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-rw-r--r--Makefile32
-rw-r--r--backends/hol4/ilistScript.sml3
-rw-r--r--backends/lean/Base.lean6
-rw-r--r--backends/lean/Base/Arith.lean2
-rw-r--r--backends/lean/Base/Arith/Arith.lean0
-rw-r--r--backends/lean/Base/Arith/Base.lean60
-rw-r--r--backends/lean/Base/Arith/Int.lean280
-rw-r--r--backends/lean/Base/Arith/Scalar.lean49
-rw-r--r--backends/lean/Base/Diverge.lean7
-rw-r--r--backends/lean/Base/Diverge/Base.lean1138
-rw-r--r--backends/lean/Base/Diverge/Elab.lean1162
-rw-r--r--backends/lean/Base/Diverge/ElabBase.lean15
-rw-r--r--backends/lean/Base/IList.lean1
-rw-r--r--backends/lean/Base/IList/IList.lean284
-rw-r--r--backends/lean/Base/Primitives.lean3
-rw-r--r--backends/lean/Base/Primitives/Base.lean130
-rw-r--r--backends/lean/Base/Primitives/Scalar.lean831
-rw-r--r--backends/lean/Base/Primitives/Vec.lean145
-rw-r--r--backends/lean/Base/Progress.lean1
-rw-r--r--backends/lean/Base/Progress/Base.lean316
-rw-r--r--backends/lean/Base/Progress/Progress.lean377
-rw-r--r--backends/lean/Base/Utils.lean640
-rw-r--r--backends/lean/Primitives.lean583
-rw-r--r--backends/lean/lake-manifest.json20
-rw-r--r--backends/lean/lakefile.lean3
-rw-r--r--backends/lean/lean-toolchain1
-rw-r--r--compiler/Config.ml23
-rw-r--r--compiler/Driver.ml10
-rw-r--r--compiler/Extract.ml353
-rw-r--r--compiler/ExtractBase.ml120
-rw-r--r--compiler/Pure.ml10
-rw-r--r--compiler/Translate.ml295
-rw-r--r--tests/coq/betree/BetreeMain_Funs.v118
-rw-r--r--tests/coq/betree/BetreeMain_Opaque.v12
-rw-r--r--tests/coq/betree/_CoqProject2
-rw-r--r--tests/coq/hashmap/Hashmap_Funs.v85
-rw-r--r--tests/coq/hashmap/_CoqProject2
-rw-r--r--tests/coq/hashmap_on_disk/HashmapMain_Funs.v89
-rw-r--r--tests/coq/hashmap_on_disk/HashmapMain_Opaque.v6
-rw-r--r--tests/coq/misc/Constants.v16
-rw-r--r--tests/coq/misc/External_Funs.v18
-rw-r--r--tests/coq/misc/External_Opaque.v12
-rw-r--r--tests/coq/misc/Loops.v124
-rw-r--r--tests/coq/misc/NoNestedBorrows.v112
-rw-r--r--tests/coq/misc/Paper.v21
-rw-r--r--tests/coq/misc/PoloniusList.v4
-rw-r--r--tests/coq/misc/_CoqProject6
-rw-r--r--tests/fstar/betree/BetreeMain.Funs.fst118
-rw-r--r--tests/fstar/betree/BetreeMain.Opaque.fsti12
-rw-r--r--tests/fstar/betree_back_stateful/BetreeMain.Funs.fst128
-rw-r--r--tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti12
-rw-r--r--tests/fstar/hashmap/Hashmap.Funs.fst85
-rw-r--r--tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst89
-rw-r--r--tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti6
-rw-r--r--tests/fstar/misc/Constants.fst16
-rw-r--r--tests/fstar/misc/External.Funs.fst18
-rw-r--r--tests/fstar/misc/External.Opaque.fsti12
-rw-r--r--tests/fstar/misc/Loops.Funs.fst124
-rw-r--r--tests/fstar/misc/NoNestedBorrows.fst112
-rw-r--r--tests/fstar/misc/Paper.fst21
-rw-r--r--tests/fstar/misc/PoloniusList.fst4
-rw-r--r--tests/hol4/betree/betreeMain_FunsScript.sml118
-rw-r--r--tests/hol4/betree/betreeMain_OpaqueScript.sml12
-rw-r--r--tests/hol4/hashmap/hashmap_FunsScript.sml85
-rw-r--r--tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml89
-rw-r--r--tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml6
-rw-r--r--tests/hol4/misc-constants/constantsScript.sml16
-rw-r--r--tests/hol4/misc-external/external_FunsScript.sml18
-rw-r--r--tests/hol4/misc-external/external_OpaqueScript.sml12
-rw-r--r--tests/hol4/misc-loops/loops_FunsScript.sml124
-rw-r--r--tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml112
-rw-r--r--tests/hol4/misc-paper/paperScript.sml21
-rw-r--r--tests/hol4/misc-polonius_list/poloniusListScript.sml4
-rw-r--r--tests/lean/.gitignore4
-rw-r--r--tests/lean/BetreeMain.lean1
-rw-r--r--tests/lean/BetreeMain/Funs.lean1023
-rw-r--r--tests/lean/BetreeMain/FunsExternal.lean35
-rw-r--r--tests/lean/BetreeMain/FunsExternal_Template.lean30
-rw-r--r--tests/lean/BetreeMain/Types.lean59
-rw-r--r--tests/lean/Constants.lean128
-rw-r--r--tests/lean/External.lean (renamed from tests/lean/misc-external/External.lean)0
-rw-r--r--tests/lean/External/Funs.lean88
-rw-r--r--tests/lean/External/FunsExternal.lean33
-rw-r--r--tests/lean/External/FunsExternal_Template.lean27
-rw-r--r--tests/lean/External/Opaque.lean32
-rw-r--r--tests/lean/External/Types.lean (renamed from tests/lean/misc-external/External/Types.lean)7
-rw-r--r--tests/lean/Hashmap.lean2
-rw-r--r--tests/lean/Hashmap/Funs.lean449
-rw-r--r--tests/lean/Hashmap/Properties.lean439
-rw-r--r--tests/lean/Hashmap/Types.lean19
-rw-r--r--tests/lean/HashmapMain.lean (renamed from tests/lean/hashmap_on_disk/HashmapMain.lean)0
-rw-r--r--tests/lean/HashmapMain/Funs.lean505
-rw-r--r--tests/lean/HashmapMain/FunsExternal.lean17
-rw-r--r--tests/lean/HashmapMain/FunsExternal_Template.lean16
-rw-r--r--tests/lean/HashmapMain/Opaque.lean (renamed from tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean)14
-rw-r--r--tests/lean/HashmapMain/Types.lean22
-rw-r--r--tests/lean/Loops.lean (renamed from tests/lean/misc-loops/Loops.lean)0
-rw-r--r--tests/lean/Loops/Funs.lean611
-rw-r--r--tests/lean/Loops/Types.lean12
-rw-r--r--tests/lean/Makefile31
-rw-r--r--tests/lean/NoNestedBorrows.lean511
-rw-r--r--tests/lean/Paper.lean121
-rw-r--r--tests/lean/PoloniusList.lean34
-rw-r--r--tests/lean/hashmap/Base/Primitives.lean583
-rw-r--r--tests/lean/hashmap/Hashmap.lean1
-rw-r--r--tests/lean/hashmap/Hashmap/Clauses/Clauses.lean107
-rw-r--r--tests/lean/hashmap/Hashmap/Clauses/Template.lean108
-rw-r--r--tests/lean/hashmap/Hashmap/Funs.lean513
-rw-r--r--tests/lean/hashmap/Hashmap/Types.lean16
-rw-r--r--tests/lean/hashmap/lake-manifest.json27
-rw-r--r--tests/lean/hashmap/lakefile.lean12
-rw-r--r--tests/lean/hashmap/lean-toolchain1
-rw-r--r--tests/lean/hashmap_on_disk/.gitignore5
-rw-r--r--tests/lean/hashmap_on_disk/Base/Primitives.lean583
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean110
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean112
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean5
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/Funs.lean590
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/Types.lean19
-rw-r--r--tests/lean/hashmap_on_disk/lake-manifest.json27
-rw-r--r--tests/lean/hashmap_on_disk/lakefile.lean12
-rw-r--r--tests/lean/hashmap_on_disk/lean-toolchain1
-rw-r--r--tests/lean/lake-manifest.json40
-rw-r--r--tests/lean/lakefile.lean19
-rw-r--r--tests/lean/lean-toolchain2
-rw-r--r--tests/lean/misc-constants/Base/Primitives.lean583
-rw-r--r--tests/lean/misc-constants/Constants.lean131
-rw-r--r--tests/lean/misc-constants/lake-manifest.json27
-rw-r--r--tests/lean/misc-constants/lakefile.lean12
-rw-r--r--tests/lean/misc-constants/lean-toolchain1
-rw-r--r--tests/lean/misc-external/Base/Primitives.lean583
-rw-r--r--tests/lean/misc-external/External/ExternalFuns.lean5
-rw-r--r--tests/lean/misc-external/External/Funs.lean84
-rw-r--r--tests/lean/misc-external/External/Opaque.lean27
-rw-r--r--tests/lean/misc-external/lake-manifest.json27
-rw-r--r--tests/lean/misc-external/lakefile.lean12
-rw-r--r--tests/lean/misc-external/lean-toolchain1
-rw-r--r--tests/lean/misc-loops/Base/Primitives.lean583
-rw-r--r--tests/lean/misc-loops/Loops/Clauses/Clauses.lean205
-rw-r--r--tests/lean/misc-loops/Loops/Clauses/Template.lean205
-rw-r--r--tests/lean/misc-loops/Loops/Funs.lean705
-rw-r--r--tests/lean/misc-loops/Loops/Types.lean9
-rw-r--r--tests/lean/misc-loops/lake-manifest.json27
-rw-r--r--tests/lean/misc-loops/lakefile.lean12
-rw-r--r--tests/lean/misc-loops/lean-toolchain1
-rw-r--r--tests/lean/misc-no_nested_borrows/Base/Primitives.lean583
-rw-r--r--tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean538
-rw-r--r--tests/lean/misc-no_nested_borrows/lake-manifest.json27
-rw-r--r--tests/lean/misc-no_nested_borrows/lakefile.lean12
-rw-r--r--tests/lean/misc-no_nested_borrows/lean-toolchain1
-rw-r--r--tests/lean/misc-paper/Base/Primitives.lean583
-rw-r--r--tests/lean/misc-paper/Paper.lean123
-rw-r--r--tests/lean/misc-paper/lake-manifest.json27
-rw-r--r--tests/lean/misc-paper/lakefile.lean12
-rw-r--r--tests/lean/misc-paper/lean-toolchain1
-rw-r--r--tests/lean/misc-polonius_list/Base/Primitives.lean583
-rw-r--r--tests/lean/misc-polonius_list/PoloniusList.lean31
-rw-r--r--tests/lean/misc-polonius_list/lake-manifest.json27
-rw-r--r--tests/lean/misc-polonius_list/lakefile.lean12
-rw-r--r--tests/lean/misc-polonius_list/lean-toolchain1
160 files changed, 11401 insertions, 10464 deletions
diff --git a/Makefile b/Makefile
index a5d1fd09..1b11592f 100644
--- a/Makefile
+++ b/Makefile
@@ -117,8 +117,8 @@ trans-no_nested_borrows trans-paper: \
OPTIONS += -test-units -test-trans-units -no-split-files -no-state
trans-no_nested_borrows trans-paper: SUBDIR := misc
tfstar-no_nested_borrows tfstar-paper:
-tlean-no_nested_borrows: SUBDIR := misc-no_nested_borrows
-tlean-paper: SUBDIR := misc-paper
+tlean-no_nested_borrows: SUBDIR :=
+tlean-paper: SUBDIR :=
thol4-no_nested_borrows: SUBDIR := misc-no_nested_borrows
thol4-paper: SUBDIR := misc-paper
@@ -126,29 +126,29 @@ trans-loops: OPTIONS += -no-state
trans-loops: SUBDIR := misc
tfstar-loops: OPTIONS += -decreases-clauses -template-clauses
tcoq-loops: OPTIONS += -use-fuel -no-split-files
-tlean-loops: SUBDIR := misc-loops
-tlean-loops: OPTIONS += -decreases-clauses -template-clauses
+tlean-loops: SUBDIR :=
thol4-loops: SUBDIR := misc-loops
trans-hashmap: OPTIONS += -no-state
trans-hashmap: SUBDIR := hashmap
tfstar-hashmap: OPTIONS += -decreases-clauses -template-clauses
tcoq-hashmap: OPTIONS += -use-fuel
-tlean-hashmap: OPTIONS += -decreases-clauses -template-clauses
+tlean-hashmap: SUBDIR :=
+tlean-hashmap: OPTIONS +=
thol4-hashmap: OPTIONS +=
trans-hashmap_main: OPTIONS +=
trans-hashmap_main: SUBDIR := hashmap_on_disk
tfstar-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
tcoq-hashmap_main: OPTIONS += -use-fuel
-tlean-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
+tlean-hashmap_main: SUBDIR :=
thol4-hashmap_main: OPTIONS +=
transp-polonius_list: OPTIONS += -test-units -test-trans-units -no-split-files -no-state
transp-polonius_list: SUBDIR := misc
tfstarp-polonius_list: OPTIONS +=
tcoqp-polonius_list: OPTIONS +=
-tleanp-polonius_list: SUBDIR := misc-polonius_list
+tleanp-polonius_list: SUBDIR :=
tleanp-polonius_list: OPTIONS +=
thol4p-polonius_list: SUBDIR := misc-polonius_list
thol4p-polonius_list: OPTIONS +=
@@ -157,7 +157,7 @@ trans-constants: OPTIONS += -test-units -test-trans-units -no-split-files -no-st
trans-constants: SUBDIR := misc
tfstar-constants: OPTIONS +=
tcoq-constants: OPTIONS +=
-tlean-constants: SUBDIR := misc-constants
+tlean-constants: SUBDIR :=
tlean-constants: OPTIONS +=
thol4-constants: SUBDIR := misc-constants
thol4-constants: OPTIONS +=
@@ -166,7 +166,7 @@ trans-external: OPTIONS +=
trans-external: SUBDIR := misc
tfstar-external: OPTIONS +=
tcoq-external: OPTIONS +=
-tlean-external: SUBDIR := misc-external
+tlean-external: SUBDIR :=
tlean-external: OPTIONS +=
thol4-external: SUBDIR := misc-external
thol4-external: OPTIONS +=
@@ -176,7 +176,8 @@ transp-betree_main: OPTIONS += -backward-no-state-update
transp-betree_main: SUBDIR:=betree
tfstarp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
tcoqp-betree_main: OPTIONS += -use-fuel
-tleanp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
+tleanp-betree_main: SUBDIR :=
+tleanp-betree_main: OPTIONS +=
thol4-betree_main: OPTIONS +=
# Additional test on the betree: translate it without `-backward-no-state-update`.
@@ -249,8 +250,7 @@ tcoqp-%:
$(AENEAS_CMD)
.PHONY: tlean-%
-# TODO: add -test-trans-units once we remove all the sorry from Primitives.lean
-tlean-%: OPTIONS += -backend lean
+tlean-%: OPTIONS += -backend lean -test-trans-units
tlean-%: BACKEND_SUBDIR := lean
tlean-%:
$(AENEAS_CMD)
@@ -258,13 +258,7 @@ tlean-%:
# "p" stands for "Polonius"
.PHONY: tleanp-%
-# TODO: for now we don't extract the betree for Lean because we need to implement
-# proper support for the proofs of termination for the mutually recursive functions.
-tleanp-betree_main:
- echo "Ignoring Lean betree"
-
-# TODO: add -test-trans-units once we remove all the sorry from Primitives.lean
-tleanp-%: OPTIONS += -backend lean
+tleanp-%: OPTIONS += -backend lean -test-trans-units
tleanp-%: BACKEND_SUBDIR := lean
tleanp-%:
$(AENEAS_CMD)
diff --git a/backends/hol4/ilistScript.sml b/backends/hol4/ilistScript.sml
index fb0c7688..2b465af3 100644
--- a/backends/hol4/ilistScript.sml
+++ b/backends/hol4/ilistScript.sml
@@ -23,6 +23,8 @@ val _ = BasicProvers.export_rewrites ["len_def"]
Remark: we initially added the following case, so that we wouldn't need the
premise [i < len ls] is [index_eq_EL]:
“index (i : int) [] = EL (Num i) []”
+
+ TODO: this can be simplified. See the Lean backend.
*)
val index_def = Define ‘
index (i : int) (x :: ls) = if i = 0 then x else (if 0 < i then index (i - 1) ls else ARB)
@@ -44,6 +46,7 @@ Proof
exfalso >> cooper_tac
QED
+(* TODO: this can be simplified. See the Lean backend. *)
val update_def = Define ‘
update ([] : 'a list) (i : int) (y : 'a) : 'a list = [] ∧
diff --git a/backends/lean/Base.lean b/backends/lean/Base.lean
new file mode 100644
index 00000000..2077d410
--- /dev/null
+++ b/backends/lean/Base.lean
@@ -0,0 +1,6 @@
+import Base.Utils
+import Base.Primitives
+import Base.Diverge
+import Base.Arith
+import Base.Progress
+import Base.IList
diff --git a/backends/lean/Base/Arith.lean b/backends/lean/Base/Arith.lean
new file mode 100644
index 00000000..c0d09fd2
--- /dev/null
+++ b/backends/lean/Base/Arith.lean
@@ -0,0 +1,2 @@
+import Base.Arith.Int
+import Base.Arith.Scalar
diff --git a/backends/lean/Base/Arith/Arith.lean b/backends/lean/Base/Arith/Arith.lean
new file mode 100644
index 00000000..e69de29b
--- /dev/null
+++ b/backends/lean/Base/Arith/Arith.lean
diff --git a/backends/lean/Base/Arith/Base.lean b/backends/lean/Base/Arith/Base.lean
new file mode 100644
index 00000000..9c11ed45
--- /dev/null
+++ b/backends/lean/Base/Arith/Base.lean
@@ -0,0 +1,60 @@
+import Lean
+import Std.Data.Int.Lemmas
+import Mathlib.Tactic.Linarith
+
+namespace Arith
+
+open Lean Elab Term Meta
+
+-- We can't define and use trace classes in the same file
+initialize registerTraceClass `Arith
+
+-- TODO: move?
+theorem ne_zero_is_lt_or_gt {x : Int} (hne : x ≠ 0) : x < 0 ∨ x > 0 := by
+ cases h: x <;> simp_all
+ . rename_i n;
+ cases n <;> simp_all
+ . apply Int.negSucc_lt_zero
+
+-- TODO: move?
+theorem ne_is_lt_or_gt {x y : Int} (hne : x ≠ y) : x < y ∨ x > y := by
+ have hne : x - y ≠ 0 := by
+ simp
+ intro h
+ have: x = y := by linarith
+ simp_all
+ have h := ne_zero_is_lt_or_gt hne
+ match h with
+ | .inl _ => left; linarith
+ | .inr _ => right; linarith
+
+-- TODO: move?
+theorem add_one_le_iff_le_ne (n m : Nat) (h1 : m ≤ n) (h2 : m ≠ n) : m + 1 ≤ n := by
+ -- Damn, those proofs on natural numbers are hard - I wish Omega was in mathlib4...
+ simp [Nat.add_one_le_iff]
+ simp [Nat.lt_iff_le_and_ne]
+ simp_all
+
+/- Induction over positive integers -/
+-- TODO: move
+theorem int_pos_ind (p : Int → Prop) :
+ (zero:p 0) → (pos:∀ i, 0 ≤ i → p i → p (i + 1)) → ∀ i, 0 ≤ i → p i := by
+ intro h0 hr i hpos
+-- have heq : Int.toNat i = i := by
+-- cases i <;> simp_all
+ have ⟨ n, heq ⟩ : {n:Nat // n = i } := ⟨ Int.toNat i, by cases i <;> simp_all ⟩
+ revert i
+ induction n
+ . intro i hpos heq
+ cases i <;> simp_all
+ . rename_i n hi
+ intro i hpos heq
+ cases i <;> simp_all
+ rename_i m
+ cases m <;> simp_all
+
+-- We sometimes need this to make sure no natural numbers appear in the goals
+-- TODO: there is probably something more general to do
+theorem nat_zero_eq_int_zero : (0 : Nat) = (0 : Int) := by simp
+
+end Arith
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
new file mode 100644
index 00000000..7a5bbe98
--- /dev/null
+++ b/backends/lean/Base/Arith/Int.lean
@@ -0,0 +1,280 @@
+/- This file contains tactics to solve arithmetic goals -/
+
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+-- TODO: there is no Omega tactic for now - it seems it hasn't been ported yet
+--import Mathlib.Tactic.Omega
+import Base.Utils
+import Base.Arith.Base
+
+namespace Arith
+
+open Utils
+
+-- Remark: I tried a version of the shape `HasScalarProp {a : Type} (x : a)`
+-- but the lookup didn't work
+class HasIntProp (a : Sort u) where
+ prop_ty : a → Prop
+ prop : ∀ x:a, prop_ty x
+
+class PropHasImp (x : Prop) where
+ concl : Prop
+ prop : x → concl
+
+instance (p : Int → Prop) : HasIntProp (Subtype p) where
+ prop_ty := λ x => p x
+ prop := λ x => x.property
+
+-- This also works for `x ≠ y` because this expression reduces to `¬ x = y`
+-- and `Ne` is marked as `reducible`
+instance (x y : Int) : PropHasImp (¬ x = y) where
+ concl := x < y ∨ x > y
+ prop := λ (h:x ≠ y) => ne_is_lt_or_gt h
+
+-- Check if a proposition is a linear integer proposition.
+-- We notably use this to check the goals.
+class IsLinearIntProp (x : Prop) where
+
+instance (x y : Int) : IsLinearIntProp (x < y) where
+instance (x y : Int) : IsLinearIntProp (x > y) where
+instance (x y : Int) : IsLinearIntProp (x ≤ y) where
+instance (x y : Int) : IsLinearIntProp (x ≥ y) where
+instance (x y : Int) : IsLinearIntProp (x ≥ y) where
+instance (x y : Int) : IsLinearIntProp (x = y) where
+/- It seems we don't need to do any special preprocessing when the *goal*
+ has the following shape - I guess `linarith` automatically calls `intro` -/
+instance (x y : Int) : IsLinearIntProp (¬ x = y) where
+
+open Lean Lean.Elab Lean.Meta
+
+-- Explore a term by decomposing the applications (we explore the applied
+-- functions and their arguments, but ignore lambdas, forall, etc. -
+-- should we go inside?).
+partial def foldTermApps (k : α → Expr → MetaM α) (s : α) (e : Expr) : MetaM α := do
+ -- We do it in a very simpler manner: we deconstruct applications,
+ -- and recursively explore the sub-expressions. Note that we do
+ -- not go inside foralls and abstractions (should we?).
+ e.withApp fun f args => do
+ let s ← k s f
+ args.foldlM (foldTermApps k) s
+
+-- Provided a function `k` which lookups type class instances on an expression,
+-- collect all the instances lookuped by applying `k` on the sub-expressions of `e`.
+def collectInstances
+ (k : Expr → MetaM (Option Expr)) (s : HashSet Expr) (e : Expr) : MetaM (HashSet Expr) := do
+ let k s e := do
+ match ← k e with
+ | none => pure s
+ | some i => pure (s.insert i)
+ foldTermApps k s e
+
+-- Similar to `collectInstances`, but explores all the local declarations in the
+-- main context.
+def collectInstancesFromMainCtx (k : Expr → MetaM (Option Expr)) : Tactic.TacticM (HashSet Expr) := do
+ Tactic.withMainContext do
+ -- Get the local context
+ let ctx ← Lean.MonadLCtx.getLCtx
+ -- Just a matter of precaution
+ let ctx ← instantiateLCtxMVars ctx
+ -- Initialize the hashset
+ let hs := HashSet.empty
+ -- Explore the declarations
+ let decls ← ctx.getDecls
+ decls.foldlM (fun hs d => collectInstances k hs d.toExpr) hs
+
+-- Helper
+def lookupProp (fName : String) (className : Name) (e : Expr) : MetaM (Option Expr) := do
+ trace[Arith] fName
+ -- TODO: do we need Lean.observing?
+ -- This actually eliminates the error messages
+ Lean.observing? do
+ trace[Arith] m!"{fName}: observing"
+ let ty ← Lean.Meta.inferType e
+ let hasProp ← mkAppM className #[ty]
+ let hasPropInst ← trySynthInstance hasProp
+ match hasPropInst with
+ | LOption.some i =>
+ trace[Arith] "Found {fName} instance"
+ let i_prop ← mkProjection i (Name.mkSimple "prop")
+ some (← mkAppM' i_prop #[e])
+ | _ => none
+
+-- Return an instance of `HasIntProp` for `e` if it has some
+def lookupHasIntProp (e : Expr) : MetaM (Option Expr) :=
+ lookupProp "lookupHasIntProp" ``HasIntProp e
+
+-- Collect the instances of `HasIntProp` for the subexpressions in the context
+def collectHasIntPropInstancesFromMainCtx : Tactic.TacticM (HashSet Expr) := do
+ collectInstancesFromMainCtx lookupHasIntProp
+
+-- Return an instance of `PropHasImp` for `e` if it has some
+def lookupPropHasImp (e : Expr) : MetaM (Option Expr) := do
+ trace[Arith] "lookupPropHasImp"
+ -- TODO: do we need Lean.observing?
+ -- This actually eliminates the error messages
+ Lean.observing? do
+ trace[Arith] "lookupPropHasImp: observing"
+ let ty ← Lean.Meta.inferType e
+ trace[Arith] "lookupPropHasImp: ty: {ty}"
+ let cl ← mkAppM ``PropHasImp #[ty]
+ let inst ← trySynthInstance cl
+ match inst with
+ | LOption.some i =>
+ trace[Arith] "Found PropHasImp instance"
+ let i_prop ← mkProjection i (Name.mkSimple "prop")
+ some (← mkAppM' i_prop #[e])
+ | _ => none
+
+-- Collect the instances of `PropHasImp` for the subexpressions in the context
+def collectPropHasImpInstancesFromMainCtx : Tactic.TacticM (HashSet Expr) := do
+ collectInstancesFromMainCtx lookupPropHasImp
+
+elab "display_prop_has_imp_instances" : tactic => do
+ trace[Arith] "Displaying the PropHasImp instances"
+ let hs ← collectPropHasImpInstancesFromMainCtx
+ hs.forM fun e => do
+ trace[Arith] "+ PropHasImp instance: {e}"
+
+example (x y : Int) (_ : x ≠ y) (_ : ¬ x = y) : True := by
+ display_prop_has_imp_instances
+ simp
+
+-- Lookup instances in a context and introduce them with additional declarations.
+def introInstances (declToUnfold : Name) (lookup : Expr → MetaM (Option Expr)) : Tactic.TacticM (Array Expr) := do
+ let hs ← collectInstancesFromMainCtx lookup
+ hs.toArray.mapM fun e => do
+ let type ← inferType e
+ let name ← mkFreshAnonPropUserName
+ -- Add a declaration
+ let nval ← Utils.addDeclTac name e type (asLet := false)
+ -- Simplify to unfold the declaration to unfold (i.e., the projector)
+ Utils.simpAt [declToUnfold] [] [] (Tactic.Location.targets #[mkIdent name] false)
+ -- Return the new value
+ pure nval
+
+def introHasIntPropInstances : Tactic.TacticM (Array Expr) := do
+ trace[Arith] "Introducing the HasIntProp instances"
+ introInstances ``HasIntProp.prop_ty lookupHasIntProp
+
+-- Lookup the instances of `HasIntProp for all the sub-expressions in the context,
+-- and introduce the corresponding assumptions
+elab "intro_has_int_prop_instances" : tactic => do
+ let _ ← introHasIntPropInstances
+
+-- Lookup the instances of `PropHasImp for all the sub-expressions in the context,
+-- and introduce the corresponding assumptions
+elab "intro_prop_has_imp_instances" : tactic => do
+ trace[Arith] "Introducing the PropHasImp instances"
+ let _ ← introInstances ``PropHasImp.concl lookupPropHasImp
+
+example (x y : Int) (h0 : x ≤ y) (h1 : x ≠ y) : x < y := by
+ intro_prop_has_imp_instances
+ rename_i h
+ split_disj h
+ . linarith
+ . linarith
+
+/- Boosting a bit the linarith tac.
+
+ We do the following:
+ - for all the assumptions of the shape `(x : Int) ≠ y` or `¬ (x = y), we
+ introduce two goals with the assumptions `x < y` and `x > y`
+ TODO: we could create a PR for mathlib.
+ -/
+def intTacPreprocess (extraPreprocess : Tactic.TacticM Unit) : Tactic.TacticM Unit := do
+ Tactic.withMainContext do
+ -- Lookup the instances of PropHasImp (this is how we detect assumptions
+ -- of the proper shape), introduce assumptions in the context and split
+ -- on those
+ -- TODO: get rid of the assumptions that we split
+ let rec splitOnAsms (asms : List Expr) : Tactic.TacticM Unit :=
+ match asms with
+ | [] => pure ()
+ | asm :: asms =>
+ let k := splitOnAsms asms
+ Utils.splitDisjTac asm k k
+ -- Introduce the scalar bounds
+ let _ ← introHasIntPropInstances
+ -- Extra preprocessing, before we split on the disjunctions
+ extraPreprocess
+ -- Split
+ let asms ← introInstances ``PropHasImp.concl lookupPropHasImp
+ splitOnAsms asms.toList
+
+elab "int_tac_preprocess" : tactic =>
+ intTacPreprocess (do pure ())
+
+-- Check if the goal is a linear arithmetic goal
+def goalIsLinearInt : Tactic.TacticM Bool := do
+ Tactic.withMainContext do
+ let gty ← Tactic.getMainTarget
+ match ← trySynthInstance (← mkAppM ``IsLinearIntProp #[gty]) with
+ | .some _ => pure true
+ | _ => pure false
+
+def intTac (splitGoalConjs : Bool) (extraPreprocess : Tactic.TacticM Unit) : Tactic.TacticM Unit := do
+ Tactic.withMainContext do
+ Tactic.focus do
+ let g ← Tactic.getMainGoal
+ trace[Arith] "Original goal: {g}"
+ -- Introduce all the universally quantified variables (includes the assumptions)
+ let (_, g) ← g.intros
+ Tactic.setGoals [g]
+ -- Preprocess - wondering if we should do this before or after splitting
+ -- the goal. I think before leads to a smaller proof term?
+ Tactic.allGoals (intTacPreprocess extraPreprocess)
+ -- More preprocessing
+ Tactic.allGoals (Utils.simpAt [] [``nat_zero_eq_int_zero] [] .wildcard)
+ -- Split the conjunctions in the goal
+ if splitGoalConjs then Tactic.allGoals (Utils.repeatTac Utils.splitConjTarget)
+ -- Call linarith
+ let linarith := do
+ let cfg : Linarith.LinarithConfig := {
+ -- We do this with our custom preprocessing
+ splitNe := false
+ }
+ Tactic.liftMetaFinishingTactic <| Linarith.linarith false [] cfg
+ Tactic.allGoals do
+ -- We check if the goal is a linear arithmetic goal: if yes, we directly
+ -- call linarith, otherwise we first apply exfalso (we do this because
+ -- linarith is too general and sometimes fails to do this correctly).
+ if ← goalIsLinearInt then do
+ trace[Arith] "linarith goal: {← Tactic.getMainGoal}"
+ linarith
+ else do
+ let g ← Tactic.getMainGoal
+ let gs ← g.apply (Expr.const ``False.elim [.zero])
+ let goals ← Tactic.getGoals
+ Tactic.setGoals (gs ++ goals)
+ Tactic.allGoals do
+ trace[Arith] "linarith goal: {← Tactic.getMainGoal}"
+ linarith
+
+elab "int_tac" args:(" split_goal"?): tactic =>
+ let split := args.raw.getArgs.size > 0
+ intTac split (do pure ())
+
+example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
+ int_tac_preprocess
+ linarith
+ linarith
+
+example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
+ int_tac
+
+-- Checking that things append correctly when there are several disjunctions
+example (x y : Int) (h0: 0 ≤ x) (h1: x ≠ 0) (h2 : 0 ≤ y) (h3 : y ≠ 0) : 0 < x ∧ 0 < y := by
+ int_tac split_goal
+
+-- Checking that things append correctly when there are several disjunctions
+example (x y : Int) (h0: 0 ≤ x) (h1: x ≠ 0) (h2 : 0 ≤ y) (h3 : y ≠ 0) : 0 < x ∧ 0 < y ∧ x + y ≥ 2 := by
+ int_tac split_goal
+
+-- Checking that we can prove exfalso
+example (a : Prop) (x : Int) (h0: 0 < x) (h1: x < 0) : a := by
+ int_tac
+
+end Arith
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
new file mode 100644
index 00000000..b792ff21
--- /dev/null
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -0,0 +1,49 @@
+import Base.Arith.Int
+import Base.Primitives.Scalar
+
+/- Automation for scalars - TODO: not sure it is worth having two files (Int.lean and Scalar.lean) -/
+namespace Arith
+
+open Lean Lean.Elab Lean.Meta
+open Primitives
+
+def scalarTacExtraPreprocess : Tactic.TacticM Unit := do
+ Tactic.withMainContext do
+ -- Inroduce the bounds for the isize/usize types
+ let add (e : Expr) : Tactic.TacticM Unit := do
+ let ty ← inferType e
+ let _ ← Utils.addDeclTac (← Utils.mkFreshAnonPropUserName) e ty (asLet := false)
+ add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []])
+ add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
+ add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
+ -- Reveal the concrete bounds
+ Utils.simpAt [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
+ ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
+ ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
+ ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
+ ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max,
+ ``Usize.min
+ ] [] [] .wildcard
+
+elab "scalar_tac_preprocess" : tactic =>
+ intTacPreprocess scalarTacExtraPreprocess
+
+-- A tactic to solve linear arithmetic goals in the presence of scalars
+def scalarTac (splitGoalConjs : Bool) : Tactic.TacticM Unit := do
+ intTac splitGoalConjs scalarTacExtraPreprocess
+
+elab "scalar_tac" : tactic =>
+ scalarTac false
+
+instance (ty : ScalarTy) : HasIntProp (Scalar ty) where
+ -- prop_ty is inferred
+ prop := λ x => And.intro x.hmin x.hmax
+
+example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
+ intro_has_int_prop_instances
+ simp [*]
+
+example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
+ scalar_tac
+
+end Arith
diff --git a/backends/lean/Base/Diverge.lean b/backends/lean/Base/Diverge.lean
new file mode 100644
index 00000000..c9a2eec2
--- /dev/null
+++ b/backends/lean/Base/Diverge.lean
@@ -0,0 +1,7 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.Diverge.Base
+import Base.Diverge.Elab
diff --git a/backends/lean/Base/Diverge/Base.lean b/backends/lean/Base/Diverge/Base.lean
new file mode 100644
index 00000000..1d548389
--- /dev/null
+++ b/backends/lean/Base/Diverge/Base.lean
@@ -0,0 +1,1138 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.Primitives.Base
+import Base.Arith.Base
+
+/- TODO: this is very useful, but is there more? -/
+set_option profiler true
+set_option profiler.threshold 100
+
+namespace Diverge
+
+namespace Fix
+
+ open Primitives
+ open Result
+
+ variable {a : Type u} {b : a → Type v}
+ variable {c d : Type w} -- TODO: why do we have to make them both : Type w?
+
+ /-! # The least fixed point definition and its properties -/
+
+ def least_p (p : Nat → Prop) (n : Nat) : Prop := p n ∧ (∀ m, m < n → ¬ p m)
+ noncomputable def least (p : Nat → Prop) : Nat :=
+ Classical.epsilon (least_p p)
+
+ -- Auxiliary theorem for [least_spec]: if there exists an `n` satisfying `p`,
+ -- there there exists a least `m` satisfying `p`.
+ theorem least_spec_aux (p : Nat → Prop) : ∀ (n : Nat), (hn : p n) → ∃ m, least_p p m := by
+ apply Nat.strongRec'
+ intros n hi hn
+ -- Case disjunction on: is n the smallest n satisfying p?
+ match Classical.em (∀ m, m < n → ¬ p m) with
+ | .inl hlt =>
+ -- Yes: trivial
+ exists n
+ | .inr hlt =>
+ simp at *
+ let ⟨ m, ⟨ hmlt, hm ⟩ ⟩ := hlt
+ have hi := hi m hmlt hm
+ apply hi
+
+ -- The specification of [least]: either `p` is never satisfied, or it is satisfied
+ -- by `least p` and no `n < least p` satisfies `p`.
+ theorem least_spec (p : Nat → Prop) : (∀ n, ¬ p n) ∨ (p (least p) ∧ ∀ n, n < least p → ¬ p n) := by
+ -- Case disjunction on the existence of an `n` which satisfies `p`
+ match Classical.em (∀ n, ¬ p n) with
+ | .inl h =>
+ -- There doesn't exist: trivial
+ apply (Or.inl h)
+ | .inr h =>
+ -- There exists: we simply use `least_spec_aux` in combination with the property
+ -- of the epsilon operator
+ simp at *
+ let ⟨ n, hn ⟩ := h
+ apply Or.inr
+ have hl := least_spec_aux p n hn
+ have he := Classical.epsilon_spec hl
+ apply he
+
+ /-! # The fixed point definitions -/
+
+ def fix_fuel (n : Nat) (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) :
+ Result (b x) :=
+ match n with
+ | 0 => .div
+ | n + 1 =>
+ f (fix_fuel n f) x
+
+ @[simp] def fix_fuel_pred (f : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (x : a) (n : Nat) :=
+ not (div? (fix_fuel n f x))
+
+ def fix_fuel_P (f : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (x : a) (n : Nat) : Prop :=
+ fix_fuel_pred f x n
+
+ partial
+ def fixImpl (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) : Result (b x) :=
+ f (fixImpl f) x
+
+ -- The fact that `fix` is implemented by `fixImpl` allows us to not mark the
+ -- functions defined with the fixed-point as noncomputable. One big advantage
+ -- is that it allows us to evaluate those functions, for instance with #eval.
+ @[implemented_by fixImpl]
+ def fix (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) : Result (b x) :=
+ fix_fuel (least (fix_fuel_P f x)) f x
+
+ /-! # The validity property -/
+
+ -- Monotonicity relation over results
+ -- TODO: generalize (we should parameterize the definition by a relation over `a`)
+ def result_rel {a : Type u} (x1 x2 : Result a) : Prop :=
+ match x1 with
+ | div => True
+ | fail _ => x2 = x1
+ | ret _ => x2 = x1 -- TODO: generalize
+
+ -- Monotonicity relation over monadic arrows (i.e., Kleisli arrows)
+ def karrow_rel (k1 k2 : (x:a) → Result (b x)) : Prop :=
+ ∀ x, result_rel (k1 x) (k2 x)
+
+ -- Monotonicity property for function bodies
+ def is_mono (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) : Prop :=
+ ∀ {{k1 k2}}, karrow_rel k1 k2 → karrow_rel (f k1) (f k2)
+
+ -- "Continuity" property.
+ -- We need this, and this looks a lot like continuity. Also see this paper:
+ -- https://inria.hal.science/file/index/docid/216187/filename/tarski.pdf
+ -- We define our "continuity" criteria so that it gives us what we need to
+ -- prove the fixed-point equation, and we can also easily manipulate it.
+ def is_cont (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) : Prop :=
+ ∀ x, (Hdiv : ∀ n, fix_fuel (.succ n) f x = div) → f (fix f) x = div
+
+ /-! # The proof of the fixed-point equation -/
+ theorem fix_fuel_mono {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}
+ (Hmono : is_mono f) :
+ ∀ {{n m}}, n ≤ m → karrow_rel (fix_fuel n f) (fix_fuel m f) := by
+ intros n
+ induction n
+ case zero => simp [karrow_rel, fix_fuel, result_rel]
+ case succ n1 Hi =>
+ intros m Hle x
+ simp [result_rel]
+ match m with
+ | 0 =>
+ exfalso
+ zify at *
+ linarith
+ | Nat.succ m1 =>
+ simp_arith at Hle
+ simp [fix_fuel]
+ have Hi := Hi Hle
+ have Hmono := Hmono Hi x
+ simp [result_rel] at Hmono
+ apply Hmono
+
+ @[simp] theorem neg_fix_fuel_P
+ {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)} {x : a} {n : Nat} :
+ ¬ fix_fuel_P f x n ↔ (fix_fuel n f x = div) := by
+ simp [fix_fuel_P, div?]
+ cases fix_fuel n f x <;> simp
+
+ theorem fix_fuel_fix_mono {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)} (Hmono : is_mono f) :
+ ∀ n, karrow_rel (fix_fuel n f) (fix f) := by
+ intros n x
+ simp [result_rel]
+ have Hl := least_spec (fix_fuel_P f x)
+ simp at Hl
+ match Hl with
+ | .inl Hl => simp [*]
+ | .inr ⟨ Hl, Hn ⟩ =>
+ match Classical.em (fix_fuel n f x = div) with
+ | .inl Hd =>
+ simp [*]
+ | .inr Hd =>
+ have Hineq : least (fix_fuel_P f x) ≤ n := by
+ -- Proof by contradiction
+ cases Classical.em (least (fix_fuel_P f x) ≤ n) <;> simp [*]
+ simp at *
+ rename_i Hineq
+ have Hn := Hn n Hineq
+ contradiction
+ have Hfix : ¬ (fix f x = div) := by
+ simp [fix]
+ -- By property of the least upper bound
+ revert Hd Hl
+ -- TODO: there is no conversion to select the head of a function!
+ conv => lhs; apply congr_fun; apply congr_fun; apply congr_fun; simp [fix_fuel_P, div?]
+ cases fix_fuel (least (fix_fuel_P f x)) f x <;> simp
+ have Hmono := fix_fuel_mono Hmono Hineq x
+ simp [result_rel] at Hmono
+ simp [fix] at *
+ cases Heq: fix_fuel (least (fix_fuel_P f x)) f x <;>
+ cases Heq':fix_fuel n f x <;>
+ simp_all
+
+ theorem fix_fuel_P_least {f : ((x:a) → Result (b x)) → (x:a) → Result (b x)} (Hmono : is_mono f) :
+ ∀ {{x n}}, fix_fuel_P f x n → fix_fuel_P f x (least (fix_fuel_P f x)) := by
+ intros x n Hf
+ have Hfmono := fix_fuel_fix_mono Hmono n x
+ -- TODO: there is no conversion to select the head of a function!
+ conv => apply congr_fun; simp [fix_fuel_P]
+ simp [fix_fuel_P] at Hf
+ revert Hf Hfmono
+ simp [div?, result_rel, fix]
+ cases fix_fuel n f x <;> simp_all
+
+ -- Prove the fixed point equation in the case there exists some fuel for which
+ -- the execution terminates
+ theorem fix_fixed_eq_terminates (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (Hmono : is_mono f)
+ (x : a) (n : Nat) (He : fix_fuel_P f x n) :
+ fix f x = f (fix f) x := by
+ have Hl := fix_fuel_P_least Hmono He
+ -- TODO: better control of simplification
+ conv at Hl =>
+ apply congr_fun
+ simp [fix_fuel_P]
+ -- The least upper bound is > 0
+ have ⟨ n, Hsucc ⟩ : ∃ n, least (fix_fuel_P f x) = Nat.succ n := by
+ revert Hl
+ simp [div?]
+ cases least (fix_fuel_P f x) <;> simp [fix_fuel]
+ simp [Hsucc] at Hl
+ revert Hl
+ simp [*, div?, fix, fix_fuel]
+ -- Use the monotonicity
+ have Hfixmono := fix_fuel_fix_mono Hmono n
+ have Hvm := Hmono Hfixmono x
+ -- Use functional extensionality
+ simp [result_rel, fix] at Hvm
+ revert Hvm
+ split <;> simp [*] <;> intros <;> simp [*]
+
+ theorem fix_fixed_eq_forall {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+ (Hmono : is_mono f) (Hcont : is_cont f) :
+ ∀ x, fix f x = f (fix f) x := by
+ intros x
+ -- Case disjunction: is there a fuel such that the execution successfully execute?
+ match Classical.em (∃ n, fix_fuel_P f x n) with
+ | .inr He =>
+ -- No fuel: the fixed point evaluates to `div`
+ --simp [fix] at *
+ simp at *
+ conv => lhs; simp [fix]
+ have Hel := He (Nat.succ (least (fix_fuel_P f x))); simp [*, fix_fuel] at *; clear Hel
+ -- Use the "continuity" of `f`
+ have He : ∀ n, fix_fuel (.succ n) f x = div := by intros; simp [*]
+ have Hcont := Hcont x He
+ simp [Hcont]
+ | .inl ⟨ n, He ⟩ => apply fix_fixed_eq_terminates f Hmono x n He
+
+ -- The final fixed point equation
+ theorem fix_fixed_eq {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+ (Hmono : is_mono f) (Hcont : is_cont f) :
+ fix f = f (fix f) := by
+ have Heq := fix_fixed_eq_forall Hmono Hcont
+ have Heq1 : fix f = (λ x => fix f x) := by simp
+ rw [Heq1]
+ conv => lhs; ext; simp [Heq]
+
+ /-! # Making the proofs of validity manageable (and automatable) -/
+
+ -- Monotonicity property for expressions
+ def is_mono_p (e : ((x:a) → Result (b x)) → Result c) : Prop :=
+ ∀ {{k1 k2}}, karrow_rel k1 k2 → result_rel (e k1) (e k2)
+
+ theorem is_mono_p_same (x : Result c) :
+ @is_mono_p a b c (λ _ => x) := by
+ simp [is_mono_p, karrow_rel, result_rel]
+ split <;> simp
+
+ theorem is_mono_p_rec (x : a) :
+ @is_mono_p a b (b x) (λ f => f x) := by
+ simp_all [is_mono_p, karrow_rel, result_rel]
+
+ -- The important lemma about `is_mono_p`
+ theorem is_mono_p_bind
+ (g : ((x:a) → Result (b x)) → Result c)
+ (h : c → ((x:a) → Result (b x)) → Result d) :
+ is_mono_p g →
+ (∀ y, is_mono_p (h y)) →
+ @is_mono_p a b d (λ k => @Bind.bind Result _ c d (g k) (fun y => h y k)) := by
+-- @is_mono_p a b d (λ k => do let (y : c) ← g k; h y k) := by
+ intro hg hh
+ simp [is_mono_p]
+ intro fg fh Hrgh
+ simp [karrow_rel, result_rel]
+ have hg := hg Hrgh; simp [result_rel] at hg
+ cases heq0: g fg <;> simp_all
+ rename_i y _
+ have hh := hh y Hrgh; simp [result_rel] at hh
+ simp_all
+
+ -- Continuity property for expressions - note that we take the continuation
+ -- as parameter
+ def is_cont_p (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (e : ((x:a) → Result (b x)) → Result c) : Prop :=
+ (Hc : ∀ n, e (fix_fuel n k) = .div) →
+ e (fix k) = .div
+
+ theorem is_cont_p_same (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (x : Result c) :
+ is_cont_p k (λ _ => x) := by
+ simp [is_cont_p]
+
+ theorem is_cont_p_rec (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) :
+ is_cont_p f (λ f => f x) := by
+ simp_all [is_cont_p, fix]
+
+ -- The important lemma about `is_cont_p`
+ theorem is_cont_p_bind
+ (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (Hkmono : is_mono k)
+ (g : ((x:a) → Result (b x)) → Result c)
+ (h : c → ((x:a) → Result (b x)) → Result d) :
+ is_mono_p g →
+ is_cont_p k g →
+ (∀ y, is_mono_p (h y)) →
+ (∀ y, is_cont_p k (h y)) →
+ is_cont_p k (λ k => do let y ← g k; h y k) := by
+ intro Hgmono Hgcont Hhmono Hhcont
+ simp [is_cont_p]
+ intro Hdiv
+ -- Case on `g (fix... k)`: is there an n s.t. it terminates?
+ cases Classical.em (∀ n, g (fix_fuel n k) = .div) <;> rename_i Hn
+ . -- Case 1: g diverges
+ have Hgcont := Hgcont Hn
+ simp_all
+ . -- Case 2: g doesn't diverge
+ simp at Hn
+ let ⟨ n, Hn ⟩ := Hn
+ have Hdivn := Hdiv n
+ have Hffmono := fix_fuel_fix_mono Hkmono n
+ have Hgeq := Hgmono Hffmono
+ simp [result_rel] at Hgeq
+ cases Heq: g (fix_fuel n k) <;> rename_i y <;> simp_all
+ -- Remains the .ret case
+ -- Use Hdiv to prove that: ∀ n, h y (fix_fuel n f) = div
+ -- We do this in two steps: first we prove it for m ≥ n
+ have Hhdiv: ∀ m, h y (fix_fuel m k) = .div := by
+ have Hhdiv : ∀ m, n ≤ m → h y (fix_fuel m k) = .div := by
+ -- We use the fact that `g (fix_fuel n f) = .div`, combined with Hdiv
+ intro m Hle
+ have Hdivm := Hdiv m
+ -- Monotonicity of g
+ have Hffmono := fix_fuel_mono Hkmono Hle
+ have Hgmono := Hgmono Hffmono
+ -- We need to clear Hdiv because otherwise simp_all rewrites Hdivm with Hdiv
+ clear Hdiv
+ simp_all [result_rel]
+ intro m
+ -- TODO: we shouldn't need the excluded middle here because it is decidable
+ cases Classical.em (n ≤ m) <;> rename_i Hl
+ . apply Hhdiv; assumption
+ . simp at Hl
+ -- Make a case disjunction on `h y (fix_fuel m k)`: if it is not equal
+ -- to div, use the monotonicity of `h y`
+ have Hle : m ≤ n := by linarith
+ have Hffmono := fix_fuel_mono Hkmono Hle
+ have Hmono := Hhmono y Hffmono
+ simp [result_rel] at Hmono
+ cases Heq: h y (fix_fuel m k) <;> simp_all
+ -- We can now use the continuity hypothesis for h
+ apply Hhcont; assumption
+
+ -- The validity property for an expression
+ def is_valid_p (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (e : ((x:a) → Result (b x)) → Result c) : Prop :=
+ is_mono_p e ∧
+ (is_mono k → is_cont_p k e)
+
+ @[simp] theorem is_valid_p_same
+ (k : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : Result c) :
+ is_valid_p k (λ _ => x) := by
+ simp [is_valid_p, is_mono_p_same, is_cont_p_same]
+
+ @[simp] theorem is_valid_p_rec
+ (k : ((x:a) → Result (b x)) → (x:a) → Result (b x)) (x : a) :
+ is_valid_p k (λ k => k x) := by
+ simp_all [is_valid_p, is_mono_p_rec, is_cont_p_rec]
+
+ theorem is_valid_p_ite
+ (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (cond : Prop) [h : Decidable cond]
+ {e1 e2 : ((x:a) → Result (b x)) → Result c}
+ (he1: is_valid_p k e1) (he2 : is_valid_p k e2) :
+ is_valid_p k (ite cond e1 e2) := by
+ split <;> assumption
+
+ theorem is_valid_p_dite
+ (k : ((x:a) → Result (b x)) → (x:a) → Result (b x))
+ (cond : Prop) [h : Decidable cond]
+ {e1 : cond → ((x:a) → Result (b x)) → Result c}
+ {e2 : Not cond → ((x:a) → Result (b x)) → Result c}
+ (he1: ∀ x, is_valid_p k (e1 x)) (he2 : ∀ x, is_valid_p k (e2 x)) :
+ is_valid_p k (dite cond e1 e2) := by
+ split <;> simp [*]
+
+ -- Lean is good at unification: we can write a very general version
+ -- (in particular, it will manage to figure out `g` and `h` when we
+ -- apply the lemma)
+ theorem is_valid_p_bind
+ {{k : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+ {{g : ((x:a) → Result (b x)) → Result c}}
+ {{h : c → ((x:a) → Result (b x)) → Result d}}
+ (Hgvalid : is_valid_p k g)
+ (Hhvalid : ∀ y, is_valid_p k (h y)) :
+ is_valid_p k (λ k => do let y ← g k; h y k) := by
+ let ⟨ Hgmono, Hgcont ⟩ := Hgvalid
+ simp [is_valid_p, forall_and] at Hhvalid
+ have ⟨ Hhmono, Hhcont ⟩ := Hhvalid
+ simp [← imp_forall_iff] at Hhcont
+ simp [is_valid_p]; constructor
+ . -- Monotonicity
+ apply is_mono_p_bind <;> assumption
+ . -- Continuity
+ intro Hkmono
+ have Hgcont := Hgcont Hkmono
+ have Hhcont := Hhcont Hkmono
+ apply is_cont_p_bind <;> assumption
+
+ def is_valid (f : ((x:a) → Result (b x)) → (x:a) → Result (b x)) : Prop :=
+ ∀ k x, is_valid_p k (λ k => f k x)
+
+ theorem is_valid_p_imp_is_valid {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+ (Hvalid : is_valid f) :
+ is_mono f ∧ is_cont f := by
+ have Hmono : is_mono f := by
+ intro f h Hr x
+ have Hmono := Hvalid (λ _ _ => .div) x
+ have Hmono := Hmono.left
+ apply Hmono; assumption
+ have Hcont : is_cont f := by
+ intro x Hdiv
+ have Hcont := (Hvalid f x).right Hmono
+ simp [is_cont_p] at Hcont
+ apply Hcont
+ intro n
+ have Hdiv := Hdiv n
+ simp [fix_fuel] at Hdiv
+ simp [*]
+ simp [*]
+
+ theorem is_valid_fix_fixed_eq {{f : ((x:a) → Result (b x)) → (x:a) → Result (b x)}}
+ (Hvalid : is_valid f) :
+ fix f = f (fix f) := by
+ have ⟨ Hmono, Hcont ⟩ := is_valid_p_imp_is_valid Hvalid
+ exact fix_fixed_eq Hmono Hcont
+
+end Fix
+
+namespace FixI
+ /- Indexed fixed-point: definitions with indexed types, convenient to use for mutually
+ recursive definitions. We simply port the definitions and proofs from Fix to a more
+ specific case.
+ -/
+ open Primitives Fix
+
+ -- The index type
+ variable {id : Type u}
+
+ -- The input/output types
+ variable {a : id → Type v} {b : (i:id) → a i → Type w}
+
+ -- Monotonicity relation over monadic arrows (i.e., Kleisli arrows)
+ def karrow_rel (k1 k2 : (i:id) → (x:a i) → Result (b i x)) : Prop :=
+ ∀ i x, result_rel (k1 i x) (k2 i x)
+
+ def kk_to_gen (k : (i:id) → (x:a i) → Result (b i x)) :
+ (x: (i:id) × a i) → Result (b x.fst x.snd) :=
+ λ ⟨ i, x ⟩ => k i x
+
+ def kk_of_gen (k : (x: (i:id) × a i) → Result (b x.fst x.snd)) :
+ (i:id) → (x:a i) → Result (b i x) :=
+ λ i x => k ⟨ i, x ⟩
+
+ def k_to_gen (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) :
+ ((x: (i:id) × a i) → Result (b x.fst x.snd)) → (x: (i:id) × a i) → Result (b x.fst x.snd) :=
+ λ kk => kk_to_gen (k (kk_of_gen kk))
+
+ def k_of_gen (k : ((x: (i:id) × a i) → Result (b x.fst x.snd)) → (x: (i:id) × a i) → Result (b x.fst x.snd)) :
+ ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x) :=
+ λ kk => kk_of_gen (k (kk_to_gen kk))
+
+ def e_to_gen (e : ((i:id) → (x:a i) → Result (b i x)) → Result c) :
+ ((x: (i:id) × a i) → Result (b x.fst x.snd)) → Result c :=
+ λ k => e (kk_of_gen k)
+
+ def is_valid_p (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
+ (e : ((i:id) → (x:a i) → Result (b i x)) → Result c) : Prop :=
+ Fix.is_valid_p (k_to_gen k) (e_to_gen e)
+
+ def is_valid (f : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) : Prop :=
+ ∀ k i x, is_valid_p k (λ k => f k i x)
+
+ def fix
+ (f : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) :
+ (i:id) → (x:a i) → Result (b i x) :=
+ kk_of_gen (Fix.fix (k_to_gen f))
+
+ theorem is_valid_fix_fixed_eq
+ {{f : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)}}
+ (Hvalid : is_valid f) :
+ fix f = f (fix f) := by
+ have Hvalid' : Fix.is_valid (k_to_gen f) := by
+ intro k x
+ simp only [is_valid, is_valid_p] at Hvalid
+ let ⟨ i, x ⟩ := x
+ have Hvalid := Hvalid (k_of_gen k) i x
+ simp only [k_to_gen, k_of_gen, kk_to_gen, kk_of_gen] at Hvalid
+ refine Hvalid
+ have Heq := Fix.is_valid_fix_fixed_eq Hvalid'
+ simp [fix]
+ conv => lhs; rw [Heq]
+
+ /- Some utilities to define the mutually recursive functions -/
+
+ -- TODO: use more
+ abbrev kk_ty (id : Type u) (a : id → Type v) (b : (i:id) → (x:a i) → Type w) :=
+ (i:id) → (x:a i) → Result (b i x)
+ abbrev k_ty (id : Type u) (a : id → Type v) (b : (i:id) → (x:a i) → Type w) :=
+ kk_ty id a b → kk_ty id a b
+
+ abbrev in_out_ty : Type (imax (u + 1) (v + 1)) := (in_ty : Type u) × ((x:in_ty) → Type v)
+ -- TODO: remove?
+ abbrev mk_in_out_ty (in_ty : Type u) (out_ty : in_ty → Type v) :
+ in_out_ty :=
+ Sigma.mk in_ty out_ty
+
+ -- Initially, we had left out the parameters id, a and b.
+ -- However, by parameterizing Funs with those parameters, we can state
+ -- and prove lemmas like Funs.is_valid_p_is_valid_p
+ inductive Funs (id : Type u) (a : id → Type v) (b : (i:id) → (x:a i) → Type w) :
+ List in_out_ty.{v, w} → Type (max (u + 1) (max (v + 1) (w + 1))) :=
+ | Nil : Funs id a b []
+ | Cons {ity : Type v} {oty : ity → Type w} {tys : List in_out_ty}
+ (f : kk_ty id a b → (x:ity) → Result (oty x)) (tl : Funs id a b tys) :
+ Funs id a b (⟨ ity, oty ⟩ :: tys)
+
+ def get_fun {tys : List in_out_ty} (fl : Funs id a b tys) :
+ (i : Fin tys.length) → kk_ty id a b → (x : (tys.get i).fst) →
+ Result ((tys.get i).snd x) :=
+ match fl with
+ | .Nil => λ i => by have h:= i.isLt; simp at h
+ | @Funs.Cons id a b ity oty tys1 f tl =>
+ λ ⟨ i, iLt ⟩ =>
+ match i with
+ | 0 =>
+ Eq.mp (by simp [List.get]) f
+ | .succ j =>
+ have jLt: j < tys1.length := by
+ simp at iLt
+ revert iLt
+ simp_arith
+ let j: Fin tys1.length := ⟨ j, jLt ⟩
+ Eq.mp (by simp) (get_fun tl j)
+
+ def for_all_fin_aux {n : Nat} (f : Fin n → Prop) (m : Nat) (h : m ≤ n) : Prop :=
+ if heq: m = n then True
+ else
+ f ⟨ m, by simp_all [Nat.lt_iff_le_and_ne] ⟩ ∧
+ for_all_fin_aux f (m + 1) (by simp_all [Arith.add_one_le_iff_le_ne])
+ termination_by for_all_fin_aux n _ m h => n - m
+ decreasing_by
+ simp_wf
+ apply Nat.sub_add_lt_sub <;> simp
+ simp_all [Arith.add_one_le_iff_le_ne]
+
+ def for_all_fin {n : Nat} (f : Fin n → Prop) := for_all_fin_aux f 0 (by simp)
+
+ theorem for_all_fin_aux_imp_forall {n : Nat} (f : Fin n → Prop) (m : Nat) :
+ (h : m ≤ n) →
+ for_all_fin_aux f m h → ∀ i, m ≤ i.val → f i
+ := by
+ generalize h: (n - m) = k
+ revert m
+ induction k -- TODO: induction h rather?
+ case zero =>
+ simp_all
+ intro m h1 h2
+ have h: n = m := by
+ linarith
+ unfold for_all_fin_aux; simp_all
+ simp_all
+ -- There is no i s.t. m ≤ i
+ intro i h3; cases i; simp_all
+ linarith
+ case succ k hi =>
+ simp_all
+ intro m hk hmn
+ intro hf i hmi
+ have hne: m ≠ n := by
+ have hineq := Nat.lt_of_sub_eq_succ hk
+ linarith
+ -- m = i?
+ if heq: m = i then
+ -- Yes: simply use the `for_all_fin_aux` hyp
+ unfold for_all_fin_aux at hf
+ simp_all
+ tauto
+ else
+ -- No: use the induction hypothesis
+ have hlt: m < i := by simp_all [Nat.lt_iff_le_and_ne]
+ have hineq: m + 1 ≤ n := by
+ have hineq := Nat.lt_of_sub_eq_succ hk
+ simp [*, Nat.add_one_le_iff]
+ have heq1: n - (m + 1) = k := by
+ -- TODO: very annoying arithmetic proof
+ simp [Nat.sub_eq_iff_eq_add hineq]
+ have hineq1: m ≤ n := by linarith
+ simp [Nat.sub_eq_iff_eq_add hineq1] at hk
+ simp_arith [hk]
+ have hi := hi (m + 1) heq1 hineq
+ apply hi <;> simp_all
+ . unfold for_all_fin_aux at hf
+ simp_all
+ . simp_all [Arith.add_one_le_iff_le_ne]
+
+ -- TODO: this is not necessary anymore
+ theorem for_all_fin_imp_forall (n : Nat) (f : Fin n → Prop) :
+ for_all_fin f → ∀ i, f i
+ := by
+ intro Hf i
+ apply for_all_fin_aux_imp_forall <;> try assumption
+ simp
+
+ /- Automating the proofs -/
+ @[simp] theorem is_valid_p_same
+ (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (x : Result c) :
+ is_valid_p k (λ _ => x) := by
+ simp [is_valid_p, k_to_gen, e_to_gen]
+
+ @[simp] theorem is_valid_p_rec
+ (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)) (i : id) (x : a i) :
+ is_valid_p k (λ k => k i x) := by
+ simp [is_valid_p, k_to_gen, e_to_gen, kk_to_gen, kk_of_gen]
+
+ theorem is_valid_p_ite
+ (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
+ (cond : Prop) [h : Decidable cond]
+ {e1 e2 : ((i:id) → (x:a i) → Result (b i x)) → Result c}
+ (he1: is_valid_p k e1) (he2 : is_valid_p k e2) :
+ is_valid_p k (λ k => ite cond (e1 k) (e2 k)) := by
+ split <;> assumption
+
+ theorem is_valid_p_dite
+ (k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x))
+ (cond : Prop) [h : Decidable cond]
+ {e1 : ((i:id) → (x:a i) → Result (b i x)) → cond → Result c}
+ {e2 : ((i:id) → (x:a i) → Result (b i x)) → Not cond → Result c}
+ (he1: ∀ x, is_valid_p k (λ k => e1 k x))
+ (he2 : ∀ x, is_valid_p k (λ k => e2 k x)) :
+ is_valid_p k (λ k => dite cond (e1 k) (e2 k)) := by
+ split <;> simp [*]
+
+ theorem is_valid_p_bind
+ {{k : ((i:id) → (x:a i) → Result (b i x)) → (i:id) → (x:a i) → Result (b i x)}}
+ {{g : ((i:id) → (x:a i) → Result (b i x)) → Result c}}
+ {{h : c → ((i:id) → (x:a i) → Result (b i x)) → Result d}}
+ (Hgvalid : is_valid_p k g)
+ (Hhvalid : ∀ y, is_valid_p k (h y)) :
+ is_valid_p k (λ k => do let y ← g k; h y k) := by
+ apply Fix.is_valid_p_bind
+ . apply Hgvalid
+ . apply Hhvalid
+
+ def Funs.is_valid_p
+ (k : k_ty id a b)
+ (fl : Funs id a b tys) :
+ Prop :=
+ match fl with
+ | .Nil => True
+ | .Cons f fl => (∀ x, FixI.is_valid_p k (λ k => f k x)) ∧ fl.is_valid_p k
+
+ theorem Funs.is_valid_p_Nil (k : k_ty id a b) :
+ Funs.is_valid_p k Funs.Nil := by simp [Funs.is_valid_p]
+
+ def Funs.is_valid_p_is_valid_p_aux
+ {k : k_ty id a b}
+ {tys : List in_out_ty}
+ (fl : Funs id a b tys) (Hvalid : is_valid_p k fl) :
+ ∀ (i : Fin tys.length) (x : (tys.get i).fst), FixI.is_valid_p k (fun k => get_fun fl i k x) := by
+ -- Prepare the induction
+ have ⟨ n, Hn ⟩ : { n : Nat // tys.length = n } := ⟨ tys.length, by rfl ⟩
+ revert tys fl Hvalid
+ induction n
+ --
+ case zero =>
+ intro tys fl Hvalid Hlen;
+ have Heq: tys = [] := by cases tys <;> simp_all
+ intro i x
+ simp_all
+ have Hi := i.isLt
+ simp_all
+ case succ n Hn =>
+ intro tys fl Hvalid Hlen i x;
+ cases fl <;> simp at Hlen i x Hvalid
+ rename_i ity oty tys f fl
+ have ⟨ Hvf, Hvalid ⟩ := Hvalid
+ have Hvf1: is_valid_p k fl := by
+ simp [Hvalid, Funs.is_valid_p]
+ have Hn := @Hn tys fl Hvf1 (by simp [*])
+ -- Case disjunction on i
+ match i with
+ | ⟨ 0, _ ⟩ =>
+ simp at x
+ simp [get_fun]
+ apply (Hvf x)
+ | ⟨ .succ j, HiLt ⟩ =>
+ simp_arith at HiLt
+ simp at x
+ let j : Fin (List.length tys) := ⟨ j, by simp_arith [HiLt] ⟩
+ have Hn := Hn j x
+ apply Hn
+
+ def Funs.is_valid_p_is_valid_p
+ (tys : List in_out_ty)
+ (k : k_ty (Fin (List.length tys)) (λ i => (tys.get i).fst) (fun i x => (List.get tys i).snd x))
+ (fl : Funs (Fin tys.length) (λ i => (tys.get i).fst) (λ i x => (tys.get i).snd x) tys) :
+ fl.is_valid_p k →
+ ∀ (i : Fin tys.length) (x : (tys.get i).fst),
+ FixI.is_valid_p k (fun k => get_fun fl i k x)
+ := by
+ intro Hvalid
+ apply is_valid_p_is_valid_p_aux; simp [*]
+
+end FixI
+
+namespace Ex1
+ /- An example of use of the fixed-point -/
+ open Primitives Fix
+
+ variable {a : Type} (k : (List a × Int) → Result a)
+
+ def list_nth_body (x : (List a × Int)) : Result a :=
+ let (ls, i) := x
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else k (tl, i - 1)
+
+ theorem list_nth_body_is_valid: ∀ k x, is_valid_p k (λ k => @list_nth_body a k x) := by
+ intro k x
+ simp [list_nth_body]
+ split <;> simp
+ split <;> simp
+
+ def list_nth (ls : List a) (i : Int) : Result a := fix list_nth_body (ls, i)
+
+ -- The unfolding equation - diverges if `i < 0`
+ theorem list_nth_eq (ls : List a) (i : Int) :
+ list_nth ls i =
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else list_nth tl (i - 1)
+ := by
+ have Heq := is_valid_fix_fixed_eq (@list_nth_body_is_valid a)
+ simp [list_nth]
+ conv => lhs; rw [Heq]
+
+end Ex1
+
+namespace Ex2
+ /- Same as Ex1, but we make the body of nth non tail-rec (this is mostly
+ to see what happens when there are let-bindings) -/
+ open Primitives Fix
+
+ variable {a : Type} (k : (List a × Int) → Result a)
+
+ def list_nth_body (x : (List a × Int)) : Result a :=
+ let (ls, i) := x
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else
+ do
+ let y ← k (tl, i - 1)
+ .ret y
+
+ theorem list_nth_body_is_valid: ∀ k x, is_valid_p k (λ k => @list_nth_body a k x) := by
+ intro k x
+ simp [list_nth_body]
+ split <;> simp
+ split <;> simp
+ apply is_valid_p_bind <;> intros <;> simp_all
+
+ def list_nth (ls : List a) (i : Int) : Result a := fix list_nth_body (ls, i)
+
+ -- The unfolding equation - diverges if `i < 0`
+ theorem list_nth_eq (ls : List a) (i : Int) :
+ (list_nth ls i =
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else
+ do
+ let y ← list_nth tl (i - 1)
+ .ret y)
+ := by
+ have Heq := is_valid_fix_fixed_eq (@list_nth_body_is_valid a)
+ simp [list_nth]
+ conv => lhs; rw [Heq]
+
+end Ex2
+
+namespace Ex3
+ /- Mutually recursive functions - first encoding (see Ex4 for a better encoding) -/
+ open Primitives Fix
+
+ /- Because we have mutually recursive functions, we use a sum for the inputs
+ and the output types:
+ - inputs: the sum allows to select the function to call in the recursive
+ calls (and the functions may not have the same input types)
+ - outputs: this case is degenerate because `even` and `odd` have the same
+ return type `Bool`, but generally speaking we need a sum type because
+ the functions in the mutually recursive group may have different
+ return types.
+ -/
+ variable (k : (Int ⊕ Int) → Result (Bool ⊕ Bool))
+
+ def is_even_is_odd_body (x : (Int ⊕ Int)) : Result (Bool ⊕ Bool) :=
+ match x with
+ | .inl i =>
+ -- Body of `is_even`
+ if i = 0
+ then .ret (.inl true) -- We use .inl because this is `is_even`
+ else
+ do
+ let b ←
+ do
+ -- Call `odd`: we need to wrap the input value in `.inr`, then
+ -- extract the output value
+ let r ← k (.inr (i- 1))
+ match r with
+ | .inl _ => .fail .panic -- Invalid output
+ | .inr b => .ret b
+ -- Wrap the return value
+ .ret (.inl b)
+ | .inr i =>
+ -- Body of `is_odd`
+ if i = 0
+ then .ret (.inr false) -- We use .inr because this is `is_odd`
+ else
+ do
+ let b ←
+ do
+ -- Call `is_even`: we need to wrap the input value in .inr, then
+ -- extract the output value
+ let r ← k (.inl (i- 1))
+ match r with
+ | .inl b => .ret b
+ | .inr _ => .fail .panic -- Invalid output
+ -- Wrap the return value
+ .ret (.inr b)
+
+ theorem is_even_is_odd_body_is_valid:
+ ∀ k x, is_valid_p k (λ k => is_even_is_odd_body k x) := by
+ intro k x
+ simp [is_even_is_odd_body]
+ split <;> simp <;> split <;> simp
+ apply is_valid_p_bind; simp
+ intros; split <;> simp
+ apply is_valid_p_bind; simp
+ intros; split <;> simp
+
+ def is_even (i : Int): Result Bool :=
+ do
+ let r ← fix is_even_is_odd_body (.inl i)
+ match r with
+ | .inl b => .ret b
+ | .inr _ => .fail .panic
+
+ def is_odd (i : Int): Result Bool :=
+ do
+ let r ← fix is_even_is_odd_body (.inr i)
+ match r with
+ | .inl _ => .fail .panic
+ | .inr b => .ret b
+
+ -- The unfolding equation for `is_even` - diverges if `i < 0`
+ theorem is_even_eq (i : Int) :
+ is_even i = (if i = 0 then .ret true else is_odd (i - 1))
+ := by
+ have Heq := is_valid_fix_fixed_eq is_even_is_odd_body_is_valid
+ simp [is_even, is_odd]
+ conv => lhs; rw [Heq]; simp; rw [is_even_is_odd_body]; simp
+ -- Very annoying: we need to swap the matches
+ -- Doing this with rewriting lemmas is hard generally speaking
+ -- (especially as we may have to generate lemmas for user-defined
+ -- inductives on the fly).
+ -- The simplest is to repeatedly split then simplify (we identify
+ -- the outer match or monadic let-binding, and split on its scrutinee)
+ split <;> simp
+ cases H0 : fix is_even_is_odd_body (Sum.inr (i - 1)) <;> simp
+ rename_i v
+ split <;> simp
+
+ -- The unfolding equation for `is_odd` - diverges if `i < 0`
+ theorem is_odd_eq (i : Int) :
+ is_odd i = (if i = 0 then .ret false else is_even (i - 1))
+ := by
+ have Heq := is_valid_fix_fixed_eq is_even_is_odd_body_is_valid
+ simp [is_even, is_odd]
+ conv => lhs; rw [Heq]; simp; rw [is_even_is_odd_body]; simp
+ -- Same remark as for `even`
+ split <;> simp
+ cases H0 : fix is_even_is_odd_body (Sum.inl (i - 1)) <;> simp
+ rename_i v
+ split <;> simp
+
+end Ex3
+
+namespace Ex4
+ /- Mutually recursive functions - 2nd encoding -/
+ open Primitives FixI
+
+ /- We make the input type and output types dependent on a parameter -/
+ @[simp] def tys : List in_out_ty := [mk_in_out_ty Int (λ _ => Bool), mk_in_out_ty Int (λ _ => Bool)]
+ @[simp] def input_ty (i : Fin 2) : Type := (tys.get i).fst
+ @[simp] def output_ty (i : Fin 2) (x : input_ty i) : Type :=
+ (tys.get i).snd x
+
+ /- The bodies are more natural -/
+ def is_even_body (k : (i : Fin 2) → (x : input_ty i) → Result (output_ty i x)) (i : Int) : Result Bool :=
+ if i = 0
+ then .ret true
+ else do
+ let b ← k 1 (i - 1)
+ .ret b
+
+ def is_odd_body (k : (i : Fin 2) → (x : input_ty i) → Result (output_ty i x)) (i : Int) : Result Bool :=
+ if i = 0
+ then .ret false
+ else do
+ let b ← k 0 (i - 1)
+ .ret b
+
+ @[simp] def bodies :
+ Funs (Fin 2) input_ty output_ty
+ [mk_in_out_ty Int (λ _ => Bool), mk_in_out_ty Int (λ _ => Bool)] :=
+ Funs.Cons (is_even_body) (Funs.Cons (is_odd_body) Funs.Nil)
+
+ def body (k : (i : Fin 2) → (x : input_ty i) → Result (output_ty i x)) (i: Fin 2) :
+ (x : input_ty i) → Result (output_ty i x) := get_fun bodies i k
+
+ theorem body_is_valid : is_valid body := by
+ -- Split the proof into proofs of validity of the individual bodies
+ rw [is_valid]
+ simp only [body]
+ intro k
+ apply (Funs.is_valid_p_is_valid_p tys)
+ simp [Funs.is_valid_p]
+ (repeat (apply And.intro)) <;> intro x <;> simp at x <;>
+ simp only [is_even_body, is_odd_body]
+ -- Prove the validity of the individual bodies
+ . split <;> simp
+ apply is_valid_p_bind <;> simp
+ . split <;> simp
+ apply is_valid_p_bind <;> simp
+
+ theorem body_fix_eq : fix body = body (fix body) :=
+ is_valid_fix_fixed_eq body_is_valid
+
+ def is_even (i : Int) : Result Bool := fix body 0 i
+ def is_odd (i : Int) : Result Bool := fix body 1 i
+
+ theorem is_even_eq (i : Int) : is_even i =
+ (if i = 0
+ then .ret true
+ else do
+ let b ← is_odd (i - 1)
+ .ret b) := by
+ simp [is_even, is_odd];
+ conv => lhs; rw [body_fix_eq]
+
+ theorem is_odd_eq (i : Int) : is_odd i =
+ (if i = 0
+ then .ret false
+ else do
+ let b ← is_even (i - 1)
+ .ret b) := by
+ simp [is_even, is_odd];
+ conv => lhs; rw [body_fix_eq]
+end Ex4
+
+namespace Ex5
+ /- Higher-order example -/
+ open Primitives Fix
+
+ variable {a b : Type}
+
+ /- An auxiliary function, which doesn't require the fixed-point -/
+ def map (f : a → Result b) (ls : List a) : Result (List b) :=
+ match ls with
+ | [] => .ret []
+ | hd :: tl =>
+ do
+ let hd ← f hd
+ let tl ← map f tl
+ .ret (hd :: tl)
+
+ /- The validity theorem for `map`, generic in `f` -/
+ theorem map_is_valid
+ {{f : (a → Result b) → a → Result c}}
+ (Hfvalid : ∀ k x, is_valid_p k (λ k => f k x))
+ (k : (a → Result b) → a → Result b)
+ (ls : List a) :
+ is_valid_p k (λ k => map (f k) ls) := by
+ induction ls <;> simp [map]
+ apply is_valid_p_bind <;> simp_all
+ intros
+ apply is_valid_p_bind <;> simp_all
+
+ /- An example which uses map -/
+ inductive Tree (a : Type) :=
+ | leaf (x : a)
+ | node (tl : List (Tree a))
+
+ def id_body (k : Tree a → Result (Tree a)) (t : Tree a) : Result (Tree a) :=
+ match t with
+ | .leaf x => .ret (.leaf x)
+ | .node tl =>
+ do
+ let tl ← map k tl
+ .ret (.node tl)
+
+ theorem id_body_is_valid :
+ ∀ k x, is_valid_p k (λ k => @id_body a k x) := by
+ intro k x
+ simp only [id_body]
+ split <;> simp
+ apply is_valid_p_bind <;> simp [*]
+ -- We have to show that `map k tl` is valid
+ apply map_is_valid;
+ -- Remark: if we don't do the intro, then the last step is expensive:
+ -- "typeclass inference of Nonempty took 119ms"
+ intro k x
+ simp only [is_valid_p_same, is_valid_p_rec]
+
+ def id (t : Tree a) := fix id_body t
+
+ -- The unfolding equation
+ theorem id_eq (t : Tree a) :
+ (id t =
+ match t with
+ | .leaf x => .ret (.leaf x)
+ | .node tl =>
+ do
+ let tl ← map id tl
+ .ret (.node tl))
+ := by
+ have Heq := is_valid_fix_fixed_eq (@id_body_is_valid a)
+ simp [id]
+ conv => lhs; rw [Heq]; simp; rw [id_body]
+
+end Ex5
+
+namespace Ex6
+ /- `list_nth` again, but this time we use FixI -/
+ open Primitives FixI
+
+ @[simp] def tys.{u} : List in_out_ty :=
+ [mk_in_out_ty ((a:Type u) × (List a × Int)) (λ ⟨ a, _ ⟩ => a)]
+
+ @[simp] def input_ty (i : Fin 1) := (tys.get i).fst
+ @[simp] def output_ty (i : Fin 1) (x : input_ty i) :=
+ (tys.get i).snd x
+
+ def list_nth_body.{u} (k : (i:Fin 1) → (x:input_ty i) → Result (output_ty i x))
+ (x : (a : Type u) × List a × Int) : Result x.fst :=
+ let ⟨ a, ls, i ⟩ := x
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else k 0 ⟨ a, tl, i - 1 ⟩
+
+ @[simp] def bodies :
+ Funs (Fin 1) input_ty output_ty tys :=
+ Funs.Cons list_nth_body Funs.Nil
+
+ def body (k : (i : Fin 1) → (x : input_ty i) → Result (output_ty i x)) (i: Fin 1) :
+ (x : input_ty i) → Result (output_ty i x) := get_fun bodies i k
+
+ theorem body_is_valid: is_valid body := by
+ -- Split the proof into proofs of validity of the individual bodies
+ rw [is_valid]
+ simp only [body]
+ intro k
+ apply (Funs.is_valid_p_is_valid_p tys)
+ simp [Funs.is_valid_p]
+ (repeat (apply And.intro)); intro x; simp at x
+ simp only [list_nth_body]
+ -- Prove the validity of the individual bodies
+ intro k x
+ simp [list_nth_body]
+ split <;> simp
+ split <;> simp
+
+ -- Writing the proof terms explicitly
+ theorem list_nth_body_is_valid' (k : k_ty (Fin 1) input_ty output_ty)
+ (x : (a : Type u) × List a × Int) : is_valid_p k (fun k => list_nth_body k x) :=
+ let ⟨ a, ls, i ⟩ := x
+ match ls with
+ | [] => is_valid_p_same k (.fail .panic)
+ | hd :: tl =>
+ is_valid_p_ite k (Eq i 0) (is_valid_p_same k (.ret hd)) (is_valid_p_rec k 0 ⟨a, tl, i-1⟩)
+
+ theorem body_is_valid' : is_valid body :=
+ fun k =>
+ Funs.is_valid_p_is_valid_p tys k bodies
+ (And.intro (list_nth_body_is_valid' k) (Funs.is_valid_p_Nil k))
+
+ def list_nth {a: Type u} (ls : List a) (i : Int) : Result a :=
+ fix body 0 ⟨ a, ls , i ⟩
+
+ -- The unfolding equation - diverges if `i < 0`
+ theorem list_nth_eq (ls : List a) (i : Int) :
+ list_nth ls i =
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else list_nth tl (i - 1)
+ := by
+ have Heq := is_valid_fix_fixed_eq body_is_valid
+ simp [list_nth]
+ conv => lhs; rw [Heq]
+
+ -- Write the proof term explicitly: the generation of the proof term (without tactics)
+ -- is automatable, and the proof term is actually a lot simpler and smaller when we
+ -- don't use tactics.
+ theorem list_nth_eq'.{u} {a : Type u} (ls : List a) (i : Int) :
+ list_nth ls i =
+ match ls with
+ | [] => .fail .panic
+ | hd :: tl =>
+ if i = 0 then .ret hd
+ else list_nth tl (i - 1)
+ :=
+ -- Use the fixed-point equation
+ have Heq := is_valid_fix_fixed_eq body_is_valid.{u}
+ -- Add the index
+ have Heqi := congr_fun Heq 0
+ -- Add the input
+ have Heqix := congr_fun Heqi { fst := a, snd := (ls, i) }
+ -- Done
+ Heqix
+
+end Ex6
diff --git a/backends/lean/Base/Diverge/Elab.lean b/backends/lean/Base/Diverge/Elab.lean
new file mode 100644
index 00000000..f109e847
--- /dev/null
+++ b/backends/lean/Base/Diverge/Elab.lean
@@ -0,0 +1,1162 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Base.Utils
+import Base.Diverge.Base
+import Base.Diverge.ElabBase
+
+namespace Diverge
+
+/- Automating the generation of the encoding and the proofs so as to use nice
+ syntactic sugar. -/
+
+syntax (name := divergentDef)
+ declModifiers "divergent" "def" declId ppIndent(optDeclSig) declVal : command
+
+open Lean Elab Term Meta Primitives Lean.Meta
+open Utils
+
+/- The following was copied from the `wfRecursion` function. -/
+
+open WF in
+
+def mkProd (x y : Expr) : MetaM Expr :=
+ mkAppM ``Prod.mk #[x, y]
+
+def mkInOutTy (x y : Expr) : MetaM Expr :=
+ mkAppM ``FixI.mk_in_out_ty #[x, y]
+
+-- Return the `a` in `Return a`
+def getResultTy (ty : Expr) : MetaM Expr :=
+ ty.withApp fun f args => do
+ if ¬ f.isConstOf ``Result ∨ args.size ≠ 1 then
+ throwError "Invalid argument to getResultTy: {ty}"
+ else
+ pure (args.get! 0)
+
+/- Deconstruct a sigma type.
+
+ For instance, deconstructs `(a : Type) × List a` into
+ `Type` and `λ a => List a`.
+ -/
+def getSigmaTypes (ty : Expr) : MetaM (Expr × Expr) := do
+ ty.withApp fun f args => do
+ if ¬ f.isConstOf ``Sigma ∨ args.size ≠ 2 then
+ throwError "Invalid argument to getSigmaTypes: {ty}"
+ else
+ pure (args.get! 0, args.get! 1)
+
+/- Generate a Sigma type from a list of *variables* (all the expressions
+ must be variables).
+
+ Example:
+ - xl = [(a:Type), (ls:List a), (i:Int)]
+
+ Generates:
+ `(a:Type) × (ls:List a) × (i:Int)`
+
+ -/
+def mkSigmasType (xl : List Expr) : MetaM Expr :=
+ match xl with
+ | [] => do
+ trace[Diverge.def.sigmas] "mkSigmasOfTypes: []"
+ pure (Expr.const ``PUnit.unit [])
+ | [x] => do
+ trace[Diverge.def.sigmas] "mkSigmasOfTypes: [{x}]"
+ let ty ← Lean.Meta.inferType x
+ pure ty
+ | x :: xl => do
+ trace[Diverge.def.sigmas] "mkSigmasOfTypes: [{x}::{xl}]"
+ let alpha ← Lean.Meta.inferType x
+ let sty ← mkSigmasType xl
+ trace[Diverge.def.sigmas] "mkSigmasOfTypes: [{x}::{xl}]: alpha={alpha}, sty={sty}"
+ let beta ← mkLambdaFVars #[x] sty
+ trace[Diverge.def.sigmas] "mkSigmasOfTypes: ({alpha}) ({beta})"
+ mkAppOptM ``Sigma #[some alpha, some beta]
+
+/- Apply a lambda expression to some arguments, simplifying the lambdas -/
+def applyLambdaToArgs (e : Expr) (xs : Array Expr) : MetaM Expr := do
+ lambdaTelescopeN e xs.size fun vars body =>
+ -- Create the substitution
+ let s : HashMap FVarId Expr := HashMap.ofList (List.zip (vars.toList.map Expr.fvarId!) xs.toList)
+ -- Substitute in the body
+ pure (body.replace fun e =>
+ match e with
+ | Expr.fvar fvarId => match s.find? fvarId with
+ | none => e
+ | some v => v
+ | _ => none)
+
+/- Group a list of expressions into a dependent tuple.
+
+ Example:
+ xl = [`a : Type`, `ls : List a`]
+ returns:
+ `⟨ (a:Type), (ls: List a) ⟩`
+
+ We need the type argument because as the elements in the tuple are
+ "concrete", we can't in all generality figure out the type of the tuple.
+
+ Example:
+ `⟨ True, 3 ⟩ : (x : Bool) × (if x then Int else Unit)`
+ -/
+def mkSigmasVal (ty : Expr) (xl : List Expr) : MetaM Expr :=
+ match xl with
+ | [] => do
+ trace[Diverge.def.sigmas] "mkSigmasVal: []"
+ pure (Expr.const ``PUnit.unit [])
+ | [x] => do
+ trace[Diverge.def.sigmas] "mkSigmasVal: [{x}]"
+ pure x
+ | fst :: xl => do
+ trace[Diverge.def.sigmas] "mkSigmasVal: [{fst}::{xl}]"
+ -- Deconstruct the type
+ let (alpha, beta) ← getSigmaTypes ty
+ -- Compute the "second" field
+ -- Specialize beta for fst
+ let nty ← applyLambdaToArgs beta #[fst]
+ -- Recursive call
+ let snd ← mkSigmasVal nty xl
+ -- Put everything together
+ trace[Diverge.def.sigmas] "mkSigmasVal:\n{alpha}\n{beta}\n{fst}\n{snd}"
+ mkAppOptM ``Sigma.mk #[some alpha, some beta, some fst, some snd]
+
+def mkAnonymous (s : String) (i : Nat) : Name :=
+ .num (.str .anonymous s) i
+
+/- Given a list of values `[x0:ty0, ..., xn:ty1]`, where every `xi` might use the previous
+ `xj` (j < i) and a value `out` which uses `x0`, ..., `xn`, generate the following
+ expression:
+ ```
+ fun x:((x0:ty0) × ... × (xn:tyn) => -- **Dependent** tuple
+ match x with
+ | (x0, ..., xn) => out
+ ```
+
+ The `index` parameter is used for naming purposes: we use it to numerotate the
+ bound variables that we introduce.
+
+ We use this function to currify functions (the function bodies given to the
+ fixed-point operator must be unary functions).
+
+ Example:
+ ========
+ - xl = `[a:Type, ls:List a, i:Int]`
+ - out = `a`
+ - index = 0
+
+ generates (getting rid of most of the syntactic sugar):
+ ```
+ λ scrut0 => match scrut0 with
+ | Sigma.mk x scrut1 =>
+ match scrut1 with
+ | Sigma.mk ls i =>
+ a
+ ```
+-/
+partial def mkSigmasMatch (xl : List Expr) (out : Expr) (index : Nat := 0) : MetaM Expr :=
+ match xl with
+ | [] => do
+ -- This would be unexpected
+ throwError "mkSigmasMatch: empyt list of input parameters"
+ | [x] => do
+ -- In the example given for the explanations: this is the inner match case
+ trace[Diverge.def.sigmas] "mkSigmasMatch: [{x}]"
+ mkLambdaFVars #[x] out
+ | fst :: xl => do
+ -- In the example given for the explanations: this is the outer match case
+ -- Remark: for the naming purposes, we use the same convention as for the
+ -- fields and parameters in `Sigma.casesOn` and `Sigma.mk` (looking at
+ -- those definitions might help)
+ --
+ -- We want to build the match expression:
+ -- ```
+ -- λ scrut =>
+ -- match scrut with
+ -- | Sigma.mk x ... -- the hole is given by a recursive call on the tail
+ -- ```
+ trace[Diverge.def.sigmas] "mkSigmasMatch: [{fst}::{xl}]"
+ let alpha ← Lean.Meta.inferType fst
+ let snd_ty ← mkSigmasType xl
+ let beta ← mkLambdaFVars #[fst] snd_ty
+ let snd ← mkSigmasMatch xl out (index + 1)
+ let mk ← mkLambdaFVars #[fst] snd
+ -- Introduce the "scrut" variable
+ let scrut_ty ← mkSigmasType (fst :: xl)
+ withLocalDeclD (mkAnonymous "scrut" index) scrut_ty fun scrut => do
+ trace[Diverge.def.sigmas] "mkSigmasMatch: scrut: ({scrut}) : ({← inferType scrut})"
+ -- TODO: make the computation of the motive more efficient
+ let motive ← do
+ let out_ty ← inferType out
+ match out_ty with
+ | .sort _ | .lit _ | .const .. =>
+ -- The type of the motive doesn't depend on the scrutinee
+ mkLambdaFVars #[scrut] out_ty
+ | _ =>
+ -- The type of the motive *may* depend on the scrutinee
+ -- TODO: make this more efficient (we could change the output type of
+ -- mkSigmasMatch
+ mkSigmasMatch (fst :: xl) out_ty
+ -- The final expression: putting everything together
+ trace[Diverge.def.sigmas] "mkSigmasMatch:\n ({alpha})\n ({beta})\n ({motive})\n ({scrut})\n ({mk})"
+ let sm ← mkAppOptM ``Sigma.casesOn #[some alpha, some beta, some motive, some scrut, some mk]
+ -- Abstracting the "scrut" variable
+ let sm ← mkLambdaFVars #[scrut] sm
+ trace[Diverge.def.sigmas] "mkSigmasMatch: sm: {sm}"
+ pure sm
+
+/- Small tests for list_nth: give a model of what `mkSigmasMatch` should generate -/
+private def list_nth_out_ty_inner (a :Type) (scrut1: @Sigma (List a) (fun (_ls : List a) => Int)) :=
+ @Sigma.casesOn (List a)
+ (fun (_ls : List a) => Int)
+ (fun (_scrut1:@Sigma (List a) (fun (_ls : List a) => Int)) => Type)
+ scrut1
+ (fun (_ls : List a) (_i : Int) => Primitives.Result a)
+
+private def list_nth_out_ty_outer (scrut0 : @Sigma (Type) (fun (a:Type) =>
+ @Sigma (List a) (fun (_ls : List a) => Int))) :=
+ @Sigma.casesOn (Type)
+ (fun (a:Type) => @Sigma (List a) (fun (_ls : List a) => Int))
+ (fun (_scrut0:@Sigma (Type) (fun (a:Type) => @Sigma (List a) (fun (_ls : List a) => Int))) => Type)
+ scrut0
+ (fun (a : Type) (scrut1: @Sigma (List a) (fun (_ls : List a) => Int)) =>
+ list_nth_out_ty_inner a scrut1)
+/- -/
+
+-- Return the expression: `Fin n`
+-- TODO: use more
+def mkFin (n : Nat) : Expr :=
+ mkAppN (.const ``Fin []) #[.lit (.natVal n)]
+
+-- Return the expression: `i : Fin n`
+def mkFinVal (n i : Nat) : MetaM Expr := do
+ let n_lit : Expr := .lit (.natVal (n - 1))
+ let i_lit : Expr := .lit (.natVal i)
+ -- We could use `trySynthInstance`, but as we know the instance that we are
+ -- going to use, we can save the lookup
+ let ofNat ← mkAppOptM ``Fin.instOfNatFinHAddNatInstHAddInstAddNatOfNat #[n_lit, i_lit]
+ mkAppOptM ``OfNat.ofNat #[none, none, ofNat]
+
+/- Generate and declare as individual definitions the bodies for the individual funcions:
+ - replace the recursive calls with calls to the continutation `k`
+ - make those bodies take one single dependent tuple as input
+
+ We name the declarations: "[original_name].body".
+ We return the new declarations.
+ -/
+def mkDeclareUnaryBodies (grLvlParams : List Name) (kk_var : Expr)
+ (inOutTys : Array (Expr × Expr)) (preDefs : Array PreDefinition) :
+ MetaM (Array Expr) := do
+ let grSize := preDefs.size
+
+ -- Compute the map from name to (index × input type).
+ -- Remark: the continuation has an indexed type; we use the index (a finite number of
+ -- type `Fin`) to control which function we call at the recursive call site.
+ let nameToInfo : HashMap Name (Nat × Expr) :=
+ let bl := preDefs.mapIdx fun i d => (d.declName, (i.val, (inOutTys.get! i.val).fst))
+ HashMap.ofList bl.toList
+
+ trace[Diverge.def.genBody] "nameToId: {nameToInfo.toList}"
+
+ -- Auxiliary function to explore the function bodies and replace the
+ -- recursive calls
+ let visit_e (i : Nat) (e : Expr) : MetaM Expr := do
+ trace[Diverge.def.genBody] "visiting expression (dept: {i}): {e}"
+ let ne ← do
+ match e with
+ | .app .. => do
+ e.withApp fun f args => do
+ trace[Diverge.def.genBody] "this is an app: {f} {args}"
+ -- Check if this is a recursive call
+ if f.isConst then
+ let name := f.constName!
+ match nameToInfo.find? name with
+ | none => pure e
+ | some (id, in_ty) =>
+ trace[Diverge.def.genBody] "this is a recursive call"
+ -- This is a recursive call: replace it
+ -- Compute the index
+ let i ← mkFinVal grSize id
+ -- Put the arguments in one big dependent tuple
+ let args ← mkSigmasVal in_ty args.toList
+ mkAppM' kk_var #[i, args]
+ else
+ -- Not a recursive call: do nothing
+ pure e
+ | .const name _ =>
+ -- Sanity check: we eliminated all the recursive calls
+ if (nameToInfo.find? name).isSome then
+ throwError "mkUnaryBodies: a recursive call was not eliminated"
+ else pure e
+ | _ => pure e
+ trace[Diverge.def.genBody] "done with expression (depth: {i}): {e}"
+ pure ne
+
+ -- Explore the bodies
+ preDefs.mapM fun preDef => do
+ -- Replace the recursive calls
+ trace[Diverge.def.genBody] "About to replace recursive calls in {preDef.declName}"
+ let body ← mapVisit visit_e preDef.value
+ trace[Diverge.def.genBody] "Body after replacement of the recursive calls: {body}"
+
+ -- Currify the function by grouping the arguments into a dependent tuple
+ -- (over which we match to retrieve the individual arguments).
+ lambdaTelescope body fun args body => do
+ let body ← mkSigmasMatch args.toList body 0
+
+ -- Add the declaration
+ let value ← mkLambdaFVars #[kk_var] body
+ let name := preDef.declName.append "body"
+ let levelParams := grLvlParams
+ let decl := Declaration.defnDecl {
+ name := name
+ levelParams := levelParams
+ type := ← inferType value -- TODO: change the type
+ value := value
+ hints := ReducibilityHints.regular (getMaxHeight (← getEnv) value + 1)
+ safety := .safe
+ all := [name]
+ }
+ addDecl decl
+ trace[Diverge.def] "individual body of {preDef.declName}: {body}"
+ -- Return the constant
+ let body := Lean.mkConst name (levelParams.map .param)
+ -- let body ← mkAppM' body #[kk_var]
+ trace[Diverge.def] "individual body (after decl): {body}"
+ pure body
+
+-- Generate a unique function body from the bodies of the mutually recursive group,
+-- and add it as a declaration in the context.
+-- We return the list of bodies (of type `FixI.Funs ...`) and the mutually recursive body.
+def mkDeclareMutRecBody (grName : Name) (grLvlParams : List Name)
+ (kk_var i_var : Expr)
+ (in_ty out_ty : Expr) (inOutTys : List (Expr × Expr))
+ (bodies : Array Expr) : MetaM (Expr × Expr) := do
+ -- Generate the body
+ let grSize := bodies.size
+ let finTypeExpr := mkFin grSize
+ -- TODO: not very clean
+ let inOutTyType ← do
+ let (x, y) := inOutTys.get! 0
+ inferType (← mkInOutTy x y)
+ let rec mkFuns (inOutTys : List (Expr × Expr)) (bl : List Expr) : MetaM Expr :=
+ match inOutTys, bl with
+ | [], [] =>
+ mkAppOptM ``FixI.Funs.Nil #[finTypeExpr, in_ty, out_ty]
+ | (ity, oty) :: inOutTys, b :: bl => do
+ -- Retrieving ity and oty - this is not very clean
+ let inOutTysExpr ← mkListLit inOutTyType (← inOutTys.mapM (λ (x, y) => mkInOutTy x y))
+ let fl ← mkFuns inOutTys bl
+ mkAppOptM ``FixI.Funs.Cons #[finTypeExpr, in_ty, out_ty, ity, oty, inOutTysExpr, b, fl]
+ | _, _ => throwError "mkDeclareMutRecBody: `tys` and `bodies` don't have the same length"
+ let bodyFuns ← mkFuns inOutTys bodies.toList
+ -- Wrap in `get_fun`
+ let body ← mkAppM ``FixI.get_fun #[bodyFuns, i_var, kk_var]
+ -- Add the index `i` and the continuation `k` as a variables
+ let body ← mkLambdaFVars #[kk_var, i_var] body
+ trace[Diverge.def] "mkDeclareMutRecBody: body: {body}"
+ -- Add the declaration
+ let name := grName.append "mut_rec_body"
+ let levelParams := grLvlParams
+ let decl := Declaration.defnDecl {
+ name := name
+ levelParams := levelParams
+ type := ← inferType body
+ value := body
+ hints := ReducibilityHints.regular (getMaxHeight (← getEnv) body + 1)
+ safety := .safe
+ all := [name]
+ }
+ addDecl decl
+ -- Return the bodies and the constant
+ pure (bodyFuns, Lean.mkConst name (levelParams.map .param))
+
+def isCasesExpr (e : Expr) : MetaM Bool := do
+ let e := e.getAppFn
+ if e.isConst then
+ return isCasesOnRecursor (← getEnv) e.constName
+ else return false
+
+structure MatchInfo where
+ matcherName : Name
+ matcherLevels : Array Level
+ params : Array Expr
+ motive : Expr
+ scruts : Array Expr
+ branchesNumParams : Array Nat
+ branches : Array Expr
+
+instance : ToMessageData MatchInfo where
+ -- This is not a very clean formatting, but we don't need more
+ toMessageData := fun me => m!"\n- matcherName: {me.matcherName}\n- params: {me.params}\n- motive: {me.motive}\n- scruts: {me.scruts}\n- branchesNumParams: {me.branchesNumParams}\n- branches: {me.branches}"
+
+-- Small helper: prove that an expression which doesn't use the continuation `kk`
+-- is valid, and return the proof.
+def proveNoKExprIsValid (k_var : Expr) (e : Expr) : MetaM Expr := do
+ trace[Diverge.def.valid] "proveNoKExprIsValid: {e}"
+ let eIsValid ← mkAppM ``FixI.is_valid_p_same #[k_var, e]
+ trace[Diverge.def.valid] "proveNoKExprIsValid: result:\n{eIsValid}:\n{← inferType eIsValid}"
+ pure eIsValid
+
+mutual
+
+/- Prove that an expression is valid, and return the proof.
+
+ More precisely, if `e` is an expression which potentially uses the continution
+ `kk`, return an expression of type:
+ ```
+ is_valid_p k (λ kk => e)
+ ```
+ -/
+partial def proveExprIsValid (k_var kk_var : Expr) (e : Expr) : MetaM Expr := do
+ trace[Diverge.def.valid] "proveValid: {e}"
+ match e with
+ | .const _ _ => throwError "Unimplemented" -- Shouldn't get there?
+ | .bvar _
+ | .fvar _
+ | .lit _
+ | .mvar _
+ | .sort _ => throwError "Unreachable"
+ | .lam .. => throwError "Unimplemented"
+ | .forallE .. => throwError "Unreachable" -- Shouldn't get there
+ | .letE .. => do
+ -- Telescope all the let-bindings (remark: this also telescopes the lambdas)
+ lambdaLetTelescope e fun xs body => do
+ -- Note that we don't visit the bound values: there shouldn't be
+ -- recursive calls, lambda expressions, etc. inside
+ -- Prove that the body is valid
+ let isValid ← proveExprIsValid k_var kk_var body
+ -- Add the let-bindings around.
+ -- Rem.: the let-binding should be *inside* the `is_valid_p`, not outside,
+ -- but because it reduces in the end it doesn't matter. More precisely:
+ -- `P (let x := v in y)` and `let x := v in P y` reduce to the same expression.
+ mkLambdaFVars xs isValid (usedLetOnly := false)
+ | .mdata _ b => proveExprIsValid k_var kk_var b
+ | .proj _ _ _ =>
+ -- The projection shouldn't use the continuation
+ proveNoKExprIsValid k_var e
+ | .app .. =>
+ e.withApp fun f args => do
+ -- There are several cases: first, check if this is a match/if
+ -- Check if the expression is a (dependent) if then else.
+ -- We treat the if then else expressions differently from the other matches,
+ -- and have dedicated theorems for them.
+ let isIte := e.isIte
+ if isIte || e.isDIte then do
+ e.withApp fun f args => do
+ trace[Diverge.def.valid] "ite/dite: {f}:\n{args}"
+ if args.size ≠ 5 then
+ throwError "Wrong number of parameters for {f}: {args}"
+ let cond := args.get! 1
+ let dec := args.get! 2
+ -- Prove that the branches are valid
+ let br0 := args.get! 3
+ let br1 := args.get! 4
+ let proveBranchValid (br : Expr) : MetaM Expr :=
+ if isIte then proveExprIsValid k_var kk_var br
+ else do
+ -- There is a lambda
+ lambdaOne br fun x br => do
+ let brValid ← proveExprIsValid k_var kk_var br
+ mkLambdaFVars #[x] brValid
+ let br0Valid ← proveBranchValid br0
+ let br1Valid ← proveBranchValid br1
+ let const := if isIte then ``FixI.is_valid_p_ite else ``FixI.is_valid_p_dite
+ let eIsValid ← mkAppOptM const #[none, none, none, none, some k_var, some cond, some dec, none, none, some br0Valid, some br1Valid]
+ trace[Diverge.def.valid] "ite/dite: result:\n{eIsValid}:\n{← inferType eIsValid}"
+ pure eIsValid
+ -- Check if the expression is a match (this case is for when the elaborator
+ -- introduces auxiliary definitions to hide the match behind syntactic
+ -- sugar):
+ else if let some me := ← matchMatcherApp? e then do
+ trace[Diverge.def.valid]
+ "matcherApp:
+ - params: {me.params}
+ - motive: {me.motive}
+ - discrs: {me.discrs}
+ - altNumParams: {me.altNumParams}
+ - alts: {me.alts}
+ - remaining: {me.remaining}"
+ -- matchMatcherApp does all the work for us: we simply need to gather
+ -- the information and call the auxiliary helper `proveMatchIsValid`
+ if me.remaining.size ≠ 0 then
+ throwError "MatcherApp: non empty remaining array: {me.remaining}"
+ let me : MatchInfo := {
+ matcherName := me.matcherName
+ matcherLevels := me.matcherLevels
+ params := me.params
+ motive := me.motive
+ scruts := me.discrs
+ branchesNumParams := me.altNumParams
+ branches := me.alts
+ }
+ proveMatchIsValid k_var kk_var me
+ -- Check if the expression is a raw match (this case is for when the expression
+ -- is a direct call to the primitive `casesOn` function, without syntactic sugar).
+ -- We have to check this case because functions like `mkSigmasMatch`, which we
+ -- use to currify function bodies, introduce such raw matches.
+ else if ← isCasesExpr f then do
+ trace[Diverge.def.valid] "rawMatch: {e}"
+ -- Deconstruct the match, and call the auxiliary helper `proveMatchIsValid`.
+ --
+ -- The casesOn definition is always of the following shape:
+ -- - input parameters (implicit parameters)
+ -- - motive (implicit), -- the motive gives the return type of the match
+ -- - scrutinee (explicit)
+ -- - branches (explicit).
+ -- In particular, we notice that the scrutinee is the first *explicit*
+ -- parameter - this is how we spot it.
+ let matcherName := f.constName!
+ let matcherLevels := f.constLevels!.toArray
+ -- Find the first explicit parameter: this is the scrutinee
+ forallTelescope (← inferType f) fun xs _ => do
+ let rec findFirstExplicit (i : Nat) : MetaM Nat := do
+ if i ≥ xs.size then throwError "Unexpected: could not find an explicit parameter"
+ else
+ let x := xs.get! i
+ let xFVarId := x.fvarId!
+ let localDecl ← xFVarId.getDecl
+ match localDecl.binderInfo with
+ | .default => pure i
+ | _ => findFirstExplicit (i + 1)
+ let scrutIdx ← findFirstExplicit 0
+ -- Split the arguments
+ let params := args.extract 0 (scrutIdx - 1)
+ let motive := args.get! (scrutIdx - 1)
+ let scrut := args.get! scrutIdx
+ let branches := args.extract (scrutIdx + 1) args.size
+ -- Compute the number of parameters for the branches: for this we use
+ -- the type of the uninstantiated casesOn constant (we can't just
+ -- destruct the lambdas in the branch expressions because the result
+ -- of a match might be a lambda expression).
+ let branchesNumParams : Array Nat ← do
+ let env ← getEnv
+ let decl := env.constants.find! matcherName
+ let ty := decl.type
+ forallTelescope ty fun xs _ => do
+ let xs := xs.extract (scrutIdx + 1) xs.size
+ xs.mapM fun x => do
+ let xty ← inferType x
+ forallTelescope xty fun ys _ => do
+ pure ys.size
+ let me : MatchInfo := {
+ matcherName,
+ matcherLevels,
+ params,
+ motive,
+ scruts := #[scrut],
+ branchesNumParams,
+ branches,
+ }
+ proveMatchIsValid k_var kk_var me
+ -- Check if this is a monadic let-binding
+ else if f.isConstOf ``Bind.bind then do
+ trace[Diverge.def.valid] "bind:\n{args}"
+ -- We simply need to prove that the subexpressions are valid, and call
+ -- the appropriate lemma.
+ let x := args.get! 4
+ let y := args.get! 5
+ -- Prove that the subexpressions are valid
+ let xValid ← proveExprIsValid k_var kk_var x
+ trace[Diverge.def.valid] "bind: xValid:\n{xValid}:\n{← inferType xValid}"
+ let yValid ← do
+ -- This is a lambda expression
+ lambdaOne y fun x y => do
+ trace[Diverge.def.valid] "bind: y: {y}"
+ let yValid ← proveExprIsValid k_var kk_var y
+ trace[Diverge.def.valid] "bind: yValid (no forall): {yValid}"
+ trace[Diverge.def.valid] "bind: yValid: x: {x}"
+ let yValid ← mkLambdaFVars #[x] yValid
+ trace[Diverge.def.valid] "bind: yValid (forall): {yValid}: {← inferType yValid}"
+ pure yValid
+ -- Put everything together
+ trace[Diverge.def.valid] "bind:\n- xValid: {xValid}: {← inferType xValid}\n- yValid: {yValid}: {← inferType yValid}"
+ mkAppM ``FixI.is_valid_p_bind #[xValid, yValid]
+ -- Check if this is a recursive call, i.e., a call to the continuation `kk`
+ else if f.isFVarOf kk_var.fvarId! then do
+ trace[Diverge.def.valid] "rec: args: \n{args}"
+ if args.size ≠ 2 then throwError "Recursive call with invalid number of parameters: {args}"
+ let i_arg := args.get! 0
+ let x_arg := args.get! 1
+ let eIsValid ← mkAppM ``FixI.is_valid_p_rec #[k_var, i_arg, x_arg]
+ trace[Diverge.def.valid] "rec: result: \n{eIsValid}"
+ pure eIsValid
+ else do
+ -- Remaining case: normal application.
+ -- It shouldn't use the continuation.
+ proveNoKExprIsValid k_var e
+
+-- Prove that a match expression is valid.
+partial def proveMatchIsValid (k_var kk_var : Expr) (me : MatchInfo) : MetaM Expr := do
+ trace[Diverge.def.valid] "proveMatchIsValid: {me}"
+ -- Prove the validity of the branch expressions
+ let branchesValid:Array Expr ← me.branches.mapIdxM fun idx br => do
+ -- Go inside the lambdas - note that we have to be careful: some of the
+ -- binders might come from the match, and some of the binders might come
+ -- from the fact that the expression in the match is a lambda expression:
+ -- we use the branchesNumParams field for this reason
+ let numParams := me.branchesNumParams.get! idx
+ lambdaTelescopeN br numParams fun xs br => do
+ -- Prove that the branch expression is valid
+ let brValid ← proveExprIsValid k_var kk_var br
+ -- Reconstruct the lambda expression
+ mkLambdaFVars xs brValid
+ trace[Diverge.def.valid] "branchesValid:\n{branchesValid}"
+ -- Compute the motive, which has the following shape:
+ -- ```
+ -- λ scrut => is_valid_p k (λ k => match scrut with ...)
+ -- ^^^^^^^^^^^^^^^^^^^^
+ -- this is the original match expression, with the
+ -- the difference that the scrutinee(s) is a variable
+ -- ```
+ let validMotive : Expr ← do
+ -- The motive is a function of the scrutinees (i.e., a lambda expression):
+ -- introduce binders for the scrutinees
+ let declInfos := me.scruts.mapIdx fun idx scrut =>
+ let name : Name := mkAnonymous "scrut" idx
+ let ty := λ (_ : Array Expr) => inferType scrut
+ (name, ty)
+ withLocalDeclsD declInfos fun scrutVars => do
+ -- Create a match expression but where the scrutinees have been replaced
+ -- by variables
+ let params : Array (Option Expr) := me.params.map some
+ let motive : Option Expr := some me.motive
+ let scruts : Array (Option Expr) := scrutVars.map some
+ let branches : Array (Option Expr) := me.branches.map some
+ let args := params ++ [motive] ++ scruts ++ branches
+ let matchE ← mkAppOptM me.matcherName args
+ -- Wrap in the `is_valid_p` predicate
+ let matchE ← mkLambdaFVars #[kk_var] matchE
+ let validMotive ← mkAppM ``FixI.is_valid_p #[k_var, matchE]
+ -- Abstract away the scrutinee variables
+ mkLambdaFVars scrutVars validMotive
+ trace[Diverge.def.valid] "valid motive: {validMotive}"
+ -- Put together
+ let valid ← do
+ -- We let Lean infer the parameters
+ let params : Array (Option Expr) := me.params.map (λ _ => none)
+ let motive := some validMotive
+ let scruts := me.scruts.map some
+ let branches := branchesValid.map some
+ let args := params ++ [motive] ++ scruts ++ branches
+ mkAppOptM me.matcherName args
+ trace[Diverge.def.valid] "proveMatchIsValid:\n{valid}:\n{← inferType valid}"
+ pure valid
+
+end
+
+-- Prove that a single body (in the mutually recursive group) is valid.
+--
+-- For instance, if we define the mutually recursive group [`is_even`, `is_odd`],
+-- we prove that `is_even.body` and `is_odd.body` are valid.
+partial def proveSingleBodyIsValid
+ (k_var : Expr) (preDef : PreDefinition) (bodyConst : Expr) :
+ MetaM Expr := do
+ trace[Diverge.def.valid] "proveSingleBodyIsValid: bodyConst: {bodyConst}"
+ -- Lookup the definition (`bodyConst` is a const, we want to retrieve its
+ -- definition to dive inside)
+ let name := bodyConst.constName!
+ let env ← getEnv
+ let body := (env.constants.find! name).value!
+ trace[Diverge.def.valid] "body: {body}"
+ lambdaTelescope body fun xs body => do
+ assert! xs.size = 2
+ let kk_var := xs.get! 0
+ let x_var := xs.get! 1
+ -- State the type of the theorem to prove
+ let thmTy ← mkAppM ``FixI.is_valid_p
+ #[k_var, ← mkLambdaFVars #[kk_var] (← mkAppM' bodyConst #[kk_var, x_var])]
+ trace[Diverge.def.valid] "thmTy: {thmTy}"
+ -- Prove that the body is valid
+ let proof ← proveExprIsValid k_var kk_var body
+ let proof ← mkLambdaFVars #[k_var, x_var] proof
+ trace[Diverge.def.valid] "proveSingleBodyIsValid: proof:\n{proof}:\n{← inferType proof}"
+ -- The target type (we don't have to do this: this is simply a sanity check,
+ -- and this allows a nicer debugging output)
+ let thmTy ← do
+ let body ← mkAppM' bodyConst #[kk_var, x_var]
+ let body ← mkLambdaFVars #[kk_var] body
+ let ty ← mkAppM ``FixI.is_valid_p #[k_var, body]
+ mkForallFVars #[k_var, x_var] ty
+ trace[Diverge.def.valid] "proveSingleBodyIsValid: thmTy\n{thmTy}:\n{← inferType thmTy}"
+ -- Save the theorem
+ let name := preDef.declName ++ "body_is_valid"
+ let decl := Declaration.thmDecl {
+ name
+ levelParams := preDef.levelParams
+ type := thmTy
+ value := proof
+ all := [name]
+ }
+ addDecl decl
+ trace[Diverge.def.valid] "proveSingleBodyIsValid: added thm: {name}"
+ -- Return the theorem
+ pure (Expr.const name (preDef.levelParams.map .param))
+
+-- Prove that the list of bodies are valid.
+--
+-- For instance, if we define the mutually recursive group [`is_even`, `is_odd`],
+-- we prove that `Funs.Cons is_even.body (Funs.Cons is_odd.body Funs.Nil)` is
+-- valid.
+partial def proveFunsBodyIsValid (inOutTys: Expr) (bodyFuns : Expr)
+ (k_var : Expr) (bodiesValid : Array Expr) : MetaM Expr := do
+ -- Create the big "and" expression, which groups the validity proof of the individual bodies
+ let rec mkValidConj (i : Nat) : MetaM Expr := do
+ if i = bodiesValid.size then
+ -- We reached the end
+ mkAppM ``FixI.Funs.is_valid_p_Nil #[k_var]
+ else do
+ -- We haven't reached the end: introduce a conjunction
+ let valid := bodiesValid.get! i
+ let valid ← mkAppM' valid #[k_var]
+ mkAppM ``And.intro #[valid, ← mkValidConj (i + 1)]
+ let andExpr ← mkValidConj 0
+ -- Wrap in the `is_valid_p_is_valid_p` theorem, and abstract the continuation
+ let isValid ← mkAppM ``FixI.Funs.is_valid_p_is_valid_p #[inOutTys, k_var, bodyFuns, andExpr]
+ mkLambdaFVars #[k_var] isValid
+
+-- Prove that the mut rec body (i.e., the unary body which groups the bodies
+-- of all the functions in the mutually recursive group and on which we will
+-- apply the fixed-point operator) is valid.
+--
+-- We save the proof in the theorem "[GROUP_NAME]."mut_rec_body_is_valid",
+-- which we return.
+--
+-- TODO: maybe this function should introduce k_var itself
+def proveMutRecIsValid
+ (grName : Name) (grLvlParams : List Name)
+ (inOutTys : Expr) (bodyFuns mutRecBodyConst : Expr)
+ (k_var : Expr) (preDefs : Array PreDefinition)
+ (bodies : Array Expr) : MetaM Expr := do
+ -- First prove that the individual bodies are valid
+ let bodiesValid ←
+ bodies.mapIdxM fun idx body => do
+ let preDef := preDefs.get! idx
+ trace[Diverge.def.valid] "## Proving that the body {body} is valid"
+ proveSingleBodyIsValid k_var preDef body
+ -- Then prove that the mut rec body is valid
+ trace[Diverge.def.valid] "## Proving that the 'Funs' body is valid"
+ let isValid ← proveFunsBodyIsValid inOutTys bodyFuns k_var bodiesValid
+ -- Save the theorem
+ let thmTy ← mkAppM ``FixI.is_valid #[mutRecBodyConst]
+ let name := grName ++ "mut_rec_body_is_valid"
+ let decl := Declaration.thmDecl {
+ name
+ levelParams := grLvlParams
+ type := thmTy
+ value := isValid
+ all := [name]
+ }
+ addDecl decl
+ trace[Diverge.def.valid] "proveFunsBodyIsValid: added thm: {name}:\n{thmTy}"
+ -- Return the theorem
+ pure (Expr.const name (grLvlParams.map .param))
+
+-- Generate the final definions by using the mutual body and the fixed point operator.
+--
+-- For instance:
+-- ```
+-- def is_even (i : Int) : Result Bool := mut_rec_body 0 i
+-- def is_odd (i : Int) : Result Bool := mut_rec_body 1 i
+-- ```
+def mkDeclareFixDefs (mutRecBody : Expr) (inOutTys : Array (Expr × Expr)) (preDefs : Array PreDefinition) :
+ TermElabM (Array Name) := do
+ let grSize := preDefs.size
+ let defs ← preDefs.mapIdxM fun idx preDef => do
+ lambdaTelescope preDef.value fun xs _ => do
+ -- Retrieve the input type
+ let in_ty := (inOutTys.get! idx.val).fst
+ -- Create the index
+ let idx ← mkFinVal grSize idx.val
+ -- Group the inputs into a dependent tuple
+ let input ← mkSigmasVal in_ty xs.toList
+ -- Apply the fixed point
+ let fixedBody ← mkAppM ``FixI.fix #[mutRecBody, idx, input]
+ let fixedBody ← mkLambdaFVars xs fixedBody
+ -- Create the declaration
+ let name := preDef.declName
+ let decl := Declaration.defnDecl {
+ name := name
+ levelParams := preDef.levelParams
+ type := preDef.type
+ value := fixedBody
+ hints := ReducibilityHints.regular (getMaxHeight (← getEnv) fixedBody + 1)
+ safety := .safe
+ all := [name]
+ }
+ addDecl decl
+ pure name
+ pure defs
+
+-- Prove the equations that we will use as unfolding theorems
+partial def proveUnfoldingThms (isValidThm : Expr) (inOutTys : Array (Expr × Expr))
+ (preDefs : Array PreDefinition) (decls : Array Name) : MetaM Unit := do
+ let grSize := preDefs.size
+ let proveIdx (i : Nat) : MetaM Unit := do
+ let preDef := preDefs.get! i
+ let defName := decls.get! i
+ -- Retrieve the arguments
+ lambdaTelescope preDef.value fun xs body => do
+ trace[Diverge.def.unfold] "proveUnfoldingThms: xs: {xs}"
+ trace[Diverge.def.unfold] "proveUnfoldingThms: body: {body}"
+ -- The theorem statement
+ let thmTy ← do
+ -- The equation: the declaration gives the lhs, the pre-def gives the rhs
+ let lhs ← mkAppOptM defName (xs.map some)
+ let rhs := body
+ let eq ← mkAppM ``Eq #[lhs, rhs]
+ mkForallFVars xs eq
+ trace[Diverge.def.unfold] "proveUnfoldingThms: thm statement: {thmTy}"
+ -- The proof
+ -- Use the fixed-point equation
+ let proof ← mkAppM ``FixI.is_valid_fix_fixed_eq #[isValidThm]
+ -- Add the index
+ let idx ← mkFinVal grSize i
+ let proof ← mkAppM ``congr_fun #[proof, idx]
+ -- Add the input argument
+ let arg ← mkSigmasVal (inOutTys.get! i).fst xs.toList
+ let proof ← mkAppM ``congr_fun #[proof, arg]
+ -- Abstract the arguments away
+ let proof ← mkLambdaFVars xs proof
+ trace[Diverge.def.unfold] "proveUnfoldingThms: proof: {proof}:\n{← inferType proof}"
+ -- Declare the theorem
+ let name := preDef.declName ++ "unfold"
+ let decl := Declaration.thmDecl {
+ name
+ levelParams := preDef.levelParams
+ type := thmTy
+ value := proof
+ all := [name]
+ }
+ addDecl decl
+ -- Add the unfolding theorem to the equation compiler
+ eqnsAttribute.add preDef.declName #[name]
+ trace[Diverge.def.unfold] "proveUnfoldingThms: added thm: {name}:\n{thmTy}"
+ let rec prove (i : Nat) : MetaM Unit := do
+ if i = preDefs.size then pure ()
+ else do
+ proveIdx i
+ prove (i + 1)
+ --
+ prove 0
+
+def divRecursion (preDefs : Array PreDefinition) : TermElabM Unit := do
+ let msg := toMessageData <| preDefs.map fun pd => (pd.declName, pd.levelParams, pd.type, pd.value)
+ trace[Diverge.def] ("divRecursion: defs:\n" ++ msg)
+
+ -- TODO: what is this?
+ for preDef in preDefs do
+ applyAttributesOf #[preDef] AttributeApplicationTime.afterCompilation
+
+ -- Retrieve the name of the first definition, that we will use as the namespace
+ -- for the definitions common to the group
+ let def0 := preDefs[0]!
+ let grName := def0.declName
+ trace[Diverge.def] "group name: {grName}"
+
+ /- # Compute the input/output types of the continuation `k`. -/
+ let grLvlParams := def0.levelParams
+ trace[Diverge.def] "def0 universe levels: {def0.levelParams}"
+
+ -- We first compute the list of pairs: (input type × output type)
+ let inOutTys : Array (Expr × Expr) ←
+ preDefs.mapM (fun preDef => do
+ withRef preDef.ref do -- is the withRef useful?
+ -- Check the universe parameters - TODO: I'm not sure what the best thing
+ -- to do is. In practice, all the type parameters should be in Type 0, so
+ -- we shouldn't have universe issues.
+ if preDef.levelParams ≠ grLvlParams then
+ throwError "Non-uniform polymorphism in the universes"
+ forallTelescope preDef.type (fun in_tys out_ty => do
+ let in_ty ← liftM (mkSigmasType in_tys.toList)
+ -- Retrieve the type in the "Result"
+ let out_ty ← getResultTy out_ty
+ let out_ty ← liftM (mkSigmasMatch in_tys.toList out_ty)
+ pure (in_ty, out_ty)
+ )
+ )
+ trace[Diverge.def] "inOutTys: {inOutTys}"
+ -- Turn the list of input/output type pairs into an expresion
+ let inOutTysExpr ← inOutTys.mapM (λ (x, y) => mkInOutTy x y)
+ let inOutTysExpr ← mkListLit (← inferType (inOutTysExpr.get! 0)) inOutTysExpr.toList
+
+ -- From the list of pairs of input/output types, actually compute the
+ -- type of the continuation `k`.
+ -- We first introduce the index `i : Fin n` where `n` is the number of
+ -- functions in the group.
+ let i_var_ty := mkFin preDefs.size
+ withLocalDeclD (mkAnonymous "i" 0) i_var_ty fun i_var => do
+ let in_out_ty ← mkAppM ``List.get #[inOutTysExpr, i_var]
+ trace[Diverge.def] "in_out_ty := {in_out_ty} : {← inferType in_out_ty}"
+ -- Add an auxiliary definition for `in_out_ty`
+ let in_out_ty ← do
+ let value ← mkLambdaFVars #[i_var] in_out_ty
+ let name := grName.append "in_out_ty"
+ let levelParams := grLvlParams
+ let decl := Declaration.defnDecl {
+ name := name
+ levelParams := levelParams
+ type := ← inferType value
+ value := value
+ hints := .abbrev
+ safety := .safe
+ all := [name]
+ }
+ addDecl decl
+ -- Return the constant
+ let in_out_ty := Lean.mkConst name (levelParams.map .param)
+ mkAppM' in_out_ty #[i_var]
+ trace[Diverge.def] "in_out_ty (after decl) := {in_out_ty} : {← inferType in_out_ty}"
+ let in_ty ← mkAppM ``Sigma.fst #[in_out_ty]
+ trace[Diverge.def] "in_ty: {in_ty}"
+ withLocalDeclD (mkAnonymous "x" 1) in_ty fun input => do
+ let out_ty ← mkAppM' (← mkAppM ``Sigma.snd #[in_out_ty]) #[input]
+ trace[Diverge.def] "out_ty: {out_ty}"
+
+ -- Introduce the continuation `k`
+ let in_ty ← mkLambdaFVars #[i_var] in_ty
+ let out_ty ← mkLambdaFVars #[i_var, input] out_ty
+ let kk_var_ty ← mkAppM ``FixI.kk_ty #[i_var_ty, in_ty, out_ty]
+ trace[Diverge.def] "kk_var_ty: {kk_var_ty}"
+ withLocalDeclD (mkAnonymous "kk" 2) kk_var_ty fun kk_var => do
+ trace[Diverge.def] "kk_var: {kk_var}"
+
+ -- Replace the recursive calls in all the function bodies by calls to the
+ -- continuation `k` and and generate for those bodies declarations
+ trace[Diverge.def] "# Generating the unary bodies"
+ let bodies ← mkDeclareUnaryBodies grLvlParams kk_var inOutTys preDefs
+ trace[Diverge.def] "Unary bodies (after decl): {bodies}"
+ -- Generate the mutually recursive body
+ trace[Diverge.def] "# Generating the mut rec body"
+ let (bodyFuns, mutRecBody) ← mkDeclareMutRecBody grName grLvlParams kk_var i_var in_ty out_ty inOutTys.toList bodies
+ trace[Diverge.def] "mut rec body (after decl): {mutRecBody}"
+
+ -- Prove that the mut rec body satisfies the validity criteria required by
+ -- our fixed-point
+ let k_var_ty ← mkAppM ``FixI.k_ty #[i_var_ty, in_ty, out_ty]
+ withLocalDeclD (mkAnonymous "k" 3) k_var_ty fun k_var => do
+ trace[Diverge.def] "# Proving that the mut rec body is valid"
+ let isValidThm ← proveMutRecIsValid grName grLvlParams inOutTysExpr bodyFuns mutRecBody k_var preDefs bodies
+
+ -- Generate the final definitions
+ trace[Diverge.def] "# Generating the final definitions"
+ let decls ← mkDeclareFixDefs mutRecBody inOutTys preDefs
+
+ -- Prove the unfolding theorems
+ trace[Diverge.def] "# Proving the unfolding theorems"
+ proveUnfoldingThms isValidThm inOutTys preDefs decls
+
+ -- Generating code -- TODO
+ addAndCompilePartialRec preDefs
+
+-- The following function is copy&pasted from Lean.Elab.PreDefinition.Main
+-- This is the only part where we make actual changes and hook into the equation compiler.
+-- (I've removed all the well-founded stuff to make it easier to read though.)
+
+open private ensureNoUnassignedMVarsAtPreDef betaReduceLetRecApps partitionPreDefs
+ addAndCompilePartial addAsAxioms from Lean.Elab.PreDefinition.Main
+
+def addPreDefinitions (preDefs : Array PreDefinition) : TermElabM Unit := withLCtx {} {} do
+ for preDef in preDefs do
+ trace[Diverge.elab] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
+ let preDefs ← preDefs.mapM ensureNoUnassignedMVarsAtPreDef
+ let preDefs ← betaReduceLetRecApps preDefs
+ let cliques := partitionPreDefs preDefs
+ let mut hasErrors := false
+ for preDefs in cliques do
+ trace[Diverge.elab] "{preDefs.map (·.declName)}"
+ try
+ withRef (preDefs[0]!.ref) do
+ divRecursion preDefs
+ catch ex =>
+ -- If it failed, we add the functions as partial functions
+ hasErrors := true
+ logException ex
+ let s ← saveState
+ try
+ if preDefs.all fun preDef => preDef.kind == DefKind.def ||
+ preDefs.all fun preDef => preDef.kind == DefKind.abbrev then
+ -- try to add as partial definition
+ try
+ addAndCompilePartial preDefs (useSorry := true)
+ catch _ =>
+ -- Compilation failed try again just as axiom
+ s.restore
+ addAsAxioms preDefs
+ else return ()
+ catch _ => s.restore
+
+-- The following two functions are copy-pasted from Lean.Elab.MutualDef
+
+open private elabHeaders levelMVarToParamHeaders getAllUserLevelNames withFunLocalDecls elabFunValues
+ instantiateMVarsAtHeader instantiateMVarsAtLetRecToLift checkLetRecsToLiftTypes withUsed from Lean.Elab.MutualDef
+
+def Term.elabMutualDef (vars : Array Expr) (views : Array DefView) : TermElabM Unit := do
+ let scopeLevelNames ← getLevelNames
+ let headers ← elabHeaders views
+ let headers ← levelMVarToParamHeaders views headers
+ let allUserLevelNames := getAllUserLevelNames headers
+ withFunLocalDecls headers fun funFVars => do
+ for view in views, funFVar in funFVars do
+ addLocalVarInfo view.declId funFVar
+ -- Add fake use site to prevent "unused variable" warning (if the
+ -- function is actually not recursive, Lean would print this warning).
+ -- Remark: we could detect this case and encode the function without
+ -- using the fixed-point. In practice it shouldn't happen however:
+ -- we define non-recursive functions with the `divergent` keyword
+ -- only for testing purposes.
+ addTermInfo' view.declId funFVar
+ let values ←
+ try
+ let values ← elabFunValues headers
+ Term.synthesizeSyntheticMVarsNoPostponing
+ values.mapM (instantiateMVars ·)
+ catch ex =>
+ logException ex
+ headers.mapM fun header => mkSorry header.type (synthetic := true)
+ let headers ← headers.mapM instantiateMVarsAtHeader
+ let letRecsToLift ← getLetRecsToLift
+ let letRecsToLift ← letRecsToLift.mapM instantiateMVarsAtLetRecToLift
+ checkLetRecsToLiftTypes funFVars letRecsToLift
+ withUsed vars headers values letRecsToLift fun vars => do
+ let preDefs ← MutualClosure.main vars headers funFVars values letRecsToLift
+ for preDef in preDefs do
+ trace[Diverge.elab] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
+ let preDefs ← withLevelNames allUserLevelNames <| levelMVarToParamPreDecls preDefs
+ let preDefs ← instantiateMVarsAtPreDecls preDefs
+ let preDefs ← fixLevelParams preDefs scopeLevelNames allUserLevelNames
+ for preDef in preDefs do
+ trace[Diverge.elab] "after eraseAuxDiscr, {preDef.declName} : {preDef.type} :=\n{preDef.value}"
+ checkForHiddenUnivLevels allUserLevelNames preDefs
+ addPreDefinitions preDefs
+
+open Command in
+def Command.elabMutualDef (ds : Array Syntax) : CommandElabM Unit := do
+ let views ← ds.mapM fun d => do
+ let `($mods:declModifiers divergent def $id:declId $sig:optDeclSig $val:declVal) := d
+ | throwUnsupportedSyntax
+ let modifiers ← elabModifiers mods
+ let (binders, type) := expandOptDeclSig sig
+ let deriving? := none
+ pure { ref := d, kind := DefKind.def, modifiers,
+ declId := id, binders, type? := type, value := val, deriving? }
+ runTermElabM fun vars => Term.elabMutualDef vars views
+
+-- Special command so that we don't fall back to the built-in mutual when we produce an error.
+local syntax "_divergent" Parser.Command.mutual : command
+elab_rules : command | `(_divergent mutual $decls* end) => Command.elabMutualDef decls
+
+macro_rules
+ | `(mutual $decls* end) => do
+ unless !decls.isEmpty && decls.all (·.1.getKind == ``divergentDef) do
+ Macro.throwUnsupported
+ `(command| _divergent mutual $decls* end)
+
+open private setDeclIdName from Lean.Elab.Declaration
+elab_rules : command
+ | `($mods:declModifiers divergent%$tk def $id:declId $sig:optDeclSig $val:declVal) => do
+ let (name, _) := expandDeclIdCore id
+ if (`_root_).isPrefixOf name then throwUnsupportedSyntax
+ let view := extractMacroScopes name
+ let .str ns shortName := view.name | throwUnsupportedSyntax
+ let shortName' := { view with name := shortName }.review
+ let cmd ← `(mutual $mods:declModifiers divergent%$tk def $(⟨setDeclIdName id shortName'⟩):declId $sig:optDeclSig $val:declVal end)
+ if ns matches .anonymous then
+ Command.elabCommand cmd
+ else
+ Command.elabCommand <| ← `(namespace $(mkIdentFrom id ns) $cmd end $(mkIdentFrom id ns))
+
+namespace Tests
+ /- Some examples of partial functions -/
+
+ divergent def list_nth {a: Type} (ls : List a) (i : Int) : Result a :=
+ match ls with
+ | [] => .fail .panic
+ | x :: ls =>
+ if i = 0 then return x
+ else return (← list_nth ls (i - 1))
+
+ #check list_nth.unfold
+
+ example {a: Type} (ls : List a) :
+ ∀ (i : Int),
+ 0 ≤ i → i < ls.length →
+ ∃ x, list_nth ls i = .ret x := by
+ induction ls
+ . intro i hpos h; simp at h; linarith
+ . rename_i hd tl ih
+ intro i hpos h
+ -- We can directly use `rw [list_nth]`!
+ rw [list_nth]; simp
+ split <;> simp [*]
+ . tauto
+ . -- TODO: we shouldn't have to do that
+ have hneq : 0 < i := by cases i <;> rename_i a _ <;> simp_all; cases a <;> simp_all
+ simp at h
+ have ⟨ x, ih ⟩ := ih (i - 1) (by linarith) (by linarith)
+ simp [ih]
+ tauto
+
+ mutual
+ divergent def is_even (i : Int) : Result Bool :=
+ if i = 0 then return true else return (← is_odd (i - 1))
+
+ divergent def is_odd (i : Int) : Result Bool :=
+ if i = 0 then return false else return (← is_even (i - 1))
+ end
+
+ #check is_even.unfold
+ #check is_odd.unfold
+
+ mutual
+ divergent def foo (i : Int) : Result Nat :=
+ if i > 10 then return (← foo (i / 10)) + (← bar i) else bar 10
+
+ divergent def bar (i : Int) : Result Nat :=
+ if i > 20 then foo (i / 20) else .ret 42
+ end
+
+ #check foo.unfold
+ #check bar.unfold
+
+ -- Testing dependent branching and let-bindings
+ -- TODO: why the linter warning?
+ divergent def isNonZero (i : Int) : Result Bool :=
+ if _h:i = 0 then return false
+ else
+ let b := true
+ return b
+
+ #check isNonZero.unfold
+
+ -- Testing let-bindings
+ divergent def iInBounds {a : Type} (ls : List a) (i : Int) : Result Bool :=
+ let i0 := ls.length
+ if i < i0
+ then Result.ret True
+ else Result.ret False
+
+ #check iInBounds.unfold
+
+ divergent def isCons
+ {a : Type} (ls : List a) : Result Bool :=
+ let ls1 := ls
+ match ls1 with
+ | [] => Result.ret False
+ | _ :: _ => Result.ret True
+
+ #check isCons.unfold
+
+ -- Testing what happens when we use concrete arguments in dependent tuples
+ divergent def test1
+ (_ : Option Bool) (_ : Unit) :
+ Result Unit
+ :=
+ test1 Option.none ()
+
+ #check test1.unfold
+
+end Tests
+
+end Diverge
diff --git a/backends/lean/Base/Diverge/ElabBase.lean b/backends/lean/Base/Diverge/ElabBase.lean
new file mode 100644
index 00000000..fedb1c74
--- /dev/null
+++ b/backends/lean/Base/Diverge/ElabBase.lean
@@ -0,0 +1,15 @@
+import Lean
+
+namespace Diverge
+
+open Lean Elab Term Meta
+
+-- We can't define and use trace classes in the same file
+initialize registerTraceClass `Diverge.elab
+initialize registerTraceClass `Diverge.def
+initialize registerTraceClass `Diverge.def.sigmas
+initialize registerTraceClass `Diverge.def.genBody
+initialize registerTraceClass `Diverge.def.valid
+initialize registerTraceClass `Diverge.def.unfold
+
+end Diverge
diff --git a/backends/lean/Base/IList.lean b/backends/lean/Base/IList.lean
new file mode 100644
index 00000000..31b66ffa
--- /dev/null
+++ b/backends/lean/Base/IList.lean
@@ -0,0 +1 @@
+import Base.IList.IList
diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean
new file mode 100644
index 00000000..93047a1b
--- /dev/null
+++ b/backends/lean/Base/IList/IList.lean
@@ -0,0 +1,284 @@
+/- Complementary list functions and lemmas which operate on integers rather
+ than natural numbers. -/
+
+import Std.Data.Int.Lemmas
+import Base.Arith
+
+namespace List
+
+def len (ls : List α) : Int :=
+ match ls with
+ | [] => 0
+ | _ :: tl => 1 + len tl
+
+@[simp] theorem len_nil : len ([] : List α) = 0 := by simp [len]
+@[simp] theorem len_cons : len ((x :: tl) : List α) = 1 + len tl := by simp [len]
+
+theorem len_pos : 0 ≤ (ls : List α).len := by
+ induction ls <;> simp [*]
+ linarith
+
+instance (a : Type u) : Arith.HasIntProp (List a) where
+ prop_ty := λ ls => 0 ≤ ls.len
+ prop := λ ls => ls.len_pos
+
+-- Remark: if i < 0, then the result is none
+def indexOpt (ls : List α) (i : Int) : Option α :=
+ match ls with
+ | [] => none
+ | hd :: tl => if i = 0 then some hd else indexOpt tl (i - 1)
+
+@[simp] theorem indexOpt_nil : indexOpt ([] : List α) i = none := by simp [indexOpt]
+@[simp] theorem indexOpt_zero_cons : indexOpt ((x :: tl) : List α) 0 = some x := by simp [indexOpt]
+@[simp] theorem indexOpt_nzero_cons (hne : i ≠ 0) : indexOpt ((x :: tl) : List α) i = indexOpt tl (i - 1) := by simp [*, indexOpt]
+
+-- Remark: if i < 0, then the result is the defaul element
+def index [Inhabited α] (ls : List α) (i : Int) : α :=
+ match ls with
+ | [] => Inhabited.default
+ | x :: tl =>
+ if i = 0 then x else index tl (i - 1)
+
+@[simp] theorem index_zero_cons [Inhabited α] : index ((x :: tl) : List α) 0 = x := by simp [index]
+@[simp] theorem index_nzero_cons [Inhabited α] (hne : i ≠ 0) : index ((x :: tl) : List α) i = index tl (i - 1) := by simp [*, index]
+
+theorem indexOpt_bounds (ls : List α) (i : Int) :
+ ls.indexOpt i = none ↔ i < 0 ∨ ls.len ≤ i :=
+ match ls with
+ | [] =>
+ have : ¬ (i < 0) → 0 ≤ i := by int_tac
+ by simp; tauto
+ | _ :: tl =>
+ have := indexOpt_bounds tl (i - 1)
+ if h: i = 0 then
+ by
+ simp [*];
+ int_tac
+ else by
+ simp [*]
+ constructor <;> intros <;>
+ casesm* _ ∨ _ <;> -- splits all the disjunctions
+ first | left; int_tac | right; int_tac
+
+theorem indexOpt_eq_index [Inhabited α] (ls : List α) (i : Int) :
+ 0 ≤ i →
+ i < ls.len →
+ ls.indexOpt i = some (ls.index i) :=
+ match ls with
+ | [] => by simp; intros; linarith
+ | hd :: tl =>
+ if h: i = 0 then
+ by simp [*]
+ else
+ have hi := indexOpt_eq_index tl (i - 1)
+ by simp [*]; intros; apply hi <;> int_tac
+
+-- Remark: the list is unchanged if the index is not in bounds (in particular
+-- if it is < 0)
+def update (ls : List α) (i : Int) (y : α) : List α :=
+ match ls with
+ | [] => []
+ | x :: tl => if i = 0 then y :: tl else x :: update tl (i - 1) y
+
+-- Remark: the whole list is dropped if the index is not in bounds (in particular
+-- if it is < 0)
+def idrop (i : Int) (ls : List α) : List α :=
+ match ls with
+ | [] => []
+ | x :: tl => if i = 0 then x :: tl else idrop (i - 1) tl
+
+section Lemmas
+
+variable {α : Type u}
+
+@[simp] theorem update_nil : update ([] : List α) i y = [] := by simp [update]
+@[simp] theorem update_zero_cons : update ((x :: tl) : List α) 0 y = y :: tl := by simp [update]
+@[simp] theorem update_nzero_cons (hne : i ≠ 0) : update ((x :: tl) : List α) i y = x :: update tl (i - 1) y := by simp [*, update]
+
+@[simp] theorem idrop_nil : idrop i ([] : List α) = [] := by simp [idrop]
+@[simp] theorem idrop_zero : idrop 0 (ls : List α) = ls := by cases ls <;> simp [idrop]
+@[simp] theorem idrop_nzero_cons (hne : i ≠ 0) : idrop i ((x :: tl) : List α) = idrop (i - 1) tl := by simp [*, idrop]
+
+theorem len_eq_length (ls : List α) : ls.len = ls.length := by
+ induction ls
+ . rfl
+ . simp [*, Int.ofNat_succ, Int.add_comm]
+
+@[simp] theorem len_append (l1 l2 : List α) : (l1 ++ l2).len = l1.len + l2.len := by
+ -- Remark: simp loops here because of the following rewritings:
+ -- @Nat.cast_add: ↑(List.length l1 + List.length l2) ==> ↑(List.length l1) + ↑(List.length l2)
+ -- Int.ofNat_add_ofNat: ↑(List.length l1) + ↑(List.length l2) ==> ↑(List.length l1 + List.length l2)
+ -- TODO: post an issue?
+ simp only [len_eq_length]
+ simp only [length_append]
+ simp only [Int.ofNat_add]
+
+@[simp]
+theorem length_update (ls : List α) (i : Int) (x : α) : (ls.update i x).length = ls.length := by
+ revert i
+ induction ls <;> simp_all [length, update]
+ intro; split <;> simp [*]
+
+@[simp]
+theorem len_update (ls : List α) (i : Int) (x : α) : (ls.update i x).len = ls.len := by
+ simp [len_eq_length]
+
+@[simp]
+theorem len_map (ls : List α) (f : α → β) : (ls.map f).len = ls.len := by
+ simp [len_eq_length]
+
+theorem left_length_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l1.length = l1'.length) :
+ l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+ revert l1'
+ induction l1
+ . intro l1'; cases l1' <;> simp [*]
+ . intro l1'; cases l1' <;> simp_all; tauto
+
+theorem right_length_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l2.length = l2'.length) :
+ l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+ have := left_length_eq_append_eq l1 l2 l1' l2'
+ constructor <;> intro heq2 <;>
+ have : l1.length + l2.length = l1'.length + l2'.length := by
+ have : (l1 ++ l2).length = (l1' ++ l2').length := by simp [*]
+ simp only [length_append] at this
+ apply this
+ . simp [heq] at this
+ tauto
+ . tauto
+
+theorem left_len_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l1.len = l1'.len) :
+ l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+ simp [len_eq_length] at heq
+ apply left_length_eq_append_eq
+ assumption
+
+theorem right_len_eq_append_eq (l1 l2 l1' l2' : List α) (heq : l2.len = l2'.len) :
+ l1 ++ l2 = l1' ++ l2' ↔ l1 = l1' ∧ l2 = l2' := by
+ simp [len_eq_length] at heq
+ apply right_length_eq_append_eq
+ assumption
+
+open Arith in
+theorem idrop_eq_nil_of_le (hineq : ls.len ≤ i) : idrop i ls = [] := by
+ revert i
+ induction ls <;> simp [*]
+ rename_i hd tl hi
+ intro i hineq
+ if heq: i = 0 then
+ simp [*] at *
+ have := tl.len_pos
+ linarith
+ else
+ simp at hineq
+ have : 0 < i := by int_tac
+ simp [*]
+ apply hi
+ linarith
+
+@[simp]
+theorem index_ne
+ {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (j: ℤ) (x: α) :
+ 0 ≤ i → i < l.len → 0 ≤ j → j < l.len → j ≠ i →
+ (l.update i x).index j = l.index j
+ :=
+ λ _ _ _ _ _ => match l with
+ | [] => by simp at *
+ | hd :: tl =>
+ if h: i = 0 then
+ have : j ≠ 0 := by scalar_tac
+ by simp [*]
+ else if h : j = 0 then
+ have : i ≠ 0 := by scalar_tac
+ by simp [*]
+ else
+ by
+ simp [*]
+ simp at *
+ apply index_ne <;> scalar_tac
+
+@[simp]
+theorem index_eq
+ {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (x: α) :
+ 0 ≤ i → i < l.len →
+ (l.update i x).index i = x
+ :=
+ fun _ _ => match l with
+ | [] => by simp at *; scalar_tac
+ | hd :: tl =>
+ if h: i = 0 then
+ by
+ simp [*]
+ else
+ by
+ simp [*]
+ simp at *
+ apply index_eq <;> scalar_tac
+
+theorem update_map_eq {α : Type u} {β : Type v} (ls : List α) (i : Int) (x : α) (f : α → β) :
+ (ls.update i x).map f = (ls.map f).update i (f x) :=
+ match ls with
+ | [] => by simp
+ | hd :: tl =>
+ if h : i = 0 then by simp [*]
+ else
+ have hi := update_map_eq tl (i - 1) x f
+ by simp [*]
+
+theorem len_flatten_update_eq {α : Type u} (ls : List (List α)) (i : Int) (x : List α)
+ (h0 : 0 ≤ i) (h1 : i < ls.len) :
+ (ls.update i x).flatten.len = ls.flatten.len + x.len - (ls.index i).len :=
+ match ls with
+ | [] => by simp at h1; int_tac
+ | hd :: tl => by
+ simp at h1
+ if h : i = 0 then simp [*]; int_tac
+ else
+ have hi := len_flatten_update_eq tl (i - 1) x (by int_tac) (by int_tac)
+ simp [*]
+ int_tac
+
+@[simp]
+theorem index_map_eq {α : Type u} {β : Type v} [Inhabited α] [Inhabited β] (ls : List α) (i : Int) (f : α → β)
+ (h0 : 0 ≤ i) (h1 : i < ls.len) :
+ (ls.map f).index i = f (ls.index i) :=
+ match ls with
+ | [] => by simp at h1; int_tac
+ | hd :: tl =>
+ if h : i = 0 then by
+ simp [*]
+ else
+ have hi := index_map_eq tl (i - 1) f (by int_tac) (by simp at h1; int_tac)
+ by
+ simp [*]
+
+def allP {α : Type u} (l : List α) (p: α → Prop) : Prop :=
+ foldr (fun a r => p a ∧ r) True l
+
+@[simp]
+theorem allP_nil {α : Type u} (p: α → Prop) : allP [] p :=
+ by simp [allP, foldr]
+
+@[simp]
+theorem allP_cons {α : Type u} (hd: α) (tl : List α) (p: α → Prop) :
+ allP (hd :: tl) p ↔ p hd ∧ allP tl p
+ := by simp [allP, foldr]
+
+def pairwise_rel
+ {α : Type u} (rel : α → α → Prop) (l: List α) : Prop
+ := match l with
+ | [] => True
+ | hd :: tl => allP tl (rel hd) ∧ pairwise_rel rel tl
+
+@[simp]
+theorem pairwise_rel_nil {α : Type u} (rel : α → α → Prop) :
+ pairwise_rel rel []
+ := by simp [pairwise_rel]
+
+@[simp]
+theorem pairwise_rel_cons {α : Type u} (rel : α → α → Prop) (hd: α) (tl: List α) :
+ pairwise_rel rel (hd :: tl) ↔ allP tl (rel hd) ∧ pairwise_rel rel tl
+ := by simp [pairwise_rel]
+
+end Lemmas
+
+end List
diff --git a/backends/lean/Base/Primitives.lean b/backends/lean/Base/Primitives.lean
new file mode 100644
index 00000000..91823cb6
--- /dev/null
+++ b/backends/lean/Base/Primitives.lean
@@ -0,0 +1,3 @@
+import Base.Primitives.Base
+import Base.Primitives.Scalar
+import Base.Primitives.Vec
diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean
new file mode 100644
index 00000000..7c0fa3bb
--- /dev/null
+++ b/backends/lean/Base/Primitives/Base.lean
@@ -0,0 +1,130 @@
+import Lean
+
+namespace Primitives
+
+--------------------
+-- ASSERT COMMAND --Std.
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+unsafe
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+ runTermElabM (fun _ => do
+ let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
+ if not r then
+ logInfo ("Assertion failed for:\n" ++ _stx[1])
+ throwError ("Expression reduced to false:\n" ++ _stx[1])
+ pure ())
+
+#eval 2 == 2
+#assert (2 == 2)
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | divisionByZero: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
+deriving Repr, BEq
+
+open Error
+
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
+ | div
+deriving Repr, BEq
+
+open Result
+
+instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
+ Inhabited.mk (fail panic)
+
+instance Result_Nonempty (α : Type u) : Nonempty (Result α) :=
+ Nonempty.intro div
+
+/- HELPERS -/
+
+def ret? {α: Type u} (r: Result α): Bool :=
+ match r with
+ | ret _ => true
+ | fail _ | div => false
+
+def div? {α: Type u} (r: Result α): Bool :=
+ match r with
+ | div => true
+ | ret _ | fail _ => false
+
+def massert (b:Bool) : Result Unit :=
+ if b then ret () else fail assertionFailure
+
+def eval_global {α: Type u} (x: Result α) (_: ret? x): α :=
+ match x with
+ | fail _ | div => by contradiction
+ | ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind {α : Type u} {β : Type v} (x: Result α) (f: α → Result β) : Result β :=
+ match x with
+ | ret v => f v
+ | fail v => fail v
+ | div => div
+
+-- Allows using Result in do-blocks
+instance : Bind Result where
+ bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure Result where
+ pure := fun x => ret x
+
+@[simp] theorem bind_ret (x : α) (f : α → Result β) : bind (.ret x) f = f x := by simp [bind]
+@[simp] theorem bind_fail (x : Error) (f : α → Result β) : bind (.fail x) f = .fail x := by simp [bind]
+@[simp] theorem bind_div (f : α → Result β) : bind .div f = .div := by simp [bind]
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the Result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
+ match o with
+ | ret x => ret ⟨x, rfl⟩
+ | fail e => fail e
+ | div => div
+
+@[simp] theorem bind_tc_ret (x : α) (f : α → Result β) :
+ (do let y ← .ret x; f y) = f x := by simp [Bind.bind, bind]
+
+@[simp] theorem bind_tc_fail (x : Error) (f : α → Result β) :
+ (do let y ← fail x; f y) = fail x := by simp [Bind.bind, bind]
+
+@[simp] theorem bind_tc_div (f : α → Result β) :
+ (do let y ← div; f y) = div := by simp [Bind.bind, bind]
+
+----------
+-- MISC --
+----------
+
+@[simp] def mem.replace (a : Type) (x : a) (_ : a) : a := x
+@[simp] def mem.replace_back (a : Type) (_ : a) (y : a) : a := y
+
+/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
+ Use with `simp [ aeneas ]` -/
+register_simp_attr aeneas
+
+end Primitives
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
new file mode 100644
index 00000000..2e5be8bf
--- /dev/null
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -0,0 +1,831 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Mathlib.Tactic.Linarith
+import Base.Primitives.Base
+import Base.Diverge.Base
+import Base.Progress.Base
+import Base.Arith.Int
+
+namespace Primitives
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- We redefine our machine integers types.
+
+-- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
+-- using the simplifier, meaning that proofs do not depend on the compile-time value of
+-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
+-- least officially, 16-bit microcontrollers, so this seems like a fine design decision
+-- for now.)
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." So, we will not add refinements on the return values of the
+-- operations defined on Primitives, but will rather rely on custom lemmas to
+-- invert on possible return values of the primitive operations.
+
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
+
+open Result Error
+open System.Platform.getNumBits
+
+-- TODO: is there a way of only importing System.Platform.getNumBits?
+--
+@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
+
+-- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
+
+-- The "structured" bounds
+def Isize.smin : Int := - (HPow.hPow 2 (size_num_bits - 1))
+def Isize.smax : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
+def I8.smin : Int := - (HPow.hPow 2 7)
+def I8.smax : Int := HPow.hPow 2 7 - 1
+def I16.smin : Int := - (HPow.hPow 2 15)
+def I16.smax : Int := HPow.hPow 2 15 - 1
+def I32.smin : Int := -(HPow.hPow 2 31)
+def I32.smax : Int := HPow.hPow 2 31 - 1
+def I64.smin : Int := -(HPow.hPow 2 63)
+def I64.smax : Int := HPow.hPow 2 63 - 1
+def I128.smin : Int := -(HPow.hPow 2 127)
+def I128.smax : Int := HPow.hPow 2 127 - 1
+def Usize.smin : Int := 0
+def Usize.smax : Int := HPow.hPow 2 size_num_bits - 1
+def U8.smin : Int := 0
+def U8.smax : Int := HPow.hPow 2 8 - 1
+def U16.smin : Int := 0
+def U16.smax : Int := HPow.hPow 2 16 - 1
+def U32.smin : Int := 0
+def U32.smax : Int := HPow.hPow 2 32 - 1
+def U64.smin : Int := 0
+def U64.smax : Int := HPow.hPow 2 64 - 1
+def U128.smin : Int := 0
+def U128.smax : Int := HPow.hPow 2 128 - 1
+
+-- The "normalized" bounds, that we use in practice
+def I8.min : Int := -128
+def I8.max : Int := 127
+def I16.min : Int := -32768
+def I16.max : Int := 32767
+def I32.min : Int := -2147483648
+def I32.max : Int := 2147483647
+def I64.min : Int := -9223372036854775808
+def I64.max : Int := 9223372036854775807
+def I128.min : Int := -170141183460469231731687303715884105728
+def I128.max : Int := 170141183460469231731687303715884105727
+@[simp]
+def U8.min : Int := 0
+def U8.max : Int := 255
+@[simp]
+def U16.min : Int := 0
+def U16.max : Int := 65535
+@[simp]
+def U32.min : Int := 0
+def U32.max : Int := 4294967295
+@[simp]
+def U64.min : Int := 0
+def U64.max : Int := 18446744073709551615
+@[simp]
+def U128.min : Int := 0
+def U128.max : Int := 340282366920938463463374607431768211455
+@[simp]
+def Usize.min : Int := 0
+
+def Isize.refined_min : { n:Int // n = I32.min ∨ n = I64.min } :=
+ ⟨ Isize.smin, by
+ simp [Isize.smin]
+ cases System.Platform.numBits_eq <;>
+ unfold System.Platform.numBits at * <;> simp [*] ⟩
+
+def Isize.refined_max : { n:Int // n = I32.max ∨ n = I64.max } :=
+ ⟨ Isize.smax, by
+ simp [Isize.smax]
+ cases System.Platform.numBits_eq <;>
+ unfold System.Platform.numBits at * <;> simp [*] ⟩
+
+def Usize.refined_max : { n:Int // n = U32.max ∨ n = U64.max } :=
+ ⟨ Usize.smax, by
+ simp [Usize.smax]
+ cases System.Platform.numBits_eq <;>
+ unfold System.Platform.numBits at * <;> simp [*] ⟩
+
+def Isize.min := Isize.refined_min.val
+def Isize.max := Isize.refined_max.val
+def Usize.max := Usize.refined_max.val
+
+inductive ScalarTy :=
+| Isize
+| I8
+| I16
+| I32
+| I64
+| I128
+| Usize
+| U8
+| U16
+| U32
+| U64
+| U128
+
+def ScalarTy.isSigned (ty : ScalarTy) : Bool :=
+ match ty with
+ | Isize
+ | I8
+ | I16
+ | I32
+ | I64
+ | I128 => true
+ | Usize
+ | U8
+ | U16
+ | U32
+ | U64
+ | U128 => false
+
+
+def Scalar.smin (ty : ScalarTy) : Int :=
+ match ty with
+ | .Isize => Isize.smin
+ | .I8 => I8.smin
+ | .I16 => I16.smin
+ | .I32 => I32.smin
+ | .I64 => I64.smin
+ | .I128 => I128.smin
+ | .Usize => Usize.smin
+ | .U8 => U8.smin
+ | .U16 => U16.smin
+ | .U32 => U32.smin
+ | .U64 => U64.smin
+ | .U128 => U128.smin
+
+def Scalar.smax (ty : ScalarTy) : Int :=
+ match ty with
+ | .Isize => Isize.smax
+ | .I8 => I8.smax
+ | .I16 => I16.smax
+ | .I32 => I32.smax
+ | .I64 => I64.smax
+ | .I128 => I128.smax
+ | .Usize => Usize.smax
+ | .U8 => U8.smax
+ | .U16 => U16.smax
+ | .U32 => U32.smax
+ | .U64 => U64.smax
+ | .U128 => U128.smax
+
+def Scalar.min (ty : ScalarTy) : Int :=
+ match ty with
+ | .Isize => Isize.min
+ | .I8 => I8.min
+ | .I16 => I16.min
+ | .I32 => I32.min
+ | .I64 => I64.min
+ | .I128 => I128.min
+ | .Usize => Usize.min
+ | .U8 => U8.min
+ | .U16 => U16.min
+ | .U32 => U32.min
+ | .U64 => U64.min
+ | .U128 => U128.min
+
+def Scalar.max (ty : ScalarTy) : Int :=
+ match ty with
+ | .Isize => Isize.max
+ | .I8 => I8.max
+ | .I16 => I16.max
+ | .I32 => I32.max
+ | .I64 => I64.max
+ | .I128 => I128.max
+ | .Usize => Usize.max
+ | .U8 => U8.max
+ | .U16 => U16.max
+ | .U32 => U32.max
+ | .U64 => U64.max
+ | .U128 => U128.max
+
+def Scalar.smin_eq (ty : ScalarTy) : Scalar.min ty = Scalar.smin ty := by
+ cases ty <;> rfl
+
+def Scalar.smax_eq (ty : ScalarTy) : Scalar.max ty = Scalar.smax ty := by
+ cases ty <;> rfl
+
+-- "Conservative" bounds
+-- We use those because we can't compare to the isize bounds (which can't
+-- reduce at compile-time). Whenever we perform an arithmetic operation like
+-- addition we need to check that the result is in bounds: we first compare
+-- to the conservative bounds, which reduce, then compare to the real bounds.
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+def Scalar.cMin (ty : ScalarTy) : Int :=
+ match ty with
+ | .Isize => Scalar.min .I32
+ | _ => Scalar.min ty
+
+def Scalar.cMax (ty : ScalarTy) : Int :=
+ match ty with
+ | .Isize => Scalar.max .I32
+ | .Usize => Scalar.max .U32
+ | _ => Scalar.max ty
+
+theorem Scalar.cMin_bound ty : Scalar.min ty ≤ Scalar.cMin ty := by
+ cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at *
+ have h := Isize.refined_min.property
+ cases h <;> simp [*, Isize.min]
+
+theorem Scalar.cMax_bound ty : Scalar.cMax ty ≤ Scalar.max ty := by
+ cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at *
+ . have h := Isize.refined_max.property
+ cases h <;> simp [*, Isize.max]
+ . have h := Usize.refined_max.property
+ cases h <;> simp [*, Usize.max]
+
+theorem Scalar.cMin_suffices ty (h : Scalar.cMin ty ≤ x) : Scalar.min ty ≤ x := by
+ have := Scalar.cMin_bound ty
+ linarith
+
+theorem Scalar.cMax_suffices ty (h : x ≤ Scalar.cMax ty) : x ≤ Scalar.max ty := by
+ have := Scalar.cMax_bound ty
+ linarith
+
+structure Scalar (ty : ScalarTy) where
+ val : Int
+ hmin : Scalar.min ty ≤ val
+ hmax : val ≤ Scalar.max ty
+deriving Repr
+
+theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
+ Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty ->
+ Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty
+ :=
+ λ h => by
+ apply And.intro <;> have hmin := Scalar.cMin_bound ty <;> have hmax := Scalar.cMax_bound ty <;> linarith
+
+def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
+ (hmin : Scalar.min ty ≤ x) (hmax : x ≤ Scalar.max ty) : Scalar ty :=
+ { val := x, hmin := hmin, hmax := hmax }
+
+-- Tactic to prove that integers are in bounds
+-- TODO: use this: https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/instance.20with.20tactic.20autoparam
+syntax "intlit" : tactic
+macro_rules
+ | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices; decide)
+
+def Scalar.ofInt {ty : ScalarTy} (x : Int)
+ (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty := by intlit) : Scalar ty :=
+ -- Remark: we initially wrote:
+ -- let ⟨ hmin, hmax ⟩ := h
+ -- Scalar.ofIntCore x hmin hmax
+ -- We updated to the line below because a similar pattern in `Scalar.tryMk`
+ -- made reduction block. Both versions seem to work for `Scalar.ofInt`, though.
+ -- TODO: investigate
+ Scalar.ofIntCore x h.left h.right
+
+@[simp] def Scalar.check_bounds (ty : ScalarTy) (x : Int) : Bool :=
+ (Scalar.cMin ty ≤ x || Scalar.min ty ≤ x) ∧ (x ≤ Scalar.cMax ty || x ≤ Scalar.max ty)
+
+theorem Scalar.check_bounds_prop {ty : ScalarTy} {x : Int} (h: Scalar.check_bounds ty x) :
+ Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty := by
+ simp at *
+ have ⟨ hmin, hmax ⟩ := h
+ have hbmin := Scalar.cMin_bound ty
+ have hbmax := Scalar.cMax_bound ty
+ cases hmin <;> cases hmax <;> apply And.intro <;> linarith
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
+ if h:Scalar.check_bounds ty x then
+ -- If we do:
+ -- ```
+ -- let ⟨ hmin, hmax ⟩ := (Scalar.check_bounds_prop h)
+ -- Scalar.ofIntCore x hmin hmax
+ -- ```
+ -- then normalization blocks (for instance, some proofs which use reflexivity fail).
+ -- However, the version below doesn't block reduction (TODO: investigate):
+ return Scalar.ofInt x (Scalar.check_bounds_prop h)
+ else fail integerOverflow
+
+def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
+
+-- Our custom remainder operation, which satisfies the semantics of Rust
+-- TODO: is there a better way?
+def scalar_rem (x y : Int) : Int :=
+ if 0 ≤ x then x % y
+ else - (|x| % |y|)
+
+@[simp]
+def scalar_rem_nonneg {x y : Int} (hx : 0 ≤ x) : scalar_rem x y = x % y := by
+ intros
+ simp [*, scalar_rem]
+
+-- Our custom division operation, which satisfies the semantics of Rust
+-- TODO: is there a better way?
+def scalar_div (x y : Int) : Int :=
+ if 0 ≤ x && 0 ≤ y then x / y
+ else if 0 ≤ x && y < 0 then - (|x| / |y|)
+ else if x < 0 && 0 ≤ y then - (|x| / |y|)
+ else |x| / |y|
+
+@[simp]
+def scalar_div_nonneg {x y : Int} (hx : 0 ≤ x) (hy : 0 ≤ y) : scalar_div x y = x / y := by
+ intros
+ simp [*, scalar_div]
+
+-- Checking that the remainder operation is correct
+#assert scalar_rem 1 2 = 1
+#assert scalar_rem (-1) 2 = -1
+#assert scalar_rem 1 (-2) = 1
+#assert scalar_rem (-1) (-2) = -1
+#assert scalar_rem 7 3 = (1:Int)
+#assert scalar_rem (-7) 3 = -1
+#assert scalar_rem 7 (-3) = 1
+#assert scalar_rem (-7) (-3) = -1
+
+-- Checking that the division operation is correct
+#assert scalar_div 3 2 = 1
+#assert scalar_div (-3) 2 = -1
+#assert scalar_div 3 (-2) = -1
+#assert scalar_div (-3) (-2) = 1
+#assert scalar_div 7 3 = 2
+#assert scalar_div (-7) 3 = -2
+#assert scalar_div 7 (-3) = -2
+#assert scalar_div (-7) (-3) = 2
+
+def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+ if y.val != 0 then Scalar.tryMk ty (scalar_div x.val y.val) else fail divisionByZero
+
+def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+ if y.val != 0 then Scalar.tryMk ty (scalar_rem x.val y.val) else fail divisionByZero
+
+def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+ Scalar.tryMk ty (x.val + y.val)
+
+def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+ Scalar.tryMk ty (x.val - y.val)
+
+def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
+ Scalar.tryMk ty (x.val * y.val)
+
+-- TODO: instances of +, -, * etc. for scalars
+
+-- Cast an integer from a [src_ty] to a [tgt_ty]
+-- TODO: check the semantics of casts in Rust
+def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
+ Scalar.tryMk tgt_ty x.val
+
+-- The scalar types
+-- We declare the definitions as reducible so that Lean can unfold them (useful
+-- for type class resolution for instance).
+@[reducible] def Isize := Scalar .Isize
+@[reducible] def I8 := Scalar .I8
+@[reducible] def I16 := Scalar .I16
+@[reducible] def I32 := Scalar .I32
+@[reducible] def I64 := Scalar .I64
+@[reducible] def I128 := Scalar .I128
+@[reducible] def Usize := Scalar .Usize
+@[reducible] def U8 := Scalar .U8
+@[reducible] def U16 := Scalar .U16
+@[reducible] def U32 := Scalar .U32
+@[reducible] def U64 := Scalar .U64
+@[reducible] def U128 := Scalar .U128
+
+-- TODO: below: not sure this is the best way.
+-- Should we rather overload operations like +, -, etc.?
+-- Also, it is possible to automate the generation of those definitions
+-- with macros (but would it be a good idea? It would be less easy to
+-- read the file, which is not supposed to change a lot)
+
+-- Negation
+
+/--
+Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
+one here.
+
+The notation typeclass for heterogeneous addition.
+This enables the notation `- a : β` where `a : α`.
+-/
+class HNeg (α : Type u) (β : outParam (Type v)) where
+ /-- `- a` computes the negation of `a`.
+ The meaning of this notation is type-dependent. -/
+ hNeg : α → β
+
+prefix:75 "-" => HNeg.hNeg
+
+instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
+instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
+instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
+instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
+instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
+instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
+
+-- Addition
+instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+ hAdd x y := Scalar.add x y
+
+-- Substraction
+instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+ hSub x y := Scalar.sub x y
+
+-- Multiplication
+instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+ hMul x y := Scalar.mul x y
+
+-- Division
+instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+ hDiv x y := Scalar.div x y
+
+-- Remainder
+instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
+ hMod x y := Scalar.rem x y
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.add_spec {ty} {x y : Scalar ty}
+ (hmin : Scalar.min ty ≤ x.val + y.val)
+ (hmax : x.val + y.val ≤ Scalar.max ty) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ simp [HAdd.hAdd, add, Add.add]
+ simp [tryMk]
+ split
+ . simp [pure]
+ rfl
+ . tauto
+
+theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
+ (hmax : x.val + y.val ≤ Scalar.max ty) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ have hmin : Scalar.min ty ≤ x.val + y.val := by
+ have hx := x.hmin
+ have hy := y.hmin
+ cases ty <;> simp [min] at * <;> linarith
+ apply add_spec <;> assumption
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.add_spec {x y : Usize} (hmax : x.val + y.val ≤ Usize.max) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U8.add_spec {x y : U8} (hmax : x.val + y.val ≤ U8.max) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U16.add_spec {x y : U16} (hmax : x.val + y.val ≤ U16.max) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U32.add_spec {x y : U32} (hmax : x.val + y.val ≤ U32.max) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U64.add_spec {x y : U64} (hmax : x.val + y.val ≤ U64.max) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U128.add_spec {x y : U128} (hmax : x.val + y.val ≤ U128.max) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *]
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.sub_spec {ty} {x y : Scalar ty}
+ (hmin : Scalar.min ty ≤ x.val - y.val)
+ (hmax : x.val - y.val ≤ Scalar.max ty) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ simp [HSub.hSub, sub, Sub.sub]
+ simp [tryMk]
+ split
+ . simp [pure]
+ rfl
+ . tauto
+
+theorem Scalar.sub_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
+ (hmin : Scalar.min ty ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ have : x.val - y.val ≤ Scalar.max ty := by
+ have hx := x.hmin
+ have hxm := x.hmax
+ have hy := y.hmin
+ cases ty <;> simp [min, max] at * <;> linarith
+ intros
+ apply sub_spec <;> assumption
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.sub_spec {x y : Usize} (hmin : Usize.min ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U8.sub_spec {x y : U8} (hmin : U8.min ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U16.sub_spec {x y : U16} (hmin : U16.min ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U32.sub_spec {x y : U32} (hmin : U32.min ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U64.sub_spec {x y : U64} (hmin : U64.min ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+@[cepspec] theorem U128.sub_spec {x y : U128} (hmin : U128.min ≤ x.val - y.val) :
+ ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by
+ apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *]
+
+-- Generic theorem - shouldn't be used much
+theorem Scalar.mul_spec {ty} {x y : Scalar ty}
+ (hmin : Scalar.min ty ≤ x.val * y.val)
+ (hmax : x.val * y.val ≤ Scalar.max ty) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ simp [HMul.hMul, mul, Mul.mul]
+ simp [tryMk]
+ split
+ . simp [pure]
+ rfl
+ . tauto
+
+theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
+ (hmax : x.val * y.val ≤ Scalar.max ty) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ have : Scalar.min ty ≤ x.val * y.val := by
+ have hx := x.hmin
+ have hy := y.hmin
+ cases ty <;> simp at * <;> apply mul_nonneg hx hy
+ apply mul_spec <;> assumption
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.mul_spec {x y : Usize} (hmax : x.val * y.val ≤ Usize.max) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U8.mul_spec {x y : U8} (hmax : x.val * y.val ≤ U8.max) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U16.mul_spec {x y : U16} (hmax : x.val * y.val ≤ U16.max) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U32.mul_spec {x y : U32} (hmax : x.val * y.val ≤ U32.max) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U64.mul_spec {x y : U64} (hmax : x.val * y.val ≤ U64.max) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+@[cepspec] theorem U128.mul_spec {x y : U128} (hmax : x.val * y.val ≤ U128.max) :
+ ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by
+ apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *]
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.div_spec {ty} {x y : Scalar ty}
+ (hnz : y.val ≠ 0)
+ (hmin : Scalar.min ty ≤ scalar_div x.val y.val)
+ (hmax : scalar_div x.val y.val ≤ Scalar.max ty) :
+ ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := by
+ simp [HDiv.hDiv, div, Div.div]
+ simp [tryMk, *]
+ simp [pure]
+ rfl
+
+theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty}
+ (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ have h : Scalar.min ty = 0 := by cases ty <;> simp at *
+ have hx := x.hmin
+ have hy := y.hmin
+ simp [h] at hx hy
+ have hmin : 0 ≤ x.val / y.val := Int.ediv_nonneg hx hy
+ have hmax : x.val / y.val ≤ Scalar.max ty := by
+ have := Int.ediv_le_self y.val hx
+ have := x.hmax
+ linarith
+ have hs := @div_spec ty x y hnz
+ simp [*] at hs
+ apply hs
+
+/- Fine-grained theorems -/
+@[cepspec] theorem Usize.div_spec (x : Usize) {y : Usize} (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ apply Scalar.div_unsigned_spec <;> simp [*]
+
+@[cepspec] theorem U8.div_spec (x : U8) {y : U8} (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U16.div_spec (x : U16) {y : U16} (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U32.div_spec (x : U32) {y : U32} (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U64.div_spec (x : U64) {y : U64} (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U128.div_spec (x : U128) {y : U128} (hnz : y.val ≠ 0) :
+ ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by
+ apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *]
+
+-- Generic theorem - shouldn't be used much
+@[cpspec]
+theorem Scalar.rem_spec {ty} {x y : Scalar ty}
+ (hnz : y.val ≠ 0)
+ (hmin : Scalar.min ty ≤ scalar_rem x.val y.val)
+ (hmax : scalar_rem x.val y.val ≤ Scalar.max ty) :
+ ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := by
+ simp [HMod.hMod, rem]
+ simp [tryMk, *]
+ simp [pure]
+ rfl
+
+theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty}
+ (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ have h : Scalar.min ty = 0 := by cases ty <;> simp at *
+ have hx := x.hmin
+ have hy := y.hmin
+ simp [h] at hx hy
+ have hmin : 0 ≤ x.val % y.val := Int.emod_nonneg x.val hnz
+ have hmax : x.val % y.val ≤ Scalar.max ty := by
+ have h : 0 < y.val := by int_tac
+ have h := Int.emod_lt_of_pos x.val h
+ have := y.hmax
+ linarith
+ have hs := @rem_spec ty x y hnz
+ simp [*] at hs
+ simp [*]
+
+@[cepspec] theorem Usize.rem_spec (x : Usize) {y : Usize} (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ apply Scalar.rem_unsigned_spec <;> simp [*]
+
+@[cepspec] theorem U8.rem_spec (x : U8) {y : U8} (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U16.rem_spec (x : U16) {y : U16} (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U32.rem_spec (x : U32) {y : U32} (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U64.rem_spec (x : U64) {y : U64} (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+@[cepspec] theorem U128.rem_spec (x : U128) {y : U128} (hnz : y.val ≠ 0) :
+ ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by
+ apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *]
+
+-- ofIntCore
+-- TODO: typeclass?
+def Isize.ofIntCore := @Scalar.ofIntCore .Isize
+def I8.ofIntCore := @Scalar.ofIntCore .I8
+def I16.ofIntCore := @Scalar.ofIntCore .I16
+def I32.ofIntCore := @Scalar.ofIntCore .I32
+def I64.ofIntCore := @Scalar.ofIntCore .I64
+def I128.ofIntCore := @Scalar.ofIntCore .I128
+def Usize.ofIntCore := @Scalar.ofIntCore .Usize
+def U8.ofIntCore := @Scalar.ofIntCore .U8
+def U16.ofIntCore := @Scalar.ofIntCore .U16
+def U32.ofIntCore := @Scalar.ofIntCore .U32
+def U64.ofIntCore := @Scalar.ofIntCore .U64
+def U128.ofIntCore := @Scalar.ofIntCore .U128
+
+-- ofInt
+-- TODO: typeclass?
+def Isize.ofInt := @Scalar.ofInt .Isize
+def I8.ofInt := @Scalar.ofInt .I8
+def I16.ofInt := @Scalar.ofInt .I16
+def I32.ofInt := @Scalar.ofInt .I32
+def I64.ofInt := @Scalar.ofInt .I64
+def I128.ofInt := @Scalar.ofInt .I128
+def Usize.ofInt := @Scalar.ofInt .Usize
+def U8.ofInt := @Scalar.ofInt .U8
+def U16.ofInt := @Scalar.ofInt .U16
+def U32.ofInt := @Scalar.ofInt .U32
+def U64.ofInt := @Scalar.ofInt .U64
+def U128.ofInt := @Scalar.ofInt .U128
+
+-- TODO: factor those lemmas out
+@[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by
+ simp [Scalar.ofInt, Scalar.ofIntCore]
+
+@[simp] theorem Isize.ofInt_val_eq (h : Scalar.min ScalarTy.Isize ≤ x ∧ x ≤ Scalar.max ScalarTy.Isize) : (Isize.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I8.ofInt_val_eq (h : Scalar.min ScalarTy.I8 ≤ x ∧ x ≤ Scalar.max ScalarTy.I8) : (I8.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I16.ofInt_val_eq (h : Scalar.min ScalarTy.I16 ≤ x ∧ x ≤ Scalar.max ScalarTy.I16) : (I16.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I32.ofInt_val_eq (h : Scalar.min ScalarTy.I32 ≤ x ∧ x ≤ Scalar.max ScalarTy.I32) : (I32.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I64.ofInt_val_eq (h : Scalar.min ScalarTy.I64 ≤ x ∧ x ≤ Scalar.max ScalarTy.I64) : (I64.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I128.ofInt_val_eq (h : Scalar.min ScalarTy.I128 ≤ x ∧ x ≤ Scalar.max ScalarTy.I128) : (I128.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem Usize.ofInt_val_eq (h : Scalar.min ScalarTy.Usize ≤ x ∧ x ≤ Scalar.max ScalarTy.Usize) : (Usize.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U8.ofInt_val_eq (h : Scalar.min ScalarTy.U8 ≤ x ∧ x ≤ Scalar.max ScalarTy.U8) : (U8.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U16.ofInt_val_eq (h : Scalar.min ScalarTy.U16 ≤ x ∧ x ≤ Scalar.max ScalarTy.U16) : (U16.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U32.ofInt_val_eq (h : Scalar.min ScalarTy.U32 ≤ x ∧ x ≤ Scalar.max ScalarTy.U32) : (U32.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U64.ofInt_val_eq (h : Scalar.min ScalarTy.U64 ≤ x ∧ x ≤ Scalar.max ScalarTy.U64) : (U64.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by
+ apply Scalar.ofInt_val_eq h
+
+
+-- Comparisons
+instance {ty} : LT (Scalar ty) where
+ lt a b := LT.lt a.val b.val
+
+instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
+
+instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
+instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
+
+theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
+ | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
+
+theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
+ h ▸ rfl
+
+theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
+ fun h' => absurd (val_eq_of_eq h') h
+
+instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
+ fun i j =>
+ match decEq i.val j.val with
+ | isTrue h => isTrue (Scalar.eq_of_val_eq h)
+ | isFalse h => isFalse (Scalar.ne_of_val_ne h)
+
+/- Remark: we can't write the following instance because of restrictions about
+ the type class parameters (`ty` doesn't appear in the return type, which is
+ forbidden):
+
+ ```
+ instance Scalar.cast (ty : ScalarTy) : Coe (Scalar ty) Int where coe := λ v => v.val
+ ```
+ -/
+def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
+
+-- -- We now define a type class that subsumes the various machine integer types, so
+-- -- as to write a concise definition for scalar_cast, rather than exhaustively
+-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
+-- -- and fails if a cast operation would involve a truncation or modulo.
+
+-- class MachineInteger (t: Type) where
+-- size: Nat
+-- val: t -> Fin size
+-- ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+-- set_option hygiene false in
+-- run_cmd
+-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+-- Lean.Elab.Command.elabCommand (← `(
+-- namespace $typeName
+-- instance: MachineInteger $typeName where
+-- size := size
+-- val := val
+-- ofNatCore := ofNatCore
+-- end $typeName
+-- ))
+
+-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
+-- -- Lean to infer `src`.
+
+-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
+-- if h: MachineInteger.val x < MachineInteger.size dst then
+-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+-- else
+-- .fail integerOverflow
+
+end Primitives
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
new file mode 100644
index 00000000..a09d6ac2
--- /dev/null
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -0,0 +1,145 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.IList
+import Base.Primitives.Scalar
+import Base.Arith
+import Base.Progress.Base
+
+namespace Primitives
+
+open Result Error
+
+-------------
+-- VECTORS --
+-------------
+
+def Vec (α : Type u) := { l : List α // l.length ≤ Usize.max }
+
+-- TODO: do we really need it? It should be with Subtype by default
+instance Vec.cast (a : Type u): Coe (Vec a) (List a) where coe := λ v => v.val
+
+instance (a : Type u) : Arith.HasIntProp (Vec a) where
+ prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize
+ prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
+
+@[simp]
+abbrev Vec.length {α : Type u} (v : Vec α) : Int := v.val.len
+
+@[simp]
+abbrev Vec.v {α : Type u} (v : Vec α) : List α := v.val
+
+example {a: Type u} (v : Vec a) : v.length ≤ Scalar.max ScalarTy.Usize := by
+ scalar_tac
+
+def Vec.new (α : Type u): Vec α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩
+
+-- TODO: very annoying that the α is an explicit parameter
+def Vec.len (α : Type u) (v : Vec α) : Usize :=
+ Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac)
+
+@[simp]
+theorem Vec.len_val {α : Type u} (v : Vec α) : (Vec.len α v).val = v.length :=
+ by rfl
+
+-- This shouldn't be used
+def Vec.push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
+
+-- This is actually the backward function
+def Vec.push (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
+ :=
+ let nlen := List.length v.val + 1
+ if h : nlen ≤ U32.max || nlen ≤ Usize.max then
+ have h : nlen ≤ Usize.max := by
+ simp [Usize.max] at *
+ have hm := Usize.refined_max.property
+ cases h <;> cases hm <;> simp [U32.max, U64.max] at * <;> try linarith
+ return ⟨ List.concat v.val x, by simp at *; assumption ⟩
+ else
+ fail maximumSizeExceeded
+
+-- This shouldn't be used
+def Vec.insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
+ if i.val < v.length then
+ .ret ()
+ else
+ .fail arrayOutOfBounds
+
+-- This is actually the backward function
+def Vec.insert (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
+ if i.val < v.length then
+ .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+ else
+ .fail arrayOutOfBounds
+
+@[pspec]
+theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α)
+ (hbound : i.val < v.length) :
+ ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by
+ simp [insert, *]
+
+def Vec.index (α : Type u) (v: Vec α) (i: Usize) : Result α :=
+ match v.val.indexOpt i.val with
+ | none => fail .arrayOutOfBounds
+ | some x => ret x
+
+/- In the theorems below: we don't always need the `∃ ..`, but we use one
+ so that `progress` introduces an opaque variable and an equality. This
+ helps control the context.
+ -/
+
+@[pspec]
+theorem Vec.index_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+ (hbound : i.val < v.length) :
+ ∃ x, v.index α i = ret x ∧ x = v.val.index i.val := by
+ simp only [index]
+ -- TODO: dependent rewrite
+ have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
+ simp [*]
+
+-- This shouldn't be used
+def Vec.index_back (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
+ if i.val < List.length v.val then
+ .ret ()
+ else
+ .fail arrayOutOfBounds
+
+def Vec.index_mut (α : Type u) (v: Vec α) (i: Usize) : Result α :=
+ match v.val.indexOpt i.val with
+ | none => fail .arrayOutOfBounds
+ | some x => ret x
+
+@[pspec]
+theorem Vec.index_mut_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+ (hbound : i.val < v.length) :
+ ∃ x, v.index_mut α i = ret x ∧ x = v.val.index i.val := by
+ simp only [index_mut]
+ -- TODO: dependent rewrite
+ have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
+ simp [*]
+
+instance {α : Type u} (p : Vec α → Prop) : Arith.HasIntProp (Subtype p) where
+ prop_ty := λ x => p x
+ prop := λ x => x.property
+
+def Vec.index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
+ match v.val.indexOpt i.val with
+ | none => fail .arrayOutOfBounds
+ | some _ =>
+ .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+
+@[pspec]
+theorem Vec.index_mut_back_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
+ (hbound : i.val < v.length) :
+ ∃ nv, v.index_mut_back α i x = ret nv ∧
+ nv.val = v.val.update i.val x
+ := by
+ simp only [index_mut_back]
+ have h := List.indexOpt_bounds v.val i.val
+ split
+ . simp_all [length]; cases h <;> scalar_tac
+ . simp_all
+
+end Primitives
diff --git a/backends/lean/Base/Progress.lean b/backends/lean/Base/Progress.lean
new file mode 100644
index 00000000..d812b896
--- /dev/null
+++ b/backends/lean/Base/Progress.lean
@@ -0,0 +1 @@
+import Base.Progress.Progress
diff --git a/backends/lean/Base/Progress/Base.lean b/backends/lean/Base/Progress/Base.lean
new file mode 100644
index 00000000..6f820a84
--- /dev/null
+++ b/backends/lean/Base/Progress/Base.lean
@@ -0,0 +1,316 @@
+import Lean
+import Std.Lean.HashSet
+import Base.Utils
+import Base.Primitives.Base
+
+namespace Progress
+
+open Lean Elab Term Meta
+open Utils
+
+-- We can't define and use trace classes in the same file
+initialize registerTraceClass `Progress
+
+/- # Progress tactic -/
+
+structure PSpecDesc where
+ -- The universally quantified variables
+ fvars : Array Expr
+ -- The existentially quantified variables
+ evars : Array Expr
+ -- The function
+ fExpr : Expr
+ fName : Name
+ -- The function arguments
+ fLevels : List Level
+ args : Array Expr
+ -- The universally quantified variables which appear in the function arguments
+ argsFVars : Array FVarId
+ -- The returned value
+ ret : Expr
+ -- The postcondition (if there is)
+ post : Option Expr
+
+section Methods
+ variable [MonadLiftT MetaM m] [MonadControlT MetaM m] [Monad m] [MonadOptions m]
+ variable [MonadTrace m] [MonadLiftT IO m] [MonadRef m] [AddMessageContext m]
+ variable [MonadError m]
+ variable {a : Type}
+
+ /- Analyze a pspec theorem to decompose its arguments.
+
+ PSpec theorems should be of the following shape:
+ ```
+ ∀ x1 ... xn, H1 → ... Hn → ∃ y1 ... ym. f x1 ... xn = .ret ... ∧ Post1 ∧ ... ∧ Postk
+ ```
+
+ The continuation `k` receives the following inputs:
+ - universally quantified variables
+ - assumptions
+ - existentially quantified variables
+ - function name
+ - function arguments
+ - return
+ - postconditions
+
+ TODO: generalize for when we do inductive proofs
+ -/
+ partial
+ def withPSpec [Inhabited (m a)] [Nonempty (m a)] (th : Expr) (k : PSpecDesc → m a)
+ (sanityChecks : Bool := false) :
+ m a := do
+ trace[Progress] "Proposition: {th}"
+ -- Dive into the quantified variables and the assumptions
+ forallTelescope th.consumeMData fun fvars th => do
+ trace[Progress] "Universally quantified arguments and assumptions: {fvars}"
+ -- Dive into the existentials
+ existsTelescope th.consumeMData fun evars th => do
+ trace[Progress] "Existentials: {evars}"
+ trace[Progress] "Proposition after stripping the quantifiers: {th}"
+ -- Take the first conjunct
+ let (th, post) ← optSplitConj th.consumeMData
+ trace[Progress] "After splitting the conjunction:\n- eq: {th}\n- post: {post}"
+ -- Destruct the equality
+ let (mExpr, ret) ← destEq th.consumeMData
+ trace[Progress] "After splitting the equality:\n- lhs: {th}\n- rhs: {ret}"
+ -- Destruct the monadic application to dive into the bind, if necessary (this
+ -- is for when we use `withPSpec` inside of the `progress` tactic), and
+ -- destruct the application to get the function name
+ mExpr.consumeMData.withApp fun mf margs => do
+ trace[Progress] "After stripping the arguments of the monad expression:\n- mf: {mf}\n- margs: {margs}"
+ let (fExpr, f, args) ← do
+ if mf.isConst ∧ mf.constName = ``Bind.bind then do
+ -- Dive into the bind
+ let fExpr := (margs.get! 4).consumeMData
+ fExpr.withApp fun f args => pure (fExpr, f, args)
+ else pure (mExpr, mf, margs)
+ trace[Progress] "After stripping the arguments of the function call:\n- f: {f}\n- args: {args}"
+ if ¬ f.isConst then throwError "Not a constant: {f}"
+ -- Compute the set of universally quantified variables which appear in the function arguments
+ let allArgsFVars ← args.foldlM (fun hs arg => getFVarIds arg hs) HashSet.empty
+ -- Sanity check
+ if sanityChecks then
+ -- All the variables which appear in the inputs given to the function are
+ -- universally quantified (in particular, they are not *existentially* quantified)
+ let fvarsSet : HashSet FVarId := HashSet.ofArray (fvars.map (fun x => x.fvarId!))
+ let filtArgsFVars := allArgsFVars.toArray.filter (fun fvar => ¬ fvarsSet.contains fvar)
+ if ¬ filtArgsFVars.isEmpty then
+ let filtArgsFVars := filtArgsFVars.map (fun fvarId => Expr.fvar fvarId)
+ throwError "Some of the function inputs are not universally quantified: {filtArgsFVars}"
+ let argsFVars := fvars.map (fun x => x.fvarId!)
+ let argsFVars := argsFVars.filter (fun fvar => allArgsFVars.contains fvar)
+ -- Return
+ trace[Progress] "Function: {f.constName!}";
+ let thDesc := {
+ fvars := fvars
+ evars := evars
+ fExpr
+ fName := f.constName!
+ fLevels := f.constLevels!
+ args := args
+ argsFVars
+ ret := ret
+ post := post
+ }
+ k thDesc
+
+end Methods
+
+def getPSpecFunName (th : Expr) : MetaM Name :=
+ withPSpec th (fun d => do pure d.fName) true
+
+def getPSpecClassFunNames (th : Expr) : MetaM (Name × Name) :=
+ withPSpec th (fun d => do
+ let arg0 := d.args.get! 0
+ arg0.withApp fun f _ => do
+ if ¬ f.isConst then throwError "Not a constant: {f}"
+ pure (d.fName, f.constName)
+ ) true
+
+def getPSpecClassFunNameArg (th : Expr) : MetaM (Name × Expr) :=
+ withPSpec th (fun d => do
+ let arg0 := d.args.get! 0
+ pure (d.fName, arg0)
+ ) true
+
+-- "Regular" pspec attribute
+structure PSpecAttr where
+ attr : AttributeImpl
+ ext : MapDeclarationExtension Name
+ deriving Inhabited
+
+/- pspec attribute for type classes: we use the name of the type class to
+ lookup another map. We use the *first* argument of the type class to lookup
+ into this second map.
+
+ Example:
+ ========
+ We use type classes for addition. For instance, the addition between two
+ U32 is written (without syntactic sugar) as `HAdd.add (Scalar ty) x y`. As a consequence,
+ we store the theorem through the bindings: HAdd.add → Scalar → ...
+
+ SH: TODO: this (and `PSpecClassExprAttr`) is a bit ad-hoc. For now it works for the
+ specs of the scalar operations, which is what I really need, but I'm not sure it
+ applies well to other situations. A better way would probably to use type classes, but
+ I couldn't get them to work on those cases. It is worth retrying.
+-/
+structure PSpecClassAttr where
+ attr : AttributeImpl
+ ext : MapDeclarationExtension (NameMap Name)
+ deriving Inhabited
+
+/- Same as `PSpecClassAttr` but we use the full first argument (it works when it
+ is a constant). -/
+structure PSpecClassExprAttr where
+ attr : AttributeImpl
+ ext : MapDeclarationExtension (HashMap Expr Name)
+ deriving Inhabited
+
+-- TODO: the original function doesn't define correctly the `addImportedFn`. Do a PR?
+def mkMapDeclarationExtension [Inhabited α] (name : Name := by exact decl_name%) : IO (MapDeclarationExtension α) :=
+ registerSimplePersistentEnvExtension {
+ name := name,
+ addImportedFn := fun a => a.foldl (fun s a => a.foldl (fun s (k, v) => s.insert k v) s) RBMap.empty,
+ addEntryFn := fun s n => s.insert n.1 n.2 ,
+ toArrayFn := fun es => es.toArray.qsort (fun a b => Name.quickLt a.1 b.1)
+ }
+
+/- The persistent map from function to pspec theorems. -/
+initialize pspecAttr : PSpecAttr ← do
+ let ext ← mkMapDeclarationExtension `pspecMap
+ let attrImpl : AttributeImpl := {
+ name := `pspec
+ descr := "Marks theorems to use with the `progress` tactic"
+ add := fun thName stx attrKind => do
+ Attribute.Builtin.ensureNoArgs stx
+ -- TODO: use the attribute kind
+ unless attrKind == AttributeKind.global do
+ throwError "invalid attribute 'pspec', must be global"
+ -- Lookup the theorem
+ let env ← getEnv
+ let thDecl := env.constants.find! thName
+ let fName ← MetaM.run' (getPSpecFunName thDecl.type)
+ trace[Progress] "Registering spec theorem for {fName}"
+ let env := ext.addEntry env (fName, thName)
+ setEnv env
+ pure ()
+ }
+ registerBuiltinAttribute attrImpl
+ pure { attr := attrImpl, ext := ext }
+
+/- The persistent map from type classes to pspec theorems -/
+initialize pspecClassAttr : PSpecClassAttr ← do
+ let ext : MapDeclarationExtension (NameMap Name) ← mkMapDeclarationExtension `pspecClassMap
+ let attrImpl : AttributeImpl := {
+ name := `cpspec
+ descr := "Marks theorems to use for type classes with the `progress` tactic"
+ add := fun thName stx attrKind => do
+ Attribute.Builtin.ensureNoArgs stx
+ -- TODO: use the attribute kind
+ unless attrKind == AttributeKind.global do
+ throwError "invalid attribute 'cpspec', must be global"
+ -- Lookup the theorem
+ let env ← getEnv
+ let thDecl := env.constants.find! thName
+ let (fName, argName) ← MetaM.run' (getPSpecClassFunNames thDecl.type)
+ trace[Progress] "Registering class spec theorem for ({fName}, {argName})"
+ -- Update the entry if there is one, add an entry if there is none
+ let env :=
+ match (ext.getState (← getEnv)).find? fName with
+ | none =>
+ let m := RBMap.ofList [(argName, thName)]
+ ext.addEntry env (fName, m)
+ | some m =>
+ let m := m.insert argName thName
+ ext.addEntry env (fName, m)
+ setEnv env
+ pure ()
+ }
+ registerBuiltinAttribute attrImpl
+ pure { attr := attrImpl, ext := ext }
+
+/- The 2nd persistent map from type classes to pspec theorems -/
+initialize pspecClassExprAttr : PSpecClassExprAttr ← do
+ let ext : MapDeclarationExtension (HashMap Expr Name) ← mkMapDeclarationExtension `pspecClassExprMap
+ let attrImpl : AttributeImpl := {
+ name := `cepspec
+ descr := "Marks theorems to use for type classes with the `progress` tactic"
+ add := fun thName stx attrKind => do
+ Attribute.Builtin.ensureNoArgs stx
+ -- TODO: use the attribute kind
+ unless attrKind == AttributeKind.global do
+ throwError "invalid attribute 'cpspec', must be global"
+ -- Lookup the theorem
+ let env ← getEnv
+ let thDecl := env.constants.find! thName
+ let (fName, arg) ← MetaM.run' (getPSpecClassFunNameArg thDecl.type)
+ -- Sanity check: no variables appear in the argument
+ MetaM.run' do
+ let fvars ← getFVarIds arg
+ if ¬ fvars.isEmpty then throwError "The first argument ({arg}) contains variables"
+ -- We store two bindings:
+ -- - arg to theorem name
+ -- - reduced arg to theorem name
+ let rarg ← MetaM.run' (reduceAll arg)
+ trace[Progress] "Registering class spec theorem for ({fName}, {arg}) and ({fName}, {rarg})"
+ -- Update the entry if there is one, add an entry if there is none
+ let env :=
+ match (ext.getState (← getEnv)).find? fName with
+ | none =>
+ let m := HashMap.ofList [(arg, thName), (rarg, thName)]
+ ext.addEntry env (fName, m)
+ | some m =>
+ let m := m.insert arg thName
+ let m := m.insert rarg thName
+ ext.addEntry env (fName, m)
+ setEnv env
+ pure ()
+ }
+ registerBuiltinAttribute attrImpl
+ pure { attr := attrImpl, ext := ext }
+
+
+def PSpecAttr.find? (s : PSpecAttr) (name : Name) : MetaM (Option Name) := do
+ return (s.ext.getState (← getEnv)).find? name
+
+def PSpecClassAttr.find? (s : PSpecClassAttr) (className argName : Name) : MetaM (Option Name) := do
+ match (s.ext.getState (← getEnv)).find? className with
+ | none => return none
+ | some map => return map.find? argName
+
+def PSpecClassExprAttr.find? (s : PSpecClassExprAttr) (className : Name) (arg : Expr) : MetaM (Option Name) := do
+ match (s.ext.getState (← getEnv)).find? className with
+ | none => return none
+ | some map => return map.find? arg
+
+def PSpecAttr.getState (s : PSpecAttr) : MetaM (NameMap Name) := do
+ pure (s.ext.getState (← getEnv))
+
+def PSpecClassAttr.getState (s : PSpecClassAttr) : MetaM (NameMap (NameMap Name)) := do
+ pure (s.ext.getState (← getEnv))
+
+def PSpecClassExprAttr.getState (s : PSpecClassExprAttr) : MetaM (NameMap (HashMap Expr Name)) := do
+ pure (s.ext.getState (← getEnv))
+
+def showStoredPSpec : MetaM Unit := do
+ let st ← pspecAttr.getState
+ let s := st.toList.foldl (fun s (f, th) => f!"{s}\n{f} → {th}") f!""
+ IO.println s
+
+def showStoredPSpecClass : MetaM Unit := do
+ let st ← pspecClassAttr.getState
+ let s := st.toList.foldl (fun s (f, m) =>
+ let ms := m.toList.foldl (fun s (f, th) =>
+ f!"{s}\n {f} → {th}") f!""
+ f!"{s}\n{f} → [{ms}]") f!""
+ IO.println s
+
+def showStoredPSpecExprClass : MetaM Unit := do
+ let st ← pspecClassExprAttr.getState
+ let s := st.toList.foldl (fun s (f, m) =>
+ let ms := m.toList.foldl (fun s (f, th) =>
+ f!"{s}\n {f} → {th}") f!""
+ f!"{s}\n{f} → [{ms}]") f!""
+ IO.println s
+
+end Progress
diff --git a/backends/lean/Base/Progress/Progress.lean b/backends/lean/Base/Progress/Progress.lean
new file mode 100644
index 00000000..6a4729dc
--- /dev/null
+++ b/backends/lean/Base/Progress/Progress.lean
@@ -0,0 +1,377 @@
+import Lean
+import Base.Arith
+import Base.Progress.Base
+import Base.Primitives -- TODO: remove?
+
+namespace Progress
+
+open Lean Elab Term Meta Tactic
+open Utils
+
+inductive TheoremOrLocal where
+| Theorem (thName : Name)
+| Local (asm : LocalDecl)
+
+instance : ToMessageData TheoremOrLocal where
+ toMessageData := λ x => match x with | .Theorem thName => m!"{thName}" | .Local asm => m!"{asm.userName}"
+
+/- Type to propagate the errors of `progressWith`.
+ We need this because we use the exceptions to backtrack, when trying to
+ use the assumptions for instance. When there is actually an error we want
+ to propagate to the user, we return it. -/
+inductive ProgressError
+| Ok
+| Error (msg : MessageData)
+deriving Inhabited
+
+def progressWith (fExpr : Expr) (th : TheoremOrLocal)
+ (keep : Option Name) (ids : Array (Option Name)) (splitPost : Bool)
+ (asmTac : TacticM Unit) : TacticM ProgressError := do
+ /- Apply the theorem
+ We try to match the theorem with the goal
+ In order to do so, we introduce meta-variables for all the parameters
+ (i.e., quantified variables and assumpions), and unify those with the goal.
+ Remark: we do not introduce meta-variables for the quantified variables
+ which don't appear in the function arguments (we want to let them
+ quantified).
+ We also make sure that all the meta variables which appear in the
+ function arguments have been instantiated
+ -/
+ let env ← getEnv
+ let thTy ← do
+ match th with
+ | .Theorem thName =>
+ let thDecl := env.constants.find! thName
+ -- We have to introduce fresh meta-variables for the universes already
+ let ul : List (Name × Level) ←
+ thDecl.levelParams.mapM (λ x => do pure (x, ← mkFreshLevelMVar))
+ let ulMap : HashMap Name Level := HashMap.ofList ul
+ let thTy := thDecl.type.instantiateLevelParamsCore (λ x => ulMap.find! x)
+ pure thTy
+ | .Local asmDecl => pure asmDecl.type
+ trace[Progress] "Looked up theorem/assumption type: {thTy}"
+ -- TODO: the tactic fails if we uncomment withNewMCtxDepth
+ -- withNewMCtxDepth do
+ let (mvars, binders, thExBody) ← forallMetaTelescope thTy
+ trace[Progress] "After stripping foralls: {thExBody}"
+ -- Introduce the existentially quantified variables and the post-condition
+ -- in the context
+ let thBody ←
+ existsTelescope thExBody.consumeMData fun _evars thBody => do
+ trace[Progress] "After stripping existentials: {thBody}"
+ let (thBody, _) ← optSplitConj thBody
+ trace[Progress] "After splitting the conjunction: {thBody}"
+ let (thBody, _) ← destEq thBody
+ trace[Progress] "After splitting equality: {thBody}"
+ -- There shouldn't be any existential variables in thBody
+ pure thBody.consumeMData
+ -- Match the body with the target
+ trace[Progress] "Matching:\n- body:\n{thBody}\n- target:\n{fExpr}"
+ let ok ← isDefEq thBody fExpr
+ if ¬ ok then throwError "Could not unify the theorem with the target:\n- theorem: {thBody}\n- target: {fExpr}"
+ let mgoal ← Tactic.getMainGoal
+ postprocessAppMVars `progress mgoal mvars binders true true
+ Term.synthesizeSyntheticMVarsNoPostponing
+ let thBody ← instantiateMVars thBody
+ trace[Progress] "thBody (after instantiation): {thBody}"
+ -- Add the instantiated theorem to the assumptions (we apply it on the metavariables).
+ let th ← do
+ match th with
+ | .Theorem thName => mkAppOptM thName (mvars.map some)
+ | .Local decl => mkAppOptM' (mkFVar decl.fvarId) (mvars.map some)
+ let asmName ← do match keep with | none => mkFreshAnonPropUserName | some n => do pure n
+ let thTy ← inferType th
+ let thAsm ← Utils.addDeclTac asmName th thTy (asLet := false)
+ withMainContext do -- The context changed - TODO: remove once addDeclTac is updated
+ let ngoal ← getMainGoal
+ trace[Progress] "current goal: {ngoal}"
+ trace[Progress] "current goal: {← ngoal.isAssigned}"
+ -- The assumption should be of the shape:
+ -- `∃ x1 ... xn, f args = ... ∧ ...`
+ -- We introduce the existentially quantified variables and split the top-most
+ -- conjunction if there is one. We use the provided `ids` list to name the
+ -- introduced variables.
+ let res ← splitAllExistsTac thAsm ids.toList fun h ids => do
+ -- Split the conjunctions.
+ -- For the conjunctions, we split according once to separate the equality `f ... = .ret ...`
+ -- from the postcondition, if there is, then continue to split the postcondition if there
+ -- are remaining ids.
+ let splitEqAndPost (k : Expr → Option Expr → List (Option Name) → TacticM ProgressError) : TacticM ProgressError := do
+ if ← isConj (← inferType h) then do
+ let hName := (← h.fvarId!.getDecl).userName
+ let (optIds, ids) ← do
+ match ids with
+ | [] => do pure (some (hName, ← mkFreshAnonPropUserName), [])
+ | none :: ids => do pure (some (hName, ← mkFreshAnonPropUserName), ids)
+ | some id :: ids => do pure (some (hName, id), ids)
+ splitConjTac h optIds (fun hEq hPost => k hEq (some hPost) ids)
+ else k h none ids
+ -- Simplify the target by using the equality and some monad simplifications,
+ -- then continue splitting the post-condition
+ splitEqAndPost fun hEq hPost ids => do
+ trace[Progress] "eq and post:\n{hEq} : {← inferType hEq}\n{hPost}"
+ simpAt [] [``Primitives.bind_tc_ret, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
+ [hEq.fvarId!] (.targets #[] true)
+ -- Clear the equality, unless the user requests not to do so
+ let mgoal ← do
+ if keep.isSome then getMainGoal
+ else do
+ let mgoal ← getMainGoal
+ mgoal.tryClearMany #[hEq.fvarId!]
+ setGoals (mgoal :: (← getUnsolvedGoals))
+ trace[Progress] "Goal after splitting eq and post and simplifying the target: {mgoal}"
+ -- Continue splitting following the post following the user's instructions
+ match hPost with
+ | none =>
+ -- Sanity check
+ if ¬ ids.isEmpty then
+ return (.Error m!"Too many ids provided ({ids}): there is no postcondition to split")
+ else return .Ok
+ | some hPost => do
+ let rec splitPostWithIds (prevId : Name) (hPost : Expr) (ids0 : List (Option Name)) : TacticM ProgressError := do
+ match ids0 with
+ | [] =>
+ /- We used all the user provided ids.
+ Split the remaining conjunctions by using fresh ids if the user
+ instructed to fully split the post-condition, otherwise stop -/
+ if splitPost then
+ splitFullConjTac true hPost (λ _ => pure .Ok)
+ else pure .Ok
+ | nid :: ids => do
+ trace[Progress] "Splitting post: {← inferType hPost}"
+ -- Split
+ let nid ← do
+ match nid with
+ | none => mkFreshAnonPropUserName
+ | some nid => pure nid
+ trace[Progress] "\n- prevId: {prevId}\n- nid: {nid}\n- remaining ids: {ids}"
+ if ← isConj (← inferType hPost) then
+ splitConjTac hPost (some (prevId, nid)) (λ _ nhPost => splitPostWithIds nid nhPost ids)
+ else return (.Error m!"Too many ids provided ({ids0}) not enough conjuncts to split in the postcondition")
+ let curPostId := (← hPost.fvarId!.getDecl).userName
+ splitPostWithIds curPostId hPost ids
+ match res with
+ | .Error _ => return res -- Can we get there? We're using "return"
+ | .Ok =>
+ -- Update the set of goals
+ let curGoals ← getUnsolvedGoals
+ let newGoals := mvars.map Expr.mvarId!
+ let newGoals ← newGoals.filterM fun mvar => not <$> mvar.isAssigned
+ trace[Progress] "new goals: {newGoals}"
+ setGoals newGoals.toList
+ allGoals asmTac
+ let newGoals ← getUnsolvedGoals
+ setGoals (newGoals ++ curGoals)
+ trace[Progress] "progress: replaced the goals"
+ --
+ pure .Ok
+
+-- Small utility: if `args` is not empty, return the name of the app in the first
+-- arg, if it is a const.
+def getFirstArgAppName (args : Array Expr) : MetaM (Option Name) := do
+ if args.size = 0 then pure none
+ else
+ (args.get! 0).withApp fun f _ => do
+ if f.isConst then pure (some f.constName)
+ else pure none
+
+def getFirstArg (args : Array Expr) : Option Expr := do
+ if args.size = 0 then none
+ else some (args.get! 0)
+
+/- Helper: try to lookup a theorem and apply it, or continue with another tactic
+ if it fails -/
+def tryLookupApply (keep : Option Name) (ids : Array (Option Name)) (splitPost : Bool)
+ (asmTac : TacticM Unit) (fExpr : Expr)
+ (kind : String) (th : Option TheoremOrLocal) (x : TacticM Unit) : TacticM Unit := do
+ let res ← do
+ match th with
+ | none =>
+ trace[Progress] "Could not find a {kind}"
+ pure none
+ | some th => do
+ trace[Progress] "Lookuped up {kind}: {th}"
+ -- Apply the theorem
+ let res ← do
+ try
+ let res ← progressWith fExpr th keep ids splitPost asmTac
+ pure (some res)
+ catch _ => none
+ match res with
+ | some .Ok => return ()
+ | some (.Error msg) => throwError msg
+ | none => x
+
+-- The array of ids are identifiers to use when introducing fresh variables
+def progressAsmsOrLookupTheorem (keep : Option Name) (withTh : Option TheoremOrLocal)
+ (ids : Array (Option Name)) (splitPost : Bool) (asmTac : TacticM Unit) : TacticM Unit := do
+ withMainContext do
+ -- Retrieve the goal
+ let mgoal ← Tactic.getMainGoal
+ let goalTy ← mgoal.getType
+ trace[Progress] "goal: {goalTy}"
+ -- Dive into the goal to lookup the theorem
+ let (fExpr, fName, args) ← do
+ withPSpec goalTy fun desc =>
+ -- TODO: check that no quantified variables in the arguments
+ pure (desc.fExpr, desc.fName, desc.args)
+ trace[Progress] "Function: {fName}"
+ -- If the user provided a theorem/assumption: use it.
+ -- Otherwise, lookup one.
+ match withTh with
+ | some th => do
+ match ← progressWith fExpr th keep ids splitPost asmTac with
+ | .Ok => return ()
+ | .Error msg => throwError msg
+ | none =>
+ -- Try all the assumptions one by one and if it fails try to lookup a theorem.
+ let ctx ← Lean.MonadLCtx.getLCtx
+ let decls ← ctx.getDecls
+ for decl in decls.reverse do
+ trace[Progress] "Trying assumption: {decl.userName} : {decl.type}"
+ let res ← do try progressWith fExpr (.Local decl) keep ids splitPost asmTac catch _ => continue
+ match res with
+ | .Ok => return ()
+ | .Error msg => throwError msg
+ -- It failed: try to lookup a theorem
+ -- TODO: use a list of theorems, and try them one by one?
+ trace[Progress] "No assumption succeeded: trying to lookup a theorem"
+ let pspec ← do
+ let thName ← pspecAttr.find? fName
+ pure (thName.map fun th => .Theorem th)
+ tryLookupApply keep ids splitPost asmTac fExpr "pspec theorem" pspec do
+ -- It failed: try to lookup a *class* expr spec theorem (those are more
+ -- specific than class spec theorems)
+ let pspecClassExpr ← do
+ match getFirstArg args with
+ | none => pure none
+ | some arg => do
+ let thName ← pspecClassExprAttr.find? fName arg
+ pure (thName.map fun th => .Theorem th)
+ tryLookupApply keep ids splitPost asmTac fExpr "pspec class expr theorem" pspecClassExpr do
+ -- It failed: try to lookup a *class* spec theorem
+ let pspecClass ← do
+ match ← getFirstArgAppName args with
+ | none => pure none
+ | some argName => do
+ let thName ← pspecClassAttr.find? fName argName
+ pure (thName.map fun th => .Theorem th)
+ tryLookupApply keep ids splitPost asmTac fExpr "pspec class theorem" pspecClass do
+ -- Try a recursive call - we try the assumptions of kind "auxDecl"
+ let ctx ← Lean.MonadLCtx.getLCtx
+ let decls ← ctx.getAllDecls
+ let decls := decls.filter (λ decl => match decl.kind with
+ | .default | .implDetail => false | .auxDecl => true)
+ for decl in decls.reverse do
+ trace[Progress] "Trying recursive assumption: {decl.userName} : {decl.type}"
+ let res ← do try progressWith fExpr (.Local decl) keep ids splitPost asmTac catch _ => continue
+ match res with
+ | .Ok => return ()
+ | .Error msg => throwError msg
+ -- Nothing worked: failed
+ throwError "Progress failed"
+
+syntax progressArgs := ("keep" (ident <|> "_"))? ("with" ident)? ("as" " ⟨ " (ident <|> "_"),* " .."? " ⟩")?
+
+def evalProgress (args : TSyntax `Progress.progressArgs) : TacticM Unit := do
+ let args := args.raw
+ -- Process the arguments to retrieve the identifiers to use
+ trace[Progress] "Progress arguments: {args}"
+ let (keepArg, withArg, asArgs) ←
+ match args.getArgs.toList with
+ | [keepArg, withArg, asArgs] => do pure (keepArg, withArg, asArgs)
+ | _ => throwError "Unexpected: invalid arguments"
+ let keep : Option Name ← do
+ trace[Progress] "Keep arg: {keepArg}"
+ let args := keepArg.getArgs
+ if args.size > 0 then do
+ trace[Progress] "Keep args: {args}"
+ let arg := args.get! 1
+ trace[Progress] "Keep arg: {arg}"
+ if arg.isIdent then pure (some arg.getId)
+ else do pure (some (← mkFreshAnonPropUserName))
+ else do pure none
+ trace[Progress] "Keep: {keep}"
+ let withArg ← do
+ let withArg := withArg.getArgs
+ if withArg.size > 0 then
+ let id := withArg.get! 1
+ trace[Progress] "With arg: {id}"
+ -- Attempt to lookup a local declaration
+ match (← getLCtx).findFromUserName? id.getId with
+ | some decl => do
+ trace[Progress] "With arg: local decl"
+ pure (some (.Local decl))
+ | none => do
+ -- Not a local declaration: should be a theorem
+ trace[Progress] "With arg: theorem"
+ addCompletionInfo <| CompletionInfo.id id id.getId (danglingDot := false) {} none
+ let cs ← resolveGlobalConstWithInfos id
+ match cs with
+ | [] => throwError "Could not find theorem {id}"
+ | id :: _ =>
+ pure (some (.Theorem id))
+ else pure none
+ let ids :=
+ let args := asArgs.getArgs
+ let args := (args.get! 2).getSepArgs
+ args.map (λ s => if s.isIdent then some s.getId else none)
+ trace[Progress] "User-provided ids: {ids}"
+ let splitPost : Bool :=
+ let args := asArgs.getArgs
+ (args.get! 3).getArgs.size > 0
+ trace[Progress] "Split post: {splitPost}"
+ /- For scalarTac we have a fast track: if the goal is not a linear
+ arithmetic goal, we skip (note that otherwise, scalarTac would try
+ to prove a contradiction) -/
+ let scalarTac : TacticM Unit := do
+ if ← Arith.goalIsLinearInt then
+ -- Also: we don't try to split the goal if it is a conjunction
+ -- (it shouldn't be)
+ Arith.scalarTac false
+ else
+ throwError "Not a linear arithmetic goal"
+ progressAsmsOrLookupTheorem keep withArg ids splitPost (
+ withMainContext do
+ trace[Progress] "trying to solve assumption: {← getMainGoal}"
+ firstTac [assumptionTac, scalarTac])
+ trace[Diverge] "Progress done"
+
+elab "progress" args:progressArgs : tactic =>
+ evalProgress args
+
+namespace Test
+ open Primitives Result
+
+ set_option trace.Progress true
+ set_option pp.rawOnError true
+
+ #eval showStoredPSpec
+ #eval showStoredPSpecClass
+
+ example {ty} {x y : Scalar ty}
+ (hmin : Scalar.min ty ≤ x.val + y.val)
+ (hmax : x.val + y.val ≤ Scalar.max ty) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ progress keep _ as ⟨ z, h1 .. ⟩
+ simp [*, h1]
+
+ example {ty} {x y : Scalar ty}
+ (hmin : Scalar.min ty ≤ x.val + y.val)
+ (hmax : x.val + y.val ≤ Scalar.max ty) :
+ ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by
+ progress keep h with Scalar.add_spec as ⟨ z ⟩
+ simp [*, h]
+
+ /- Checking that universe instantiation works: the original spec uses
+ `α : Type u` where u is quantified, while here we use `α : Type 0` -/
+ example {α : Type} (v: Vec α) (i: Usize) (x : α)
+ (hbounds : i.val < v.length) :
+ ∃ nv, v.index_mut_back α i x = ret nv ∧
+ nv.val = v.val.update i.val x := by
+ progress
+ simp [*]
+
+end Test
+
+end Progress
diff --git a/backends/lean/Base/Utils.lean b/backends/lean/Base/Utils.lean
new file mode 100644
index 00000000..1f8f1455
--- /dev/null
+++ b/backends/lean/Base/Utils.lean
@@ -0,0 +1,640 @@
+import Lean
+import Mathlib.Tactic.Core
+import Mathlib.Tactic.LeftRight
+import Base.UtilsBase
+
+/-
+Mathlib tactics:
+- rcases: https://leanprover-community.github.io/mathlib_docs/tactics.html#rcases
+- split_ifs: https://leanprover-community.github.io/mathlib_docs/tactics.html#split_ifs
+- norm_num: https://leanprover-community.github.io/mathlib_docs/tactics.html#norm_num
+- should we use linarith or omega?
+- hint: https://leanprover-community.github.io/mathlib_docs/tactics.html#hint
+- classical: https://leanprover-community.github.io/mathlib_docs/tactics.html#classical
+-/
+
+/-
+TODO:
+- we want an easier to use cases:
+ - keeps in the goal an equation of the shape: `t = case`
+ - if called on Prop terms, uses Classical.em
+ Actually, the cases from mathlib seems already quite powerful
+ (https://leanprover-community.github.io/mathlib_docs/tactics.html#cases)
+ For instance: cases h : e
+ Also: **casesm**
+- better split tactic
+- we need conversions to operate on the head of applications.
+ Actually, something like this works:
+ ```
+ conv at Hl =>
+ apply congr_fun
+ simp [fix_fuel_P]
+ ```
+ Maybe we need a rpt ... ; focus?
+- simplifier/rewriter have a strange behavior sometimes
+-/
+
+
+namespace List
+
+ -- TODO: I could not find this function??
+ @[simp] def flatten {a : Type u} : List (List a) → List a
+ | [] => []
+ | x :: ls => x ++ flatten ls
+
+end List
+
+-- TODO: move?
+@[simp]
+theorem neq_imp {α : Type u} {x y : α} (h : ¬ x = y) : ¬ y = x := by intro; simp_all
+
+namespace Lean
+
+namespace LocalContext
+
+ open Lean Lean.Elab Command Term Lean.Meta
+
+ -- Small utility: return the list of declarations in the context, from
+ -- the last to the first.
+ def getAllDecls (lctx : Lean.LocalContext) : MetaM (List Lean.LocalDecl) :=
+ lctx.foldrM (fun d ls => do let d ← instantiateLocalDeclMVars d; pure (d :: ls)) []
+
+ -- Return the list of declarations in the context, but filter the
+ -- declarations which are considered as implementation details
+ def getDecls (lctx : Lean.LocalContext) : MetaM (List Lean.LocalDecl) := do
+ let ls ← lctx.getAllDecls
+ pure (ls.filter (fun d => not d.isImplementationDetail))
+
+end LocalContext
+
+end Lean
+
+namespace Utils
+
+open Lean Elab Term Meta Tactic
+
+-- Useful helper to explore definitions and figure out the variant
+-- of their sub-expressions.
+def explore_term (incr : String) (e : Expr) : MetaM Unit :=
+ match e with
+ | .bvar _ => do logInfo m!"{incr}bvar: {e}"; return ()
+ | .fvar _ => do logInfo m!"{incr}fvar: {e}"; return ()
+ | .mvar _ => do logInfo m!"{incr}mvar: {e}"; return ()
+ | .sort _ => do logInfo m!"{incr}sort: {e}"; return ()
+ | .const _ _ => do logInfo m!"{incr}const: {e}"; return ()
+ | .app fn arg => do
+ logInfo m!"{incr}app: {e}"
+ explore_term (incr ++ " ") fn
+ explore_term (incr ++ " ") arg
+ | .lam _bName bTy body _binfo => do
+ logInfo m!"{incr}lam: {e}"
+ explore_term (incr ++ " ") bTy
+ explore_term (incr ++ " ") body
+ | .forallE _bName bTy body _bInfo => do
+ logInfo m!"{incr}forallE: {e}"
+ explore_term (incr ++ " ") bTy
+ explore_term (incr ++ " ") body
+ | .letE _dName ty val body _nonDep => do
+ logInfo m!"{incr}letE: {e}"
+ explore_term (incr ++ " ") ty
+ explore_term (incr ++ " ") val
+ explore_term (incr ++ " ") body
+ | .lit _ => do logInfo m!"{incr}lit: {e}"; return ()
+ | .mdata _ e => do
+ logInfo m!"{incr}mdata: {e}"
+ explore_term (incr ++ " ") e
+ | .proj _ _ struct => do
+ logInfo m!"{incr}proj: {e}"
+ explore_term (incr ++ " ") struct
+
+def explore_decl (n : Name) : TermElabM Unit := do
+ logInfo m!"Name: {n}"
+ let env ← getEnv
+ let decl := env.constants.find! n
+ match decl with
+ | .defnInfo val =>
+ logInfo m!"About to explore defn: {decl.name}"
+ logInfo m!"# Type:"
+ explore_term "" val.type
+ logInfo m!"# Value:"
+ explore_term "" val.value
+ | .axiomInfo _ => throwError m!"axiom: {n}"
+ | .thmInfo _ => throwError m!"thm: {n}"
+ | .opaqueInfo _ => throwError m!"opaque: {n}"
+ | .quotInfo _ => throwError m!"quot: {n}"
+ | .inductInfo _ => throwError m!"induct: {n}"
+ | .ctorInfo _ => throwError m!"ctor: {n}"
+ | .recInfo _ => throwError m!"rec: {n}"
+
+syntax (name := printDecl) "print_decl " ident : command
+
+open Lean.Elab.Command
+
+@[command_elab printDecl] def elabPrintDecl : CommandElab := fun stx => do
+ liftTermElabM do
+ let id := stx[1]
+ addCompletionInfo <| CompletionInfo.id id id.getId (danglingDot := false) {} none
+ let cs ← resolveGlobalConstWithInfos id
+ explore_decl cs[0]!
+
+private def test1 : Nat := 0
+private def test2 (x : Nat) : Nat := x
+print_decl test1
+print_decl test2
+
+def printDecls (decls : List LocalDecl) : MetaM Unit := do
+ let decls ← decls.foldrM (λ decl msg => do
+ pure (m!"\n{decl.toExpr} : {← inferType decl.toExpr}" ++ msg)) m!""
+ logInfo m!"# Ctx decls:{decls}"
+
+-- Small utility: print all the declarations in the context (including the "implementation details")
+elab "print_all_ctx_decls" : tactic => do
+ let ctx ← Lean.MonadLCtx.getLCtx
+ let decls ← ctx.getAllDecls
+ printDecls decls
+
+-- Small utility: print all declarations in the context
+elab "print_ctx_decls" : tactic => do
+ let ctx ← Lean.MonadLCtx.getLCtx
+ let decls ← ctx.getDecls
+ printDecls decls
+
+-- A map visitor function for expressions (adapted from `AbstractNestedProofs.visit`)
+-- The continuation takes as parameters:
+-- - the current depth of the expression (useful for printing/debugging)
+-- - the expression to explore
+partial def mapVisit (k : Nat → Expr → MetaM Expr) (e : Expr) : MetaM Expr := do
+ let mapVisitBinders (xs : Array Expr) (k2 : MetaM Expr) : MetaM Expr := do
+ let localInstances ← getLocalInstances
+ let mut lctx ← getLCtx
+ for x in xs do
+ let xFVarId := x.fvarId!
+ let localDecl ← xFVarId.getDecl
+ let type ← mapVisit k localDecl.type
+ let localDecl := localDecl.setType type
+ let localDecl ← match localDecl.value? with
+ | some value => let value ← mapVisit k value; pure <| localDecl.setValue value
+ | none => pure localDecl
+ lctx :=lctx.modifyLocalDecl xFVarId fun _ => localDecl
+ withLCtx lctx localInstances k2
+ -- TODO: use a cache? (Lean.checkCache)
+ let rec visit (i : Nat) (e : Expr) : MetaM Expr := do
+ -- Explore
+ let e ← k i e
+ match e with
+ | .bvar _
+ | .fvar _
+ | .mvar _
+ | .sort _
+ | .lit _
+ | .const _ _ => pure e
+ | .app .. => do e.withApp fun f args => return mkAppN f (← args.mapM (visit (i + 1)))
+ | .lam .. =>
+ lambdaLetTelescope e fun xs b =>
+ mapVisitBinders xs do mkLambdaFVars xs (← visit (i + 1) b) (usedLetOnly := false)
+ | .forallE .. => do
+ forallTelescope e fun xs b => mapVisitBinders xs do mkForallFVars xs (← visit (i + 1) b)
+ | .letE .. => do
+ lambdaLetTelescope e fun xs b => mapVisitBinders xs do
+ mkLambdaFVars xs (← visit (i + 1) b) (usedLetOnly := false)
+ | .mdata _ b => return e.updateMData! (← visit (i + 1) b)
+ | .proj _ _ b => return e.updateProj! (← visit (i + 1) b)
+ visit 0 e
+
+-- Generate a fresh user name for an anonymous proposition to introduce in the
+-- assumptions
+def mkFreshAnonPropUserName := mkFreshUserName `_
+
+section Methods
+ variable [MonadLiftT MetaM m] [MonadControlT MetaM m] [Monad m] [MonadError m]
+ variable {a : Type}
+
+ /- Like `lambdaTelescopeN` but only destructs a fixed number of lambdas -/
+ def lambdaTelescopeN (e : Expr) (n : Nat) (k : Array Expr → Expr → m a) : m a :=
+ lambdaTelescope e fun xs body => do
+ if xs.size < n then throwError "lambdaTelescopeN: not enough lambdas"
+ let xs := xs.extract 0 n
+ let ys := xs.extract n xs.size
+ let body ← liftMetaM (mkLambdaFVars ys body)
+ k xs body
+
+ /- Like `lambdaTelescope`, but only destructs one lambda
+ TODO: is there an equivalent of this function somewhere in the
+ standard library? -/
+ def lambdaOne (e : Expr) (k : Expr → Expr → m a) : m a :=
+ lambdaTelescopeN e 1 λ xs b => k (xs.get! 0) b
+
+ def isExists (e : Expr) : Bool := e.getAppFn.isConstOf ``Exists ∧ e.getAppNumArgs = 2
+
+ -- Remark: Lean doesn't find the inhabited and nonempty instances if we don'
+ -- put them explicitely in the signature
+ partial def existsTelescopeProcess [Inhabited (m a)] [Nonempty (m a)]
+ (fvars : Array Expr) (e : Expr) (k : Array Expr → Expr → m a) : m a := do
+ -- Attempt to deconstruct an existential
+ if isExists e then do
+ let p := e.appArg!
+ lambdaOne p fun x ne =>
+ existsTelescopeProcess (fvars.push x) ne k
+ else
+ -- No existential: call the continuation
+ k fvars e
+
+ def existsTelescope [Inhabited (m a)] [Nonempty (m a)] (e : Expr) (k : Array Expr → Expr → m a) : m a := do
+ existsTelescopeProcess #[] e k
+
+end Methods
+
+-- TODO: this should take a continuation
+def addDeclTac (name : Name) (val : Expr) (type : Expr) (asLet : Bool) : TacticM Expr :=
+ -- I don't think we need that
+ withMainContext do
+ -- Insert the new declaration
+ let withDecl := if asLet then withLetDecl name type val else withLocalDeclD name type
+ withDecl fun nval => do
+ -- For debugging
+ let lctx ← Lean.MonadLCtx.getLCtx
+ let fid := nval.fvarId!
+ let decl := lctx.get! fid
+ trace[Arith] " new decl: \"{decl.userName}\" ({nval}) : {decl.type} := {decl.value}"
+ --
+ -- Tranform the main goal `?m0` to `let x = nval in ?m1`
+ let mvarId ← getMainGoal
+ let newMVar ← mkFreshExprSyntheticOpaqueMVar (← mvarId.getType)
+ let newVal ← mkLetFVars #[nval] newMVar
+ -- There are two cases:
+ -- - asLet is true: newVal is `let $name := $val in $newMVar`
+ -- - asLet is false: ewVal is `λ $name => $newMVar`
+ -- We need to apply it to `val`
+ let newVal := if asLet then newVal else mkAppN newVal #[val]
+ -- Assign the main goal and update the current goal
+ mvarId.assign newVal
+ let goals ← getUnsolvedGoals
+ setGoals (newMVar.mvarId! :: goals)
+ -- Return the new value - note: we are in the *new* context, created
+ -- after the declaration was added, so it will persist
+ pure nval
+
+def addDeclTacSyntax (name : Name) (val : Syntax) (asLet : Bool) : TacticM Unit :=
+ -- I don't think we need that
+ withMainContext do
+ --
+ let val ← Term.elabTerm val .none
+ let type ← inferType val
+ -- In some situations, the type will be left as a metavariable (for instance,
+ -- if the term is `3`, Lean has the choice between `Nat` and `Int` and will
+ -- not choose): we force the instantiation of the meta-variable
+ synthesizeSyntheticMVarsUsingDefault
+ --
+ let _ ← addDeclTac name val type asLet
+
+elab "custom_let " n:ident " := " v:term : tactic => do
+ addDeclTacSyntax n.getId v (asLet := true)
+
+elab "custom_have " n:ident " := " v:term : tactic =>
+ addDeclTacSyntax n.getId v (asLet := false)
+
+example : Nat := by
+ custom_let x := 4
+ custom_have y := 4
+ apply y
+
+example (x : Bool) : Nat := by
+ cases x <;> custom_let x := 3 <;> apply x
+
+-- Repeatedly apply a tactic
+partial def repeatTac (tac : TacticM Unit) : TacticM Unit := do
+ try
+ tac
+ allGoals (focus (repeatTac tac))
+ -- TODO: does this restore the state?
+ catch _ => pure ()
+
+def firstTac (tacl : List (TacticM Unit)) : TacticM Unit := do
+ match tacl with
+ | [] => pure ()
+ | tac :: tacl =>
+ -- Should use try ... catch or Lean.observing?
+ -- Generally speaking we should use Lean.observing? to restore the state,
+ -- but with tactics the try ... catch variant seems to work
+ try do
+ tac
+ -- Check that there are no remaining goals
+ let gl ← Tactic.getUnsolvedGoals
+ if ¬ gl.isEmpty then throwError "tactic failed"
+ catch _ => firstTac tacl
+/- let res ← Lean.observing? do
+ tac
+ -- Check that there are no remaining goals
+ let gl ← Tactic.getUnsolvedGoals
+ if ¬ gl.isEmpty then throwError "tactic failed"
+ match res with
+ | some _ => pure ()
+ | none => firstTac tacl -/
+
+-- Taken from Lean.Elab.evalAssumption
+def assumptionTac : TacticM Unit :=
+ liftMetaTactic fun mvarId => do mvarId.assumption; pure []
+
+def isConj (e : Expr) : MetaM Bool :=
+ e.consumeMData.withApp fun f args => pure (f.isConstOf ``And ∧ args.size = 2)
+
+-- Return the first conjunct if the expression is a conjunction, or the
+-- expression itself otherwise. Also return the second conjunct if it is a
+-- conjunction.
+def optSplitConj (e : Expr) : MetaM (Expr × Option Expr) := do
+ e.consumeMData.withApp fun f args =>
+ if f.isConstOf ``And ∧ args.size = 2 then pure (args.get! 0, some (args.get! 1))
+ else pure (e, none)
+
+-- Split the goal if it is a conjunction
+def splitConjTarget : TacticM Unit := do
+ withMainContext do
+ let g ← getMainTarget
+ trace[Utils] "splitConjTarget: goal: {g}"
+ -- The tactic was initially implemened with `_root_.Lean.MVarId.apply`
+ -- but it tended to mess the goal by unfolding terms, even when it failed
+ let (l, r) ← optSplitConj g
+ match r with
+ | none => do throwError "The goal is not a conjunction"
+ | some r => do
+ let lmvar ← mkFreshExprSyntheticOpaqueMVar l
+ let rmvar ← mkFreshExprSyntheticOpaqueMVar r
+ let and_intro ← mkAppM ``And.intro #[lmvar, rmvar]
+ let g ← getMainGoal
+ g.assign and_intro
+ let goals ← getUnsolvedGoals
+ setGoals (lmvar.mvarId! :: rmvar.mvarId! :: goals)
+
+-- Destruct an equaliy and return the two sides
+def destEq (e : Expr) : MetaM (Expr × Expr) := do
+ e.withApp fun f args =>
+ if f.isConstOf ``Eq ∧ args.size = 3 then pure (args.get! 1, args.get! 2)
+ else throwError "Not an equality: {e}"
+
+-- Return the set of FVarIds in the expression
+partial def getFVarIds (e : Expr) (hs : HashSet FVarId := HashSet.empty) : MetaM (HashSet FVarId) := do
+ e.withApp fun body args => do
+ let hs := if body.isFVar then hs.insert body.fvarId! else hs
+ args.foldlM (fun hs arg => getFVarIds arg hs) hs
+
+-- Tactic to split on a disjunction.
+-- The expression `h` should be an fvar.
+-- TODO: there must be simpler. Use use _root_.Lean.MVarId.cases for instance
+def splitDisjTac (h : Expr) (kleft kright : TacticM Unit) : TacticM Unit := do
+ trace[Arith] "assumption on which to split: {h}"
+ -- Retrieve the main goal
+ withMainContext do
+ let goalType ← getMainTarget
+ let hDecl := (← getLCtx).get! h.fvarId!
+ let hName := hDecl.userName
+ -- Case disjunction
+ let hTy ← inferType h
+ hTy.withApp fun f xs => do
+ trace[Arith] "as app: {f} {xs}"
+ -- Sanity check
+ if ¬ (f.isConstOf ``Or ∧ xs.size = 2) then throwError "Invalid argument to splitDisjTac"
+ let a := xs.get! 0
+ let b := xs.get! 1
+ -- Introduce the new goals
+ -- Returns:
+ -- - the match branch
+ -- - a fresh new mvar id
+ let mkGoal (hTy : Expr) (nGoalName : String) : MetaM (Expr × MVarId) := do
+ -- Introduce a variable for the assumption (`a` or `b`). Note that we reuse
+ -- the name of the assumption we split.
+ withLocalDeclD hName hTy fun var => do
+ -- The new goal
+ let mgoal ← mkFreshExprSyntheticOpaqueMVar goalType (tag := Name.mkSimple nGoalName)
+ -- Clear the assumption that we split
+ let mgoal ← mgoal.mvarId!.tryClearMany #[h.fvarId!]
+ -- The branch expression
+ let branch ← mkLambdaFVars #[var] (mkMVar mgoal)
+ pure (branch, mgoal)
+ let (inl, mleft) ← mkGoal a "left"
+ let (inr, mright) ← mkGoal b "right"
+ trace[Arith] "left: {inl}: {mleft}"
+ trace[Arith] "right: {inr}: {mright}"
+ -- Create the match expression
+ withLocalDeclD (← mkFreshAnonPropUserName) hTy fun hVar => do
+ let motive ← mkLambdaFVars #[hVar] goalType
+ let casesExpr ← mkAppOptM ``Or.casesOn #[a, b, motive, h, inl, inr]
+ let mgoal ← getMainGoal
+ trace[Arith] "goals: {← getUnsolvedGoals}"
+ trace[Arith] "main goal: {mgoal}"
+ mgoal.assign casesExpr
+ let goals ← getUnsolvedGoals
+ -- Focus on the left
+ setGoals [mleft]
+ withMainContext kleft
+ let leftGoals ← getUnsolvedGoals
+ -- Focus on the right
+ setGoals [mright]
+ withMainContext kright
+ let rightGoals ← getUnsolvedGoals
+ -- Put all the goals back
+ setGoals (leftGoals ++ rightGoals ++ goals)
+ trace[Arith] "new goals: {← getUnsolvedGoals}"
+
+elab "split_disj " n:ident : tactic => do
+ withMainContext do
+ let decl ← Lean.Meta.getLocalDeclFromUserName n.getId
+ let fvar := mkFVar decl.fvarId
+ splitDisjTac fvar (fun _ => pure ()) (fun _ => pure ())
+
+example (x y : Int) (h0 : x ≤ y ∨ x ≥ y) : x ≤ y ∨ x ≥ y := by
+ split_disj h0
+ . left; assumption
+ . right; assumption
+
+
+-- Tactic to split on an exists.
+-- `h` must be an FVar
+def splitExistsTac (h : Expr) (optId : Option Name) (k : Expr → Expr → TacticM α) : TacticM α := do
+ withMainContext do
+ let goal ← getMainGoal
+ let hTy ← inferType h
+ if isExists hTy then do
+ -- Try to use the user-provided names
+ let altVarNames ← do
+ let hDecl ← h.fvarId!.getDecl
+ let id ← do
+ match optId with
+ | none => mkFreshUserName `x
+ | some id => pure id
+ pure #[{ varNames := [id, hDecl.userName] }]
+ let newGoals ← goal.cases h.fvarId! altVarNames
+ -- There should be exactly one goal
+ match newGoals.toList with
+ | [ newGoal ] =>
+ -- Set the new goal
+ let goals ← getUnsolvedGoals
+ setGoals (newGoal.mvarId :: goals)
+ -- There should be exactly two fields
+ let fields := newGoal.fields
+ withMainContext do
+ k (fields.get! 0) (fields.get! 1)
+ | _ =>
+ throwError "Unreachable"
+ else
+ throwError "Not a conjunction"
+
+-- TODO: move
+def listTryPopHead (ls : List α) : Option α × List α :=
+ match ls with
+ | [] => (none, ls)
+ | hd :: tl => (some hd, tl)
+
+/- Destruct all the existentials appearing in `h`, and introduce them as variables
+ in the context.
+
+ If `ids` is not empty, we use it to name the introduced variables. We
+ transmit the stripped expression and the remaining ids to the continuation.
+ -/
+partial def splitAllExistsTac [Inhabited α] (h : Expr) (ids : List (Option Name)) (k : Expr → List (Option Name) → TacticM α) : TacticM α := do
+ try
+ let (optId, ids) :=
+ match ids with
+ | [] => (none, [])
+ | x :: ids => (x, ids)
+ splitExistsTac h optId (fun _ body => splitAllExistsTac body ids k)
+ catch _ => k h ids
+
+-- Tactic to split on a conjunction.
+def splitConjTac (h : Expr) (optIds : Option (Name × Name)) (k : Expr → Expr → TacticM α) : TacticM α := do
+ withMainContext do
+ let goal ← getMainGoal
+ let hTy ← inferType h
+ if ← isConj hTy then do
+ -- Try to use the user-provided names
+ let altVarNames ←
+ match optIds with
+ | none => do
+ let id0 ← mkFreshAnonPropUserName
+ let id1 ← mkFreshAnonPropUserName
+ pure #[{ varNames := [id0, id1] }]
+ | some (id0, id1) => do
+ pure #[{ varNames := [id0, id1] }]
+ let newGoals ← goal.cases h.fvarId! altVarNames
+ -- There should be exactly one goal
+ match newGoals.toList with
+ | [ newGoal ] =>
+ -- Set the new goal
+ let goals ← getUnsolvedGoals
+ setGoals (newGoal.mvarId :: goals)
+ -- There should be exactly two fields
+ let fields := newGoal.fields
+ withMainContext do
+ k (fields.get! 0) (fields.get! 1)
+ | _ =>
+ throwError "Unreachable"
+ else
+ throwError "Not a conjunction"
+
+-- Tactic to fully split a conjunction
+partial def splitFullConjTacAux [Inhabited α] [Nonempty α] (keepCurrentName : Bool) (l : List Expr) (h : Expr) (k : List Expr → TacticM α) : TacticM α := do
+ try
+ let ids ← do
+ if keepCurrentName then do
+ let cur := (← h.fvarId!.getDecl).userName
+ let nid ← mkFreshAnonPropUserName
+ pure (some (cur, nid))
+ else
+ pure none
+ splitConjTac h ids (λ h1 h2 =>
+ splitFullConjTacAux keepCurrentName l h1 (λ l1 =>
+ splitFullConjTacAux keepCurrentName l1 h2 (λ l2 =>
+ k l2)))
+ catch _ =>
+ k (h :: l)
+
+-- Tactic to fully split a conjunction
+-- `keepCurrentName`: if `true`, then the first conjunct has the name of the original assumption
+def splitFullConjTac [Inhabited α] [Nonempty α] (keepCurrentName : Bool) (h : Expr) (k : List Expr → TacticM α) : TacticM α := do
+ splitFullConjTacAux keepCurrentName [] h (λ l => k l.reverse)
+
+syntax optAtArgs := ("at" ident)?
+def elabOptAtArgs (args : TSyntax `Utils.optAtArgs) : TacticM (Option Expr) := do
+ withMainContext do
+ let args := (args.raw.getArgs.get! 0).getArgs
+ if args.size > 0 then do
+ let n := (args.get! 1).getId
+ let decl ← Lean.Meta.getLocalDeclFromUserName n
+ let fvar := mkFVar decl.fvarId
+ pure (some fvar)
+ else
+ pure none
+
+elab "split_conj" args:optAtArgs : tactic => do
+ withMainContext do
+ match ← elabOptAtArgs args with
+ | some fvar => do
+ trace[Utils] "split at {fvar}"
+ splitConjTac fvar none (fun _ _ => pure ())
+ | none => do
+ trace[Utils] "split goal"
+ splitConjTarget
+
+elab "split_conjs" args:optAtArgs : tactic => do
+ withMainContext do
+ match ← elabOptAtArgs args with
+ | some fvar =>
+ trace[Utils] "split at {fvar}"
+ splitFullConjTac false fvar (fun _ => pure ())
+ | none =>
+ trace[Utils] "split goal"
+ repeatTac splitConjTarget
+
+elab "split_existsl" " at " n:ident : tactic => do
+ withMainContext do
+ let decl ← Lean.Meta.getLocalDeclFromUserName n.getId
+ let fvar := mkFVar decl.fvarId
+ splitAllExistsTac fvar [] (fun _ _ => pure ())
+
+example (h : a ∧ b) : a := by
+ split_existsl at h
+ split_conj at h
+ assumption
+
+example (h : ∃ x y z, x + y + z ≥ 0) : ∃ x, x ≥ 0 := by
+ split_existsl at h
+ rename_i x y z
+ exists x + y + z
+
+/- Call the simp tactic.
+ The initialization of the context is adapted from Tactic.elabSimpArgs.
+ Something very annoying is that there is no function which allows to
+ initialize a simp context without doing an elaboration - as a consequence
+ we write our own here. -/
+def simpAt (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
+ (loc : Tactic.Location) :
+ Tactic.TacticM Unit := do
+ -- Initialize with the builtin simp theorems
+ let simpThms ← Tactic.simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems)
+ -- Add the equational theorem for the declarations to unfold
+ let simpThms ←
+ declsToUnfold.foldlM (fun thms decl => thms.addDeclToUnfold decl) simpThms
+ -- Add the hypotheses and the rewriting theorems
+ let simpThms ←
+ hypsToUse.foldlM (fun thms fvarId =>
+ -- post: TODO: don't know what that is
+ -- inv: invert the equality
+ thms.add (.fvar fvarId) #[] (mkFVar fvarId) (post := false) (inv := false)
+ -- thms.eraseCore (.fvar fvar)
+ ) simpThms
+ -- Add the rewriting theorems to use
+ let simpThms ←
+ thms.foldlM (fun thms thmName => do
+ let info ← getConstInfo thmName
+ if (← isProp info.type) then
+ -- post: TODO: don't know what that is
+ -- inv: invert the equality
+ thms.addConst thmName (post := false) (inv := false)
+ else
+ throwError "Not a proposition: {thmName}"
+ ) simpThms
+ let congrTheorems ← getSimpCongrTheorems
+ let ctx : Simp.Context := { simpTheorems := #[simpThms], congrTheorems }
+ -- Apply the simplifier
+ let _ ← Tactic.simpLocation ctx (discharge? := .none) loc
+
+end Utils
diff --git a/backends/lean/Primitives.lean b/backends/lean/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/backends/lean/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/backends/lean/lake-manifest.json b/backends/lean/lake-manifest.json
index 7b23fc19..5a089838 100644
--- a/backends/lean/lake-manifest.json
+++ b/backends/lean/lake-manifest.json
@@ -2,26 +2,38 @@
"packagesDir": "lake-packages",
"packages":
[{"git":
+ {"url": "https://github.com/EdAyers/ProofWidgets4",
+ "subDir?": null,
+ "rev": "c43db94a8f495dad37829e9d7ad65483d68c86b8",
+ "name": "proofwidgets",
+ "inputRev?": "v0.0.11"}},
+ {"git":
+ {"url": "https://github.com/mhuisi/lean4-cli.git",
+ "subDir?": null,
+ "rev": "5a858c32963b6b19be0d477a30a1f4b6c120be7e",
+ "name": "Cli",
+ "inputRev?": "nightly"}},
+ {"git":
{"url": "https://github.com/leanprover-community/mathlib4.git",
"subDir?": null,
- "rev": "f89ee53085b8aad0bacd3bc94d7ef4b8d9aba643",
+ "rev": "fa05951a270fef2873666c46f138e90338cd48d6",
"name": "mathlib",
"inputRev?": null}},
{"git":
{"url": "https://github.com/gebner/quote4",
"subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
+ "rev": "c0d9516f44d07feee01c1103c8f2f7c24a822b55",
"name": "Qq",
"inputRev?": "master"}},
{"git":
{"url": "https://github.com/JLimperg/aesop",
"subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
+ "rev": "f04538ab6ad07642368cf11d2702acc0a9b4bcee",
"name": "aesop",
"inputRev?": "master"}},
{"git":
{"url": "https://github.com/leanprover/std4",
"subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
+ "rev": "dff883c55395438ae2a5c65ad5ddba084b600feb",
"name": "std",
"inputRev?": "main"}}]}
diff --git a/backends/lean/lakefile.lean b/backends/lean/lakefile.lean
index 9633e1e8..21a4a332 100644
--- a/backends/lean/lakefile.lean
+++ b/backends/lean/lakefile.lean
@@ -1,10 +1,11 @@
import Lake
open Lake DSL
+-- Important: mathlib imports std4 and quote4: we mustn't add a `require std4` line
require mathlib from git
"https://github.com/leanprover-community/mathlib4.git"
package «base» {}
@[default_target]
-lean_lib «Primitives» {}
+lean_lib «Base» {}
diff --git a/backends/lean/lean-toolchain b/backends/lean/lean-toolchain
new file mode 100644
index 00000000..334c5053
--- /dev/null
+++ b/backends/lean/lean-toolchain
@@ -0,0 +1 @@
+leanprover/lean4:nightly-2023-07-12 \ No newline at end of file
diff --git a/compiler/Config.ml b/compiler/Config.ml
index ce9b0e0c..0475899c 100644
--- a/compiler/Config.ml
+++ b/compiler/Config.ml
@@ -162,6 +162,11 @@ let backward_no_state_update = ref false
*)
let split_files = ref true
+(** For Lean, controls whether we generate a lakefile or not.
+
+ *)
+let lean_gen_lakefile = ref false
+
(** If true, treat the unit functions (function taking no inputs and returning
no outputs) as unit tests: evaluate them with the interpreter and check that
they don't panic.
@@ -292,3 +297,21 @@ let filter_useless_monadic_calls = ref true
dynamically check for that).
*)
let filter_useless_functions = ref true
+
+(** Obsolete. TODO: remove.
+
+ For Lean we used to parameterize the entire development by a section variable
+ called opaque_defs, of type OpaqueDefs.
+ *)
+let wrap_opaque_in_sig = ref false
+
+(** Use short names for the record fields.
+
+ Some backends can't disambiguate records when their field names have collisions.
+ When this happens, we use long names, by which we concatenate the record
+ names with the field names, and check whether there are name collisions.
+
+ For backends which can disambiguate records (typically by using the typing
+ information), we use short names (i.e., the original field names).
+ *)
+let record_fields_short_names = ref false
diff --git a/compiler/Driver.ml b/compiler/Driver.ml
index 2ff9e295..166ef11b 100644
--- a/compiler/Driver.ml
+++ b/compiler/Driver.ml
@@ -107,6 +107,9 @@ let () =
Arg.Clear check_invariants,
" Deactivate the invariant sanity checks performed at every evaluation \
step. Dramatically increases speed." );
+ ( "-lean-default-lakefile",
+ Arg.Clear lean_gen_lakefile,
+ " Generate a default lakefile.lean (Lean only)" );
]
in
@@ -130,6 +133,9 @@ let () =
(not !use_fuel)
|| (not !extract_decreases_clauses)
&& not !extract_template_decreases_clauses);
+ if !lean_gen_lakefile && not (!backend = Lean) then
+ log#error
+ "The -lean-default-lakefile option is valid only for the Lean backend";
(* Check that the user specified a backend *)
let _ =
@@ -157,7 +163,9 @@ let () =
(* We don't support fuel for the Lean backend *)
if !use_fuel then (
log#error "The Lean backend doesn't support the -use-fuel option";
- fail ())
+ fail ());
+ (* Lean can disambiguate the field names *)
+ record_fields_short_names := true
| HOL4 ->
(* We don't support fuel for the HOL4 backend *)
if !use_fuel then (
diff --git a/compiler/Extract.ml b/compiler/Extract.ml
index d624d9ca..b16f9639 100644
--- a/compiler/Extract.ml
+++ b/compiler/Extract.ml
@@ -300,23 +300,40 @@ let assumed_variants () : (assumed_ty * VariantId.id * string) list =
(Option, option_none_id, "NONE");
]
-let assumed_llbc_functions :
+let assumed_llbc_functions () :
(A.assumed_fun_id * T.RegionGroupId.id option * string) list =
let rg0 = Some T.RegionGroupId.zero in
- [
- (Replace, None, "mem_replace_fwd");
- (Replace, rg0, "mem_replace_back");
- (VecNew, None, "vec_new");
- (VecPush, None, "vec_push_fwd") (* Shouldn't be used *);
- (VecPush, rg0, "vec_push_back");
- (VecInsert, None, "vec_insert_fwd") (* Shouldn't be used *);
- (VecInsert, rg0, "vec_insert_back");
- (VecLen, None, "vec_len");
- (VecIndex, None, "vec_index_fwd");
- (VecIndex, rg0, "vec_index_back") (* shouldn't be used *);
- (VecIndexMut, None, "vec_index_mut_fwd");
- (VecIndexMut, rg0, "vec_index_mut_back");
- ]
+ match !backend with
+ | FStar | Coq | HOL4 ->
+ [
+ (Replace, None, "mem_replace_fwd");
+ (Replace, rg0, "mem_replace_back");
+ (VecNew, None, "vec_new");
+ (VecPush, None, "vec_push_fwd") (* Shouldn't be used *);
+ (VecPush, rg0, "vec_push_back");
+ (VecInsert, None, "vec_insert_fwd") (* Shouldn't be used *);
+ (VecInsert, rg0, "vec_insert_back");
+ (VecLen, None, "vec_len");
+ (VecIndex, None, "vec_index_fwd");
+ (VecIndex, rg0, "vec_index_back") (* shouldn't be used *);
+ (VecIndexMut, None, "vec_index_mut_fwd");
+ (VecIndexMut, rg0, "vec_index_mut_back");
+ ]
+ | Lean ->
+ [
+ (Replace, None, "mem.replace");
+ (Replace, rg0, "mem.replace_back");
+ (VecNew, None, "Vec.new");
+ (VecPush, None, "Vec.push_fwd") (* Shouldn't be used *);
+ (VecPush, rg0, "Vec.push");
+ (VecInsert, None, "Vec.insert_fwd") (* Shouldn't be used *);
+ (VecInsert, rg0, "Vec.insert");
+ (VecLen, None, "Vec.len");
+ (VecIndex, None, "Vec.index");
+ (VecIndex, rg0, "Vec.index_back") (* shouldn't be used *);
+ (VecIndexMut, None, "Vec.index_mut");
+ (VecIndexMut, rg0, "Vec.index_mut_back");
+ ]
let assumed_pure_functions () : (pure_assumed_fun_id * string) list =
match !backend with
@@ -344,7 +361,7 @@ let names_map_init () : names_map_init =
assumed_adts = assumed_adts ();
assumed_structs;
assumed_variants = assumed_variants ();
- assumed_llbc_functions;
+ assumed_llbc_functions = assumed_llbc_functions ();
assumed_pure_functions = assumed_pure_functions ();
}
@@ -505,10 +522,10 @@ let fun_decl_kind_to_qualif (kind : decl_kind) : string option =
| Lean -> (
match kind with
| SingleNonRec -> Some "def"
- | SingleRec -> Some "def"
- | MutRecFirst -> Some "mutual def"
- | MutRecInner -> Some "def"
- | MutRecLast -> Some "def"
+ | SingleRec -> Some "divergent def"
+ | MutRecFirst -> Some "mutual divergent def"
+ | MutRecInner -> Some "divergent def"
+ | MutRecLast -> Some "divergent def"
| Assumed -> Some "axiom"
| Declared -> Some "axiom")
| HOL4 -> None
@@ -601,34 +618,48 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
| FStar | Lean | HOL4 -> name
| Coq -> capitalize_first_letter name
in
- let type_name name = type_name_to_snake_case name ^ "_t" in
+ let type_name name =
+ match !backend with
+ | FStar | Coq | HOL4 -> type_name_to_snake_case name ^ "_t"
+ | Lean -> String.concat "." (get_type_name name)
+ in
let field_name (def_name : name) (field_id : FieldId.id)
(field_name : string option) : string =
- let def_name = type_name_to_snake_case def_name ^ "_" in
- match field_name with
- | Some field_name -> def_name ^ field_name
- | None -> def_name ^ FieldId.to_string field_id
+ let field_name =
+ match field_name with
+ | Some field_name -> field_name
+ | None -> FieldId.to_string field_id
+ in
+ if !Config.record_fields_short_names then field_name
+ else
+ let def_name = type_name_to_snake_case def_name ^ "_" in
+ def_name ^ field_name
in
let variant_name (def_name : name) (variant : string) : string =
- let variant = to_camel_case variant in
- if variant_concatenate_type_name then
- type_name_to_camel_case def_name ^ variant
- else variant
+ match !backend with
+ | FStar | Coq | HOL4 ->
+ let variant = to_camel_case variant in
+ if variant_concatenate_type_name then
+ type_name_to_camel_case def_name ^ variant
+ else variant
+ | Lean -> variant
in
let struct_constructor (basename : name) : string =
let tname = type_name basename in
let prefix =
- match !backend with FStar -> "Mk" | Lean | Coq | HOL4 -> "mk"
+ match !backend with FStar -> "Mk" | Coq | HOL4 -> "mk" | Lean -> ""
+ in
+ let suffix =
+ match !backend with FStar | Coq | HOL4 -> "" | Lean -> ".mk"
in
- prefix ^ tname
+ prefix ^ tname ^ suffix
in
- let get_fun_name = get_name in
- let fun_name_to_snake_case (fname : fun_name) : string =
- let fname = get_fun_name fname in
- (* Converting to snake case should be a no-op, but it doesn't cost much *)
- let fname = List.map to_snake_case fname in
- (* Concatenate the elements *)
- String.concat "_" fname
+ let get_fun_name fname =
+ let fname = get_name fname in
+ (* TODO: don't convert to snake case for Coq, HOL4, F* *)
+ match !backend with
+ | FStar | Coq | HOL4 -> String.concat "_" (List.map to_snake_case fname)
+ | Lean -> String.concat "." fname
in
let global_name (name : global_name) : string =
(* Converting to snake case also lowercases the letters (in Rust, global
@@ -639,7 +670,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
let fun_name (fname : fun_name) (num_loops : int) (loop_id : LoopId.id option)
(num_rgs : int) (rg : region_group_info option) (filter_info : bool * int)
: string =
- let fname = fun_name_to_snake_case fname in
+ let fname = get_fun_name fname in
(* Compute the suffix *)
let suffix = default_fun_suffix num_loops loop_id num_rgs rg filter_info in
(* Concatenate *)
@@ -648,7 +679,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
let termination_measure_name (_fid : A.FunDeclId.id) (fname : fun_name)
(num_loops : int) (loop_id : LoopId.id option) : string =
- let fname = fun_name_to_snake_case fname in
+ let fname = get_fun_name fname in
let lp_suffix = default_fun_loop_suffix num_loops loop_id in
(* Compute the suffix *)
let suffix =
@@ -663,7 +694,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
let decreases_proof_name (_fid : A.FunDeclId.id) (fname : fun_name)
(num_loops : int) (loop_id : LoopId.id option) : string =
- let fname = fun_name_to_snake_case fname in
+ let fname = get_fun_name fname in
let lp_suffix = default_fun_loop_suffix num_loops loop_id in
(* Compute the suffix *)
let suffix =
@@ -678,7 +709,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
let opaque_pre () =
match !Config.backend with
| FStar | Coq | HOL4 -> ""
- | Lean -> "opaque_defs."
+ | Lean -> if !Config.wrap_opaque_in_sig then "opaque_defs." else ""
in
let var_basename (_varset : StringSet.t) (basename : string option) (ty : ty)
@@ -789,7 +820,7 @@ let mk_formatter (ctx : trans_ctx) (crate_name : string)
F.pp_print_string fmt ")";
F.pp_print_string fmt ")")
else Z.pp_print fmt sv.value;
- F.pp_print_string fmt " (by intlit))")
+ F.pp_print_string fmt ")")
| Bool b ->
let b =
match !backend with
@@ -1007,6 +1038,11 @@ let end_type_decl_group (fmt : F.formatter) (is_rec : bool)
let unit_name () =
match !backend with Lean -> "Unit" | Coq | FStar | HOL4 -> "unit"
+(** Small helper *)
+let extract_arrow (fmt : F.formatter) () : unit =
+ if !Config.backend = Lean then F.pp_print_string fmt "→"
+ else F.pp_print_string fmt "->"
+
(** [inside] constrols whether we should add parentheses or not around type
applications (if [true] we add parentheses).
@@ -1100,7 +1136,7 @@ let rec extract_ty (ctx : extraction_ctx) (fmt : F.formatter)
if inside then F.pp_print_string fmt "(";
extract_rec false arg_ty;
F.pp_print_space fmt ();
- F.pp_print_string fmt "->";
+ extract_arrow fmt ();
F.pp_print_space fmt ();
extract_rec false ret_ty;
if inside then F.pp_print_string fmt ")"
@@ -1188,7 +1224,7 @@ let extract_type_decl_variant (ctx : extraction_ctx) (fmt : F.formatter)
(* Print the arrow [->] *)
if !backend <> HOL4 then (
F.pp_print_space fmt ();
- F.pp_print_string fmt "->");
+ extract_arrow fmt ());
(* Close the field box *)
F.pp_close_box fmt ();
(* Return *)
@@ -1326,7 +1362,8 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
F.pp_print_string fmt (unit_name ()))
else if !backend = Lean && fields = [] then ()
(* If the definition is recursive, we may need to extract it as an inductive
- (instead of a record) *)
+ (instead of a record). We start with the "normal" case: we extract it
+ as a record. *)
else if (not is_rec) || (!backend <> Coq && !backend <> Lean) then (
if !backend <> Lean then F.pp_print_space fmt ();
(* If Coq: print the constructor name *)
@@ -1379,7 +1416,14 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
a group of mutually recursive types: we extract it as an inductive type *)
assert (is_rec && (!backend = Coq || !backend = Lean));
let with_opaque_pre = false in
- let cons_name = ctx_get_struct with_opaque_pre (AdtId def.def_id) ctx in
+ (* Small trick: in Lean we use namespaces, meaning we don't need to prefix
+ the constructor name with the name of the type at definition site,
+ i.e., instead of generating `inductive Foo := | MkFoo ...` like in Coq
+ we generate `inductive Foo := | mk ... *)
+ let cons_name =
+ if !backend = Lean then "mk"
+ else ctx_get_struct with_opaque_pre (AdtId def.def_id) ctx
+ in
let def_name = ctx_get_local_type with_opaque_pre def.def_id ctx in
extract_type_decl_variant ctx fmt type_decl_group def_name type_params
cons_name fields)
@@ -1387,16 +1431,26 @@ let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
()
(** Extract a nestable, muti-line comment *)
-let extract_comment (fmt : F.formatter) (s : string) : unit =
- match !backend with
- | Coq | FStar | HOL4 ->
- F.pp_print_string fmt "(** ";
- F.pp_print_string fmt s;
- F.pp_print_string fmt " *)"
- | Lean ->
- F.pp_print_string fmt "/- ";
+let extract_comment (fmt : F.formatter) (sl : string list) : unit =
+ (* Delimiters, space after we break a line *)
+ let ld, space, rd =
+ match !backend with
+ | Coq | FStar | HOL4 -> ("(** ", 4, " *)")
+ | Lean -> ("/- ", 3, " -/")
+ in
+ F.pp_open_vbox fmt space;
+ F.pp_print_string fmt ld;
+ (match sl with
+ | [] -> ()
+ | s :: sl ->
F.pp_print_string fmt s;
- F.pp_print_string fmt " -/"
+ List.iter
+ (fun s ->
+ F.pp_print_space fmt ();
+ F.pp_print_string fmt s)
+ sl);
+ F.pp_print_string fmt rd;
+ F.pp_close_box fmt ()
(** Extract a type declaration.
@@ -1436,7 +1490,7 @@ let extract_type_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
if !backend <> HOL4 || not (decl_is_first_from_group kind) then
F.pp_print_break fmt 0 0;
(* Print a comment to link the extracted type to its original rust definition *)
- extract_comment fmt ("[" ^ Print.name_to_string def.name ^ "]");
+ extract_comment fmt [ "[" ^ Print.name_to_string def.name ^ "]" ];
F.pp_print_break fmt 0 0;
(* Open a box for the definition, so that whenever possible it gets printed on
* one line. Note however that in the case of Lean line breaks are important
@@ -1833,7 +1887,7 @@ let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
(* Add a break before *)
F.pp_print_break fmt 0 0;
(* Print a comment *)
- extract_comment fmt "The state type used in the state-error monad";
+ extract_comment fmt [ "The state type used in the state-error monad" ];
F.pp_print_break fmt 0 0;
(* Open a box for the definition, so that whenever possible it gets printed on
* one line *)
@@ -1950,14 +2004,17 @@ let extract_global_decl_register_names (ctx : extraction_ctx)
Note that patterns can introduce new variables: we thus return an extraction
context updated with new bindings.
+ [is_single_pat]: are we extracting a single pattern (a pattern for a let-binding
+ or a lambda).
+
TODO: we don't need something very generic anymore (some definitions used
to be polymorphic).
*)
let extract_adt_g_value
(extract_value : extraction_ctx -> bool -> 'v -> extraction_ctx)
- (fmt : F.formatter) (ctx : extraction_ctx) (inside : bool)
- (variant_id : VariantId.id option) (field_values : 'v list) (ty : ty) :
- extraction_ctx =
+ (fmt : F.formatter) (ctx : extraction_ctx) (is_single_pat : bool)
+ (inside : bool) (variant_id : VariantId.id option) (field_values : 'v list)
+ (ty : ty) : extraction_ctx =
match ty with
| Adt (Tuple, type_args) ->
(* Tuple *)
@@ -1982,36 +2039,57 @@ let extract_adt_g_value
ctx)
| Adt (adt_id, _) ->
(* "Regular" ADT *)
- (* We print something of the form: [Cons field0 ... fieldn].
- * We could update the code to print something of the form:
- * [{ field0=...; ...; fieldn=...; }] in case of structures.
- *)
- let cons =
- (* The ADT shouldn't be opaque *)
- let with_opaque_pre = false in
- match variant_id with
- | Some vid -> (
- (* In the case of Lean, we might have to add the type name as a prefix *)
- match (!backend, adt_id) with
- | Lean, Assumed _ ->
- ctx_get_type with_opaque_pre adt_id ctx
- ^ "."
- ^ ctx_get_variant adt_id vid ctx
- | _ -> ctx_get_variant adt_id vid ctx)
- | None -> ctx_get_struct with_opaque_pre adt_id ctx
- in
- let use_parentheses = inside && field_values <> [] in
- if use_parentheses then F.pp_print_string fmt "(";
- F.pp_print_string fmt cons;
- let ctx =
- Collections.List.fold_left
- (fun ctx v ->
- F.pp_print_space fmt ();
- extract_value ctx true v)
- ctx field_values
- in
- if use_parentheses then F.pp_print_string fmt ")";
- ctx
+
+ (* If we are generating a pattern for a let-binding and we target Lean,
+ the syntax is: `let ⟨ x0, ..., xn ⟩ := ...`.
+
+ Otherwise, it is: `let Cons x0 ... xn = ...`
+ *)
+ if is_single_pat && !Config.backend = Lean then (
+ F.pp_print_string fmt "⟨";
+ F.pp_print_space fmt ();
+ let ctx =
+ Collections.List.fold_left_link
+ (fun _ ->
+ F.pp_print_string fmt ",";
+ F.pp_print_space fmt ())
+ (fun ctx v -> extract_value ctx true v)
+ ctx field_values
+ in
+ F.pp_print_space fmt ();
+ F.pp_print_string fmt "⟩";
+ ctx)
+ else
+ (* We print something of the form: [Cons field0 ... fieldn].
+ * We could update the code to print something of the form:
+ * [{ field0=...; ...; fieldn=...; }] in case of structures.
+ *)
+ let cons =
+ (* The ADT shouldn't be opaque *)
+ let with_opaque_pre = false in
+ match variant_id with
+ | Some vid -> (
+ (* In the case of Lean, we might have to add the type name as a prefix *)
+ match (!backend, adt_id) with
+ | Lean, Assumed _ ->
+ ctx_get_type with_opaque_pre adt_id ctx
+ ^ "."
+ ^ ctx_get_variant adt_id vid ctx
+ | _ -> ctx_get_variant adt_id vid ctx)
+ | None -> ctx_get_struct with_opaque_pre adt_id ctx
+ in
+ let use_parentheses = inside && field_values <> [] in
+ if use_parentheses then F.pp_print_string fmt "(";
+ F.pp_print_string fmt cons;
+ let ctx =
+ Collections.List.fold_left
+ (fun ctx v ->
+ F.pp_print_space fmt ();
+ extract_value ctx true v)
+ ctx field_values
+ in
+ if use_parentheses then F.pp_print_string fmt ")";
+ ctx
| _ -> raise (Failure "Inconsistent typed value")
(* Extract globals in the same way as variables *)
@@ -2026,7 +2104,7 @@ let extract_global (ctx : extraction_ctx) (fmt : F.formatter)
updated with new bindings.
*)
let rec extract_typed_pattern (ctx : extraction_ctx) (fmt : F.formatter)
- (inside : bool) (v : typed_pattern) : extraction_ctx =
+ (is_let : bool) (inside : bool) (v : typed_pattern) : extraction_ctx =
match v.value with
| PatConstant cv ->
ctx.fmt.extract_primitive_value fmt inside cv;
@@ -2042,8 +2120,10 @@ let rec extract_typed_pattern (ctx : extraction_ctx) (fmt : F.formatter)
F.pp_print_string fmt "_";
ctx
| PatAdt av ->
- let extract_value ctx inside v = extract_typed_pattern ctx fmt inside v in
- extract_adt_g_value extract_value fmt ctx inside av.variant_id
+ let extract_value ctx inside v =
+ extract_typed_pattern ctx fmt is_let inside v
+ in
+ extract_adt_g_value extract_value fmt ctx is_let inside av.variant_id
av.field_values v.ty
(** [inside]: controls the introduction of parentheses. See [extract_ty]
@@ -2173,12 +2253,13 @@ and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
(adt_cons : adt_cons_id) (type_args : ty list) (args : texpression list) :
unit =
let e_ty = Adt (adt_cons.adt_id, type_args) in
+ let is_single_pat = false in
let _ =
extract_adt_g_value
(fun ctx inside e ->
extract_texpression ctx fmt inside e;
ctx)
- fmt ctx inside adt_cons.variant_id args e_ty
+ fmt ctx is_single_pat inside adt_cons.variant_id args e_ty
in
()
@@ -2226,11 +2307,12 @@ and extract_Abs (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
List.fold_left
(fun ctx x ->
F.pp_print_space fmt ();
- extract_typed_pattern ctx fmt true x)
+ extract_typed_pattern ctx fmt true true x)
ctx xl
in
F.pp_print_space fmt ();
- F.pp_print_string fmt "->";
+ if !backend = Lean then F.pp_print_string fmt "=>"
+ else F.pp_print_string fmt "->";
F.pp_print_space fmt ();
(* Print the body *)
extract_texpression ctx fmt false e;
@@ -2295,7 +2377,7 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
* TODO: cleanup
* *)
if monadic && (!backend = Coq || !backend = HOL4) then (
- let ctx = extract_typed_pattern ctx fmt true lv in
+ let ctx = extract_typed_pattern ctx fmt true true lv in
F.pp_print_space fmt ();
let arrow =
match !backend with
@@ -2321,15 +2403,13 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
else (
F.pp_print_string fmt "let";
F.pp_print_space fmt ());
- let ctx = extract_typed_pattern ctx fmt true lv in
+ let ctx = extract_typed_pattern ctx fmt true true lv in
F.pp_print_space fmt ();
let eq =
match !backend with
| FStar -> "="
| Coq -> ":="
- | Lean ->
- (* TODO: switch to ⟵ once issues are fixed *)
- if monadic then "←" else ":="
+ | Lean -> if monadic then "←" else ":="
| HOL4 -> if monadic then "<-" else "="
in
F.pp_print_string fmt eq;
@@ -2409,7 +2489,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (_inside : bool)
(* Open a box for the [if e] *)
F.pp_open_hovbox fmt ctx.indent_incr;
F.pp_print_string fmt "if";
- if !backend = Lean then F.pp_print_string fmt " h:";
+ if !backend = Lean && ctx.use_dep_ite then F.pp_print_string fmt " h:";
F.pp_print_space fmt ();
let scrut_inside = PureUtils.texpression_requires_parentheses scrut in
extract_texpression ctx fmt scrut_inside scrut;
@@ -2470,7 +2550,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (_inside : bool)
match !backend with
| FStar -> "begin match"
| Coq -> "match"
- | Lean -> "match h:"
+ | Lean -> if ctx.use_dep_ite then "match h:" else "match"
| HOL4 ->
(* We're being extra safe in the case of HOL4 *)
"(case"
@@ -2497,7 +2577,7 @@ and extract_Switch (ctx : extraction_ctx) (fmt : F.formatter) (_inside : bool)
(* Print the pattern *)
F.pp_print_string fmt "|";
F.pp_print_space fmt ();
- let ctx = extract_typed_pattern ctx fmt false br.pat in
+ let ctx = extract_typed_pattern ctx fmt false false br.pat in
F.pp_print_space fmt ();
let arrow =
match !backend with FStar -> "->" | Coq | Lean | HOL4 -> "=>"
@@ -2689,7 +2769,7 @@ let extract_fun_parameters (space : bool ref) (ctx : extraction_ctx)
(* Open a box for the input parameter *)
F.pp_open_hovbox fmt 0;
F.pp_print_string fmt "(";
- let ctx = extract_typed_pattern ctx fmt false lv in
+ let ctx = extract_typed_pattern ctx fmt true false lv in
F.pp_print_space fmt ();
F.pp_print_string fmt ":";
F.pp_print_space fmt ();
@@ -2714,7 +2794,7 @@ let extract_fun_input_parameters_types (ctx : extraction_ctx)
let inside = false in
extract_ty ctx fmt TypeDeclId.Set.empty inside ty;
F.pp_print_space fmt ();
- F.pp_print_string fmt "->";
+ extract_arrow fmt ();
F.pp_print_space fmt ()
in
List.iter extract_param def.signature.inputs
@@ -2752,7 +2832,7 @@ let extract_template_fstar_decreases_clause (ctx : extraction_ctx)
F.pp_print_break fmt 0 0;
(* Print a comment to link the extracted type to its original rust definition *)
extract_comment fmt
- ("[" ^ Print.fun_name_to_string def.basename ^ "]: decreases clause");
+ [ "[" ^ Print.fun_name_to_string def.basename ^ "]: decreases clause" ];
F.pp_print_space fmt ();
(* Open a box for the definition, so that whenever possible it gets printed on
* one line *)
@@ -2814,7 +2894,7 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
F.pp_print_break fmt 0 0;
(* Print a comment to link the extracted type to its original rust definition *)
extract_comment fmt
- ("[" ^ Print.fun_name_to_string def.basename ^ "]: termination measure");
+ [ "[" ^ Print.fun_name_to_string def.basename ^ "]: termination measure" ];
F.pp_print_space fmt ();
(* Open a box for the definition, so that whenever possible it gets printed on
* one line *)
@@ -2868,7 +2948,7 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
(* syntax <def_name> term ... term : tactic *)
F.pp_print_break fmt 0 0;
extract_comment fmt
- ("[" ^ Print.fun_name_to_string def.basename ^ "]: decreases_by tactic");
+ [ "[" ^ Print.fun_name_to_string def.basename ^ "]: decreases_by tactic" ];
F.pp_print_space fmt ();
F.pp_open_hvbox fmt 0;
F.pp_print_string fmt "syntax \"";
@@ -2897,6 +2977,40 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
F.pp_close_box fmt ();
F.pp_print_break fmt 0 0
+let extract_fun_comment (ctx : extraction_ctx) (fmt : F.formatter)
+ (def : fun_decl) : unit =
+ let { keep_fwd; num_backs } =
+ PureUtils.RegularFunIdMap.find
+ (A.Regular def.def_id, def.loop_id, def.back_id)
+ ctx.fun_name_info
+ in
+ let comment_pre = "[" ^ Print.fun_name_to_string def.basename ^ "]: " in
+ let comment =
+ let loop_comment =
+ match def.loop_id with
+ | None -> ""
+ | Some id -> "loop " ^ LoopId.to_string id ^ ": "
+ in
+ let fwd_back_comment =
+ match def.back_id with
+ | None -> [ "forward function" ]
+ | Some id ->
+ (* Check if there is only one backward function, and no forward function *)
+ if (not keep_fwd) && num_backs = 1 then
+ [
+ "merged forward/backward function";
+ "(there is a single backward function, and the forward function \
+ returns ())";
+ ]
+ else [ "backward function " ^ T.RegionGroupId.to_string id ]
+ in
+ match fwd_back_comment with
+ | [] -> raise (Failure "Unreachable")
+ | [ s ] -> [ comment_pre ^ loop_comment ^ s ]
+ | s :: sl -> (comment_pre ^ loop_comment ^ s) :: sl
+ in
+ extract_comment fmt comment
+
(** Extract a function declaration.
This function is for all function declarations and all backends **at the exception**
@@ -2916,8 +3030,8 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
(* Add a break before *)
if !backend <> HOL4 || not (decl_is_first_from_group kind) then
F.pp_print_break fmt 0 0;
- (* Print a comment to link the extracted type to its original rust definition *)
- extract_comment fmt ("[" ^ Print.fun_name_to_string def.basename ^ "]");
+ (* Print a comment to link the extracted definition to its original rust definition *)
+ extract_fun_comment ctx fmt def;
F.pp_print_space fmt ();
(* Open two boxes for the definition, so that whenever possible it gets printed on
* one line and indents are correct *)
@@ -2939,8 +3053,11 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
let use_forall = is_opaque_coq && def.signature.type_params <> [] in
(* Print the qualifier ("assume", etc.).
- For Lean: we generate a record of assumed functions *)
- (if not (!backend = Lean && (kind = Assumed || kind = Declared)) then
+ if `wrap_opaque_in_sig`: we generate a record of assumed funcions.
+ TODO: this is obsolete.
+ *)
+ (if not (!Config.wrap_opaque_in_sig && (kind = Assumed || kind = Declared))
+ then
let qualif = ctx.fmt.fun_decl_kind_to_qualif kind in
match qualif with
| Some qualif ->
@@ -3034,7 +3151,7 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
List.fold_left
(fun ctx (lv : typed_pattern) ->
F.pp_print_space fmt ();
- let ctx = extract_typed_pattern ctx fmt false lv in
+ let ctx = extract_typed_pattern ctx fmt true false lv in
ctx)
ctx inputs_lvs
in
@@ -3168,6 +3285,8 @@ let extract_fun_decl_hol4_opaque (ctx : extraction_ctx) (fmt : F.formatter)
F.pp_print_break fmt 0 0;
(* Open a box for the whole definition *)
F.pp_open_hvbox fmt ctx.indent_incr;
+ (* Print a comment to link the extracted definition to its original rust definition *)
+ extract_fun_comment ctx fmt def;
(* Generate: `val _ = new_constant ("...",` *)
F.pp_print_string fmt ("val _ = new_constant (\"" ^ def_name ^ "\",");
F.pp_print_space fmt ();
@@ -3343,7 +3462,7 @@ let extract_global_decl (ctx : extraction_ctx) (fmt : F.formatter)
(* Add a break then the name of the corresponding LLBC declaration *)
F.pp_print_break fmt 0 0;
- extract_comment fmt ("[" ^ Print.global_name_to_string global.name ^ "]");
+ extract_comment fmt [ "[" ^ Print.global_name_to_string global.name ^ "]" ];
F.pp_print_space fmt ();
let with_opaque_pre = false in
@@ -3417,7 +3536,7 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
F.pp_print_break fmt 0 0;
(* Print a comment *)
extract_comment fmt
- ("Unit test for [" ^ Print.fun_name_to_string def.basename ^ "]");
+ [ "Unit test for [" ^ Print.fun_name_to_string def.basename ^ "]" ];
F.pp_print_space fmt ();
(* Open a box for the test *)
F.pp_open_hovbox fmt ctx.indent_incr;
diff --git a/compiler/ExtractBase.ml b/compiler/ExtractBase.ml
index 0a5d7df2..655bb033 100644
--- a/compiler/ExtractBase.ml
+++ b/compiler/ExtractBase.ml
@@ -240,7 +240,9 @@ type formatter = {
- loop identifier, if this is for a loop
*)
opaque_pre : unit -> string;
- (** The prefix to use for opaque definitions.
+ (** TODO: obsolete, remove.
+
+ The prefix to use for opaque definitions.
We need this because for some backends like Lean and Coq, we group
opaque definitions in module signatures, meaning that using those
@@ -414,7 +416,7 @@ module IdSet = Collections.MakeSet (IdOrderedType)
We use it for lookups (during the translation) and to check for name clashes.
- [id_to_string] is for debugging.
+ [id_to_name] is for debugging.
*)
type names_map = {
id_to_name : string IdMap.t;
@@ -425,7 +427,9 @@ type names_map = {
*)
names_set : StringSet.t;
opaque_ids : IdSet.t;
- (** The set of opaque definitions.
+ (** TODO: this is obsolete. Remove.
+
+ The set of opaque definitions.
See {!formatter.opaque_pre} for detailed explanations about why
we need to know which definitions are opaque to compute names.
@@ -486,6 +490,20 @@ let names_map_add_function (id_to_string : id -> string) (is_opaque : bool)
(fid : fun_id) (name : string) (nm : names_map) : names_map =
names_map_add id_to_string is_opaque (FunId fid) name nm
+(** The unsafe names map stores mappings from identifiers to names which might
+ collide. For some backends and some names, it might be acceptable to have
+ collisions. For instance, in Lean, different records can have fields with
+ the same name because Lean uses the typing information to resolve the
+ ambiguities.
+
+ This map complements the {!names_map}, which checks for collisions.
+ *)
+type unsafe_names_map = { id_to_name : string IdMap.t }
+
+let unsafe_names_map_add (id : id) (name : string) (nm : unsafe_names_map) :
+ unsafe_names_map =
+ { id_to_name = IdMap.add id name nm.id_to_name }
+
(** Make a (variable) basename unique (by adding an index).
We do this in an inefficient manner (by testing all indices starting from
@@ -518,6 +536,8 @@ let basename_to_unique (names_set : StringSet.t)
in
if StringSet.mem basename names_set then gen 0 else basename
+type fun_name_info = { keep_fwd : bool; num_backs : int }
+
(** Extraction context.
Note that the extraction context contains information coming from the
@@ -528,6 +548,11 @@ let basename_to_unique (names_set : StringSet.t)
type extraction_ctx = {
trans_ctx : trans_ctx;
names_map : names_map;
+ (** The map for id to names, where we forbid name collisions
+ (ex.: we always forbid function name collisions). *)
+ unsafe_names_map : unsafe_names_map;
+ (** The map for id to names, where we allow name collisions
+ (ex.: we might allow record field name collisions). *)
fmt : formatter;
indent_incr : int;
(** The indent increment we insert whenever we need to indent more *)
@@ -539,6 +564,25 @@ type extraction_ctx = {
use it.
Also see {!names_map.opaque_ids}.
*)
+ use_dep_ite : bool;
+ (** For Lean: do we use dependent-if then else expressions?
+
+ Example:
+ {[
+ if h: b then ... else ...
+ -- ^^
+ -- makes the if then else dependent
+ ]}
+ *)
+ fun_name_info : fun_name_info PureUtils.RegularFunIdMap.t;
+ (** Information used to filter and name functions - we use it
+ to print comments in the generated code, to help link
+ the generated code to the original code (information such
+ as: "this function is the backward function of ...", or
+ "this function is the merged forward/backward function of ..."
+ in case a Rust function only has one backward translation
+ and we filter the forward function because it returns unit.
+ *)
}
(** Debugging function, used when communicating name collisions to the user,
@@ -667,23 +711,42 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
| TypeVarId id -> "type_var_id: " ^ TypeVarId.to_string id
| VarId id -> "var_id: " ^ VarId.to_string id
+(** We might not check for collisions for some specific ids (ex.: field names) *)
+let allow_collisions (id : id) : bool =
+ match id with
+ | FieldId (_, _) -> !Config.record_fields_short_names
+ | _ -> false
+
let ctx_add (is_opaque : bool) (id : id) (name : string) (ctx : extraction_ctx)
: extraction_ctx =
- (* The id_to_string function to print nice debugging messages if there are
- * collisions *)
- let id_to_string (id : id) : string = id_to_string id ctx in
- let names_map = names_map_add id_to_string is_opaque id name ctx.names_map in
- { ctx with names_map }
+ (* We do not use the same name map if we allow/disallow collisions *)
+ if allow_collisions id then (
+ assert (not is_opaque);
+ {
+ ctx with
+ unsafe_names_map = unsafe_names_map_add id name ctx.unsafe_names_map;
+ })
+ else
+ (* The id_to_string function to print nice debugging messages if there are
+ * collisions *)
+ let id_to_string (id : id) : string = id_to_string id ctx in
+ let names_map =
+ names_map_add id_to_string is_opaque id name ctx.names_map
+ in
+ { ctx with names_map }
(** [with_opaque_pre]: if [true] and the definition is opaque, add the opaque prefix *)
let ctx_get (with_opaque_pre : bool) (id : id) (ctx : extraction_ctx) : string =
- match IdMap.find_opt id ctx.names_map.id_to_name with
- | Some s ->
- let is_opaque = IdSet.mem id ctx.names_map.opaque_ids in
- if with_opaque_pre && is_opaque then ctx.fmt.opaque_pre () ^ s else s
- | None ->
- log#serror ("Could not find: " ^ id_to_string id ctx);
- raise Not_found
+ (* We do not use the same name map if we allow/disallow collisions *)
+ if allow_collisions id then IdMap.find id ctx.unsafe_names_map.id_to_name
+ else
+ match IdMap.find_opt id ctx.names_map.id_to_name with
+ | Some s ->
+ let is_opaque = IdSet.mem id ctx.names_map.opaque_ids in
+ if with_opaque_pre && is_opaque then ctx.fmt.opaque_pre () ^ s else s
+ | None ->
+ log#serror ("Could not find: " ^ id_to_string id ctx);
+ raise Not_found
let ctx_get_global (with_opaque_pre : bool) (id : A.GlobalDeclId.id)
(ctx : extraction_ctx) : string =
@@ -918,9 +981,15 @@ let ctx_add_fun_decl (trans_group : bool * pure_fun_translation)
ctx.fmt.fun_name def.basename def.num_loops def.loop_id num_rgs rg_info
(keep_fwd, num_backs)
in
- ctx_add is_opaque
- (FunId (FromLlbc (A.Regular def_id, def.loop_id, def.back_id)))
- def_name ctx
+ let fun_id = (A.Regular def_id, def.loop_id, def.back_id) in
+ let ctx = ctx_add is_opaque (FunId (FromLlbc fun_id)) def_name ctx in
+ (* Add the name info *)
+ {
+ ctx with
+ fun_name_info =
+ PureUtils.RegularFunIdMap.add fun_id { keep_fwd; num_backs }
+ ctx.fun_name_info;
+ }
type names_map_init = {
keywords : string list;
@@ -1041,13 +1110,24 @@ let default_fun_suffix (num_loops : int) (loop_id : LoopId.id option)
definitions (in particular between type and function definitions).
*)
let rg_suff =
+ (* TODO: make all the backends match what is done for Lean *)
match rg with
- | None -> "_fwd"
+ | None -> (
+ match !Config.backend with
+ | FStar | Coq | HOL4 -> "_fwd"
+ | Lean ->
+ (* In order to avoid name conflicts:
+ * - if the forward is eliminated, we add the suffix "_fwd" (it won't be used)
+ * - otherwise, no suffix (because the backward functions will have a suffix)
+ *)
+ if num_backs = 1 && not keep_fwd then "_fwd" else "")
| Some rg ->
assert (num_region_groups > 0 && num_backs > 0);
if num_backs = 1 then
(* Exactly one backward function *)
- if not keep_fwd then "_fwd_back" else "_back"
+ match !Config.backend with
+ | FStar | Coq | HOL4 -> if not keep_fwd then "_fwd_back" else "_back"
+ | Lean -> if not keep_fwd then "" else "_back"
else if
(* Several region groups/backward functions:
- if all the regions in the group have names, we use those names
diff --git a/compiler/Pure.ml b/compiler/Pure.ml
index 4a00dfb2..b251a005 100644
--- a/compiler/Pure.ml
+++ b/compiler/Pure.ml
@@ -18,16 +18,19 @@ module GlobalDeclId = A.GlobalDeclId
(they monotonically increase across functions) while in {!module:Pure} we want
the indices to start at 0 for every function.
*)
-module LoopId = IdGen ()
+module LoopId =
+IdGen ()
type loop_id = LoopId.id [@@deriving show, ord]
(** We give an identifier to every phase of the synthesis (forward, backward
for group of regions 0, etc.) *)
-module SynthPhaseId = IdGen ()
+module SynthPhaseId =
+IdGen ()
(** Pay attention to the fact that we also define a {!E.VarId} module in Values *)
-module VarId = IdGen ()
+module VarId =
+IdGen ()
type integer_type = T.integer_type [@@deriving show, ord]
@@ -723,6 +726,7 @@ type fun_sig_info = {
*)
type fun_sig = {
type_params : type_var list;
+ (** TODO: we should analyse the signature to make the type parameters implicit whenever possible *)
inputs : ty list;
(** The input types.
diff --git a/compiler/Translate.ml b/compiler/Translate.ml
index 75fc7fe9..c5f7df92 100644
--- a/compiler/Translate.ml
+++ b/compiler/Translate.ml
@@ -750,18 +750,17 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
if config.extract_state_type && config.extract_fun_decls then
export_state_type ();
- (* For Lean, we parameterize the entire development by a section variable
- called opaque_defs, of type OpaqueDefs. The code below emits the type
- definition for OpaqueDefs, which is a structure, in which each field is one
- of the functions marked as Opaque. We emit the `structure ...` bit here,
- then rely on `extract_fun_decl` to be aware of this, and skip the keyword
- (e.g. "axiom" or "val") so as to generate valid syntax for records.
-
- We also generate such a structure only if there actually are opaque
- definitions.
- *)
+ (* Obsolete: (TODO: remove) For Lean we parameterize the entire development by a section
+ variable called opaque_defs, of type OpaqueDefs. The code below emits the type
+ definition for OpaqueDefs, which is a structure, in which each field is one of the
+ functions marked as Opaque. We emit the `structure ...` bit here, then rely on
+ `extract_fun_decl` to be aware of this, and skip the keyword (e.g. "axiom" or "val")
+ so as to generate valid syntax for records.
+
+ We also generate such a structure only if there actually are opaque definitions. *)
let wrap_in_sig =
- config.extract_opaque && config.extract_fun_decls && !Config.backend = Lean
+ config.extract_opaque && config.extract_fun_decls
+ && !Config.wrap_opaque_in_sig
&&
let _, opaque_funs = module_has_opaque_decls ctx in
opaque_funs
@@ -783,11 +782,22 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
if wrap_in_sig then Format.pp_close_box fmt ()
-let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
- (rust_module_name : string) (module_name : string) (custom_msg : string)
- (custom_imports : string list) (custom_includes : string list) : unit =
+type extract_file_info = {
+ filename : string;
+ namespace : string;
+ in_namespace : bool;
+ crate_name : string;
+ rust_module_name : string;
+ module_name : string;
+ custom_msg : string;
+ custom_imports : string list;
+ custom_includes : string list;
+}
+
+let extract_file (config : gen_config) (ctx : gen_ctx) (fi : extract_file_info)
+ : unit =
(* Open the file and create the formatter *)
- let out = open_out filename in
+ let out = open_out fi.filename in
let fmt = Format.formatter_of_out_channel out in
(* Print the headers.
@@ -801,19 +811,22 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
(match !Config.backend with
| Lean ->
Printf.fprintf out "-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS\n";
- Printf.fprintf out "-- [%s]%s\n" rust_module_name custom_msg
+ Printf.fprintf out "-- [%s]%s\n" fi.rust_module_name fi.custom_msg
| Coq | FStar | HOL4 ->
Printf.fprintf out
"(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)\n";
- Printf.fprintf out "(** [%s]%s *)\n" rust_module_name custom_msg);
+ Printf.fprintf out "(** [%s]%s *)\n" fi.rust_module_name fi.custom_msg);
+ (* Generate the imports *)
(match !Config.backend with
| FStar ->
- Printf.fprintf out "module %s\n" module_name;
+ Printf.fprintf out "module %s\n" fi.module_name;
Printf.fprintf out "open Primitives\n";
(* Add the custom imports *)
- List.iter (fun m -> Printf.fprintf out "open %s\n" m) custom_imports;
+ List.iter (fun m -> Printf.fprintf out "open %s\n" m) fi.custom_imports;
(* Add the custom includes *)
- List.iter (fun m -> Printf.fprintf out "include %s\n" m) custom_includes;
+ List.iter
+ (fun m -> Printf.fprintf out "include %s\n" m)
+ fi.custom_includes;
(* Z3 options - note that we use fuel 1 because it its useful for the decrease clauses *)
Printf.fprintf out "\n#set-options \"--z3rlimit 50 --fuel 1 --ifuel 1\"\n"
| Coq ->
@@ -825,24 +838,29 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
(* Add the custom imports *)
List.iter
(fun m -> Printf.fprintf out "Require Import %s.\n" m)
- custom_imports;
+ fi.custom_imports;
(* Add the custom includes *)
List.iter
(fun m ->
Printf.fprintf out "Require Export %s.\n" m;
Printf.fprintf out "Import %s.\n" m)
- custom_includes;
- Printf.fprintf out "Module %s.\n" module_name
+ fi.custom_includes;
+ Printf.fprintf out "Module %s.\n" fi.module_name
| Lean ->
- Printf.fprintf out "import Base.Primitives\n";
+ Printf.fprintf out "import Base\n";
(* Add the custom imports *)
- List.iter (fun m -> Printf.fprintf out "import %s\n" m) custom_imports;
+ List.iter (fun m -> Printf.fprintf out "import %s\n" m) fi.custom_imports;
(* Add the custom includes *)
- List.iter (fun m -> Printf.fprintf out "import %s\n" m) custom_includes
+ List.iter (fun m -> Printf.fprintf out "import %s\n" m) fi.custom_includes;
+ (* Always open the Primitives namespace *)
+ Printf.fprintf out "open Primitives\n";
+ (* If we are inside the namespace: declare it, otherwise: open it *)
+ if fi.in_namespace then Printf.fprintf out "namespace %s\n" fi.namespace
+ else Printf.fprintf out "open %s\n" fi.namespace
| HOL4 ->
Printf.fprintf out "open primitivesLib divDefLib\n";
(* Add the custom imports and includes *)
- let imports = custom_imports @ custom_includes in
+ let imports = fi.custom_imports @ fi.custom_includes in
(* The imports are a list of module names: we need to add a "Theory" suffix *)
let imports = List.map (fun s -> s ^ "Theory") imports in
if imports <> [] then
@@ -850,7 +868,7 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
Printf.fprintf out "open %s\n\n" imports
else Printf.fprintf out "\n";
(* Initialize the theory *)
- Printf.fprintf out "val _ = new_theory \"%s\"\n\n" module_name);
+ Printf.fprintf out "val _ = new_theory \"%s\"\n\n" fi.module_name);
(* From now onwards, we use the formatter *)
(* Set the margin *)
Format.pp_set_margin fmt 80;
@@ -867,12 +885,13 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (filename : string)
(* Close the module *)
(match !Config.backend with
- | FStar | Lean -> ()
+ | FStar -> ()
+ | Lean -> if fi.in_namespace then Printf.fprintf out "end %s\n" fi.namespace
| HOL4 -> Printf.fprintf out "val _ = export_theory ()\n"
- | Coq -> Printf.fprintf out "End %s .\n" module_name);
+ | Coq -> Printf.fprintf out "End %s .\n" fi.module_name);
(* Some logging *)
- log#linfo (lazy ("Generated: " ^ filename));
+ log#linfo (lazy ("Generated: " ^ fi.filename));
(* Flush and close the file *)
close_out out
@@ -891,18 +910,24 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
prefixed with the type name to prevent collisions *)
match !Config.backend with Coq | FStar | HOL4 -> true | Lean -> false
in
+ (* Initialize the names map (we insert the names of the "primitives"
+ declarations, and insert the names of the local declarations later) *)
let mk_formatter_and_names_map = Extract.mk_formatter_and_names_map in
let fmt, names_map =
mk_formatter_and_names_map trans_ctx crate.name
variant_concatenate_type_name
in
+ (* Put everything in the context *)
let ctx =
{
ExtractBase.trans_ctx;
names_map;
+ unsafe_names_map = { id_to_name = ExtractBase.IdMap.empty };
fmt;
indent_incr = 2;
use_opaque_pre = !Config.split_files;
+ use_dep_ite = !Config.backend = Lean && !Config.extract_decreases_clauses;
+ fun_name_info = PureUtils.RegularFunIdMap.empty;
}
in
@@ -968,7 +993,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
(* Open the output file *)
(* First compute the filename by replacing the extension and converting the
* case (rust module names are snake case) *)
- let module_name, extract_filebasename =
+ let namespace, crate_name, extract_filebasename =
match Filename.chop_suffix_opt ~suffix:".llbc" filename with
| None ->
(* Note that we already checked the suffix upon opening the file *)
@@ -977,14 +1002,20 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
(* Retrieve the file basename *)
let basename = Filename.basename filename in
(* Convert the case *)
- let module_name = StringUtils.to_camel_case basename in
- let module_name =
+ let crate_name = StringUtils.to_camel_case basename in
+ let crate_name =
if !Config.backend = HOL4 then
- StringUtils.lowercase_first_letter module_name
- else module_name
+ StringUtils.lowercase_first_letter crate_name
+ else crate_name
+ in
+ (* We use the raw crate name for the namespaces *)
+ let namespace =
+ match !Config.backend with
+ | FStar | Coq | HOL4 -> crate.name
+ | Lean -> crate.name
in
(* Concatenate *)
- (module_name, Filename.concat dest_dir module_name)
+ (namespace, crate_name, Filename.concat dest_dir crate_name)
in
(* Put the translated definitions in maps *)
@@ -1019,11 +1050,10 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
create more directories *)
if !Config.backend = Lean then (
let ( ^^ ) = Filename.concat in
- mkdir_if (dest_dir ^^ "Base");
- if !Config.split_files then mkdir_if (dest_dir ^^ module_name);
+ if !Config.split_files then mkdir_if (dest_dir ^^ crate_name);
if needs_clauses_module then (
assert !Config.split_files;
- mkdir_if (dest_dir ^^ module_name ^^ "Clauses")));
+ mkdir_if (dest_dir ^^ crate_name ^^ "Clauses")));
(* Copy the "Primitives" file, if necessary *)
let _ =
@@ -1033,7 +1063,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
match !Config.backend with
| FStar -> Some ("/backends/fstar/Primitives.fst", "Primitives.fst")
| Coq -> Some ("/backends/coq/Primitives.v", "Primitives.v")
- | Lean -> Some ("/backends/lean/Primitives.lean", "Base/Primitives.lean")
+ | Lean -> None
| HOL4 -> None
in
match primitives_src_dest with
@@ -1117,6 +1147,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
(* Extract the types *)
(* If there are opaque types, we extract in an interface *)
+ (* TODO: for Lean and Coq: generate a template file *)
let types_filename_ext =
match !Config.backend with
| FStar -> if has_opaque_types then ".fsti" else ".fst"
@@ -1127,7 +1158,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
let types_filename =
extract_filebasename ^ file_delimiter ^ "Types" ^ types_filename_ext
in
- let types_module = module_name ^ module_delimiter ^ "Types" in
+ let types_module = crate_name ^ module_delimiter ^ "Types" in
let types_config =
{
base_gen_config with
@@ -1137,8 +1168,20 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
interface = has_opaque_types;
}
in
- extract_file types_config gen_ctx types_filename crate.A.name types_module
- ": type definitions" [] [];
+ let file_info =
+ {
+ filename = types_filename;
+ namespace;
+ in_namespace = true;
+ crate_name;
+ rust_module_name = crate.A.name;
+ module_name = types_module;
+ custom_msg = ": type definitions";
+ custom_imports = [];
+ custom_includes = [];
+ }
+ in
+ extract_file types_config gen_ctx file_info;
(* Extract the template clauses *)
(if needs_clauses_module && !Config.extract_template_decreases_clauses then
@@ -1147,33 +1190,49 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
^ "Template" ^ ext
in
let template_clauses_module =
- module_name ^ module_delimiter ^ "Clauses" ^ module_delimiter
+ crate_name ^ module_delimiter ^ "Clauses" ^ module_delimiter
^ "Template"
in
let template_clauses_config =
{ base_gen_config with extract_template_decreases_clauses = true }
in
- extract_file template_clauses_config gen_ctx template_clauses_filename
- crate.A.name template_clauses_module
- ": templates for the decreases clauses" [ types_module ] []);
+ let file_info =
+ {
+ filename = template_clauses_filename;
+ namespace;
+ in_namespace = true;
+ crate_name;
+ rust_module_name = crate.A.name;
+ module_name = template_clauses_module;
+ custom_msg = ": templates for the decreases clauses";
+ custom_imports = [ types_module ];
+ custom_includes = [];
+ }
+ in
+ extract_file template_clauses_config gen_ctx file_info);
(* Extract the opaque functions, if needed *)
let opaque_funs_module =
if has_opaque_funs then (
+ (* In the case of Lean we generate a template file *)
+ let module_suffix, opaque_imported_suffix, custom_msg =
+ match !Config.backend with
+ | FStar | Coq | HOL4 ->
+ ("Opaque", "Opaque", ": external function declarations")
+ | Lean ->
+ ( "FunsExternal_Template",
+ "FunsExternal",
+ ": external functions.\n\
+ -- This is a template file: rename it to \
+ \"FunsExternal.lean\" and fill the holes." )
+ in
let opaque_filename =
- extract_filebasename ^ file_delimiter ^ "Opaque" ^ opaque_ext
+ extract_filebasename ^ file_delimiter ^ module_suffix ^ opaque_ext
in
- let opaque_module = module_name ^ module_delimiter ^ "Opaque" in
+ let opaque_module = crate_name ^ module_delimiter ^ module_suffix in
let opaque_imported_module =
- (* In the case of Lean, we declare an interface (a record) containing
- the opaque definitions, and we leave it to the user to provide an
- instance of this module.
-
- TODO: do the same for Coq.
- TODO: do the same for the type definitions.
- *)
if !Config.backend = Lean then
- module_name ^ module_delimiter ^ "ExternalFuns"
+ crate_name ^ module_delimiter ^ opaque_imported_suffix
else opaque_module
in
let opaque_config =
@@ -1191,15 +1250,28 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
extract_ctx = { gen_ctx.extract_ctx with use_opaque_pre = false };
}
in
- extract_file opaque_config gen_ctx opaque_filename crate.A.name
- opaque_module ": opaque function definitions" [] [ types_module ];
+ let file_info =
+ {
+ filename = opaque_filename;
+ namespace;
+ in_namespace = false;
+ crate_name;
+ rust_module_name = crate.A.name;
+ module_name = opaque_module;
+ custom_msg;
+ custom_imports = [];
+ custom_includes = [ types_module ];
+ }
+ in
+ extract_file opaque_config gen_ctx file_info;
+ (* Return the additional dependencies *)
[ opaque_imported_module ])
else []
in
(* Extract the functions *)
let fun_filename = extract_filebasename ^ file_delimiter ^ "Funs" ^ ext in
- let fun_module = module_name ^ module_delimiter ^ "Funs" in
+ let fun_module = crate_name ^ module_delimiter ^ "Funs" in
let fun_config =
{
base_gen_config with
@@ -1213,12 +1285,24 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
let clauses_submodule =
if !Config.backend = Lean then module_delimiter ^ "Clauses" else ""
in
- [ module_name ^ clauses_submodule ^ module_delimiter ^ "Clauses" ]
+ [ crate_name ^ clauses_submodule ^ module_delimiter ^ "Clauses" ]
else []
in
- extract_file fun_config gen_ctx fun_filename crate.A.name fun_module
- ": function definitions" []
- ([ types_module ] @ opaque_funs_module @ clauses_module))
+ let file_info =
+ {
+ filename = fun_filename;
+ namespace;
+ in_namespace = true;
+ crate_name;
+ rust_module_name = crate.A.name;
+ module_name = fun_module;
+ custom_msg = ": function definitions";
+ custom_imports = [];
+ custom_includes =
+ [ types_module ] @ opaque_funs_module @ clauses_module;
+ }
+ in
+ extract_file fun_config gen_ctx file_info)
else
let gen_config =
{
@@ -1235,10 +1319,21 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
test_trans_unit_functions = !Config.test_trans_unit_functions;
}
in
+ let file_info =
+ {
+ filename = extract_filebasename ^ ext;
+ namespace;
+ in_namespace = true;
+ crate_name;
+ rust_module_name = crate.A.name;
+ module_name = crate_name;
+ custom_msg = "";
+ custom_imports = [];
+ custom_includes = [];
+ }
+ in
(* Add the extension for F* *)
- let extract_filename = extract_filebasename ^ ext in
- extract_file gen_config gen_ctx extract_filename crate.A.name module_name
- "" [] []);
+ extract_file gen_config gen_ctx file_info);
(* Generate the build file *)
match !Config.backend with
@@ -1256,47 +1351,45 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
* different files.
*)
if !Config.split_files then (
- let filename = Filename.concat dest_dir (module_name ^ ".lean") in
+ let filename = Filename.concat dest_dir (crate_name ^ ".lean") in
let out = open_out filename in
(* Write *)
- Printf.fprintf out "import %s.Funs\n" module_name;
+ Printf.fprintf out "import %s.Funs\n" crate_name;
(* Flush and close the file, log *)
close_out out;
log#linfo (lazy ("Generated: " ^ filename)));
(*
- * Generate the lakefile.lean file
+ * Generate the lakefile.lean file, if the user asks for it
*)
+ if !Config.lean_gen_lakefile then (
+ (* Open the file *)
+ let filename = Filename.concat dest_dir "lakefile.lean" in
+ let out = open_out filename in
- (* Open the file *)
- let filename = Filename.concat dest_dir "lakefile.lean" in
- let out = open_out filename in
-
- (* Generate the content *)
- Printf.fprintf out "import Lake\nopen Lake DSL\n\n";
- Printf.fprintf out "require mathlib from git\n";
- Printf.fprintf out
- " \"https://github.com/leanprover-community/mathlib4.git\"\n\n";
-
- let package_name = StringUtils.to_snake_case module_name in
- Printf.fprintf out "package «%s» {}\n\n" package_name;
-
- Printf.fprintf out "lean_lib «Base» {}\n\n";
-
- Printf.fprintf out "@[default_target]\nlean_lib «%s» {}\n" module_name;
-
- (* No default target for now.
- Format would be:
- {[
- @[default_target]
- lean_exe «package_name» {
- root := `Main
- }
- ]}
- *)
+ (* Generate the content *)
+ Printf.fprintf out "import Lake\nopen Lake DSL\n\n";
+ Printf.fprintf out "require mathlib from git\n";
+ Printf.fprintf out
+ " \"https://github.com/leanprover-community/mathlib4.git\"\n\n";
+
+ let package_name = StringUtils.to_snake_case crate_name in
+ Printf.fprintf out "package «%s» {}\n\n" package_name;
+
+ Printf.fprintf out "@[default_target]\nlean_lib «%s» {}\n" crate_name;
+
+ (* No default target for now.
+ Format would be:
+ {[
+ @[default_target]
+ lean_exe «package_name» {
+ root := `Main
+ }
+ ]}
+ *)
- (* Flush and close the file *)
- close_out out;
+ (* Flush and close the file *)
+ close_out out;
- (* Logging *)
- log#linfo (lazy ("Generated: " ^ filename))
+ (* Logging *)
+ log#linfo (lazy ("Generated: " ^ filename)))
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index 940b8650..86a9d5f2 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -10,7 +10,7 @@ Require Export BetreeMain_Opaque.
Import BetreeMain_Opaque.
Module BetreeMain_Funs.
-(** [betree_main::betree::load_internal_node] *)
+(** [betree_main::betree::load_internal_node]: forward function *)
Definition betree_load_internal_node_fwd
(id : u64) (st : state) :
result (state * (Betree_list_t (u64 * Betree_message_t)))
@@ -18,7 +18,7 @@ Definition betree_load_internal_node_fwd
betree_utils_load_internal_node_fwd id st
.
-(** [betree_main::betree::store_internal_node] *)
+(** [betree_main::betree::store_internal_node]: forward function *)
Definition betree_store_internal_node_fwd
(id : u64) (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
result (state * unit)
@@ -28,13 +28,13 @@ Definition betree_store_internal_node_fwd
Return (st0, tt)
.
-(** [betree_main::betree::load_leaf_node] *)
+(** [betree_main::betree::load_leaf_node]: forward function *)
Definition betree_load_leaf_node_fwd
(id : u64) (st : state) : result (state * (Betree_list_t (u64 * u64))) :=
betree_utils_load_leaf_node_fwd id st
.
-(** [betree_main::betree::store_leaf_node] *)
+(** [betree_main::betree::store_leaf_node]: forward function *)
Definition betree_store_leaf_node_fwd
(id : u64) (content : Betree_list_t (u64 * u64)) (st : state) :
result (state * unit)
@@ -44,29 +44,29 @@ Definition betree_store_leaf_node_fwd
Return (st0, tt)
.
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: forward function *)
Definition betree_fresh_node_id_fwd (counter : u64) : result u64 :=
_ <- u64_add counter 1%u64; Return counter
.
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: backward function 0 *)
Definition betree_fresh_node_id_back (counter : u64) : result u64 :=
u64_add counter 1%u64
.
-(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
Definition betree_node_id_counter_new_fwd : result Betree_node_id_counter_t :=
Return {| Betree_node_id_counter_next_node_id := 0%u64 |}
.
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
Definition betree_node_id_counter_fresh_id_fwd
(self : Betree_node_id_counter_t) : result u64 :=
_ <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
Return self.(Betree_node_id_counter_next_node_id)
.
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
Definition betree_node_id_counter_fresh_id_back
(self : Betree_node_id_counter_t) : result Betree_node_id_counter_t :=
i <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
@@ -79,7 +79,7 @@ Definition core_num_u64_max_body : result u64 :=
.
Definition core_num_u64_max_c : u64 := core_num_u64_max_body%global.
-(** [betree_main::betree::upsert_update] *)
+(** [betree_main::betree::upsert_update]: forward function *)
Definition betree_upsert_update_fwd
(prev : option u64) (st : Betree_upsert_fun_state_t) : result u64 :=
match prev with
@@ -99,7 +99,7 @@ Definition betree_upsert_update_fwd
end
.
-(** [betree_main::betree::List::{1}::len] *)
+(** [betree_main::betree::List::{1}::len]: forward function *)
Fixpoint betree_list_len_fwd
(T : Type) (n : nat) (self : Betree_list_t T) : result u64 :=
match n with
@@ -112,7 +112,7 @@ Fixpoint betree_list_len_fwd
end
.
-(** [betree_main::betree::List::{1}::split_at] *)
+(** [betree_main::betree::List::{1}::split_at]: forward function *)
Fixpoint betree_list_split_at_fwd
(T : Type) (n : nat) (self : Betree_list_t T) (n0 : u64) :
result ((Betree_list_t T) * (Betree_list_t T))
@@ -135,7 +135,8 @@ Fixpoint betree_list_split_at_fwd
end
.
-(** [betree_main::betree::List::{1}::push_front] *)
+(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition betree_list_push_front_fwd_back
(T : Type) (self : Betree_list_t T) (x : T) : result (Betree_list_t T) :=
let tl := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
@@ -143,7 +144,7 @@ Definition betree_list_push_front_fwd_back
Return (BetreeListCons x l)
.
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: forward function *)
Definition betree_list_pop_front_fwd
(T : Type) (self : Betree_list_t T) : result T :=
let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
@@ -153,7 +154,7 @@ Definition betree_list_pop_front_fwd
end
.
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
Definition betree_list_pop_front_back
(T : Type) (self : Betree_list_t T) : result (Betree_list_t T) :=
let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
@@ -163,7 +164,7 @@ Definition betree_list_pop_front_back
end
.
-(** [betree_main::betree::List::{1}::hd] *)
+(** [betree_main::betree::List::{1}::hd]: forward function *)
Definition betree_list_hd_fwd (T : Type) (self : Betree_list_t T) : result T :=
match self with
| BetreeListCons hd l => Return hd
@@ -171,7 +172,7 @@ Definition betree_list_hd_fwd (T : Type) (self : Betree_list_t T) : result T :=
end
.
-(** [betree_main::betree::List::{2}::head_has_key] *)
+(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
Definition betree_list_head_has_key_fwd
(T : Type) (self : Betree_list_t (u64 * T)) (key : u64) : result bool :=
match self with
@@ -180,7 +181,7 @@ Definition betree_list_head_has_key_fwd
end
.
-(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
Fixpoint betree_list_partition_at_pivot_fwd
(T : Type) (n : nat) (self : Betree_list_t (u64 * T)) (pivot : u64) :
result ((Betree_list_t (u64 * T)) * (Betree_list_t (u64 * T)))
@@ -203,7 +204,7 @@ Fixpoint betree_list_partition_at_pivot_fwd
end
.
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: forward function *)
Definition betree_leaf_split_fwd
(n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
(params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
@@ -236,7 +237,7 @@ Definition betree_leaf_split_fwd
Return (st1, mkBetree_internal_t self.(Betree_leaf_id) pivot n0 n1)
.
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
Definition betree_leaf_split_back
(n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
(params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
@@ -257,7 +258,7 @@ Definition betree_leaf_split_back
betree_node_id_counter_fresh_id_back node_id_cnt0
.
-(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
Fixpoint betree_node_lookup_in_bindings_fwd
(n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
result (option u64)
@@ -279,7 +280,7 @@ Fixpoint betree_node_lookup_in_bindings_fwd
end
.
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
Fixpoint betree_node_lookup_first_message_for_key_fwd
(n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
result (Betree_list_t (u64 * Betree_message_t))
@@ -298,7 +299,7 @@ Fixpoint betree_node_lookup_first_message_for_key_fwd
end
.
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
Fixpoint betree_node_lookup_first_message_for_key_back
(n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
(ret : Betree_list_t (u64 * Betree_message_t)) :
@@ -321,7 +322,7 @@ Fixpoint betree_node_lookup_first_message_for_key_back
end
.
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
Fixpoint betree_node_apply_upserts_fwd
(n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
@@ -353,7 +354,7 @@ Fixpoint betree_node_apply_upserts_fwd
end
.
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
Fixpoint betree_node_apply_upserts_back
(n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
@@ -383,7 +384,7 @@ Fixpoint betree_node_apply_upserts_back
end
.
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: forward function *)
Fixpoint betree_node_lookup_fwd
(n : nat) (self : Betree_node_t) (key : u64) (st : state) :
result (state * (option u64))
@@ -455,7 +456,7 @@ Fixpoint betree_node_lookup_fwd
end
end
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
with betree_node_lookup_back
(n : nat) (self : Betree_node_t) (key : u64) (st : state) :
result Betree_node_t
@@ -524,7 +525,7 @@ with betree_node_lookup_back
end
end
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
with betree_internal_lookup_in_children_fwd
(n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
result (state * (option u64))
@@ -537,7 +538,7 @@ with betree_internal_lookup_in_children_fwd
else betree_node_lookup_fwd n0 self.(Betree_internal_right) key st
end
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
with betree_internal_lookup_in_children_back
(n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
result Betree_internal_t
@@ -557,7 +558,7 @@ with betree_internal_lookup_in_children_back
end
.
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
Fixpoint betree_node_lookup_mut_in_bindings_fwd
(n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
result (Betree_list_t (u64 * u64))
@@ -576,7 +577,7 @@ Fixpoint betree_node_lookup_mut_in_bindings_fwd
end
.
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
Fixpoint betree_node_lookup_mut_in_bindings_back
(n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64))
(ret : Betree_list_t (u64 * u64)) :
@@ -598,7 +599,8 @@ Fixpoint betree_node_lookup_mut_in_bindings_back
end
.
-(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition betree_node_apply_to_leaf_fwd_back
(n : nat) (bindings : Betree_list_t (u64 * u64)) (key : u64)
(new_msg : Betree_message_t) :
@@ -642,7 +644,8 @@ Definition betree_node_apply_to_leaf_fwd_back
end
.
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint betree_node_apply_messages_to_leaf_fwd_back
(n : nat) (bindings : Betree_list_t (u64 * u64))
(new_msgs : Betree_list_t (u64 * Betree_message_t)) :
@@ -661,7 +664,8 @@ Fixpoint betree_node_apply_messages_to_leaf_fwd_back
end
.
-(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint betree_node_filter_messages_for_key_fwd_back
(n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
result (Betree_list_t (u64 * Betree_message_t))
@@ -684,7 +688,7 @@ Fixpoint betree_node_filter_messages_for_key_fwd_back
end
.
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
Fixpoint betree_node_lookup_first_message_after_key_fwd
(n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
result (Betree_list_t (u64 * Betree_message_t))
@@ -703,7 +707,7 @@ Fixpoint betree_node_lookup_first_message_after_key_fwd
end
.
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
Fixpoint betree_node_lookup_first_message_after_key_back
(n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
(ret : Betree_list_t (u64 * Betree_message_t)) :
@@ -726,7 +730,8 @@ Fixpoint betree_node_lookup_first_message_after_key_back
end
.
-(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition betree_node_apply_to_internal_fwd_back
(n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (key : u64)
(new_msg : Betree_message_t) :
@@ -784,7 +789,8 @@ Definition betree_node_apply_to_internal_fwd_back
betree_node_lookup_first_message_for_key_back n key msgs msgs1)
.
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint betree_node_apply_messages_to_internal_fwd_back
(n : nat) (msgs : Betree_list_t (u64 * Betree_message_t))
(new_msgs : Betree_list_t (u64 * Betree_message_t)) :
@@ -803,7 +809,7 @@ Fixpoint betree_node_apply_messages_to_internal_fwd_back
end
.
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
Fixpoint betree_node_apply_messages_fwd
(n : nat) (self : Betree_node_t) (params : Betree_params_t)
(node_id_cnt : Betree_node_id_counter_t)
@@ -859,7 +865,7 @@ Fixpoint betree_node_apply_messages_fwd
end
end
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
with betree_node_apply_messages_back
(n : nat) (self : Betree_node_t) (params : Betree_params_t)
(node_id_cnt : Betree_node_id_counter_t)
@@ -915,7 +921,7 @@ with betree_node_apply_messages_back
end
end
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: forward function *)
with betree_internal_flush_fwd
(n : nat) (self : Betree_internal_t) (params : Betree_params_t)
(node_id_cnt : Betree_node_id_counter_t)
@@ -963,7 +969,7 @@ with betree_internal_flush_fwd
Return (st0, msgs_left))
end
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
with betree_internal_flush_back
(n : nat) (self : Betree_internal_t) (params : Betree_params_t)
(node_id_cnt : Betree_node_id_counter_t)
@@ -1012,7 +1018,7 @@ with betree_internal_flush_back
end
.
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: forward function *)
Definition betree_node_apply_fwd
(n : nat) (self : Betree_node_t) (params : Betree_params_t)
(node_id_cnt : Betree_node_id_counter_t) (key : u64)
@@ -1030,7 +1036,7 @@ Definition betree_node_apply_fwd
Return (st0, tt)
.
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
Definition betree_node_apply_back
(n : nat) (self : Betree_node_t) (params : Betree_params_t)
(node_id_cnt : Betree_node_id_counter_t) (key : u64)
@@ -1042,7 +1048,7 @@ Definition betree_node_apply_back
(key, new_msg) l) st
.
-(** [betree_main::betree::BeTree::{6}::new] *)
+(** [betree_main::betree::BeTree::{6}::new]: forward function *)
Definition betree_be_tree_new_fwd
(min_flush_size : u64) (split_size : u64) (st : state) :
result (state * Betree_be_tree_t)
@@ -1065,7 +1071,7 @@ Definition betree_be_tree_new_fwd
|})
.
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
Definition betree_be_tree_apply_fwd
(n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
(st : state) :
@@ -1081,7 +1087,7 @@ Definition betree_be_tree_apply_fwd
Return (st0, tt)
.
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
Definition betree_be_tree_apply_back
(n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
(st : state) :
@@ -1099,7 +1105,7 @@ Definition betree_be_tree_apply_back
|}
.
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
Definition betree_be_tree_insert_fwd
(n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result (state * unit)
@@ -1110,7 +1116,7 @@ Definition betree_be_tree_insert_fwd
Return (st0, tt)
.
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
Definition betree_be_tree_insert_back
(n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result Betree_be_tree_t
@@ -1118,7 +1124,7 @@ Definition betree_be_tree_insert_back
betree_be_tree_apply_back n self key (BetreeMessageInsert value) st
.
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
Definition betree_be_tree_delete_fwd
(n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
result (state * unit)
@@ -1129,7 +1135,7 @@ Definition betree_be_tree_delete_fwd
Return (st0, tt)
.
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
Definition betree_be_tree_delete_back
(n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
result Betree_be_tree_t
@@ -1137,7 +1143,7 @@ Definition betree_be_tree_delete_back
betree_be_tree_apply_back n self key BetreeMessageDelete st
.
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
Definition betree_be_tree_upsert_fwd
(n : nat) (self : Betree_be_tree_t) (key : u64)
(upd : Betree_upsert_fun_state_t) (st : state) :
@@ -1149,7 +1155,7 @@ Definition betree_be_tree_upsert_fwd
Return (st0, tt)
.
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
Definition betree_be_tree_upsert_back
(n : nat) (self : Betree_be_tree_t) (key : u64)
(upd : Betree_upsert_fun_state_t) (st : state) :
@@ -1158,7 +1164,7 @@ Definition betree_be_tree_upsert_back
betree_be_tree_apply_back n self key (BetreeMessageUpsert upd) st
.
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
Definition betree_be_tree_lookup_fwd
(n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
result (state * (option u64))
@@ -1166,7 +1172,7 @@ Definition betree_be_tree_lookup_fwd
betree_node_lookup_fwd n self.(Betree_be_tree_root) key st
.
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
Definition betree_be_tree_lookup_back
(n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
result Betree_be_tree_t
@@ -1180,7 +1186,7 @@ Definition betree_be_tree_lookup_back
|}
.
-(** [betree_main::main] *)
+(** [betree_main::main]: forward function *)
Definition main_fwd : result unit :=
Return tt.
diff --git a/tests/coq/betree/BetreeMain_Opaque.v b/tests/coq/betree/BetreeMain_Opaque.v
index 08ab530a..bd49500b 100644
--- a/tests/coq/betree/BetreeMain_Opaque.v
+++ b/tests/coq/betree/BetreeMain_Opaque.v
@@ -1,5 +1,5 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
Require Import Primitives.
Import Primitives.
Require Import Coq.ZArith.ZArith.
@@ -8,29 +8,29 @@ Require Export BetreeMain_Types.
Import BetreeMain_Types.
Module BetreeMain_Opaque.
-(** [betree_main::betree_utils::load_internal_node] *)
+(** [betree_main::betree_utils::load_internal_node]: forward function *)
Axiom betree_utils_load_internal_node_fwd
: u64 -> state -> result (state * (Betree_list_t (u64 * Betree_message_t)))
.
-(** [betree_main::betree_utils::store_internal_node] *)
+(** [betree_main::betree_utils::store_internal_node]: forward function *)
Axiom betree_utils_store_internal_node_fwd
:
u64 -> Betree_list_t (u64 * Betree_message_t) -> state -> result (state *
unit)
.
-(** [betree_main::betree_utils::load_leaf_node] *)
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)
Axiom betree_utils_load_leaf_node_fwd
: u64 -> state -> result (state * (Betree_list_t (u64 * u64)))
.
-(** [betree_main::betree_utils::store_leaf_node] *)
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)
Axiom betree_utils_store_leaf_node_fwd
: u64 -> Betree_list_t (u64 * u64) -> state -> result (state * unit)
.
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
Axiom core_option_option_unwrap_fwd :
forall(T : Type), option T -> state -> result (state * T)
.
diff --git a/tests/coq/betree/_CoqProject b/tests/coq/betree/_CoqProject
index e5a3f799..42c62421 100644
--- a/tests/coq/betree/_CoqProject
+++ b/tests/coq/betree/_CoqProject
@@ -3,7 +3,7 @@
-arg -w
-arg all
-Primitives.v
BetreeMain_Types.v
+Primitives.v
BetreeMain_Funs.v
BetreeMain_Opaque.v
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index 6bc82677..c8630eb6 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -8,11 +8,11 @@ Require Export Hashmap_Types.
Import Hashmap_Types.
Module Hashmap_Funs.
-(** [hashmap::hash_key] *)
+(** [hashmap::hash_key]: forward function *)
Definition hash_key_fwd (k : usize) : result usize :=
Return k.
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
Fixpoint hash_map_allocate_slots_loop_fwd
(T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
result (vec (List_t T))
@@ -29,7 +29,7 @@ Fixpoint hash_map_allocate_slots_loop_fwd
end
.
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
Definition hash_map_allocate_slots_fwd
(T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
result (vec (List_t T))
@@ -37,7 +37,7 @@ Definition hash_map_allocate_slots_fwd
hash_map_allocate_slots_loop_fwd T n slots n0
.
-(** [hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
Definition hash_map_new_with_capacity_fwd
(T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
(max_load_divisor : usize) :
@@ -56,12 +56,13 @@ Definition hash_map_new_with_capacity_fwd
|}
.
-(** [hashmap::HashMap::{0}::new] *)
+(** [hashmap::HashMap::{0}::new]: forward function *)
Definition hash_map_new_fwd (T : Type) (n : nat) : result (Hash_map_t T) :=
hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
.
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint hash_map_clear_loop_fwd_back
(T : Type) (n : nat) (slots : vec (List_t T)) (i : usize) :
result (vec (List_t T))
@@ -79,7 +80,8 @@ Fixpoint hash_map_clear_loop_fwd_back
end
.
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hash_map_clear_fwd_back
(T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
v <- hash_map_clear_loop_fwd_back T n self.(Hash_map_slots) 0%usize;
@@ -92,12 +94,12 @@ Definition hash_map_clear_fwd_back
|}
.
-(** [hashmap::HashMap::{0}::len] *)
+(** [hashmap::HashMap::{0}::len]: forward function *)
Definition hash_map_len_fwd (T : Type) (self : Hash_map_t T) : result usize :=
Return self.(Hash_map_num_entries)
.
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
Fixpoint hash_map_insert_in_list_loop_fwd
(T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
result bool
@@ -115,7 +117,7 @@ Fixpoint hash_map_insert_in_list_loop_fwd
end
.
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
Definition hash_map_insert_in_list_fwd
(T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
result bool
@@ -123,7 +125,7 @@ Definition hash_map_insert_in_list_fwd
hash_map_insert_in_list_loop_fwd T n key value ls
.
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
Fixpoint hash_map_insert_in_list_loop_back
(T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
result (List_t T)
@@ -143,7 +145,7 @@ Fixpoint hash_map_insert_in_list_loop_back
end
.
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
Definition hash_map_insert_in_list_back
(T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
result (List_t T)
@@ -151,7 +153,8 @@ Definition hash_map_insert_in_list_back
hash_map_insert_in_list_loop_back T n key value ls
.
-(** [hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hash_map_insert_no_resize_fwd_back
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
result (Hash_map_t T)
@@ -189,7 +192,8 @@ Definition hash_map_insert_no_resize_fwd_back
Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint hash_map_move_elements_from_list_loop_fwd_back
(T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
result (Hash_map_t T)
@@ -206,7 +210,8 @@ Fixpoint hash_map_move_elements_from_list_loop_fwd_back
end
.
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hash_map_move_elements_from_list_fwd_back
(T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
result (Hash_map_t T)
@@ -214,7 +219,8 @@ Definition hash_map_move_elements_from_list_fwd_back
hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
.
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint hash_map_move_elements_loop_fwd_back
(T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
(i : usize) :
@@ -237,7 +243,8 @@ Fixpoint hash_map_move_elements_loop_fwd_back
end
.
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hash_map_move_elements_fwd_back
(T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
(i : usize) :
@@ -246,7 +253,8 @@ Definition hash_map_move_elements_fwd_back
hash_map_move_elements_loop_fwd_back T n ntable slots i
.
-(** [hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hash_map_try_resize_fwd_back
(T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
@@ -278,7 +286,8 @@ Definition hash_map_try_resize_fwd_back
|}
.
-(** [hashmap::HashMap::{0}::insert] *)
+(** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hash_map_insert_fwd_back
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
result (Hash_map_t T)
@@ -290,7 +299,7 @@ Definition hash_map_insert_fwd_back
else Return self0
.
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
Fixpoint hash_map_contains_key_in_list_loop_fwd
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
match n with
@@ -306,13 +315,13 @@ Fixpoint hash_map_contains_key_in_list_loop_fwd
end
.
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
Definition hash_map_contains_key_in_list_fwd
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
hash_map_contains_key_in_list_loop_fwd T n key ls
.
-(** [hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap::HashMap::{0}::contains_key]: forward function *)
Definition hash_map_contains_key_fwd
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result bool :=
hash <- hash_key_fwd key;
@@ -322,7 +331,7 @@ Definition hash_map_contains_key_fwd
hash_map_contains_key_in_list_fwd T n key l
.
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
Fixpoint hash_map_get_in_list_loop_fwd
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
match n with
@@ -338,13 +347,13 @@ Fixpoint hash_map_get_in_list_loop_fwd
end
.
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: forward function *)
Definition hash_map_get_in_list_fwd
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
hash_map_get_in_list_loop_fwd T n key ls
.
-(** [hashmap::HashMap::{0}::get] *)
+(** [hashmap::HashMap::{0}::get]: forward function *)
Definition hash_map_get_fwd
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
hash <- hash_key_fwd key;
@@ -354,7 +363,7 @@ Definition hash_map_get_fwd
hash_map_get_in_list_fwd T n key l
.
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
Fixpoint hash_map_get_mut_in_list_loop_fwd
(T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
match n with
@@ -370,13 +379,13 @@ Fixpoint hash_map_get_mut_in_list_loop_fwd
end
.
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
Definition hash_map_get_mut_in_list_fwd
(T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
hash_map_get_mut_in_list_loop_fwd T n ls key
.
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
Fixpoint hash_map_get_mut_in_list_loop_back
(T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
result (List_t T)
@@ -396,7 +405,7 @@ Fixpoint hash_map_get_mut_in_list_loop_back
end
.
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
Definition hash_map_get_mut_in_list_back
(T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
result (List_t T)
@@ -404,7 +413,7 @@ Definition hash_map_get_mut_in_list_back
hash_map_get_mut_in_list_loop_back T n ls key ret
.
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: forward function *)
Definition hash_map_get_mut_fwd
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
hash <- hash_key_fwd key;
@@ -414,7 +423,7 @@ Definition hash_map_get_mut_fwd
hash_map_get_mut_in_list_fwd T n l key
.
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
Definition hash_map_get_mut_back
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (ret : T) :
result (Hash_map_t T)
@@ -434,7 +443,7 @@ Definition hash_map_get_mut_back
|}
.
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
Fixpoint hash_map_remove_from_list_loop_fwd
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
match n with
@@ -455,13 +464,13 @@ Fixpoint hash_map_remove_from_list_loop_fwd
end
.
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
Definition hash_map_remove_from_list_fwd
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
hash_map_remove_from_list_loop_fwd T n key ls
.
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
Fixpoint hash_map_remove_from_list_loop_back
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
match n with
@@ -484,13 +493,13 @@ Fixpoint hash_map_remove_from_list_loop_back
end
.
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
Definition hash_map_remove_from_list_back
(T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
hash_map_remove_from_list_loop_back T n key ls
.
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: forward function *)
Definition hash_map_remove_fwd
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
result (option T)
@@ -507,7 +516,7 @@ Definition hash_map_remove_fwd
end
.
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: backward function 0 *)
Definition hash_map_remove_back
(T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
result (Hash_map_t T)
@@ -542,7 +551,7 @@ Definition hash_map_remove_back
end
.
-(** [hashmap::test1] *)
+(** [hashmap::test1]: forward function *)
Definition test1_fwd (n : nat) : result unit :=
hm <- hash_map_new_fwd u64 n;
hm0 <- hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
diff --git a/tests/coq/hashmap/_CoqProject b/tests/coq/hashmap/_CoqProject
index daa9b2ba..7f80afbf 100644
--- a/tests/coq/hashmap/_CoqProject
+++ b/tests/coq/hashmap/_CoqProject
@@ -3,6 +3,6 @@
-arg -w
-arg all
-Primitives.v
Hashmap_Types.v
+Primitives.v
Hashmap_Funs.v
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index 2d1bcda6..1b7304cc 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -10,11 +10,11 @@ Require Export HashmapMain_Opaque.
Import HashmapMain_Opaque.
Module HashmapMain_Funs.
-(** [hashmap_main::hashmap::hash_key] *)
+(** [hashmap_main::hashmap::hash_key]: forward function *)
Definition hashmap_hash_key_fwd (k : usize) : result usize :=
Return k.
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
(T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
result (vec (Hashmap_list_t T))
@@ -31,7 +31,7 @@ Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
Definition hashmap_hash_map_allocate_slots_fwd
(T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
result (vec (Hashmap_list_t T))
@@ -39,7 +39,7 @@ Definition hashmap_hash_map_allocate_slots_fwd
hashmap_hash_map_allocate_slots_loop_fwd T n slots n0
.
-(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
Definition hashmap_hash_map_new_with_capacity_fwd
(T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
(max_load_divisor : usize) :
@@ -58,13 +58,14 @@ Definition hashmap_hash_map_new_with_capacity_fwd
|}
.
-(** [hashmap_main::hashmap::HashMap::{0}::new] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
Definition hashmap_hash_map_new_fwd
(T : Type) (n : nat) : result (Hashmap_hash_map_t T) :=
hashmap_hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
.
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint hashmap_hash_map_clear_loop_fwd_back
(T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (i : usize) :
result (vec (Hashmap_list_t T))
@@ -82,7 +83,8 @@ Fixpoint hashmap_hash_map_clear_loop_fwd_back
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hashmap_hash_map_clear_fwd_back
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
result (Hashmap_hash_map_t T)
@@ -100,13 +102,13 @@ Definition hashmap_hash_map_clear_fwd_back
|}
.
-(** [hashmap_main::hashmap::HashMap::{0}::len] *)
+(** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
Definition hashmap_hash_map_len_fwd
(T : Type) (self : Hashmap_hash_map_t T) : result usize :=
Return self.(Hashmap_hash_map_num_entries)
.
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
(T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
result bool
@@ -124,7 +126,7 @@ Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
Definition hashmap_hash_map_insert_in_list_fwd
(T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
result bool
@@ -132,7 +134,7 @@ Definition hashmap_hash_map_insert_in_list_fwd
hashmap_hash_map_insert_in_list_loop_fwd T n key value ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
Fixpoint hashmap_hash_map_insert_in_list_loop_back
(T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
result (Hashmap_list_t T)
@@ -153,7 +155,7 @@ Fixpoint hashmap_hash_map_insert_in_list_loop_back
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
Definition hashmap_hash_map_insert_in_list_back
(T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
result (Hashmap_list_t T)
@@ -161,7 +163,8 @@ Definition hashmap_hash_map_insert_in_list_back
hashmap_hash_map_insert_in_list_loop_back T n key value ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hashmap_hash_map_insert_no_resize_fwd_back
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
:
@@ -207,7 +210,8 @@ Definition hashmap_hash_map_insert_no_resize_fwd_back
Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
(T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
:
@@ -225,7 +229,8 @@ Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hashmap_hash_map_move_elements_from_list_fwd_back
(T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
:
@@ -234,7 +239,8 @@ Definition hashmap_hash_map_move_elements_from_list_fwd_back
hashmap_hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
(T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
(slots : vec (Hashmap_list_t T)) (i : usize) :
@@ -258,7 +264,8 @@ Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hashmap_hash_map_move_elements_fwd_back
(T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
(slots : vec (Hashmap_list_t T)) (i : usize) :
@@ -267,7 +274,8 @@ Definition hashmap_hash_map_move_elements_fwd_back
hashmap_hash_map_move_elements_loop_fwd_back T n ntable slots i
.
-(** [hashmap_main::hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hashmap_hash_map_try_resize_fwd_back
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
result (Hashmap_hash_map_t T)
@@ -302,7 +310,8 @@ Definition hashmap_hash_map_try_resize_fwd_back
|}
.
-(** [hashmap_main::hashmap::HashMap::{0}::insert] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition hashmap_hash_map_insert_fwd_back
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
:
@@ -315,7 +324,7 @@ Definition hashmap_hash_map_insert_fwd_back
else Return self0
.
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
match n with
@@ -331,13 +340,13 @@ Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
Definition hashmap_hash_map_contains_key_in_list_fwd
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
hashmap_hash_map_contains_key_in_list_loop_fwd T n key ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
Definition hashmap_hash_map_contains_key_fwd
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
result bool
@@ -349,7 +358,7 @@ Definition hashmap_hash_map_contains_key_fwd
hashmap_hash_map_contains_key_in_list_fwd T n key l
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
Fixpoint hashmap_hash_map_get_in_list_loop_fwd
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
match n with
@@ -365,13 +374,13 @@ Fixpoint hashmap_hash_map_get_in_list_loop_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
Definition hashmap_hash_map_get_in_list_fwd
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
hashmap_hash_map_get_in_list_loop_fwd T n key ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::get] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
Definition hashmap_hash_map_get_fwd
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
result T
@@ -383,7 +392,7 @@ Definition hashmap_hash_map_get_fwd
hashmap_hash_map_get_in_list_fwd T n key l
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
(T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
match n with
@@ -399,13 +408,13 @@ Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
Definition hashmap_hash_map_get_mut_in_list_fwd
(T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
hashmap_hash_map_get_mut_in_list_loop_fwd T n ls key
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
(T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
result (Hashmap_list_t T)
@@ -425,7 +434,7 @@ Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
Definition hashmap_hash_map_get_mut_in_list_back
(T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
result (Hashmap_list_t T)
@@ -433,7 +442,7 @@ Definition hashmap_hash_map_get_mut_in_list_back
hashmap_hash_map_get_mut_in_list_loop_back T n ls key ret
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
Definition hashmap_hash_map_get_mut_fwd
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
result T
@@ -446,7 +455,7 @@ Definition hashmap_hash_map_get_mut_fwd
hashmap_hash_map_get_mut_in_list_fwd T n l key
.
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
Definition hashmap_hash_map_get_mut_back
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (ret : T) :
result (Hashmap_hash_map_t T)
@@ -470,7 +479,7 @@ Definition hashmap_hash_map_get_mut_back
|}
.
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
result (option T)
@@ -495,7 +504,7 @@ Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
Definition hashmap_hash_map_remove_from_list_fwd
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
result (option T)
@@ -503,7 +512,7 @@ Definition hashmap_hash_map_remove_from_list_fwd
hashmap_hash_map_remove_from_list_loop_fwd T n key ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
Fixpoint hashmap_hash_map_remove_from_list_loop_back
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
result (Hashmap_list_t T)
@@ -530,7 +539,7 @@ Fixpoint hashmap_hash_map_remove_from_list_loop_back
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
Definition hashmap_hash_map_remove_from_list_back
(T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
result (Hashmap_list_t T)
@@ -538,7 +547,7 @@ Definition hashmap_hash_map_remove_from_list_back
hashmap_hash_map_remove_from_list_loop_back T n key ls
.
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
Definition hashmap_hash_map_remove_fwd
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
result (option T)
@@ -557,7 +566,7 @@ Definition hashmap_hash_map_remove_fwd
end
.
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
Definition hashmap_hash_map_remove_back
(T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
result (Hashmap_hash_map_t T)
@@ -599,7 +608,7 @@ Definition hashmap_hash_map_remove_back
end
.
-(** [hashmap_main::hashmap::test1] *)
+(** [hashmap_main::hashmap::test1]: forward function *)
Definition hashmap_test1_fwd (n : nat) : result unit :=
hm <- hashmap_hash_map_new_fwd u64 n;
hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
@@ -636,7 +645,7 @@ Definition hashmap_test1_fwd (n : nat) : result unit :=
end))
.
-(** [hashmap_main::insert_on_disk] *)
+(** [hashmap_main::insert_on_disk]: forward function *)
Definition insert_on_disk_fwd
(n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
p <- hashmap_utils_deserialize_fwd st;
@@ -647,7 +656,7 @@ Definition insert_on_disk_fwd
Return (st1, tt)
.
-(** [hashmap_main::main] *)
+(** [hashmap_main::main]: forward function *)
Definition main_fwd : result unit :=
Return tt.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
index 6152b94b..1ad9c697 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
@@ -1,5 +1,5 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
Require Import Primitives.
Import Primitives.
Require Import Coq.ZArith.ZArith.
@@ -8,12 +8,12 @@ Require Export HashmapMain_Types.
Import HashmapMain_Types.
Module HashmapMain_Opaque.
-(** [hashmap_main::hashmap_utils::deserialize] *)
+(** [hashmap_main::hashmap_utils::deserialize]: forward function *)
Axiom hashmap_utils_deserialize_fwd
: state -> result (state * (Hashmap_hash_map_t u64))
.
-(** [hashmap_main::hashmap_utils::serialize] *)
+(** [hashmap_main::hashmap_utils::serialize]: forward function *)
Axiom hashmap_utils_serialize_fwd
: Hashmap_hash_map_t u64 -> state -> result (state * unit)
.
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index 6a5f2696..14c05c61 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -22,7 +22,7 @@ Definition x1_c : u32 := x1_body%global.
Definition x2_body : result u32 := Return 3%u32.
Definition x2_c : u32 := x2_body%global.
-(** [constants::incr] *)
+(** [constants::incr]: forward function *)
Definition incr_fwd (n : u32) : result u32 :=
u32_add n 1%u32.
@@ -30,7 +30,7 @@ Definition incr_fwd (n : u32) : result u32 :=
Definition x3_body : result u32 := incr_fwd 32%u32.
Definition x3_c : u32 := x3_body%global.
-(** [constants::mk_pair0] *)
+(** [constants::mk_pair0]: forward function *)
Definition mk_pair0_fwd (x : u32) (y : u32) : result (u32 * u32) :=
Return (x, y)
.
@@ -42,7 +42,7 @@ Arguments mkPair_t {T1} {T2} _ _.
Arguments Pair_x {T1} {T2}.
Arguments Pair_y {T1} {T2}.
-(** [constants::mk_pair1] *)
+(** [constants::mk_pair1]: forward function *)
Definition mk_pair1_fwd (x : u32) (y : u32) : result (Pair_t u32 u32) :=
Return {| Pair_x := x; Pair_y := y |}
.
@@ -71,7 +71,7 @@ Record Wrap_t (T : Type) := mkWrap_t { Wrap_val : T; }.
Arguments mkWrap_t {T} _.
Arguments Wrap_val {T}.
-(** [constants::Wrap::{0}::new] *)
+(** [constants::Wrap::{0}::new]: forward function *)
Definition wrap_new_fwd (T : Type) (val : T) : result (Wrap_t T) :=
Return {| Wrap_val := val |}
.
@@ -80,7 +80,7 @@ Definition wrap_new_fwd (T : Type) (val : T) : result (Wrap_t T) :=
Definition y_body : result (Wrap_t i32) := wrap_new_fwd i32 2%i32.
Definition y_c : Wrap_t i32 := y_body%global.
-(** [constants::unwrap_y] *)
+(** [constants::unwrap_y]: forward function *)
Definition unwrap_y_fwd : result i32 :=
Return y_c.(Wrap_val).
@@ -92,11 +92,11 @@ Definition yval_c : i32 := yval_body%global.
Definition get_z1_z1_body : result i32 := Return 3%i32.
Definition get_z1_z1_c : i32 := get_z1_z1_body%global.
-(** [constants::get_z1] *)
+(** [constants::get_z1]: forward function *)
Definition get_z1_fwd : result i32 :=
Return get_z1_z1_c.
-(** [constants::add] *)
+(** [constants::add]: forward function *)
Definition add_fwd (a : i32) (b : i32) : result i32 :=
i32_add a b.
@@ -112,7 +112,7 @@ Definition q2_c : i32 := q2_body%global.
Definition q3_body : result i32 := add_fwd q2_c 3%i32.
Definition q3_c : i32 := q3_body%global.
-(** [constants::get_z2] *)
+(** [constants::get_z2]: forward function *)
Definition get_z2_fwd : result i32 :=
i <- get_z1_fwd; i0 <- add_fwd i q3_c; add_fwd q1_c i0
.
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index 05dd8f2e..f18bbd1f 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -10,7 +10,7 @@ Require Export External_Opaque.
Import External_Opaque.
Module External_Funs.
-(** [external::swap] *)
+(** [external::swap]: forward function *)
Definition swap_fwd
(T : Type) (x : T) (y : T) (st : state) : result (state * unit) :=
p <- core_mem_swap_fwd T x y st;
@@ -22,7 +22,7 @@ Definition swap_fwd
Return (st2, tt)
.
-(** [external::swap] *)
+(** [external::swap]: backward function 0 *)
Definition swap_back
(T : Type) (x : T) (y : T) (st : state) (st0 : state) :
result (state * (T * T))
@@ -36,7 +36,7 @@ Definition swap_back
Return (st0, (x0, y0))
.
-(** [external::test_new_non_zero_u32] *)
+(** [external::test_new_non_zero_u32]: forward function *)
Definition test_new_non_zero_u32_fwd
(x : u32) (st : state) : result (state * Core_num_nonzero_non_zero_u32_t) :=
p <- core_num_nonzero_non_zero_u32_new_fwd x st;
@@ -44,7 +44,7 @@ Definition test_new_non_zero_u32_fwd
core_option_option_unwrap_fwd Core_num_nonzero_non_zero_u32_t opt st0
.
-(** [external::test_vec] *)
+(** [external::test_vec]: forward function *)
Definition test_vec_fwd : result unit :=
let v := vec_new u32 in _ <- vec_push_back u32 v 0%u32; Return tt
.
@@ -52,7 +52,7 @@ Definition test_vec_fwd : result unit :=
(** Unit test for [external::test_vec] *)
Check (test_vec_fwd )%return.
-(** [external::custom_swap] *)
+(** [external::custom_swap]: forward function *)
Definition custom_swap_fwd
(T : Type) (x : T) (y : T) (st : state) : result (state * T) :=
p <- core_mem_swap_fwd T x y st;
@@ -64,7 +64,7 @@ Definition custom_swap_fwd
Return (st2, x0)
.
-(** [external::custom_swap] *)
+(** [external::custom_swap]: backward function 0 *)
Definition custom_swap_back
(T : Type) (x : T) (y : T) (st : state) (ret : T) (st0 : state) :
result (state * (T * T))
@@ -78,13 +78,13 @@ Definition custom_swap_back
Return (st0, (ret, y0))
.
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: forward function *)
Definition test_custom_swap_fwd
(x : u32) (y : u32) (st : state) : result (state * unit) :=
p <- custom_swap_fwd u32 x y st; let (st0, _) := p in Return (st0, tt)
.
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: backward function 0 *)
Definition test_custom_swap_back
(x : u32) (y : u32) (st : state) (st0 : state) :
result (state * (u32 * u32))
@@ -92,7 +92,7 @@ Definition test_custom_swap_back
custom_swap_back u32 x y st 1%u32 st0
.
-(** [external::test_swap_non_zero] *)
+(** [external::test_swap_non_zero]: forward function *)
Definition test_swap_non_zero_fwd
(x : u32) (st : state) : result (state * u32) :=
p <- swap_fwd u32 x 0%u32 st;
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
index d60251e0..1224f426 100644
--- a/tests/coq/misc/External_Opaque.v
+++ b/tests/coq/misc/External_Opaque.v
@@ -1,5 +1,5 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
Require Import Primitives.
Import Primitives.
Require Import Coq.ZArith.ZArith.
@@ -8,27 +8,27 @@ Require Export External_Types.
Import External_Types.
Module External_Opaque.
-(** [core::mem::swap] *)
+(** [core::mem::swap]: forward function *)
Axiom core_mem_swap_fwd :
forall(T : Type), T -> T -> state -> result (state * unit)
.
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 0 *)
Axiom core_mem_swap_back0 :
forall(T : Type), T -> T -> state -> state -> result (state * T)
.
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 1 *)
Axiom core_mem_swap_back1 :
forall(T : Type), T -> T -> state -> state -> result (state * T)
.
-(** [core::num::nonzero::NonZeroU32::{14}::new] *)
+(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
Axiom core_num_nonzero_non_zero_u32_new_fwd
: u32 -> state -> result (state * (option Core_num_nonzero_non_zero_u32_t))
.
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
Axiom core_option_option_unwrap_fwd :
forall(T : Type), option T -> state -> result (state * T)
.
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index a5cb3688..f17eb986 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -6,7 +6,7 @@ Require Import Coq.ZArith.ZArith.
Local Open Scope Primitives_scope.
Module Loops.
-(** [loops::sum] *)
+(** [loops::sum]: loop 0: forward function *)
Fixpoint sum_loop_fwd (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
match n with
| O => Fail_ OutOfFuel
@@ -17,12 +17,12 @@ Fixpoint sum_loop_fwd (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
end
.
-(** [loops::sum] *)
+(** [loops::sum]: forward function *)
Definition sum_fwd (n : nat) (max : u32) : result u32 :=
sum_loop_fwd n max 0%u32 0%u32
.
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
Fixpoint sum_with_mut_borrows_loop_fwd
(n : nat) (max : u32) (mi : u32) (ms : u32) : result u32 :=
match n with
@@ -37,12 +37,12 @@ Fixpoint sum_with_mut_borrows_loop_fwd
end
.
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: forward function *)
Definition sum_with_mut_borrows_fwd (n : nat) (max : u32) : result u32 :=
sum_with_mut_borrows_loop_fwd n max 0%u32 0%u32
.
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
Fixpoint sum_with_shared_borrows_loop_fwd
(n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
match n with
@@ -57,12 +57,13 @@ Fixpoint sum_with_shared_borrows_loop_fwd
end
.
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: forward function *)
Definition sum_with_shared_borrows_fwd (n : nat) (max : u32) : result u32 :=
sum_with_shared_borrows_loop_fwd n max 0%u32 0%u32
.
-(** [loops::clear] *)
+(** [loops::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Fixpoint clear_loop_fwd_back
(n : nat) (v : vec u32) (i : usize) : result (vec u32) :=
match n with
@@ -78,7 +79,8 @@ Fixpoint clear_loop_fwd_back
end
.
-(** [loops::clear] *)
+(** [loops::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition clear_fwd_back (n : nat) (v : vec u32) : result (vec u32) :=
clear_loop_fwd_back n v 0%usize
.
@@ -92,7 +94,7 @@ Inductive List_t (T : Type) :=
Arguments ListCons {T} _ _.
Arguments ListNil {T}.
-(** [loops::list_mem] *)
+(** [loops::list_mem]: loop 0: forward function *)
Fixpoint list_mem_loop_fwd
(n : nat) (x : u32) (ls : List_t u32) : result bool :=
match n with
@@ -106,12 +108,12 @@ Fixpoint list_mem_loop_fwd
end
.
-(** [loops::list_mem] *)
+(** [loops::list_mem]: forward function *)
Definition list_mem_fwd (n : nat) (x : u32) (ls : List_t u32) : result bool :=
list_mem_loop_fwd n x ls
.
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: forward function *)
Fixpoint list_nth_mut_loop_loop_fwd
(T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
match n with
@@ -127,13 +129,13 @@ Fixpoint list_nth_mut_loop_loop_fwd
end
.
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: forward function *)
Definition list_nth_mut_loop_fwd
(T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
list_nth_mut_loop_loop_fwd T n ls i
.
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
Fixpoint list_nth_mut_loop_loop_back
(T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -154,7 +156,7 @@ Fixpoint list_nth_mut_loop_loop_back
end
.
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: backward function 0 *)
Definition list_nth_mut_loop_back
(T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -162,7 +164,7 @@ Definition list_nth_mut_loop_back
list_nth_mut_loop_loop_back T n ls i ret
.
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: loop 0: forward function *)
Fixpoint list_nth_shared_loop_loop_fwd
(T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
match n with
@@ -178,13 +180,13 @@ Fixpoint list_nth_shared_loop_loop_fwd
end
.
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: forward function *)
Definition list_nth_shared_loop_fwd
(T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
list_nth_shared_loop_loop_fwd T n ls i
.
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: forward function *)
Fixpoint get_elem_mut_loop_fwd
(n : nat) (x : usize) (ls : List_t usize) : result usize :=
match n with
@@ -198,14 +200,14 @@ Fixpoint get_elem_mut_loop_fwd
end
.
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: forward function *)
Definition get_elem_mut_fwd
(n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
l <- vec_index_mut_fwd (List_t usize) slots 0%usize;
get_elem_mut_loop_fwd n x l
.
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: backward function 0 *)
Fixpoint get_elem_mut_loop_back
(n : nat) (x : usize) (ls : List_t usize) (ret : usize) :
result (List_t usize)
@@ -223,7 +225,7 @@ Fixpoint get_elem_mut_loop_back
end
.
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: backward function 0 *)
Definition get_elem_mut_back
(n : nat) (slots : vec (List_t usize)) (x : usize) (ret : usize) :
result (vec (List_t usize))
@@ -233,7 +235,7 @@ Definition get_elem_mut_back
vec_index_mut_back (List_t usize) slots 0%usize l0
.
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: loop 0: forward function *)
Fixpoint get_elem_shared_loop_fwd
(n : nat) (x : usize) (ls : List_t usize) : result usize :=
match n with
@@ -247,30 +249,30 @@ Fixpoint get_elem_shared_loop_fwd
end
.
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: forward function *)
Definition get_elem_shared_fwd
(n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
l <- vec_index_fwd (List_t usize) slots 0%usize;
get_elem_shared_loop_fwd n x l
.
-(** [loops::id_mut] *)
+(** [loops::id_mut]: forward function *)
Definition id_mut_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
Return ls
.
-(** [loops::id_mut] *)
+(** [loops::id_mut]: backward function 0 *)
Definition id_mut_back
(T : Type) (ls : List_t T) (ret : List_t T) : result (List_t T) :=
Return ret
.
-(** [loops::id_shared] *)
+(** [loops::id_shared]: forward function *)
Definition id_shared_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
Return ls
.
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
Fixpoint list_nth_mut_loop_with_id_loop_fwd
(T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
match n with
@@ -287,13 +289,13 @@ Fixpoint list_nth_mut_loop_with_id_loop_fwd
end
.
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: forward function *)
Definition list_nth_mut_loop_with_id_fwd
(T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
ls0 <- id_mut_fwd T ls; list_nth_mut_loop_with_id_loop_fwd T n i ls0
.
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
Fixpoint list_nth_mut_loop_with_id_loop_back
(T : Type) (n : nat) (i : u32) (ls : List_t T) (ret : T) :
result (List_t T)
@@ -314,7 +316,7 @@ Fixpoint list_nth_mut_loop_with_id_loop_back
end
.
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
Definition list_nth_mut_loop_with_id_back
(T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -324,7 +326,7 @@ Definition list_nth_mut_loop_with_id_back
id_mut_back T ls l
.
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
Fixpoint list_nth_shared_loop_with_id_loop_fwd
(T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
match n with
@@ -341,13 +343,13 @@ Fixpoint list_nth_shared_loop_with_id_loop_fwd
end
.
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: forward function *)
Definition list_nth_shared_loop_with_id_fwd
(T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
ls0 <- id_shared_fwd T ls; list_nth_shared_loop_with_id_loop_fwd T n i ls0
.
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
Fixpoint list_nth_mut_loop_pair_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -371,7 +373,7 @@ Fixpoint list_nth_mut_loop_pair_loop_fwd
end
.
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: forward function *)
Definition list_nth_mut_loop_pair_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -379,7 +381,7 @@ Definition list_nth_mut_loop_pair_fwd
list_nth_mut_loop_pair_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
Fixpoint list_nth_mut_loop_pair_loop_back'a
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -404,7 +406,7 @@ Fixpoint list_nth_mut_loop_pair_loop_back'a
end
.
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
Definition list_nth_mut_loop_pair_back'a
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -412,7 +414,7 @@ Definition list_nth_mut_loop_pair_back'a
list_nth_mut_loop_pair_loop_back'a T n ls0 ls1 i ret
.
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
Fixpoint list_nth_mut_loop_pair_loop_back'b
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -437,7 +439,7 @@ Fixpoint list_nth_mut_loop_pair_loop_back'b
end
.
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
Definition list_nth_mut_loop_pair_back'b
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -445,7 +447,7 @@ Definition list_nth_mut_loop_pair_back'b
list_nth_mut_loop_pair_loop_back'b T n ls0 ls1 i ret
.
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
Fixpoint list_nth_shared_loop_pair_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -469,7 +471,7 @@ Fixpoint list_nth_shared_loop_pair_loop_fwd
end
.
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: forward function *)
Definition list_nth_shared_loop_pair_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -477,7 +479,7 @@ Definition list_nth_shared_loop_pair_fwd
list_nth_shared_loop_pair_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -501,7 +503,7 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
end
.
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
Definition list_nth_mut_loop_pair_merge_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -509,7 +511,7 @@ Definition list_nth_mut_loop_pair_merge_fwd
list_nth_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
Fixpoint list_nth_mut_loop_pair_merge_loop_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
(ret : (T * T)) :
@@ -536,7 +538,7 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_back
end
.
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
Definition list_nth_mut_loop_pair_merge_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
(ret : (T * T)) :
@@ -545,7 +547,7 @@ Definition list_nth_mut_loop_pair_merge_back
list_nth_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
.
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -569,7 +571,7 @@ Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
end
.
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
Definition list_nth_shared_loop_pair_merge_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -577,7 +579,7 @@ Definition list_nth_shared_loop_pair_merge_fwd
list_nth_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -601,7 +603,7 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
end
.
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
Definition list_nth_mut_shared_loop_pair_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -609,7 +611,7 @@ Definition list_nth_mut_shared_loop_pair_fwd
list_nth_mut_shared_loop_pair_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
Fixpoint list_nth_mut_shared_loop_pair_loop_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -634,7 +636,7 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_back
end
.
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
Definition list_nth_mut_shared_loop_pair_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -642,7 +644,7 @@ Definition list_nth_mut_shared_loop_pair_back
list_nth_mut_shared_loop_pair_loop_back T n ls0 ls1 i ret
.
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -666,7 +668,7 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
end
.
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
Definition list_nth_mut_shared_loop_pair_merge_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -674,7 +676,7 @@ Definition list_nth_mut_shared_loop_pair_merge_fwd
list_nth_mut_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -700,7 +702,7 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
end
.
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
Definition list_nth_mut_shared_loop_pair_merge_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -708,7 +710,7 @@ Definition list_nth_mut_shared_loop_pair_merge_back
list_nth_mut_shared_loop_pair_merge_loop_back T n ls0 ls1 i ret
.
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -732,7 +734,7 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
end
.
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
Definition list_nth_shared_mut_loop_pair_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -740,7 +742,7 @@ Definition list_nth_shared_mut_loop_pair_fwd
list_nth_shared_mut_loop_pair_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
Fixpoint list_nth_shared_mut_loop_pair_loop_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -765,7 +767,7 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_back
end
.
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
Definition list_nth_shared_mut_loop_pair_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -773,7 +775,7 @@ Definition list_nth_shared_mut_loop_pair_back
list_nth_shared_mut_loop_pair_loop_back T n ls0 ls1 i ret
.
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -797,7 +799,7 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
end
.
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
Definition list_nth_shared_mut_loop_pair_merge_fwd
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
result (T * T)
@@ -805,7 +807,7 @@ Definition list_nth_shared_mut_loop_pair_merge_fwd
list_nth_shared_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
.
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
@@ -831,7 +833,7 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
end
.
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
Definition list_nth_shared_mut_loop_pair_merge_back
(T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
result (List_t T)
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index 96d62711..470a2cde 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -45,47 +45,47 @@ Inductive Sum_t (T1 T2 : Type) :=
Arguments SumLeft {T1} {T2} _.
Arguments SumRight {T1} {T2} _.
-(** [no_nested_borrows::neg_test] *)
+(** [no_nested_borrows::neg_test]: forward function *)
Definition neg_test_fwd (x : i32) : result i32 :=
i32_neg x.
-(** [no_nested_borrows::add_test] *)
+(** [no_nested_borrows::add_test]: forward function *)
Definition add_test_fwd (x : u32) (y : u32) : result u32 :=
u32_add x y.
-(** [no_nested_borrows::subs_test] *)
+(** [no_nested_borrows::subs_test]: forward function *)
Definition subs_test_fwd (x : u32) (y : u32) : result u32 :=
u32_sub x y.
-(** [no_nested_borrows::div_test] *)
+(** [no_nested_borrows::div_test]: forward function *)
Definition div_test_fwd (x : u32) (y : u32) : result u32 :=
u32_div x y.
-(** [no_nested_borrows::div_test1] *)
+(** [no_nested_borrows::div_test1]: forward function *)
Definition div_test1_fwd (x : u32) : result u32 :=
u32_div x 2%u32.
-(** [no_nested_borrows::rem_test] *)
+(** [no_nested_borrows::rem_test]: forward function *)
Definition rem_test_fwd (x : u32) (y : u32) : result u32 :=
u32_rem x y.
-(** [no_nested_borrows::cast_test] *)
+(** [no_nested_borrows::cast_test]: forward function *)
Definition cast_test_fwd (x : u32) : result i32 :=
scalar_cast U32 I32 x.
-(** [no_nested_borrows::test2] *)
+(** [no_nested_borrows::test2]: forward function *)
Definition test2_fwd : result unit :=
_ <- u32_add 23%u32 44%u32; Return tt.
(** Unit test for [no_nested_borrows::test2] *)
Check (test2_fwd )%return.
-(** [no_nested_borrows::get_max] *)
+(** [no_nested_borrows::get_max]: forward function *)
Definition get_max_fwd (x : u32) (y : u32) : result u32 :=
if x s>= y then Return x else Return y
.
-(** [no_nested_borrows::test3] *)
+(** [no_nested_borrows::test3]: forward function *)
Definition test3_fwd : result unit :=
x <- get_max_fwd 4%u32 3%u32;
y <- get_max_fwd 10%u32 11%u32;
@@ -96,7 +96,7 @@ Definition test3_fwd : result unit :=
(** Unit test for [no_nested_borrows::test3] *)
Check (test3_fwd )%return.
-(** [no_nested_borrows::test_neg1] *)
+(** [no_nested_borrows::test_neg1]: forward function *)
Definition test_neg1_fwd : result unit :=
y <- i32_neg 3%i32; if negb (y s= (-3)%i32) then Fail_ Failure else Return tt
.
@@ -104,7 +104,7 @@ Definition test_neg1_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_neg1] *)
Check (test_neg1_fwd )%return.
-(** [no_nested_borrows::refs_test1] *)
+(** [no_nested_borrows::refs_test1]: forward function *)
Definition refs_test1_fwd : result unit :=
if negb (1%i32 s= 1%i32) then Fail_ Failure else Return tt
.
@@ -112,7 +112,7 @@ Definition refs_test1_fwd : result unit :=
(** Unit test for [no_nested_borrows::refs_test1] *)
Check (refs_test1_fwd )%return.
-(** [no_nested_borrows::refs_test2] *)
+(** [no_nested_borrows::refs_test2]: forward function *)
Definition refs_test2_fwd : result unit :=
if negb (2%i32 s= 2%i32)
then Fail_ Failure
@@ -128,14 +128,14 @@ Definition refs_test2_fwd : result unit :=
(** Unit test for [no_nested_borrows::refs_test2] *)
Check (refs_test2_fwd )%return.
-(** [no_nested_borrows::test_list1] *)
+(** [no_nested_borrows::test_list1]: forward function *)
Definition test_list1_fwd : result unit :=
Return tt.
(** Unit test for [no_nested_borrows::test_list1] *)
Check (test_list1_fwd )%return.
-(** [no_nested_borrows::test_box1] *)
+(** [no_nested_borrows::test_box1]: forward function *)
Definition test_box1_fwd : result unit :=
let b := 1%i32 in
let x := b in
@@ -145,21 +145,21 @@ Definition test_box1_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_box1] *)
Check (test_box1_fwd )%return.
-(** [no_nested_borrows::copy_int] *)
+(** [no_nested_borrows::copy_int]: forward function *)
Definition copy_int_fwd (x : i32) : result i32 :=
Return x.
-(** [no_nested_borrows::test_unreachable] *)
+(** [no_nested_borrows::test_unreachable]: forward function *)
Definition test_unreachable_fwd (b : bool) : result unit :=
if b then Fail_ Failure else Return tt
.
-(** [no_nested_borrows::test_panic] *)
+(** [no_nested_borrows::test_panic]: forward function *)
Definition test_panic_fwd (b : bool) : result unit :=
if b then Fail_ Failure else Return tt
.
-(** [no_nested_borrows::test_copy_int] *)
+(** [no_nested_borrows::test_copy_int]: forward function *)
Definition test_copy_int_fwd : result unit :=
y <- copy_int_fwd 0%i32;
if negb (0%i32 s= y) then Fail_ Failure else Return tt
@@ -168,12 +168,12 @@ Definition test_copy_int_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_copy_int] *)
Check (test_copy_int_fwd )%return.
-(** [no_nested_borrows::is_cons] *)
+(** [no_nested_borrows::is_cons]: forward function *)
Definition is_cons_fwd (T : Type) (l : List_t T) : result bool :=
match l with | ListCons t l0 => Return true | ListNil => Return false end
.
-(** [no_nested_borrows::test_is_cons] *)
+(** [no_nested_borrows::test_is_cons]: forward function *)
Definition test_is_cons_fwd : result unit :=
let l := ListNil in
b <- is_cons_fwd i32 (ListCons 0%i32 l);
@@ -183,7 +183,7 @@ Definition test_is_cons_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_is_cons] *)
Check (test_is_cons_fwd )%return.
-(** [no_nested_borrows::split_list] *)
+(** [no_nested_borrows::split_list]: forward function *)
Definition split_list_fwd
(T : Type) (l : List_t T) : result (T * (List_t T)) :=
match l with
@@ -192,7 +192,7 @@ Definition split_list_fwd
end
.
-(** [no_nested_borrows::test_split_list] *)
+(** [no_nested_borrows::test_split_list]: forward function *)
Definition test_split_list_fwd : result unit :=
let l := ListNil in
p <- split_list_fwd i32 (ListCons 0%i32 l);
@@ -203,18 +203,18 @@ Definition test_split_list_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_split_list] *)
Check (test_split_list_fwd )%return.
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: forward function *)
Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
if b then Return x else Return y
.
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: backward function 0 *)
Definition choose_back
(T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
if b then Return (ret, y) else Return (x, ret)
.
-(** [no_nested_borrows::choose_test] *)
+(** [no_nested_borrows::choose_test]: forward function *)
Definition choose_test_fwd : result unit :=
z <- choose_fwd i32 true 0%i32 0%i32;
z0 <- i32_add z 1%i32;
@@ -231,7 +231,7 @@ Definition choose_test_fwd : result unit :=
(** Unit test for [no_nested_borrows::choose_test] *)
Check (choose_test_fwd )%return.
-(** [no_nested_borrows::test_char] *)
+(** [no_nested_borrows::test_char]: forward function *)
Definition test_char_fwd : result char :=
Return (char_of_byte Coq.Init.Byte.x61)
.
@@ -253,7 +253,7 @@ Arguments NodeElemNil {T}.
Arguments TreeLeaf {T} _.
Arguments TreeNode {T} _ _ _.
-(** [no_nested_borrows::list_length] *)
+(** [no_nested_borrows::list_length]: forward function *)
Fixpoint list_length_fwd (T : Type) (l : List_t T) : result u32 :=
match l with
| ListCons t l1 => i <- list_length_fwd T l1; u32_add 1%u32 i
@@ -261,7 +261,7 @@ Fixpoint list_length_fwd (T : Type) (l : List_t T) : result u32 :=
end
.
-(** [no_nested_borrows::list_nth_shared] *)
+(** [no_nested_borrows::list_nth_shared]: forward function *)
Fixpoint list_nth_shared_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
match l with
| ListCons x tl =>
@@ -272,7 +272,7 @@ Fixpoint list_nth_shared_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
end
.
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: forward function *)
Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
match l with
| ListCons x tl =>
@@ -283,7 +283,7 @@ Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
end
.
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: backward function 0 *)
Fixpoint list_nth_mut_back
(T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
match l with
@@ -298,7 +298,7 @@ Fixpoint list_nth_mut_back
end
.
-(** [no_nested_borrows::list_rev_aux] *)
+(** [no_nested_borrows::list_rev_aux]: forward function *)
Fixpoint list_rev_aux_fwd
(T : Type) (li : List_t T) (lo : List_t T) : result (List_t T) :=
match li with
@@ -307,13 +307,14 @@ Fixpoint list_rev_aux_fwd
end
.
-(** [no_nested_borrows::list_rev] *)
+(** [no_nested_borrows::list_rev]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition list_rev_fwd_back (T : Type) (l : List_t T) : result (List_t T) :=
let li := mem_replace_fwd (List_t T) l ListNil in
list_rev_aux_fwd T li ListNil
.
-(** [no_nested_borrows::test_list_functions] *)
+(** [no_nested_borrows::test_list_functions]: forward function *)
Definition test_list_functions_fwd : result unit :=
let l := ListNil in
let l0 := ListCons 2%i32 l in
@@ -350,61 +351,61 @@ Definition test_list_functions_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_list_functions] *)
Check (test_list_functions_fwd )%return.
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: forward function *)
Definition id_mut_pair1_fwd
(T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
Return (x, y)
.
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
Definition id_mut_pair1_back
(T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 * T2)) : result (T1 * T2) :=
let (t, t0) := ret in Return (t, t0)
.
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: forward function *)
Definition id_mut_pair2_fwd
(T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
let (t, t0) := p in Return (t, t0)
.
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
Definition id_mut_pair2_back
(T1 T2 : Type) (p : (T1 * T2)) (ret : (T1 * T2)) : result (T1 * T2) :=
let (t, t0) := ret in Return (t, t0)
.
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: forward function *)
Definition id_mut_pair3_fwd
(T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
Return (x, y)
.
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
Definition id_mut_pair3_back'a
(T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : result T1 :=
Return ret
.
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
Definition id_mut_pair3_back'b
(T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : result T2 :=
Return ret
.
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: forward function *)
Definition id_mut_pair4_fwd
(T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
let (t, t0) := p in Return (t, t0)
.
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
Definition id_mut_pair4_back'a
(T1 T2 : Type) (p : (T1 * T2)) (ret : T1) : result T1 :=
Return ret
.
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
Definition id_mut_pair4_back'b
(T1 T2 : Type) (p : (T1 * T2)) (ret : T2) : result T2 :=
Return ret
@@ -420,17 +421,17 @@ mkStruct_with_tuple_t {
Arguments mkStruct_with_tuple_t {T1} {T2} _.
Arguments Struct_with_tuple_p {T1} {T2}.
-(** [no_nested_borrows::new_tuple1] *)
+(** [no_nested_borrows::new_tuple1]: forward function *)
Definition new_tuple1_fwd : result (Struct_with_tuple_t u32 u32) :=
Return {| Struct_with_tuple_p := (1%u32, 2%u32) |}
.
-(** [no_nested_borrows::new_tuple2] *)
+(** [no_nested_borrows::new_tuple2]: forward function *)
Definition new_tuple2_fwd : result (Struct_with_tuple_t i16 i16) :=
Return {| Struct_with_tuple_p := (1%i16, 2%i16) |}
.
-(** [no_nested_borrows::new_tuple3] *)
+(** [no_nested_borrows::new_tuple3]: forward function *)
Definition new_tuple3_fwd : result (Struct_with_tuple_t u64 i64) :=
Return {| Struct_with_tuple_p := (1%u64, 2%i64) |}
.
@@ -445,12 +446,12 @@ mkStruct_with_pair_t {
Arguments mkStruct_with_pair_t {T1} {T2} _.
Arguments Struct_with_pair_p {T1} {T2}.
-(** [no_nested_borrows::new_pair1] *)
+(** [no_nested_borrows::new_pair1]: forward function *)
Definition new_pair1_fwd : result (Struct_with_pair_t u32 u32) :=
Return {| Struct_with_pair_p := {| Pair_x := 1%u32; Pair_y := 2%u32 |} |}
.
-(** [no_nested_borrows::test_constants] *)
+(** [no_nested_borrows::test_constants]: forward function *)
Definition test_constants_fwd : result unit :=
swt <- new_tuple1_fwd;
let (i, _) := swt.(Struct_with_tuple_p) in
@@ -476,34 +477,35 @@ Definition test_constants_fwd : result unit :=
(** Unit test for [no_nested_borrows::test_constants] *)
Check (test_constants_fwd )%return.
-(** [no_nested_borrows::test_weird_borrows1] *)
+(** [no_nested_borrows::test_weird_borrows1]: forward function *)
Definition test_weird_borrows1_fwd : result unit :=
Return tt.
(** Unit test for [no_nested_borrows::test_weird_borrows1] *)
Check (test_weird_borrows1_fwd )%return.
-(** [no_nested_borrows::test_mem_replace] *)
+(** [no_nested_borrows::test_mem_replace]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition test_mem_replace_fwd_back (px : u32) : result u32 :=
let y := mem_replace_fwd u32 px 1%u32 in
if negb (y s= 0%u32) then Fail_ Failure else Return 2%u32
.
-(** [no_nested_borrows::test_shared_borrow_bool1] *)
+(** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
Definition test_shared_borrow_bool1_fwd (b : bool) : result u32 :=
if b then Return 0%u32 else Return 1%u32
.
-(** [no_nested_borrows::test_shared_borrow_bool2] *)
+(** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
Definition test_shared_borrow_bool2_fwd : result u32 :=
Return 0%u32.
-(** [no_nested_borrows::test_shared_borrow_enum1] *)
+(** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
Definition test_shared_borrow_enum1_fwd (l : List_t u32) : result u32 :=
match l with | ListCons i l0 => Return 1%u32 | ListNil => Return 0%u32 end
.
-(** [no_nested_borrows::test_shared_borrow_enum2] *)
+(** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
Definition test_shared_borrow_enum2_fwd : result u32 :=
Return 0%u32.
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 513bc749..0f854f31 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -6,11 +6,12 @@ Require Import Coq.ZArith.ZArith.
Local Open Scope Primitives_scope.
Module Paper.
-(** [paper::ref_incr] *)
+(** [paper::ref_incr]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
Definition ref_incr_fwd_back (x : i32) : result i32 :=
i32_add x 1%i32.
-(** [paper::test_incr] *)
+(** [paper::test_incr]: forward function *)
Definition test_incr_fwd : result unit :=
x <- ref_incr_fwd_back 0%i32;
if negb (x s= 1%i32) then Fail_ Failure else Return tt
@@ -19,18 +20,18 @@ Definition test_incr_fwd : result unit :=
(** Unit test for [paper::test_incr] *)
Check (test_incr_fwd )%return.
-(** [paper::choose] *)
+(** [paper::choose]: forward function *)
Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
if b then Return x else Return y
.
-(** [paper::choose] *)
+(** [paper::choose]: backward function 0 *)
Definition choose_back
(T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
if b then Return (ret, y) else Return (x, ret)
.
-(** [paper::test_choose] *)
+(** [paper::test_choose]: forward function *)
Definition test_choose_fwd : result unit :=
z <- choose_fwd i32 true 0%i32 0%i32;
z0 <- i32_add z 1%i32;
@@ -56,7 +57,7 @@ Inductive List_t (T : Type) :=
Arguments ListCons {T} _ _.
Arguments ListNil {T}.
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: forward function *)
Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
match l with
| ListCons x tl =>
@@ -67,7 +68,7 @@ Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
end
.
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: backward function 0 *)
Fixpoint list_nth_mut_back
(T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
match l with
@@ -82,7 +83,7 @@ Fixpoint list_nth_mut_back
end
.
-(** [paper::sum] *)
+(** [paper::sum]: forward function *)
Fixpoint sum_fwd (l : List_t i32) : result i32 :=
match l with
| ListCons x tl => i <- sum_fwd tl; i32_add x i
@@ -90,7 +91,7 @@ Fixpoint sum_fwd (l : List_t i32) : result i32 :=
end
.
-(** [paper::test_nth] *)
+(** [paper::test_nth]: forward function *)
Definition test_nth_fwd : result unit :=
let l := ListNil in
let l0 := ListCons 3%i32 l in
@@ -105,7 +106,7 @@ Definition test_nth_fwd : result unit :=
(** Unit test for [paper::test_nth] *)
Check (test_nth_fwd )%return.
-(** [paper::call_choose] *)
+(** [paper::call_choose]: forward function *)
Definition call_choose_fwd (p : (u32 * u32)) : result u32 :=
let (px, py) := p in
pz <- choose_fwd u32 true px py;
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index bd6df02e..e94b6dcb 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -15,7 +15,7 @@ Inductive List_t (T : Type) :=
Arguments ListCons {T} _ _.
Arguments ListNil {T}.
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: forward function *)
Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
match ls with
| ListCons hd tl =>
@@ -24,7 +24,7 @@ Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
end
.
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: backward function 0 *)
Fixpoint get_list_at_x_back
(ls : List_t u32) (x : u32) (ret : List_t u32) : result (List_t u32) :=
match ls with
diff --git a/tests/coq/misc/_CoqProject b/tests/coq/misc/_CoqProject
index 87dea3e6..db6c2742 100644
--- a/tests/coq/misc/_CoqProject
+++ b/tests/coq/misc/_CoqProject
@@ -3,12 +3,12 @@
-arg -w
-arg all
-Constants.v
-External_Types.v
-Primitives.v
Loops.v
+Primitives.v
External_Funs.v
+Constants.v
PoloniusList.v
+External_Types.v
NoNestedBorrows.v
External_Opaque.v
Paper.v
diff --git a/tests/fstar/betree/BetreeMain.Funs.fst b/tests/fstar/betree/BetreeMain.Funs.fst
index 0c868f47..f1bc1191 100644
--- a/tests/fstar/betree/BetreeMain.Funs.fst
+++ b/tests/fstar/betree/BetreeMain.Funs.fst
@@ -8,14 +8,14 @@ include BetreeMain.Clauses
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [betree_main::betree::load_internal_node] *)
+(** [betree_main::betree::load_internal_node]: forward function *)
let betree_load_internal_node_fwd
(id : u64) (st : state) :
result (state & (betree_list_t (u64 & betree_message_t)))
=
betree_utils_load_internal_node_fwd id st
-(** [betree_main::betree::store_internal_node] *)
+(** [betree_main::betree::store_internal_node]: forward function *)
let betree_store_internal_node_fwd
(id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
result (state & unit)
@@ -23,12 +23,12 @@ let betree_store_internal_node_fwd
let* (st0, _) = betree_utils_store_internal_node_fwd id content st in
Return (st0, ())
-(** [betree_main::betree::load_leaf_node] *)
+(** [betree_main::betree::load_leaf_node]: forward function *)
let betree_load_leaf_node_fwd
(id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
betree_utils_load_leaf_node_fwd id st
-(** [betree_main::betree::store_leaf_node] *)
+(** [betree_main::betree::store_leaf_node]: forward function *)
let betree_store_leaf_node_fwd
(id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
result (state & unit)
@@ -36,25 +36,25 @@ let betree_store_leaf_node_fwd
let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in
Return (st0, ())
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: forward function *)
let betree_fresh_node_id_fwd (counter : u64) : result u64 =
let* _ = u64_add counter 1 in Return counter
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: backward function 0 *)
let betree_fresh_node_id_back (counter : u64) : result u64 =
u64_add counter 1
-(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
Return { betree_node_id_counter_next_node_id = 0 }
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
let betree_node_id_counter_fresh_id_fwd
(self : betree_node_id_counter_t) : result u64 =
let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in
Return self.betree_node_id_counter_next_node_id
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
let betree_node_id_counter_fresh_id_back
(self : betree_node_id_counter_t) : result betree_node_id_counter_t =
let* i = u64_add self.betree_node_id_counter_next_node_id 1 in
@@ -64,7 +64,7 @@ let betree_node_id_counter_fresh_id_back
let core_num_u64_max_body : result u64 = Return 18446744073709551615
let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
-(** [betree_main::betree::upsert_update] *)
+(** [betree_main::betree::upsert_update]: forward function *)
let betree_upsert_update_fwd
(prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
begin match prev with
@@ -83,7 +83,7 @@ let betree_upsert_update_fwd
end
end
-(** [betree_main::betree::List::{1}::len] *)
+(** [betree_main::betree::List::{1}::len]: forward function *)
let rec betree_list_len_fwd
(t : Type0) (self : betree_list_t t) :
Tot (result u64) (decreases (betree_list_len_decreases t self))
@@ -93,7 +93,7 @@ let rec betree_list_len_fwd
| BetreeListNil -> Return 0
end
-(** [betree_main::betree::List::{1}::split_at] *)
+(** [betree_main::betree::List::{1}::split_at]: forward function *)
let rec betree_list_split_at_fwd
(t : Type0) (self : betree_list_t t) (n : u64) :
Tot (result ((betree_list_t t) & (betree_list_t t)))
@@ -112,14 +112,15 @@ let rec betree_list_split_at_fwd
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{1}::push_front] *)
+(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let betree_list_push_front_fwd_back
(t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
let l = tl in
Return (BetreeListCons x l)
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: forward function *)
let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
begin match ls with
@@ -127,7 +128,7 @@ let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
let betree_list_pop_front_back
(t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
@@ -136,14 +137,14 @@ let betree_list_pop_front_back
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{1}::hd] *)
+(** [betree_main::betree::List::{1}::hd]: forward function *)
let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
begin match self with
| BetreeListCons hd l -> Return hd
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{2}::head_has_key] *)
+(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
let betree_list_head_has_key_fwd
(t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
begin match self with
@@ -151,7 +152,7 @@ let betree_list_head_has_key_fwd
| BetreeListNil -> Return false
end
-(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
let rec betree_list_partition_at_pivot_fwd
(t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
@@ -170,7 +171,7 @@ let rec betree_list_partition_at_pivot_fwd
| BetreeListNil -> Return (BetreeListNil, BetreeListNil)
end
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: forward function *)
let betree_leaf_split_fwd
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -202,7 +203,7 @@ let betree_leaf_split_fwd
betree_internal_right = n0
})
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
let betree_leaf_split_back
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -221,7 +222,7 @@ let betree_leaf_split_back
let* _ = betree_store_leaf_node_fwd id1 content1 st0 in
betree_node_id_counter_fresh_id_back node_id_cnt0
-(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
let rec betree_node_lookup_in_bindings_fwd
(key : u64) (bindings : betree_list_t (u64 & u64)) :
Tot (result (option u64))
@@ -239,7 +240,7 @@ let rec betree_node_lookup_in_bindings_fwd
| BetreeListNil -> Return None
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
let rec betree_node_lookup_first_message_for_key_fwd
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -254,7 +255,7 @@ let rec betree_node_lookup_first_message_for_key_fwd
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
let rec betree_node_lookup_first_message_for_key_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t))
(ret : betree_list_t (u64 & betree_message_t)) :
@@ -273,7 +274,7 @@ let rec betree_node_lookup_first_message_for_key_back
| BetreeListNil -> Return ret
end
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
let rec betree_node_apply_upserts_fwd
(msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
@@ -300,7 +301,7 @@ let rec betree_node_apply_upserts_fwd
BetreeMessageInsert v) in
Return (st0, v)
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
let rec betree_node_apply_upserts_back
(msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
@@ -325,7 +326,7 @@ let rec betree_node_apply_upserts_back
betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
BetreeMessageInsert v)
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: forward function *)
let rec betree_node_lookup_fwd
(self : betree_node_t) (key : u64) (st : state) :
Tot (result (state & (option u64)))
@@ -388,7 +389,7 @@ let rec betree_node_lookup_fwd
Return (st0, opt)
end
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
and betree_node_lookup_back
(self : betree_node_t) (key : u64) (st : state) :
Tot (result betree_node_t)
@@ -450,7 +451,7 @@ and betree_node_lookup_back
Return (BetreeNodeLeaf node)
end
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
and betree_internal_lookup_in_children_fwd
(self : betree_internal_t) (key : u64) (st : state) :
Tot (result (state & (option u64)))
@@ -460,7 +461,7 @@ and betree_internal_lookup_in_children_fwd
then betree_node_lookup_fwd self.betree_internal_left key st
else betree_node_lookup_fwd self.betree_internal_right key st
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
and betree_internal_lookup_in_children_back
(self : betree_internal_t) (key : u64) (st : state) :
Tot (result betree_internal_t)
@@ -474,7 +475,7 @@ and betree_internal_lookup_in_children_back
let* n = betree_node_lookup_back self.betree_internal_right key st in
Return { self with betree_internal_right = n }
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
let rec betree_node_lookup_mut_in_bindings_fwd
(key : u64) (bindings : betree_list_t (u64 & u64)) :
Tot (result (betree_list_t (u64 & u64)))
@@ -489,7 +490,7 @@ let rec betree_node_lookup_mut_in_bindings_fwd
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
let rec betree_node_lookup_mut_in_bindings_back
(key : u64) (bindings : betree_list_t (u64 & u64))
(ret : betree_list_t (u64 & u64)) :
@@ -507,7 +508,8 @@ let rec betree_node_lookup_mut_in_bindings_back
| BetreeListNil -> Return ret
end
-(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let betree_node_apply_to_leaf_fwd_back
(bindings : betree_list_t (u64 & u64)) (key : u64)
(new_msg : betree_message_t) :
@@ -550,7 +552,8 @@ let betree_node_apply_to_leaf_fwd_back
betree_node_lookup_mut_in_bindings_back key bindings bindings1
end
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec betree_node_apply_messages_to_leaf_fwd_back
(bindings : betree_list_t (u64 & u64))
(new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -565,7 +568,8 @@ let rec betree_node_apply_messages_to_leaf_fwd_back
| BetreeListNil -> Return bindings
end
-(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec betree_node_filter_messages_for_key_fwd_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -584,7 +588,7 @@ let rec betree_node_filter_messages_for_key_fwd_back
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
let rec betree_node_lookup_first_message_after_key_fwd
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -599,7 +603,7 @@ let rec betree_node_lookup_first_message_after_key_fwd
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
let rec betree_node_lookup_first_message_after_key_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t))
(ret : betree_list_t (u64 & betree_message_t)) :
@@ -618,7 +622,8 @@ let rec betree_node_lookup_first_message_after_key_back
| BetreeListNil -> Return ret
end
-(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let betree_node_apply_to_internal_fwd_back
(msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
(new_msg : betree_message_t) :
@@ -678,7 +683,8 @@ let betree_node_apply_to_internal_fwd_back
new_msg) in
betree_node_lookup_first_message_for_key_back key msgs msgs1
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec betree_node_apply_messages_to_internal_fwd_back
(msgs : betree_list_t (u64 & betree_message_t))
(new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -693,7 +699,7 @@ let rec betree_node_apply_messages_to_internal_fwd_back
| BetreeListNil -> Return msgs
end
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
let rec betree_node_apply_messages_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -740,7 +746,7 @@ let rec betree_node_apply_messages_fwd
Return (st1, ())
end
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
and betree_node_apply_messages_back
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -788,7 +794,7 @@ and betree_node_apply_messages_back
Return (BetreeNodeLeaf { node with betree_leaf_size = len }, node_id_cnt)
end
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: forward function *)
and betree_internal_flush_fwd
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -830,7 +836,7 @@ and betree_internal_flush_fwd
node_id_cnt msgs_right st in
Return (st0, msgs_left)
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
and betree_internal_flush_back
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -868,7 +874,7 @@ and betree_internal_flush_back
node_id_cnt msgs_right st in
Return ({ self with betree_internal_right = n }, node_id_cnt0)
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: forward function *)
let betree_node_apply_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -884,7 +890,7 @@ let betree_node_apply_fwd
(key, new_msg) l) st in
Return (st0, ())
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
let betree_node_apply_back
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -895,7 +901,7 @@ let betree_node_apply_back
betree_node_apply_messages_back self params node_id_cnt (BetreeListCons (key,
new_msg) l) st
-(** [betree_main::betree::BeTree::{6}::new] *)
+(** [betree_main::betree::BeTree::{6}::new]: forward function *)
let betree_be_tree_new_fwd
(min_flush_size : u64) (split_size : u64) (st : state) :
result (state & betree_be_tree_t)
@@ -916,7 +922,7 @@ let betree_be_tree_new_fwd
(BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 })
})
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
let betree_be_tree_apply_fwd
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
result (state & unit)
@@ -929,7 +935,7 @@ let betree_be_tree_apply_fwd
self.betree_be_tree_node_id_cnt key msg st in
Return (st0, ())
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
let betree_be_tree_apply_back
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
result betree_be_tree_t
@@ -940,7 +946,7 @@ let betree_be_tree_apply_back
Return
{ self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n }
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
let betree_be_tree_insert_fwd
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result (state & unit)
@@ -950,28 +956,28 @@ let betree_be_tree_insert_fwd
let* _ = betree_be_tree_apply_back self key (BetreeMessageInsert value) st in
Return (st0, ())
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
let betree_be_tree_insert_back
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result betree_be_tree_t
=
betree_be_tree_apply_back self key (BetreeMessageInsert value) st
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
let betree_be_tree_delete_fwd
(self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
let* _ = betree_be_tree_apply_back self key BetreeMessageDelete st in
Return (st0, ())
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
let betree_be_tree_delete_back
(self : betree_be_tree_t) (key : u64) (st : state) :
result betree_be_tree_t
=
betree_be_tree_apply_back self key BetreeMessageDelete st
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
let betree_be_tree_upsert_fwd
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
@@ -982,7 +988,7 @@ let betree_be_tree_upsert_fwd
let* _ = betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st in
Return (st0, ())
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
let betree_be_tree_upsert_back
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
@@ -990,14 +996,14 @@ let betree_be_tree_upsert_back
=
betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
let betree_be_tree_lookup_fwd
(self : betree_be_tree_t) (key : u64) (st : state) :
result (state & (option u64))
=
betree_node_lookup_fwd self.betree_be_tree_root key st
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
let betree_be_tree_lookup_back
(self : betree_be_tree_t) (key : u64) (st : state) :
result betree_be_tree_t
@@ -1005,7 +1011,7 @@ let betree_be_tree_lookup_back
let* n = betree_node_lookup_back self.betree_be_tree_root key st in
Return { self with betree_be_tree_root = n }
-(** [betree_main::main] *)
+(** [betree_main::main]: forward function *)
let main_fwd : result unit =
Return ()
diff --git a/tests/fstar/betree/BetreeMain.Opaque.fsti b/tests/fstar/betree/BetreeMain.Opaque.fsti
index dc49601a..c33cf225 100644
--- a/tests/fstar/betree/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree/BetreeMain.Opaque.fsti
@@ -1,30 +1,30 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
module BetreeMain.Opaque
open Primitives
include BetreeMain.Types
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [betree_main::betree_utils::load_internal_node] *)
+(** [betree_main::betree_utils::load_internal_node]: forward function *)
val betree_utils_load_internal_node_fwd
: u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t)))
-(** [betree_main::betree_utils::store_internal_node] *)
+(** [betree_main::betree_utils::store_internal_node]: forward function *)
val betree_utils_store_internal_node_fwd
:
u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state &
unit)
-(** [betree_main::betree_utils::load_leaf_node] *)
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)
val betree_utils_load_leaf_node_fwd
: u64 -> state -> result (state & (betree_list_t (u64 & u64)))
-(** [betree_main::betree_utils::store_leaf_node] *)
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)
val betree_utils_store_leaf_node_fwd
: u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit)
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
val core_option_option_unwrap_fwd
(t : Type0) : option t -> state -> result (state & t)
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
index c70bef08..12402fb4 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
@@ -8,14 +8,14 @@ include BetreeMain.Clauses
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [betree_main::betree::load_internal_node] *)
+(** [betree_main::betree::load_internal_node]: forward function *)
let betree_load_internal_node_fwd
(id : u64) (st : state) :
result (state & (betree_list_t (u64 & betree_message_t)))
=
betree_utils_load_internal_node_fwd id st
-(** [betree_main::betree::store_internal_node] *)
+(** [betree_main::betree::store_internal_node]: forward function *)
let betree_store_internal_node_fwd
(id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
result (state & unit)
@@ -23,12 +23,12 @@ let betree_store_internal_node_fwd
let* (st0, _) = betree_utils_store_internal_node_fwd id content st in
Return (st0, ())
-(** [betree_main::betree::load_leaf_node] *)
+(** [betree_main::betree::load_leaf_node]: forward function *)
let betree_load_leaf_node_fwd
(id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
betree_utils_load_leaf_node_fwd id st
-(** [betree_main::betree::store_leaf_node] *)
+(** [betree_main::betree::store_leaf_node]: forward function *)
let betree_store_leaf_node_fwd
(id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
result (state & unit)
@@ -36,25 +36,25 @@ let betree_store_leaf_node_fwd
let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in
Return (st0, ())
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: forward function *)
let betree_fresh_node_id_fwd (counter : u64) : result u64 =
let* _ = u64_add counter 1 in Return counter
-(** [betree_main::betree::fresh_node_id] *)
+(** [betree_main::betree::fresh_node_id]: backward function 0 *)
let betree_fresh_node_id_back (counter : u64) : result u64 =
u64_add counter 1
-(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+(** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
Return { betree_node_id_counter_next_node_id = 0 }
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
let betree_node_id_counter_fresh_id_fwd
(self : betree_node_id_counter_t) : result u64 =
let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in
Return self.betree_node_id_counter_next_node_id
-(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
let betree_node_id_counter_fresh_id_back
(self : betree_node_id_counter_t) : result betree_node_id_counter_t =
let* i = u64_add self.betree_node_id_counter_next_node_id 1 in
@@ -64,7 +64,7 @@ let betree_node_id_counter_fresh_id_back
let core_num_u64_max_body : result u64 = Return 18446744073709551615
let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
-(** [betree_main::betree::upsert_update] *)
+(** [betree_main::betree::upsert_update]: forward function *)
let betree_upsert_update_fwd
(prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
begin match prev with
@@ -83,7 +83,7 @@ let betree_upsert_update_fwd
end
end
-(** [betree_main::betree::List::{1}::len] *)
+(** [betree_main::betree::List::{1}::len]: forward function *)
let rec betree_list_len_fwd
(t : Type0) (self : betree_list_t t) :
Tot (result u64) (decreases (betree_list_len_decreases t self))
@@ -93,7 +93,7 @@ let rec betree_list_len_fwd
| BetreeListNil -> Return 0
end
-(** [betree_main::betree::List::{1}::split_at] *)
+(** [betree_main::betree::List::{1}::split_at]: forward function *)
let rec betree_list_split_at_fwd
(t : Type0) (self : betree_list_t t) (n : u64) :
Tot (result ((betree_list_t t) & (betree_list_t t)))
@@ -112,14 +112,15 @@ let rec betree_list_split_at_fwd
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{1}::push_front] *)
+(** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let betree_list_push_front_fwd_back
(t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
let l = tl in
Return (BetreeListCons x l)
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: forward function *)
let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
begin match ls with
@@ -127,7 +128,7 @@ let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{1}::pop_front] *)
+(** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
let betree_list_pop_front_back
(t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
@@ -136,14 +137,14 @@ let betree_list_pop_front_back
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{1}::hd] *)
+(** [betree_main::betree::List::{1}::hd]: forward function *)
let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
begin match self with
| BetreeListCons hd l -> Return hd
| BetreeListNil -> Fail Failure
end
-(** [betree_main::betree::List::{2}::head_has_key] *)
+(** [betree_main::betree::List::{2}::head_has_key]: forward function *)
let betree_list_head_has_key_fwd
(t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
begin match self with
@@ -151,7 +152,7 @@ let betree_list_head_has_key_fwd
| BetreeListNil -> Return false
end
-(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+(** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
let rec betree_list_partition_at_pivot_fwd
(t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
@@ -170,7 +171,7 @@ let rec betree_list_partition_at_pivot_fwd
| BetreeListNil -> Return (BetreeListNil, BetreeListNil)
end
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: forward function *)
let betree_leaf_split_fwd
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -202,7 +203,7 @@ let betree_leaf_split_fwd
betree_internal_right = n0
})
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 0 *)
let betree_leaf_split_back0
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -221,7 +222,7 @@ let betree_leaf_split_back0
let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
Return (st0, ())
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 1 *)
let betree_leaf_split_back1
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -240,7 +241,7 @@ let betree_leaf_split_back1
let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
Return (st0, ())
-(** [betree_main::betree::Leaf::{3}::split] *)
+(** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
let betree_leaf_split_back2
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -260,7 +261,7 @@ let betree_leaf_split_back2
let* node_id_cnt1 = betree_node_id_counter_fresh_id_back node_id_cnt0 in
Return (st0, node_id_cnt1)
-(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
let rec betree_node_lookup_in_bindings_fwd
(key : u64) (bindings : betree_list_t (u64 & u64)) :
Tot (result (option u64))
@@ -278,7 +279,7 @@ let rec betree_node_lookup_in_bindings_fwd
| BetreeListNil -> Return None
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
let rec betree_node_lookup_first_message_for_key_fwd
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -293,7 +294,7 @@ let rec betree_node_lookup_first_message_for_key_fwd
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
let rec betree_node_lookup_first_message_for_key_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t))
(ret : betree_list_t (u64 & betree_message_t)) :
@@ -312,7 +313,7 @@ let rec betree_node_lookup_first_message_for_key_back
| BetreeListNil -> Return ret
end
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
let rec betree_node_apply_upserts_fwd
(msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
@@ -339,7 +340,7 @@ let rec betree_node_apply_upserts_fwd
BetreeMessageInsert v) in
Return (st0, v)
-(** [betree_main::betree::Node::{5}::apply_upserts] *)
+(** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
let rec betree_node_apply_upserts_back
(msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
(key : u64) (st : state) (st0 : state) :
@@ -366,7 +367,7 @@ let rec betree_node_apply_upserts_back
BetreeMessageInsert v) in
Return (st0, msgs0)
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: forward function *)
let rec betree_node_lookup_fwd
(self : betree_node_t) (key : u64) (st : state) :
Tot (result (state & (option u64)))
@@ -430,7 +431,7 @@ let rec betree_node_lookup_fwd
Return (st0, opt)
end
-(** [betree_main::betree::Node::{5}::lookup] *)
+(** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
and betree_node_lookup_back
(self : betree_node_t) (key : u64) (st : state) (st0 : state) :
Tot (result (state & betree_node_t))
@@ -495,7 +496,7 @@ and betree_node_lookup_back
Return (st0, BetreeNodeLeaf node)
end
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
and betree_internal_lookup_in_children_fwd
(self : betree_internal_t) (key : u64) (st : state) :
Tot (result (state & (option u64)))
@@ -505,7 +506,7 @@ and betree_internal_lookup_in_children_fwd
then betree_node_lookup_fwd self.betree_internal_left key st
else betree_node_lookup_fwd self.betree_internal_right key st
-(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+(** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
and betree_internal_lookup_in_children_back
(self : betree_internal_t) (key : u64) (st : state) (st0 : state) :
Tot (result (state & betree_internal_t))
@@ -521,7 +522,7 @@ and betree_internal_lookup_in_children_back
betree_node_lookup_back self.betree_internal_right key st st0 in
Return (st1, { self with betree_internal_right = n })
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
let rec betree_node_lookup_mut_in_bindings_fwd
(key : u64) (bindings : betree_list_t (u64 & u64)) :
Tot (result (betree_list_t (u64 & u64)))
@@ -536,7 +537,7 @@ let rec betree_node_lookup_mut_in_bindings_fwd
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
let rec betree_node_lookup_mut_in_bindings_back
(key : u64) (bindings : betree_list_t (u64 & u64))
(ret : betree_list_t (u64 & u64)) :
@@ -554,7 +555,8 @@ let rec betree_node_lookup_mut_in_bindings_back
| BetreeListNil -> Return ret
end
-(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let betree_node_apply_to_leaf_fwd_back
(bindings : betree_list_t (u64 & u64)) (key : u64)
(new_msg : betree_message_t) :
@@ -597,7 +599,8 @@ let betree_node_apply_to_leaf_fwd_back
betree_node_lookup_mut_in_bindings_back key bindings bindings1
end
-(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec betree_node_apply_messages_to_leaf_fwd_back
(bindings : betree_list_t (u64 & u64))
(new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -612,7 +615,8 @@ let rec betree_node_apply_messages_to_leaf_fwd_back
| BetreeListNil -> Return bindings
end
-(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+(** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec betree_node_filter_messages_for_key_fwd_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -631,7 +635,7 @@ let rec betree_node_filter_messages_for_key_fwd_back
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
let rec betree_node_lookup_first_message_after_key_fwd
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
@@ -646,7 +650,7 @@ let rec betree_node_lookup_first_message_after_key_fwd
| BetreeListNil -> Return BetreeListNil
end
-(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
let rec betree_node_lookup_first_message_after_key_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t))
(ret : betree_list_t (u64 & betree_message_t)) :
@@ -665,7 +669,8 @@ let rec betree_node_lookup_first_message_after_key_back
| BetreeListNil -> Return ret
end
-(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let betree_node_apply_to_internal_fwd_back
(msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
(new_msg : betree_message_t) :
@@ -725,7 +730,8 @@ let betree_node_apply_to_internal_fwd_back
new_msg) in
betree_node_lookup_first_message_for_key_back key msgs msgs1
-(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec betree_node_apply_messages_to_internal_fwd_back
(msgs : betree_list_t (u64 & betree_message_t))
(new_msgs : betree_list_t (u64 & betree_message_t)) :
@@ -740,7 +746,7 @@ let rec betree_node_apply_messages_to_internal_fwd_back
| BetreeListNil -> Return msgs
end
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
let rec betree_node_apply_messages_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -788,7 +794,7 @@ let rec betree_node_apply_messages_fwd
Return (st1, ())
end
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
and betree_node_apply_messages_back'a
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -840,7 +846,7 @@ and betree_node_apply_messages_back'a
node_id_cnt))
end
-(** [betree_main::betree::Node::{5}::apply_messages] *)
+(** [betree_main::betree::Node::{5}::apply_messages]: backward function 1 *)
and betree_node_apply_messages_back1
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -889,7 +895,7 @@ and betree_node_apply_messages_back1
Return (st0, ())
end
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: forward function *)
and betree_internal_flush_fwd
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -940,7 +946,7 @@ and betree_internal_flush_fwd
node_id_cnt msgs_right st st1 in
Return (st2, msgs_left)
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
and betree_internal_flush_back'a
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -994,7 +1000,7 @@ and betree_internal_flush_back'a
node_id_cnt msgs_right st st2 in
Return (st0, ({ self with betree_internal_right = n }, node_id_cnt0))
-(** [betree_main::betree::Internal::{4}::flush] *)
+(** [betree_main::betree::Internal::{4}::flush]: backward function 1 *)
and betree_internal_flush_back1
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -1046,7 +1052,7 @@ and betree_internal_flush_back1
node_id_cnt msgs_right st st2 in
Return (st0, ())
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: forward function *)
let betree_node_apply_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1063,7 +1069,7 @@ let betree_node_apply_fwd
betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons
(key, new_msg) l) st st1
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
let betree_node_apply_back'a
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1082,7 +1088,7 @@ let betree_node_apply_back'a
(key, new_msg) l) st st2 in
Return (st0, (self0, node_id_cnt0))
-(** [betree_main::betree::Node::{5}::apply] *)
+(** [betree_main::betree::Node::{5}::apply]: backward function 1 *)
let betree_node_apply_back1
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1101,7 +1107,7 @@ let betree_node_apply_back1
(key, new_msg) l) st st2 in
Return (st0, ())
-(** [betree_main::betree::BeTree::{6}::new] *)
+(** [betree_main::betree::BeTree::{6}::new]: forward function *)
let betree_be_tree_new_fwd
(min_flush_size : u64) (split_size : u64) (st : state) :
result (state & betree_be_tree_t)
@@ -1122,7 +1128,7 @@ let betree_be_tree_new_fwd
(BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 })
})
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: forward function *)
let betree_be_tree_apply_fwd
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
result (state & unit)
@@ -1137,7 +1143,7 @@ let betree_be_tree_apply_fwd
betree_node_apply_back1 self.betree_be_tree_root self.betree_be_tree_params
self.betree_be_tree_node_id_cnt key msg st st1
-(** [betree_main::betree::BeTree::{6}::apply] *)
+(** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
let betree_be_tree_apply_back
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
(st0 : state) :
@@ -1156,7 +1162,7 @@ let betree_be_tree_apply_back
Return (st0,
{ self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n })
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: forward function *)
let betree_be_tree_insert_fwd
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result (state & unit)
@@ -1167,7 +1173,7 @@ let betree_be_tree_insert_fwd
betree_be_tree_apply_back self key (BetreeMessageInsert value) st st0 in
Return (st1, ())
-(** [betree_main::betree::BeTree::{6}::insert] *)
+(** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
let betree_be_tree_insert_back
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state)
(st0 : state) :
@@ -1179,7 +1185,7 @@ let betree_be_tree_insert_back
betree_be_tree_apply_back self key (BetreeMessageInsert value) st st1 in
Return (st0, self0)
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: forward function *)
let betree_be_tree_delete_fwd
(self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
@@ -1187,7 +1193,7 @@ let betree_be_tree_delete_fwd
in
Return (st1, ())
-(** [betree_main::betree::BeTree::{6}::delete] *)
+(** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
let betree_be_tree_delete_back
(self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
result (state & betree_be_tree_t)
@@ -1197,7 +1203,7 @@ let betree_be_tree_delete_back
betree_be_tree_apply_back self key BetreeMessageDelete st st1 in
Return (st0, self0)
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
let betree_be_tree_upsert_fwd
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
@@ -1209,7 +1215,7 @@ let betree_be_tree_upsert_fwd
betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st0 in
Return (st1, ())
-(** [betree_main::betree::BeTree::{6}::upsert] *)
+(** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
let betree_be_tree_upsert_back
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) (st0 : state) :
@@ -1221,14 +1227,14 @@ let betree_be_tree_upsert_back
betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st1 in
Return (st0, self0)
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
let betree_be_tree_lookup_fwd
(self : betree_be_tree_t) (key : u64) (st : state) :
result (state & (option u64))
=
betree_node_lookup_fwd self.betree_be_tree_root key st
-(** [betree_main::betree::BeTree::{6}::lookup] *)
+(** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
let betree_be_tree_lookup_back
(self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
result (state & betree_be_tree_t)
@@ -1237,7 +1243,7 @@ let betree_be_tree_lookup_back
in
Return (st1, { self with betree_be_tree_root = n })
-(** [betree_main::main] *)
+(** [betree_main::main]: forward function *)
let main_fwd : result unit =
Return ()
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
index dc49601a..c33cf225 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
@@ -1,30 +1,30 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
module BetreeMain.Opaque
open Primitives
include BetreeMain.Types
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [betree_main::betree_utils::load_internal_node] *)
+(** [betree_main::betree_utils::load_internal_node]: forward function *)
val betree_utils_load_internal_node_fwd
: u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t)))
-(** [betree_main::betree_utils::store_internal_node] *)
+(** [betree_main::betree_utils::store_internal_node]: forward function *)
val betree_utils_store_internal_node_fwd
:
u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state &
unit)
-(** [betree_main::betree_utils::load_leaf_node] *)
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)
val betree_utils_load_leaf_node_fwd
: u64 -> state -> result (state & (betree_list_t (u64 & u64)))
-(** [betree_main::betree_utils::store_leaf_node] *)
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)
val betree_utils_store_leaf_node_fwd
: u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit)
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
val core_option_option_unwrap_fwd
(t : Type0) : option t -> state -> result (state & t)
diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
index 44ad7463..950f1490 100644
--- a/tests/fstar/hashmap/Hashmap.Funs.fst
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -7,11 +7,11 @@ include Hashmap.Clauses
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [hashmap::hash_key] *)
+(** [hashmap::hash_key]: forward function *)
let hash_key_fwd (k : usize) : result usize =
Return k
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
let rec hash_map_allocate_slots_loop_fwd
(t : Type0) (slots : vec (list_t t)) (n : usize) :
Tot (result (vec (list_t t)))
@@ -24,12 +24,12 @@ let rec hash_map_allocate_slots_loop_fwd
hash_map_allocate_slots_loop_fwd t slots0 n0
else Return slots
-(** [hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
let hash_map_allocate_slots_fwd
(t : Type0) (slots : vec (list_t t)) (n : usize) : result (vec (list_t t)) =
hash_map_allocate_slots_loop_fwd t slots n
-(** [hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
let hash_map_new_with_capacity_fwd
(t : Type0) (capacity : usize) (max_load_dividend : usize)
(max_load_divisor : usize) :
@@ -47,11 +47,12 @@ let hash_map_new_with_capacity_fwd
hash_map_slots = slots
}
-(** [hashmap::HashMap::{0}::new] *)
+(** [hashmap::HashMap::{0}::new]: forward function *)
let hash_map_new_fwd (t : Type0) : result (hash_map_t t) =
hash_map_new_with_capacity_fwd t 32 4 5
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec hash_map_clear_loop_fwd_back
(t : Type0) (slots : vec (list_t t)) (i : usize) :
Tot (result (vec (list_t t)))
@@ -65,17 +66,18 @@ let rec hash_map_clear_loop_fwd_back
hash_map_clear_loop_fwd_back t slots0 i1
else Return slots
-(** [hashmap::HashMap::{0}::clear] *)
+(** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hash_map_clear_fwd_back
(t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
let* v = hash_map_clear_loop_fwd_back t self.hash_map_slots 0 in
Return { self with hash_map_num_entries = 0; hash_map_slots = v }
-(** [hashmap::HashMap::{0}::len] *)
+(** [hashmap::HashMap::{0}::len]: forward function *)
let hash_map_len_fwd (t : Type0) (self : hash_map_t t) : result usize =
Return self.hash_map_num_entries
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
let rec hash_map_insert_in_list_loop_fwd
(t : Type0) (key : usize) (value : t) (ls : list_t t) :
Tot (result bool)
@@ -89,12 +91,12 @@ let rec hash_map_insert_in_list_loop_fwd
| ListNil -> Return true
end
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
let hash_map_insert_in_list_fwd
(t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
hash_map_insert_in_list_loop_fwd t key value ls
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
let rec hash_map_insert_in_list_loop_back
(t : Type0) (key : usize) (value : t) (ls : list_t t) :
Tot (result (list_t t))
@@ -110,12 +112,13 @@ let rec hash_map_insert_in_list_loop_back
| ListNil -> let l = ListNil in Return (ListCons key value l)
end
-(** [hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
let hash_map_insert_in_list_back
(t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
hash_map_insert_in_list_loop_back t key value ls
-(** [hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hash_map_insert_no_resize_fwd_back
(t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
result (hash_map_t t)
@@ -140,7 +143,8 @@ let hash_map_insert_no_resize_fwd_back
let core_num_u32_max_body : result u32 = Return 4294967295
let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec hash_map_move_elements_from_list_loop_fwd_back
(t : Type0) (ntable : hash_map_t t) (ls : list_t t) :
Tot (result (hash_map_t t))
@@ -153,12 +157,14 @@ let rec hash_map_move_elements_from_list_loop_fwd_back
| ListNil -> Return ntable
end
-(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hash_map_move_elements_from_list_fwd_back
(t : Type0) (ntable : hash_map_t t) (ls : list_t t) : result (hash_map_t t) =
hash_map_move_elements_from_list_loop_fwd_back t ntable ls
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec hash_map_move_elements_loop_fwd_back
(t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
Tot (result ((hash_map_t t) & (vec (list_t t))))
@@ -176,14 +182,16 @@ let rec hash_map_move_elements_loop_fwd_back
hash_map_move_elements_loop_fwd_back t ntable0 slots0 i1
else Return (ntable, slots)
-(** [hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hash_map_move_elements_fwd_back
(t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
result ((hash_map_t t) & (vec (list_t t)))
=
hash_map_move_elements_loop_fwd_back t ntable slots i
-(** [hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hash_map_try_resize_fwd_back
(t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
let* max_usize = scalar_cast U32 Usize core_num_u32_max_c in
@@ -206,7 +214,8 @@ let hash_map_try_resize_fwd_back
}
else Return { self with hash_map_max_load_factor = (i, i0) }
-(** [hashmap::HashMap::{0}::insert] *)
+(** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hash_map_insert_fwd_back
(t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
result (hash_map_t t)
@@ -217,7 +226,7 @@ let hash_map_insert_fwd_back
then hash_map_try_resize_fwd_back t self0
else Return self0
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
let rec hash_map_contains_key_in_list_loop_fwd
(t : Type0) (key : usize) (ls : list_t t) :
Tot (result bool)
@@ -231,12 +240,12 @@ let rec hash_map_contains_key_in_list_loop_fwd
| ListNil -> Return false
end
-(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
let hash_map_contains_key_in_list_fwd
(t : Type0) (key : usize) (ls : list_t t) : result bool =
hash_map_contains_key_in_list_loop_fwd t key ls
-(** [hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap::HashMap::{0}::contains_key]: forward function *)
let hash_map_contains_key_fwd
(t : Type0) (self : hash_map_t t) (key : usize) : result bool =
let* hash = hash_key_fwd key in
@@ -245,7 +254,7 @@ let hash_map_contains_key_fwd
let* l = vec_index_fwd (list_t t) self.hash_map_slots hash_mod in
hash_map_contains_key_in_list_fwd t key l
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
let rec hash_map_get_in_list_loop_fwd
(t : Type0) (key : usize) (ls : list_t t) :
Tot (result t) (decreases (hash_map_get_in_list_loop_decreases t key ls))
@@ -258,12 +267,12 @@ let rec hash_map_get_in_list_loop_fwd
| ListNil -> Fail Failure
end
-(** [hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap::HashMap::{0}::get_in_list]: forward function *)
let hash_map_get_in_list_fwd
(t : Type0) (key : usize) (ls : list_t t) : result t =
hash_map_get_in_list_loop_fwd t key ls
-(** [hashmap::HashMap::{0}::get] *)
+(** [hashmap::HashMap::{0}::get]: forward function *)
let hash_map_get_fwd
(t : Type0) (self : hash_map_t t) (key : usize) : result t =
let* hash = hash_key_fwd key in
@@ -272,7 +281,7 @@ let hash_map_get_fwd
let* l = vec_index_fwd (list_t t) self.hash_map_slots hash_mod in
hash_map_get_in_list_fwd t key l
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
let rec hash_map_get_mut_in_list_loop_fwd
(t : Type0) (ls : list_t t) (key : usize) :
Tot (result t) (decreases (hash_map_get_mut_in_list_loop_decreases t ls key))
@@ -285,12 +294,12 @@ let rec hash_map_get_mut_in_list_loop_fwd
| ListNil -> Fail Failure
end
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
let hash_map_get_mut_in_list_fwd
(t : Type0) (ls : list_t t) (key : usize) : result t =
hash_map_get_mut_in_list_loop_fwd t ls key
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
let rec hash_map_get_mut_in_list_loop_back
(t : Type0) (ls : list_t t) (key : usize) (ret : t) :
Tot (result (list_t t))
@@ -306,12 +315,12 @@ let rec hash_map_get_mut_in_list_loop_back
| ListNil -> Fail Failure
end
-(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
let hash_map_get_mut_in_list_back
(t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
hash_map_get_mut_in_list_loop_back t ls key ret
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: forward function *)
let hash_map_get_mut_fwd
(t : Type0) (self : hash_map_t t) (key : usize) : result t =
let* hash = hash_key_fwd key in
@@ -320,7 +329,7 @@ let hash_map_get_mut_fwd
let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
hash_map_get_mut_in_list_fwd t l key
-(** [hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
let hash_map_get_mut_back
(t : Type0) (self : hash_map_t t) (key : usize) (ret : t) :
result (hash_map_t t)
@@ -333,7 +342,7 @@ let hash_map_get_mut_back
let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
Return { self with hash_map_slots = v }
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
let rec hash_map_remove_from_list_loop_fwd
(t : Type0) (key : usize) (ls : list_t t) :
Tot (result (option t))
@@ -352,12 +361,12 @@ let rec hash_map_remove_from_list_loop_fwd
| ListNil -> Return None
end
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
let hash_map_remove_from_list_fwd
(t : Type0) (key : usize) (ls : list_t t) : result (option t) =
hash_map_remove_from_list_loop_fwd t key ls
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
let rec hash_map_remove_from_list_loop_back
(t : Type0) (key : usize) (ls : list_t t) :
Tot (result (list_t t))
@@ -378,12 +387,12 @@ let rec hash_map_remove_from_list_loop_back
| ListNil -> Return ListNil
end
-(** [hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
let hash_map_remove_from_list_back
(t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
hash_map_remove_from_list_loop_back t key ls
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: forward function *)
let hash_map_remove_fwd
(t : Type0) (self : hash_map_t t) (key : usize) : result (option t) =
let* hash = hash_key_fwd key in
@@ -397,7 +406,7 @@ let hash_map_remove_fwd
let* _ = usize_sub self.hash_map_num_entries 1 in Return (Some x0)
end
-(** [hashmap::HashMap::{0}::remove] *)
+(** [hashmap::HashMap::{0}::remove]: backward function 0 *)
let hash_map_remove_back
(t : Type0) (self : hash_map_t t) (key : usize) : result (hash_map_t t) =
let* hash = hash_key_fwd key in
@@ -417,7 +426,7 @@ let hash_map_remove_back
Return { self with hash_map_num_entries = i0; hash_map_slots = v }
end
-(** [hashmap::test1] *)
+(** [hashmap::test1]: forward function *)
let test1_fwd : result unit =
let* hm = hash_map_new_fwd u64 in
let* hm0 = hash_map_insert_fwd_back u64 hm 0 42 in
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
index e8cd54c1..f6d9c8cf 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
@@ -8,11 +8,11 @@ include HashmapMain.Clauses
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [hashmap_main::hashmap::hash_key] *)
+(** [hashmap_main::hashmap::hash_key]: forward function *)
let hashmap_hash_key_fwd (k : usize) : result usize =
Return k
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
let rec hashmap_hash_map_allocate_slots_loop_fwd
(t : Type0) (slots : vec (hashmap_list_t t)) (n : usize) :
Tot (result (vec (hashmap_list_t t)))
@@ -25,14 +25,14 @@ let rec hashmap_hash_map_allocate_slots_loop_fwd
hashmap_hash_map_allocate_slots_loop_fwd t slots0 n0
else Return slots
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
let hashmap_hash_map_allocate_slots_fwd
(t : Type0) (slots : vec (hashmap_list_t t)) (n : usize) :
result (vec (hashmap_list_t t))
=
hashmap_hash_map_allocate_slots_loop_fwd t slots n
-(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
let hashmap_hash_map_new_with_capacity_fwd
(t : Type0) (capacity : usize) (max_load_dividend : usize)
(max_load_divisor : usize) :
@@ -50,11 +50,12 @@ let hashmap_hash_map_new_with_capacity_fwd
hashmap_hash_map_slots = slots
}
-(** [hashmap_main::hashmap::HashMap::{0}::new] *)
+(** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
let hashmap_hash_map_new_fwd (t : Type0) : result (hashmap_hash_map_t t) =
hashmap_hash_map_new_with_capacity_fwd t 32 4 5
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec hashmap_hash_map_clear_loop_fwd_back
(t : Type0) (slots : vec (hashmap_list_t t)) (i : usize) :
Tot (result (vec (hashmap_list_t t)))
@@ -69,7 +70,8 @@ let rec hashmap_hash_map_clear_loop_fwd_back
hashmap_hash_map_clear_loop_fwd_back t slots0 i1
else Return slots
-(** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+(** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hashmap_hash_map_clear_fwd_back
(t : Type0) (self : hashmap_hash_map_t t) : result (hashmap_hash_map_t t) =
let* v = hashmap_hash_map_clear_loop_fwd_back t self.hashmap_hash_map_slots 0
@@ -77,12 +79,12 @@ let hashmap_hash_map_clear_fwd_back
Return
{ self with hashmap_hash_map_num_entries = 0; hashmap_hash_map_slots = v }
-(** [hashmap_main::hashmap::HashMap::{0}::len] *)
+(** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
let hashmap_hash_map_len_fwd
(t : Type0) (self : hashmap_hash_map_t t) : result usize =
Return self.hashmap_hash_map_num_entries
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
let rec hashmap_hash_map_insert_in_list_loop_fwd
(t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
Tot (result bool)
@@ -96,12 +98,12 @@ let rec hashmap_hash_map_insert_in_list_loop_fwd
| HashmapListNil -> Return true
end
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
let hashmap_hash_map_insert_in_list_fwd
(t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) : result bool =
hashmap_hash_map_insert_in_list_loop_fwd t key value ls
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
let rec hashmap_hash_map_insert_in_list_loop_back
(t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
Tot (result (hashmap_list_t t))
@@ -118,14 +120,15 @@ let rec hashmap_hash_map_insert_in_list_loop_back
let l = HashmapListNil in Return (HashmapListCons key value l)
end
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
let hashmap_hash_map_insert_in_list_back
(t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
result (hashmap_list_t t)
=
hashmap_hash_map_insert_in_list_loop_back t key value ls
-(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hashmap_hash_map_insert_no_resize_fwd_back
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) (value : t) :
result (hashmap_hash_map_t t)
@@ -158,7 +161,8 @@ let hashmap_hash_map_insert_no_resize_fwd_back
let core_num_u32_max_body : result u32 = Return 4294967295
let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec hashmap_hash_map_move_elements_from_list_loop_fwd_back
(t : Type0) (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) :
Tot (result (hashmap_hash_map_t t))
@@ -172,14 +176,16 @@ let rec hashmap_hash_map_move_elements_from_list_loop_fwd_back
| HashmapListNil -> Return ntable
end
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hashmap_hash_map_move_elements_from_list_fwd_back
(t : Type0) (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) :
result (hashmap_hash_map_t t)
=
hashmap_hash_map_move_elements_from_list_loop_fwd_back t ntable ls
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec hashmap_hash_map_move_elements_loop_fwd_back
(t : Type0) (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t))
(i : usize) :
@@ -199,7 +205,8 @@ let rec hashmap_hash_map_move_elements_loop_fwd_back
hashmap_hash_map_move_elements_loop_fwd_back t ntable0 slots0 i1
else Return (ntable, slots)
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hashmap_hash_map_move_elements_fwd_back
(t : Type0) (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t))
(i : usize) :
@@ -207,7 +214,8 @@ let hashmap_hash_map_move_elements_fwd_back
=
hashmap_hash_map_move_elements_loop_fwd_back t ntable slots i
-(** [hashmap_main::hashmap::HashMap::{0}::try_resize] *)
+(** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hashmap_hash_map_try_resize_fwd_back
(t : Type0) (self : hashmap_hash_map_t t) : result (hashmap_hash_map_t t) =
let* max_usize = scalar_cast U32 Usize core_num_u32_max_c in
@@ -231,7 +239,8 @@ let hashmap_hash_map_try_resize_fwd_back
}
else Return { self with hashmap_hash_map_max_load_factor = (i, i0) }
-(** [hashmap_main::hashmap::HashMap::{0}::insert] *)
+(** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let hashmap_hash_map_insert_fwd_back
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) (value : t) :
result (hashmap_hash_map_t t)
@@ -242,7 +251,7 @@ let hashmap_hash_map_insert_fwd_back
then hashmap_hash_map_try_resize_fwd_back t self0
else Return self0
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
let rec hashmap_hash_map_contains_key_in_list_loop_fwd
(t : Type0) (key : usize) (ls : hashmap_list_t t) :
Tot (result bool)
@@ -256,12 +265,12 @@ let rec hashmap_hash_map_contains_key_in_list_loop_fwd
| HashmapListNil -> Return false
end
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
let hashmap_hash_map_contains_key_in_list_fwd
(t : Type0) (key : usize) (ls : hashmap_list_t t) : result bool =
hashmap_hash_map_contains_key_in_list_loop_fwd t key ls
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key] *)
+(** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
let hashmap_hash_map_contains_key_fwd
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result bool =
let* hash = hashmap_hash_key_fwd key in
@@ -271,7 +280,7 @@ let hashmap_hash_map_contains_key_fwd
vec_index_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod in
hashmap_hash_map_contains_key_in_list_fwd t key l
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
let rec hashmap_hash_map_get_in_list_loop_fwd
(t : Type0) (key : usize) (ls : hashmap_list_t t) :
Tot (result t)
@@ -285,12 +294,12 @@ let rec hashmap_hash_map_get_in_list_loop_fwd
| HashmapListNil -> Fail Failure
end
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
let hashmap_hash_map_get_in_list_fwd
(t : Type0) (key : usize) (ls : hashmap_list_t t) : result t =
hashmap_hash_map_get_in_list_loop_fwd t key ls
-(** [hashmap_main::hashmap::HashMap::{0}::get] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
let hashmap_hash_map_get_fwd
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result t =
let* hash = hashmap_hash_key_fwd key in
@@ -300,7 +309,7 @@ let hashmap_hash_map_get_fwd
vec_index_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod in
hashmap_hash_map_get_in_list_fwd t key l
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
let rec hashmap_hash_map_get_mut_in_list_loop_fwd
(t : Type0) (ls : hashmap_list_t t) (key : usize) :
Tot (result t)
@@ -314,12 +323,12 @@ let rec hashmap_hash_map_get_mut_in_list_loop_fwd
| HashmapListNil -> Fail Failure
end
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
let hashmap_hash_map_get_mut_in_list_fwd
(t : Type0) (ls : hashmap_list_t t) (key : usize) : result t =
hashmap_hash_map_get_mut_in_list_loop_fwd t ls key
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
let rec hashmap_hash_map_get_mut_in_list_loop_back
(t : Type0) (ls : hashmap_list_t t) (key : usize) (ret : t) :
Tot (result (hashmap_list_t t))
@@ -335,14 +344,14 @@ let rec hashmap_hash_map_get_mut_in_list_loop_back
| HashmapListNil -> Fail Failure
end
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
let hashmap_hash_map_get_mut_in_list_back
(t : Type0) (ls : hashmap_list_t t) (key : usize) (ret : t) :
result (hashmap_list_t t)
=
hashmap_hash_map_get_mut_in_list_loop_back t ls key ret
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
let hashmap_hash_map_get_mut_fwd
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result t =
let* hash = hashmap_hash_key_fwd key in
@@ -353,7 +362,7 @@ let hashmap_hash_map_get_mut_fwd
in
hashmap_hash_map_get_mut_in_list_fwd t l key
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
let hashmap_hash_map_get_mut_back
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) (ret : t) :
result (hashmap_hash_map_t t)
@@ -370,7 +379,7 @@ let hashmap_hash_map_get_mut_back
l0 in
Return { self with hashmap_hash_map_slots = v }
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
let rec hashmap_hash_map_remove_from_list_loop_fwd
(t : Type0) (key : usize) (ls : hashmap_list_t t) :
Tot (result (option t))
@@ -391,12 +400,12 @@ let rec hashmap_hash_map_remove_from_list_loop_fwd
| HashmapListNil -> Return None
end
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
let hashmap_hash_map_remove_from_list_fwd
(t : Type0) (key : usize) (ls : hashmap_list_t t) : result (option t) =
hashmap_hash_map_remove_from_list_loop_fwd t key ls
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
let rec hashmap_hash_map_remove_from_list_loop_back
(t : Type0) (key : usize) (ls : hashmap_list_t t) :
Tot (result (hashmap_list_t t))
@@ -419,14 +428,14 @@ let rec hashmap_hash_map_remove_from_list_loop_back
| HashmapListNil -> Return HashmapListNil
end
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
let hashmap_hash_map_remove_from_list_back
(t : Type0) (key : usize) (ls : hashmap_list_t t) :
result (hashmap_list_t t)
=
hashmap_hash_map_remove_from_list_loop_back t key ls
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
let hashmap_hash_map_remove_fwd
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result (option t) =
let* hash = hashmap_hash_key_fwd key in
@@ -442,7 +451,7 @@ let hashmap_hash_map_remove_fwd
let* _ = usize_sub self.hashmap_hash_map_num_entries 1 in Return (Some x0)
end
-(** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+(** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
let hashmap_hash_map_remove_back
(t : Type0) (self : hashmap_hash_map_t t) (key : usize) :
result (hashmap_hash_map_t t)
@@ -472,7 +481,7 @@ let hashmap_hash_map_remove_back
}
end
-(** [hashmap_main::hashmap::test1] *)
+(** [hashmap_main::hashmap::test1]: forward function *)
let hashmap_test1_fwd : result unit =
let* hm = hashmap_hash_map_new_fwd u64 in
let* hm0 = hashmap_hash_map_insert_fwd_back u64 hm 0 42 in
@@ -511,7 +520,7 @@ let hashmap_test1_fwd : result unit =
(** Unit test for [hashmap_main::hashmap::test1] *)
let _ = assert_norm (hashmap_test1_fwd = Return ())
-(** [hashmap_main::insert_on_disk] *)
+(** [hashmap_main::insert_on_disk]: forward function *)
let insert_on_disk_fwd
(key : usize) (value : u64) (st : state) : result (state & unit) =
let* (st0, hm) = hashmap_utils_deserialize_fwd st in
@@ -519,7 +528,7 @@ let insert_on_disk_fwd
let* (st1, _) = hashmap_utils_serialize_fwd hm0 st0 in
Return (st1, ())
-(** [hashmap_main::main] *)
+(** [hashmap_main::main]: forward function *)
let main_fwd : result unit =
Return ()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
index 6e54ea10..78a6c3ba 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
@@ -1,16 +1,16 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
module HashmapMain.Opaque
open Primitives
include HashmapMain.Types
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [hashmap_main::hashmap_utils::deserialize] *)
+(** [hashmap_main::hashmap_utils::deserialize]: forward function *)
val hashmap_utils_deserialize_fwd
: state -> result (state & (hashmap_hash_map_t u64))
-(** [hashmap_main::hashmap_utils::serialize] *)
+(** [hashmap_main::hashmap_utils::serialize]: forward function *)
val hashmap_utils_serialize_fwd
: hashmap_hash_map_t u64 -> state -> result (state & unit)
diff --git a/tests/fstar/misc/Constants.fst b/tests/fstar/misc/Constants.fst
index bf2f0b1b..aae997fa 100644
--- a/tests/fstar/misc/Constants.fst
+++ b/tests/fstar/misc/Constants.fst
@@ -21,7 +21,7 @@ let x1_c : u32 = eval_global x1_body
let x2_body : result u32 = Return 3
let x2_c : u32 = eval_global x2_body
-(** [constants::incr] *)
+(** [constants::incr]: forward function *)
let incr_fwd (n : u32) : result u32 =
u32_add n 1
@@ -29,14 +29,14 @@ let incr_fwd (n : u32) : result u32 =
let x3_body : result u32 = incr_fwd 32
let x3_c : u32 = eval_global x3_body
-(** [constants::mk_pair0] *)
+(** [constants::mk_pair0]: forward function *)
let mk_pair0_fwd (x : u32) (y : u32) : result (u32 & u32) =
Return (x, y)
(** [constants::Pair] *)
type pair_t (t1 t2 : Type0) = { pair_x : t1; pair_y : t2; }
-(** [constants::mk_pair1] *)
+(** [constants::mk_pair1]: forward function *)
let mk_pair1_fwd (x : u32) (y : u32) : result (pair_t u32 u32) =
Return { pair_x = x; pair_y = y }
@@ -59,7 +59,7 @@ let p3_c : pair_t u32 u32 = eval_global p3_body
(** [constants::Wrap] *)
type wrap_t (t : Type0) = { wrap_val : t; }
-(** [constants::Wrap::{0}::new] *)
+(** [constants::Wrap::{0}::new]: forward function *)
let wrap_new_fwd (t : Type0) (val0 : t) : result (wrap_t t) =
Return { wrap_val = val0 }
@@ -67,7 +67,7 @@ let wrap_new_fwd (t : Type0) (val0 : t) : result (wrap_t t) =
let y_body : result (wrap_t i32) = wrap_new_fwd i32 2
let y_c : wrap_t i32 = eval_global y_body
-(** [constants::unwrap_y] *)
+(** [constants::unwrap_y]: forward function *)
let unwrap_y_fwd : result i32 =
Return y_c.wrap_val
@@ -79,11 +79,11 @@ let yval_c : i32 = eval_global yval_body
let get_z1_z1_body : result i32 = Return 3
let get_z1_z1_c : i32 = eval_global get_z1_z1_body
-(** [constants::get_z1] *)
+(** [constants::get_z1]: forward function *)
let get_z1_fwd : result i32 =
Return get_z1_z1_c
-(** [constants::add] *)
+(** [constants::add]: forward function *)
let add_fwd (a : i32) (b : i32) : result i32 =
i32_add a b
@@ -99,7 +99,7 @@ let q2_c : i32 = eval_global q2_body
let q3_body : result i32 = add_fwd q2_c 3
let q3_c : i32 = eval_global q3_body
-(** [constants::get_z2] *)
+(** [constants::get_z2]: forward function *)
let get_z2_fwd : result i32 =
let* i = get_z1_fwd in let* i0 = add_fwd i q3_c in add_fwd q1_c i0
diff --git a/tests/fstar/misc/External.Funs.fst b/tests/fstar/misc/External.Funs.fst
index f70a9fc6..f118a2cf 100644
--- a/tests/fstar/misc/External.Funs.fst
+++ b/tests/fstar/misc/External.Funs.fst
@@ -7,14 +7,14 @@ include External.Opaque
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [external::swap] *)
+(** [external::swap]: forward function *)
let swap_fwd (t : Type0) (x : t) (y : t) (st : state) : result (state & unit) =
let* (st0, _) = core_mem_swap_fwd t x y st in
let* (st1, _) = core_mem_swap_back0 t x y st st0 in
let* (st2, _) = core_mem_swap_back1 t x y st st1 in
Return (st2, ())
-(** [external::swap] *)
+(** [external::swap]: backward function 0 *)
let swap_back
(t : Type0) (x : t) (y : t) (st : state) (st0 : state) :
result (state & (t & t))
@@ -24,20 +24,20 @@ let swap_back
let* (_, y0) = core_mem_swap_back1 t x y st st2 in
Return (st0, (x0, y0))
-(** [external::test_new_non_zero_u32] *)
+(** [external::test_new_non_zero_u32]: forward function *)
let test_new_non_zero_u32_fwd
(x : u32) (st : state) : result (state & core_num_nonzero_non_zero_u32_t) =
let* (st0, opt) = core_num_nonzero_non_zero_u32_new_fwd x st in
core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t opt st0
-(** [external::test_vec] *)
+(** [external::test_vec]: forward function *)
let test_vec_fwd : result unit =
let v = vec_new u32 in let* _ = vec_push_back u32 v 0 in Return ()
(** Unit test for [external::test_vec] *)
let _ = assert_norm (test_vec_fwd = Return ())
-(** [external::custom_swap] *)
+(** [external::custom_swap]: forward function *)
let custom_swap_fwd
(t : Type0) (x : t) (y : t) (st : state) : result (state & t) =
let* (st0, _) = core_mem_swap_fwd t x y st in
@@ -45,7 +45,7 @@ let custom_swap_fwd
let* (st2, _) = core_mem_swap_back1 t x y st st1 in
Return (st2, x0)
-(** [external::custom_swap] *)
+(** [external::custom_swap]: backward function 0 *)
let custom_swap_back
(t : Type0) (x : t) (y : t) (st : state) (ret : t) (st0 : state) :
result (state & (t & t))
@@ -55,19 +55,19 @@ let custom_swap_back
let* (_, y0) = core_mem_swap_back1 t x y st st2 in
Return (st0, (ret, y0))
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: forward function *)
let test_custom_swap_fwd
(x : u32) (y : u32) (st : state) : result (state & unit) =
let* (st0, _) = custom_swap_fwd u32 x y st in Return (st0, ())
-(** [external::test_custom_swap] *)
+(** [external::test_custom_swap]: backward function 0 *)
let test_custom_swap_back
(x : u32) (y : u32) (st : state) (st0 : state) :
result (state & (u32 & u32))
=
custom_swap_back u32 x y st 1 st0
-(** [external::test_swap_non_zero] *)
+(** [external::test_swap_non_zero]: forward function *)
let test_swap_non_zero_fwd (x : u32) (st : state) : result (state & u32) =
let* (st0, _) = swap_fwd u32 x 0 st in
let* (st1, (x0, _)) = swap_back u32 x 0 st st0 in
diff --git a/tests/fstar/misc/External.Opaque.fsti b/tests/fstar/misc/External.Opaque.fsti
index 7d86405a..2e19f767 100644
--- a/tests/fstar/misc/External.Opaque.fsti
+++ b/tests/fstar/misc/External.Opaque.fsti
@@ -1,27 +1,27 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
module External.Opaque
open Primitives
include External.Types
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [core::mem::swap] *)
+(** [core::mem::swap]: forward function *)
val core_mem_swap_fwd (t : Type0) : t -> t -> state -> result (state & unit)
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 0 *)
val core_mem_swap_back0
(t : Type0) : t -> t -> state -> state -> result (state & t)
-(** [core::mem::swap] *)
+(** [core::mem::swap]: backward function 1 *)
val core_mem_swap_back1
(t : Type0) : t -> t -> state -> state -> result (state & t)
-(** [core::num::nonzero::NonZeroU32::{14}::new] *)
+(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
val core_num_nonzero_non_zero_u32_new_fwd
: u32 -> state -> result (state & (option core_num_nonzero_non_zero_u32_t))
-(** [core::option::Option::{0}::unwrap] *)
+(** [core::option::Option::{0}::unwrap]: forward function *)
val core_option_option_unwrap_fwd
(t : Type0) : option t -> state -> result (state & t)
diff --git a/tests/fstar/misc/Loops.Funs.fst b/tests/fstar/misc/Loops.Funs.fst
index 7fe175e5..9a80f415 100644
--- a/tests/fstar/misc/Loops.Funs.fst
+++ b/tests/fstar/misc/Loops.Funs.fst
@@ -7,7 +7,7 @@ include Loops.Clauses
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [loops::sum] *)
+(** [loops::sum]: loop 0: forward function *)
let rec sum_loop_fwd
(max : u32) (i : u32) (s : u32) :
Tot (result u32) (decreases (sum_loop_decreases max i s))
@@ -16,11 +16,11 @@ let rec sum_loop_fwd
then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop_fwd max i0 s0
else u32_mul s 2
-(** [loops::sum] *)
+(** [loops::sum]: forward function *)
let sum_fwd (max : u32) : result u32 =
sum_loop_fwd max 0 0
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: loop 0: forward function *)
let rec sum_with_mut_borrows_loop_fwd
(max : u32) (mi : u32) (ms : u32) :
Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms))
@@ -32,11 +32,11 @@ let rec sum_with_mut_borrows_loop_fwd
sum_with_mut_borrows_loop_fwd max mi0 ms0
else u32_mul ms 2
-(** [loops::sum_with_mut_borrows] *)
+(** [loops::sum_with_mut_borrows]: forward function *)
let sum_with_mut_borrows_fwd (max : u32) : result u32 =
sum_with_mut_borrows_loop_fwd max 0 0
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: loop 0: forward function *)
let rec sum_with_shared_borrows_loop_fwd
(max : u32) (i : u32) (s : u32) :
Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s))
@@ -48,11 +48,12 @@ let rec sum_with_shared_borrows_loop_fwd
sum_with_shared_borrows_loop_fwd max i0 s0
else u32_mul s 2
-(** [loops::sum_with_shared_borrows] *)
+(** [loops::sum_with_shared_borrows]: forward function *)
let sum_with_shared_borrows_fwd (max : u32) : result u32 =
sum_with_shared_borrows_loop_fwd max 0 0
-(** [loops::clear] *)
+(** [loops::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let rec clear_loop_fwd_back
(v : vec u32) (i : usize) :
Tot (result (vec u32)) (decreases (clear_loop_decreases v i))
@@ -65,11 +66,12 @@ let rec clear_loop_fwd_back
clear_loop_fwd_back v0 i1
else Return v
-(** [loops::clear] *)
+(** [loops::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let clear_fwd_back (v : vec u32) : result (vec u32) =
clear_loop_fwd_back v 0
-(** [loops::list_mem] *)
+(** [loops::list_mem]: loop 0: forward function *)
let rec list_mem_loop_fwd
(x : u32) (ls : list_t u32) :
Tot (result bool) (decreases (list_mem_loop_decreases x ls))
@@ -79,11 +81,11 @@ let rec list_mem_loop_fwd
| ListNil -> Return false
end
-(** [loops::list_mem] *)
+(** [loops::list_mem]: forward function *)
let list_mem_fwd (x : u32) (ls : list_t u32) : result bool =
list_mem_loop_fwd x ls
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: forward function *)
let rec list_nth_mut_loop_loop_fwd
(t : Type0) (ls : list_t t) (i : u32) :
Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i))
@@ -96,11 +98,11 @@ let rec list_nth_mut_loop_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: forward function *)
let list_nth_mut_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
list_nth_mut_loop_loop_fwd t ls i
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
let rec list_nth_mut_loop_loop_back
(t : Type0) (ls : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
@@ -116,12 +118,12 @@ let rec list_nth_mut_loop_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop] *)
+(** [loops::list_nth_mut_loop]: backward function 0 *)
let list_nth_mut_loop_back
(t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
list_nth_mut_loop_loop_back t ls i ret
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: loop 0: forward function *)
let rec list_nth_shared_loop_loop_fwd
(t : Type0) (ls : list_t t) (i : u32) :
Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i))
@@ -134,11 +136,11 @@ let rec list_nth_shared_loop_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_loop] *)
+(** [loops::list_nth_shared_loop]: forward function *)
let list_nth_shared_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
list_nth_shared_loop_loop_fwd t ls i
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: forward function *)
let rec get_elem_mut_loop_fwd
(x : usize) (ls : list_t usize) :
Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
@@ -148,12 +150,12 @@ let rec get_elem_mut_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: forward function *)
let get_elem_mut_fwd (slots : vec (list_t usize)) (x : usize) : result usize =
let* l = vec_index_mut_fwd (list_t usize) slots 0 in
get_elem_mut_loop_fwd x l
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: loop 0: backward function 0 *)
let rec get_elem_mut_loop_back
(x : usize) (ls : list_t usize) (ret : usize) :
Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
@@ -166,7 +168,7 @@ let rec get_elem_mut_loop_back
| ListNil -> Fail Failure
end
-(** [loops::get_elem_mut] *)
+(** [loops::get_elem_mut]: backward function 0 *)
let get_elem_mut_back
(slots : vec (list_t usize)) (x : usize) (ret : usize) :
result (vec (list_t usize))
@@ -175,7 +177,7 @@ let get_elem_mut_back
let* l0 = get_elem_mut_loop_back x l ret in
vec_index_mut_back (list_t usize) slots 0 l0
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: loop 0: forward function *)
let rec get_elem_shared_loop_fwd
(x : usize) (ls : list_t usize) :
Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
@@ -185,25 +187,25 @@ let rec get_elem_shared_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::get_elem_shared] *)
+(** [loops::get_elem_shared]: forward function *)
let get_elem_shared_fwd
(slots : vec (list_t usize)) (x : usize) : result usize =
let* l = vec_index_fwd (list_t usize) slots 0 in get_elem_shared_loop_fwd x l
-(** [loops::id_mut] *)
+(** [loops::id_mut]: forward function *)
let id_mut_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
Return ls
-(** [loops::id_mut] *)
+(** [loops::id_mut]: backward function 0 *)
let id_mut_back
(t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
Return ret
-(** [loops::id_shared] *)
+(** [loops::id_shared]: forward function *)
let id_shared_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
Return ls
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
let rec list_nth_mut_loop_with_id_loop_fwd
(t : Type0) (i : u32) (ls : list_t t) :
Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
@@ -216,12 +218,12 @@ let rec list_nth_mut_loop_with_id_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: forward function *)
let list_nth_mut_loop_with_id_fwd
(t : Type0) (ls : list_t t) (i : u32) : result t =
let* ls0 = id_mut_fwd t ls in list_nth_mut_loop_with_id_loop_fwd t i ls0
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
let rec list_nth_mut_loop_with_id_loop_back
(t : Type0) (i : u32) (ls : list_t t) (ret : t) :
Tot (result (list_t t))
@@ -238,14 +240,14 @@ let rec list_nth_mut_loop_with_id_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_with_id] *)
+(** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
let list_nth_mut_loop_with_id_back
(t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
let* ls0 = id_mut_fwd t ls in
let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
id_mut_back t ls l
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
let rec list_nth_shared_loop_with_id_loop_fwd
(t : Type0) (i : u32) (ls : list_t t) :
Tot (result t)
@@ -259,13 +261,13 @@ let rec list_nth_shared_loop_with_id_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_loop_with_id] *)
+(** [loops::list_nth_shared_loop_with_id]: forward function *)
let list_nth_shared_loop_with_id_fwd
(t : Type0) (ls : list_t t) (i : u32) : result t =
let* ls0 = id_shared_fwd t ls in
list_nth_shared_loop_with_id_loop_fwd t i ls0
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
let rec list_nth_mut_loop_pair_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -284,12 +286,12 @@ let rec list_nth_mut_loop_pair_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: forward function *)
let list_nth_mut_loop_pair_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_mut_loop_pair_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
let rec list_nth_mut_loop_pair_loop_back'a
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t))
@@ -310,14 +312,14 @@ let rec list_nth_mut_loop_pair_loop_back'a
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 0 *)
let list_nth_mut_loop_pair_back'a
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
result (list_t t)
=
list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
let rec list_nth_mut_loop_pair_loop_back'b
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t))
@@ -338,14 +340,14 @@ let rec list_nth_mut_loop_pair_loop_back'b
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_pair] *)
+(** [loops::list_nth_mut_loop_pair]: backward function 1 *)
let list_nth_mut_loop_pair_back'b
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
result (list_t t)
=
list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
let rec list_nth_shared_loop_pair_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -365,12 +367,12 @@ let rec list_nth_shared_loop_pair_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_loop_pair] *)
+(** [loops::list_nth_shared_loop_pair]: forward function *)
let list_nth_shared_loop_pair_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_shared_loop_pair_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
let rec list_nth_mut_loop_pair_merge_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -390,12 +392,12 @@ let rec list_nth_mut_loop_pair_merge_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: forward function *)
let list_nth_mut_loop_pair_merge_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_mut_loop_pair_merge_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
let rec list_nth_mut_loop_pair_merge_loop_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
Tot (result ((list_t t) & (list_t t)))
@@ -417,14 +419,14 @@ let rec list_nth_mut_loop_pair_merge_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_loop_pair_merge] *)
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
let list_nth_mut_loop_pair_merge_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
result ((list_t t) & (list_t t))
=
list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
let rec list_nth_shared_loop_pair_merge_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -444,12 +446,12 @@ let rec list_nth_shared_loop_pair_merge_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_loop_pair_merge] *)
+(** [loops::list_nth_shared_loop_pair_merge]: forward function *)
let list_nth_shared_loop_pair_merge_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_shared_loop_pair_merge_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
let rec list_nth_mut_shared_loop_pair_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -469,12 +471,12 @@ let rec list_nth_mut_shared_loop_pair_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: forward function *)
let list_nth_mut_shared_loop_pair_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_mut_shared_loop_pair_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
let rec list_nth_mut_shared_loop_pair_loop_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t))
@@ -495,14 +497,14 @@ let rec list_nth_mut_shared_loop_pair_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_shared_loop_pair] *)
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
let list_nth_mut_shared_loop_pair_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
result (list_t t)
=
list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
let rec list_nth_mut_shared_loop_pair_merge_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -522,12 +524,12 @@ let rec list_nth_mut_shared_loop_pair_merge_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
let list_nth_mut_shared_loop_pair_merge_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_mut_shared_loop_pair_merge_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
let rec list_nth_mut_shared_loop_pair_merge_loop_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t))
@@ -549,14 +551,14 @@ let rec list_nth_mut_shared_loop_pair_merge_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_mut_shared_loop_pair_merge] *)
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
let list_nth_mut_shared_loop_pair_merge_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
result (list_t t)
=
list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
let rec list_nth_shared_mut_loop_pair_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -576,12 +578,12 @@ let rec list_nth_shared_mut_loop_pair_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: forward function *)
let list_nth_shared_mut_loop_pair_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_shared_mut_loop_pair_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
let rec list_nth_shared_mut_loop_pair_loop_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t))
@@ -602,14 +604,14 @@ let rec list_nth_shared_mut_loop_pair_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_mut_loop_pair] *)
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
let list_nth_shared_mut_loop_pair_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
result (list_t t)
=
list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
let rec list_nth_shared_mut_loop_pair_merge_loop_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
Tot (result (t & t))
@@ -629,12 +631,12 @@ let rec list_nth_shared_mut_loop_pair_merge_loop_fwd
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
let list_nth_shared_mut_loop_pair_merge_fwd
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
list_nth_shared_mut_loop_pair_merge_loop_fwd t ls0 ls1 i
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
let rec list_nth_shared_mut_loop_pair_merge_loop_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
Tot (result (list_t t))
@@ -656,7 +658,7 @@ let rec list_nth_shared_mut_loop_pair_merge_loop_back
| ListNil -> Fail Failure
end
-(** [loops::list_nth_shared_mut_loop_pair_merge] *)
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
let list_nth_shared_mut_loop_pair_merge_back
(t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
result (list_t t)
diff --git a/tests/fstar/misc/NoNestedBorrows.fst b/tests/fstar/misc/NoNestedBorrows.fst
index 3770ab5d..d790bfa9 100644
--- a/tests/fstar/misc/NoNestedBorrows.fst
+++ b/tests/fstar/misc/NoNestedBorrows.fst
@@ -30,46 +30,46 @@ type sum_t (t1 t2 : Type0) =
| SumLeft : t1 -> sum_t t1 t2
| SumRight : t2 -> sum_t t1 t2
-(** [no_nested_borrows::neg_test] *)
+(** [no_nested_borrows::neg_test]: forward function *)
let neg_test_fwd (x : i32) : result i32 =
i32_neg x
-(** [no_nested_borrows::add_test] *)
+(** [no_nested_borrows::add_test]: forward function *)
let add_test_fwd (x : u32) (y : u32) : result u32 =
u32_add x y
-(** [no_nested_borrows::subs_test] *)
+(** [no_nested_borrows::subs_test]: forward function *)
let subs_test_fwd (x : u32) (y : u32) : result u32 =
u32_sub x y
-(** [no_nested_borrows::div_test] *)
+(** [no_nested_borrows::div_test]: forward function *)
let div_test_fwd (x : u32) (y : u32) : result u32 =
u32_div x y
-(** [no_nested_borrows::div_test1] *)
+(** [no_nested_borrows::div_test1]: forward function *)
let div_test1_fwd (x : u32) : result u32 =
u32_div x 2
-(** [no_nested_borrows::rem_test] *)
+(** [no_nested_borrows::rem_test]: forward function *)
let rem_test_fwd (x : u32) (y : u32) : result u32 =
u32_rem x y
-(** [no_nested_borrows::cast_test] *)
+(** [no_nested_borrows::cast_test]: forward function *)
let cast_test_fwd (x : u32) : result i32 =
scalar_cast U32 I32 x
-(** [no_nested_borrows::test2] *)
+(** [no_nested_borrows::test2]: forward function *)
let test2_fwd : result unit =
let* _ = u32_add 23 44 in Return ()
(** Unit test for [no_nested_borrows::test2] *)
let _ = assert_norm (test2_fwd = Return ())
-(** [no_nested_borrows::get_max] *)
+(** [no_nested_borrows::get_max]: forward function *)
let get_max_fwd (x : u32) (y : u32) : result u32 =
if x >= y then Return x else Return y
-(** [no_nested_borrows::test3] *)
+(** [no_nested_borrows::test3]: forward function *)
let test3_fwd : result unit =
let* x = get_max_fwd 4 3 in
let* y = get_max_fwd 10 11 in
@@ -79,21 +79,21 @@ let test3_fwd : result unit =
(** Unit test for [no_nested_borrows::test3] *)
let _ = assert_norm (test3_fwd = Return ())
-(** [no_nested_borrows::test_neg1] *)
+(** [no_nested_borrows::test_neg1]: forward function *)
let test_neg1_fwd : result unit =
let* y = i32_neg 3 in if not (y = -3) then Fail Failure else Return ()
(** Unit test for [no_nested_borrows::test_neg1] *)
let _ = assert_norm (test_neg1_fwd = Return ())
-(** [no_nested_borrows::refs_test1] *)
+(** [no_nested_borrows::refs_test1]: forward function *)
let refs_test1_fwd : result unit =
if not (1 = 1) then Fail Failure else Return ()
(** Unit test for [no_nested_borrows::refs_test1] *)
let _ = assert_norm (refs_test1_fwd = Return ())
-(** [no_nested_borrows::refs_test2] *)
+(** [no_nested_borrows::refs_test2]: forward function *)
let refs_test2_fwd : result unit =
if not (2 = 2)
then Fail Failure
@@ -108,47 +108,47 @@ let refs_test2_fwd : result unit =
(** Unit test for [no_nested_borrows::refs_test2] *)
let _ = assert_norm (refs_test2_fwd = Return ())
-(** [no_nested_borrows::test_list1] *)
+(** [no_nested_borrows::test_list1]: forward function *)
let test_list1_fwd : result unit =
Return ()
(** Unit test for [no_nested_borrows::test_list1] *)
let _ = assert_norm (test_list1_fwd = Return ())
-(** [no_nested_borrows::test_box1] *)
+(** [no_nested_borrows::test_box1]: forward function *)
let test_box1_fwd : result unit =
let b = 1 in let x = b in if not (x = 1) then Fail Failure else Return ()
(** Unit test for [no_nested_borrows::test_box1] *)
let _ = assert_norm (test_box1_fwd = Return ())
-(** [no_nested_borrows::copy_int] *)
+(** [no_nested_borrows::copy_int]: forward function *)
let copy_int_fwd (x : i32) : result i32 =
Return x
-(** [no_nested_borrows::test_unreachable] *)
+(** [no_nested_borrows::test_unreachable]: forward function *)
let test_unreachable_fwd (b : bool) : result unit =
if b then Fail Failure else Return ()
-(** [no_nested_borrows::test_panic] *)
+(** [no_nested_borrows::test_panic]: forward function *)
let test_panic_fwd (b : bool) : result unit =
if b then Fail Failure else Return ()
-(** [no_nested_borrows::test_copy_int] *)
+(** [no_nested_borrows::test_copy_int]: forward function *)
let test_copy_int_fwd : result unit =
let* y = copy_int_fwd 0 in if not (0 = y) then Fail Failure else Return ()
(** Unit test for [no_nested_borrows::test_copy_int] *)
let _ = assert_norm (test_copy_int_fwd = Return ())
-(** [no_nested_borrows::is_cons] *)
+(** [no_nested_borrows::is_cons]: forward function *)
let is_cons_fwd (t : Type0) (l : list_t t) : result bool =
begin match l with
| ListCons x l0 -> Return true
| ListNil -> Return false
end
-(** [no_nested_borrows::test_is_cons] *)
+(** [no_nested_borrows::test_is_cons]: forward function *)
let test_is_cons_fwd : result unit =
let l = ListNil in
let* b = is_cons_fwd i32 (ListCons 0 l) in
@@ -157,14 +157,14 @@ let test_is_cons_fwd : result unit =
(** Unit test for [no_nested_borrows::test_is_cons] *)
let _ = assert_norm (test_is_cons_fwd = Return ())
-(** [no_nested_borrows::split_list] *)
+(** [no_nested_borrows::split_list]: forward function *)
let split_list_fwd (t : Type0) (l : list_t t) : result (t & (list_t t)) =
begin match l with
| ListCons hd tl -> Return (hd, tl)
| ListNil -> Fail Failure
end
-(** [no_nested_borrows::test_split_list] *)
+(** [no_nested_borrows::test_split_list]: forward function *)
let test_split_list_fwd : result unit =
let l = ListNil in
let* p = split_list_fwd i32 (ListCons 0 l) in
@@ -174,16 +174,16 @@ let test_split_list_fwd : result unit =
(** Unit test for [no_nested_borrows::test_split_list] *)
let _ = assert_norm (test_split_list_fwd = Return ())
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: forward function *)
let choose_fwd (t : Type0) (b : bool) (x : t) (y : t) : result t =
if b then Return x else Return y
-(** [no_nested_borrows::choose] *)
+(** [no_nested_borrows::choose]: backward function 0 *)
let choose_back
(t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
if b then Return (ret, y) else Return (x, ret)
-(** [no_nested_borrows::choose_test] *)
+(** [no_nested_borrows::choose_test]: forward function *)
let choose_test_fwd : result unit =
let* z = choose_fwd i32 true 0 0 in
let* z0 = i32_add z 1 in
@@ -198,7 +198,7 @@ let choose_test_fwd : result unit =
(** Unit test for [no_nested_borrows::choose_test] *)
let _ = assert_norm (choose_test_fwd = Return ())
-(** [no_nested_borrows::test_char] *)
+(** [no_nested_borrows::test_char]: forward function *)
let test_char_fwd : result char =
Return 'a'
@@ -212,14 +212,14 @@ and tree_t (t : Type0) =
| TreeLeaf : t -> tree_t t
| TreeNode : t -> node_elem_t t -> tree_t t -> tree_t t
-(** [no_nested_borrows::list_length] *)
+(** [no_nested_borrows::list_length]: forward function *)
let rec list_length_fwd (t : Type0) (l : list_t t) : result u32 =
begin match l with
| ListCons x l1 -> let* i = list_length_fwd t l1 in u32_add 1 i
| ListNil -> Return 0
end
-(** [no_nested_borrows::list_nth_shared] *)
+(** [no_nested_borrows::list_nth_shared]: forward function *)
let rec list_nth_shared_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
begin match l with
| ListCons x tl ->
@@ -229,7 +229,7 @@ let rec list_nth_shared_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
| ListNil -> Fail Failure
end
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: forward function *)
let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
begin match l with
| ListCons x tl ->
@@ -239,7 +239,7 @@ let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
| ListNil -> Fail Failure
end
-(** [no_nested_borrows::list_nth_mut] *)
+(** [no_nested_borrows::list_nth_mut]: backward function 0 *)
let rec list_nth_mut_back
(t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
begin match l with
@@ -253,7 +253,7 @@ let rec list_nth_mut_back
| ListNil -> Fail Failure
end
-(** [no_nested_borrows::list_rev_aux] *)
+(** [no_nested_borrows::list_rev_aux]: forward function *)
let rec list_rev_aux_fwd
(t : Type0) (li : list_t t) (lo : list_t t) : result (list_t t) =
begin match li with
@@ -261,12 +261,13 @@ let rec list_rev_aux_fwd
| ListNil -> Return lo
end
-(** [no_nested_borrows::list_rev] *)
+(** [no_nested_borrows::list_rev]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let list_rev_fwd_back (t : Type0) (l : list_t t) : result (list_t t) =
let li = mem_replace_fwd (list_t t) l ListNil in
list_rev_aux_fwd t li ListNil
-(** [no_nested_borrows::test_list_functions] *)
+(** [no_nested_borrows::test_list_functions]: forward function *)
let test_list_functions_fwd : result unit =
let l = ListNil in
let l0 = ListCons 2 l in
@@ -302,48 +303,48 @@ let test_list_functions_fwd : result unit =
(** Unit test for [no_nested_borrows::test_list_functions] *)
let _ = assert_norm (test_list_functions_fwd = Return ())
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: forward function *)
let id_mut_pair1_fwd (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
Return (x, y)
-(** [no_nested_borrows::id_mut_pair1] *)
+(** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
let id_mut_pair1_back
(t1 t2 : Type0) (x : t1) (y : t2) (ret : (t1 & t2)) : result (t1 & t2) =
let (x0, x1) = ret in Return (x0, x1)
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: forward function *)
let id_mut_pair2_fwd (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
let (x, x0) = p in Return (x, x0)
-(** [no_nested_borrows::id_mut_pair2] *)
+(** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
let id_mut_pair2_back
(t1 t2 : Type0) (p : (t1 & t2)) (ret : (t1 & t2)) : result (t1 & t2) =
let (x, x0) = ret in Return (x, x0)
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: forward function *)
let id_mut_pair3_fwd (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
Return (x, y)
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
let id_mut_pair3_back'a
(t1 t2 : Type0) (x : t1) (y : t2) (ret : t1) : result t1 =
Return ret
-(** [no_nested_borrows::id_mut_pair3] *)
+(** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
let id_mut_pair3_back'b
(t1 t2 : Type0) (x : t1) (y : t2) (ret : t2) : result t2 =
Return ret
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: forward function *)
let id_mut_pair4_fwd (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
let (x, x0) = p in Return (x, x0)
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
let id_mut_pair4_back'a
(t1 t2 : Type0) (p : (t1 & t2)) (ret : t1) : result t1 =
Return ret
-(** [no_nested_borrows::id_mut_pair4] *)
+(** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
let id_mut_pair4_back'b
(t1 t2 : Type0) (p : (t1 & t2)) (ret : t2) : result t2 =
Return ret
@@ -351,15 +352,15 @@ let id_mut_pair4_back'b
(** [no_nested_borrows::StructWithTuple] *)
type struct_with_tuple_t (t1 t2 : Type0) = { struct_with_tuple_p : (t1 & t2); }
-(** [no_nested_borrows::new_tuple1] *)
+(** [no_nested_borrows::new_tuple1]: forward function *)
let new_tuple1_fwd : result (struct_with_tuple_t u32 u32) =
Return { struct_with_tuple_p = (1, 2) }
-(** [no_nested_borrows::new_tuple2] *)
+(** [no_nested_borrows::new_tuple2]: forward function *)
let new_tuple2_fwd : result (struct_with_tuple_t i16 i16) =
Return { struct_with_tuple_p = (1, 2) }
-(** [no_nested_borrows::new_tuple3] *)
+(** [no_nested_borrows::new_tuple3]: forward function *)
let new_tuple3_fwd : result (struct_with_tuple_t u64 i64) =
Return { struct_with_tuple_p = (1, 2) }
@@ -369,11 +370,11 @@ type struct_with_pair_t (t1 t2 : Type0) =
struct_with_pair_p : pair_t t1 t2;
}
-(** [no_nested_borrows::new_pair1] *)
+(** [no_nested_borrows::new_pair1]: forward function *)
let new_pair1_fwd : result (struct_with_pair_t u32 u32) =
Return { struct_with_pair_p = { pair_x = 1; pair_y = 2 } }
-(** [no_nested_borrows::test_constants] *)
+(** [no_nested_borrows::test_constants]: forward function *)
let test_constants_fwd : result unit =
let* swt = new_tuple1_fwd in
let (i, _) = swt.struct_with_tuple_p in
@@ -398,31 +399,32 @@ let test_constants_fwd : result unit =
(** Unit test for [no_nested_borrows::test_constants] *)
let _ = assert_norm (test_constants_fwd = Return ())
-(** [no_nested_borrows::test_weird_borrows1] *)
+(** [no_nested_borrows::test_weird_borrows1]: forward function *)
let test_weird_borrows1_fwd : result unit =
Return ()
(** Unit test for [no_nested_borrows::test_weird_borrows1] *)
let _ = assert_norm (test_weird_borrows1_fwd = Return ())
-(** [no_nested_borrows::test_mem_replace] *)
+(** [no_nested_borrows::test_mem_replace]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let test_mem_replace_fwd_back (px : u32) : result u32 =
let y = mem_replace_fwd u32 px 1 in
if not (y = 0) then Fail Failure else Return 2
-(** [no_nested_borrows::test_shared_borrow_bool1] *)
+(** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
let test_shared_borrow_bool1_fwd (b : bool) : result u32 =
if b then Return 0 else Return 1
-(** [no_nested_borrows::test_shared_borrow_bool2] *)
+(** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
let test_shared_borrow_bool2_fwd : result u32 =
Return 0
-(** [no_nested_borrows::test_shared_borrow_enum1] *)
+(** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
let test_shared_borrow_enum1_fwd (l : list_t u32) : result u32 =
begin match l with | ListCons i l0 -> Return 1 | ListNil -> Return 0 end
-(** [no_nested_borrows::test_shared_borrow_enum2] *)
+(** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
let test_shared_borrow_enum2_fwd : result u32 =
Return 0
diff --git a/tests/fstar/misc/Paper.fst b/tests/fstar/misc/Paper.fst
index 4ab31de3..e2d692c2 100644
--- a/tests/fstar/misc/Paper.fst
+++ b/tests/fstar/misc/Paper.fst
@@ -5,11 +5,12 @@ open Primitives
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-(** [paper::ref_incr] *)
+(** [paper::ref_incr]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
let ref_incr_fwd_back (x : i32) : result i32 =
i32_add x 1
-(** [paper::test_incr] *)
+(** [paper::test_incr]: forward function *)
let test_incr_fwd : result unit =
let* x = ref_incr_fwd_back 0 in
if not (x = 1) then Fail Failure else Return ()
@@ -17,16 +18,16 @@ let test_incr_fwd : result unit =
(** Unit test for [paper::test_incr] *)
let _ = assert_norm (test_incr_fwd = Return ())
-(** [paper::choose] *)
+(** [paper::choose]: forward function *)
let choose_fwd (t : Type0) (b : bool) (x : t) (y : t) : result t =
if b then Return x else Return y
-(** [paper::choose] *)
+(** [paper::choose]: backward function 0 *)
let choose_back
(t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
if b then Return (ret, y) else Return (x, ret)
-(** [paper::test_choose] *)
+(** [paper::test_choose]: forward function *)
let test_choose_fwd : result unit =
let* z = choose_fwd i32 true 0 0 in
let* z0 = i32_add z 1 in
@@ -46,7 +47,7 @@ type list_t (t : Type0) =
| ListCons : t -> list_t t -> list_t t
| ListNil : list_t t
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: forward function *)
let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
begin match l with
| ListCons x tl ->
@@ -56,7 +57,7 @@ let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
| ListNil -> Fail Failure
end
-(** [paper::list_nth_mut] *)
+(** [paper::list_nth_mut]: backward function 0 *)
let rec list_nth_mut_back
(t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
begin match l with
@@ -70,14 +71,14 @@ let rec list_nth_mut_back
| ListNil -> Fail Failure
end
-(** [paper::sum] *)
+(** [paper::sum]: forward function *)
let rec sum_fwd (l : list_t i32) : result i32 =
begin match l with
| ListCons x tl -> let* i = sum_fwd tl in i32_add x i
| ListNil -> Return 0
end
-(** [paper::test_nth] *)
+(** [paper::test_nth]: forward function *)
let test_nth_fwd : result unit =
let l = ListNil in
let l0 = ListCons 3 l in
@@ -91,7 +92,7 @@ let test_nth_fwd : result unit =
(** Unit test for [paper::test_nth] *)
let _ = assert_norm (test_nth_fwd = Return ())
-(** [paper::call_choose] *)
+(** [paper::call_choose]: forward function *)
let call_choose_fwd (p : (u32 & u32)) : result u32 =
let (px, py) = p in
let* pz = choose_fwd u32 true px py in
diff --git a/tests/fstar/misc/PoloniusList.fst b/tests/fstar/misc/PoloniusList.fst
index e2144487..79c86606 100644
--- a/tests/fstar/misc/PoloniusList.fst
+++ b/tests/fstar/misc/PoloniusList.fst
@@ -10,7 +10,7 @@ type list_t (t : Type0) =
| ListCons : t -> list_t t -> list_t t
| ListNil : list_t t
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: forward function *)
let rec get_list_at_x_fwd (ls : list_t u32) (x : u32) : result (list_t u32) =
begin match ls with
| ListCons hd tl ->
@@ -18,7 +18,7 @@ let rec get_list_at_x_fwd (ls : list_t u32) (x : u32) : result (list_t u32) =
| ListNil -> Return ListNil
end
-(** [polonius_list::get_list_at_x] *)
+(** [polonius_list::get_list_at_x]: backward function 0 *)
let rec get_list_at_x_back
(ls : list_t u32) (x : u32) (ret : list_t u32) : result (list_t u32) =
begin match ls with
diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml
index df0c6a24..03ff2671 100644
--- a/tests/hol4/betree/betreeMain_FunsScript.sml
+++ b/tests/hol4/betree/betreeMain_FunsScript.sml
@@ -7,7 +7,7 @@ val _ = new_theory "betreeMain_Funs"
val betree_load_internal_node_fwd_def = Define ‘
- (** [betree_main::betree::load_internal_node] *)
+ (** [betree_main::betree::load_internal_node]: forward function *)
betree_load_internal_node_fwd
(id : u64) (st : state) :
(state # (u64 # betree_message_t) betree_list_t) result
@@ -16,7 +16,7 @@ val betree_load_internal_node_fwd_def = Define ‘
val betree_store_internal_node_fwd_def = Define ‘
- (** [betree_main::betree::store_internal_node] *)
+ (** [betree_main::betree::store_internal_node]: forward function *)
betree_store_internal_node_fwd
(id : u64) (content : (u64 # betree_message_t) betree_list_t) (st : state)
:
@@ -29,14 +29,14 @@ val betree_store_internal_node_fwd_def = Define ‘
val betree_load_leaf_node_fwd_def = Define ‘
- (** [betree_main::betree::load_leaf_node] *)
+ (** [betree_main::betree::load_leaf_node]: forward function *)
betree_load_leaf_node_fwd
(id : u64) (st : state) : (state # (u64 # u64) betree_list_t) result =
betree_utils_load_leaf_node_fwd id st
val betree_store_leaf_node_fwd_def = Define ‘
- (** [betree_main::betree::store_leaf_node] *)
+ (** [betree_main::betree::store_leaf_node]: forward function *)
betree_store_leaf_node_fwd
(id : u64) (content : (u64 # u64) betree_list_t) (st : state) :
(state # unit) result
@@ -48,7 +48,7 @@ val betree_store_leaf_node_fwd_def = Define ‘
val betree_fresh_node_id_fwd_def = Define ‘
- (** [betree_main::betree::fresh_node_id] *)
+ (** [betree_main::betree::fresh_node_id]: forward function *)
betree_fresh_node_id_fwd (counter : u64) : u64 result =
do
_ <- u64_add counter (int_to_u64 1);
@@ -57,19 +57,19 @@ val betree_fresh_node_id_fwd_def = Define ‘
val betree_fresh_node_id_back_def = Define ‘
- (** [betree_main::betree::fresh_node_id] *)
+ (** [betree_main::betree::fresh_node_id]: backward function 0 *)
betree_fresh_node_id_back (counter : u64) : u64 result =
u64_add counter (int_to_u64 1)
val betree_node_id_counter_new_fwd_def = Define ‘
- (** [betree_main::betree::NodeIdCounter::{0}::new] *)
+ (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
betree_node_id_counter_new_fwd : betree_node_id_counter_t result =
Return (<| betree_node_id_counter_next_node_id := (int_to_u64 0) |>)
val betree_node_id_counter_fresh_id_fwd_def = Define ‘
- (** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+ (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
betree_node_id_counter_fresh_id_fwd
(self : betree_node_id_counter_t) : u64 result =
do
@@ -79,7 +79,7 @@ val betree_node_id_counter_fresh_id_fwd_def = Define ‘
val betree_node_id_counter_fresh_id_back_def = Define ‘
- (** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+ (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
betree_node_id_counter_fresh_id_back
(self : betree_node_id_counter_t) : betree_node_id_counter_t result =
do
@@ -97,7 +97,7 @@ Definition core_num_u64_max_c_def:
End
val betree_upsert_update_fwd_def = Define ‘
- (** [betree_main::betree::upsert_update] *)
+ (** [betree_main::betree::upsert_update]: forward function *)
betree_upsert_update_fwd
(prev : u64 option) (st : betree_upsert_fun_state_t) : u64 result =
(case prev of
@@ -117,7 +117,7 @@ val betree_upsert_update_fwd_def = Define ‘
val [betree_list_len_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::List::{1}::len] *)
+ (** [betree_main::betree::List::{1}::len]: forward function *)
betree_list_len_fwd (self : 't betree_list_t) : u64 result =
(case self of
| BetreeListCons t tl =>
@@ -129,7 +129,7 @@ val [betree_list_len_fwd_def] = DefineDiv ‘
val [betree_list_split_at_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::List::{1}::split_at] *)
+ (** [betree_main::betree::List::{1}::split_at]: forward function *)
betree_list_split_at_fwd
(self : 't betree_list_t) (n : u64) :
('t betree_list_t # 't betree_list_t) result
@@ -148,7 +148,8 @@ val [betree_list_split_at_fwd_def] = DefineDiv ‘
val betree_list_push_front_fwd_back_def = Define ‘
- (** [betree_main::betree::List::{1}::push_front] *)
+ (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
betree_list_push_front_fwd_back
(self : 't betree_list_t) (x : 't) : 't betree_list_t result =
let tl = mem_replace_fwd self BetreeListNil in
@@ -157,7 +158,7 @@ val betree_list_push_front_fwd_back_def = Define ‘
val betree_list_pop_front_fwd_def = Define ‘
- (** [betree_main::betree::List::{1}::pop_front] *)
+ (** [betree_main::betree::List::{1}::pop_front]: forward function *)
betree_list_pop_front_fwd (self : 't betree_list_t) : 't result =
let ls = mem_replace_fwd self BetreeListNil in
(case ls of
@@ -166,7 +167,7 @@ val betree_list_pop_front_fwd_def = Define ‘
val betree_list_pop_front_back_def = Define ‘
- (** [betree_main::betree::List::{1}::pop_front] *)
+ (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
betree_list_pop_front_back
(self : 't betree_list_t) : 't betree_list_t result =
let ls = mem_replace_fwd self BetreeListNil in
@@ -176,7 +177,7 @@ val betree_list_pop_front_back_def = Define ‘
val betree_list_hd_fwd_def = Define ‘
- (** [betree_main::betree::List::{1}::hd] *)
+ (** [betree_main::betree::List::{1}::hd]: forward function *)
betree_list_hd_fwd (self : 't betree_list_t) : 't result =
(case self of
| BetreeListCons hd l => Return hd
@@ -184,7 +185,7 @@ val betree_list_hd_fwd_def = Define ‘
val betree_list_head_has_key_fwd_def = Define ‘
- (** [betree_main::betree::List::{2}::head_has_key] *)
+ (** [betree_main::betree::List::{2}::head_has_key]: forward function *)
betree_list_head_has_key_fwd
(self : (u64 # 't) betree_list_t) (key : u64) : bool result =
(case self of
@@ -193,7 +194,7 @@ val betree_list_head_has_key_fwd_def = Define ‘
val [betree_list_partition_at_pivot_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::List::{2}::partition_at_pivot] *)
+ (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
betree_list_partition_at_pivot_fwd
(self : (u64 # 't) betree_list_t) (pivot : u64) :
((u64 # 't) betree_list_t # (u64 # 't) betree_list_t) result
@@ -214,7 +215,7 @@ val [betree_list_partition_at_pivot_fwd_def] = DefineDiv ‘
val betree_leaf_split_fwd_def = Define ‘
- (** [betree_main::betree::Leaf::{3}::split] *)
+ (** [betree_main::betree::Leaf::{3}::split]: forward function *)
betree_leaf_split_fwd
(self : betree_leaf_t) (content : (u64 # u64) betree_list_t)
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -256,7 +257,7 @@ val betree_leaf_split_fwd_def = Define ‘
val betree_leaf_split_back_def = Define ‘
- (** [betree_main::betree::Leaf::{3}::split] *)
+ (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
betree_leaf_split_back
(self : betree_leaf_t) (content : (u64 # u64) betree_list_t)
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
@@ -279,7 +280,7 @@ val betree_leaf_split_back_def = Define ‘
val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+ (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
betree_node_lookup_in_bindings_fwd
(key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result =
(case bindings of
@@ -295,7 +296,7 @@ val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘
val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+ (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
betree_node_lookup_first_message_for_key_fwd
(key : u64) (msgs : (u64 # betree_message_t) betree_list_t) :
(u64 # betree_message_t) betree_list_t result
@@ -310,7 +311,7 @@ val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘
val [betree_node_lookup_first_message_for_key_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+ (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
betree_node_lookup_first_message_for_key_back
(key : u64) (msgs : (u64 # betree_message_t) betree_list_t)
(ret : (u64 # betree_message_t) betree_list_t) :
@@ -331,7 +332,7 @@ val [betree_node_lookup_first_message_for_key_back_def] = DefineDiv ‘
val [betree_node_apply_upserts_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::apply_upserts] *)
+ (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
betree_node_apply_upserts_fwd
(msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option)
(key : u64) (st : state) :
@@ -364,7 +365,7 @@ val [betree_node_apply_upserts_fwd_def] = DefineDiv ‘
val [betree_node_apply_upserts_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::apply_upserts] *)
+ (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
betree_node_apply_upserts_back
(msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option)
(key : u64) (st : state) :
@@ -396,7 +397,7 @@ val [betree_node_apply_upserts_back_def] = DefineDiv ‘
val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup] *)
+ (** [betree_main::betree::Node::{5}::lookup]: forward function *)
(betree_node_lookup_fwd
(self : betree_node_t) (key : u64) (st : state) :
(state # u64 option) result
@@ -466,7 +467,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
od))
/\
- (** [betree_main::betree::Node::{5}::lookup] *)
+ (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
(betree_node_lookup_back
(self : betree_node_t) (key : u64) (st : state) : betree_node_t result =
(case self of
@@ -534,7 +535,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
od))
/\
- (** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+ (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
(betree_internal_lookup_in_children_fwd
(self : betree_internal_t) (key : u64) (st : state) :
(state # u64 option) result
@@ -544,7 +545,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
else betree_node_lookup_fwd self.betree_internal_right key st)
/\
- (** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+ (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
betree_internal_lookup_in_children_back
(self : betree_internal_t) (key : u64) (st : state) :
betree_internal_t result
@@ -563,7 +564,7 @@ val [betree_node_lookup_fwd_def, betree_node_lookup_back_def, betree_internal_lo
val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+ (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
betree_node_lookup_mut_in_bindings_fwd
(key : u64) (bindings : (u64 # u64) betree_list_t) :
(u64 # u64) betree_list_t result
@@ -578,7 +579,7 @@ val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘
val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+ (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
betree_node_lookup_mut_in_bindings_back
(key : u64) (bindings : (u64 # u64) betree_list_t)
(ret : (u64 # u64) betree_list_t) :
@@ -598,7 +599,8 @@ val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘
val betree_node_apply_to_leaf_fwd_back_def = Define ‘
- (** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+ (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
betree_node_apply_to_leaf_fwd_back
(bindings : (u64 # u64) betree_list_t) (key : u64)
(new_msg : betree_message_t) :
@@ -651,7 +653,8 @@ val betree_node_apply_to_leaf_fwd_back_def = Define ‘
val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+ (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
betree_node_apply_messages_to_leaf_fwd_back
(bindings : (u64 # u64) betree_list_t)
(new_msgs : (u64 # betree_message_t) betree_list_t) :
@@ -668,7 +671,8 @@ val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘
val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+ (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
betree_node_filter_messages_for_key_fwd_back
(key : u64) (msgs : (u64 # betree_message_t) betree_list_t) :
(u64 # betree_message_t) betree_list_t result
@@ -687,7 +691,7 @@ val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘
val [betree_node_lookup_first_message_after_key_fwd_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+ (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
betree_node_lookup_first_message_after_key_fwd
(key : u64) (msgs : (u64 # betree_message_t) betree_list_t) :
(u64 # betree_message_t) betree_list_t result
@@ -702,7 +706,7 @@ val [betree_node_lookup_first_message_after_key_fwd_def] = DefineDiv ‘
val [betree_node_lookup_first_message_after_key_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+ (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
betree_node_lookup_first_message_after_key_back
(key : u64) (msgs : (u64 # betree_message_t) betree_list_t)
(ret : (u64 # betree_message_t) betree_list_t) :
@@ -723,7 +727,8 @@ val [betree_node_lookup_first_message_after_key_back_def] = DefineDiv ‘
val betree_node_apply_to_internal_fwd_back_def = Define ‘
- (** [betree_main::betree::Node::{5}::apply_to_internal] *)
+ (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
betree_node_apply_to_internal_fwd_back
(msgs : (u64 # betree_message_t) betree_list_t) (key : u64)
(new_msg : betree_message_t) :
@@ -789,7 +794,8 @@ val betree_node_apply_to_internal_fwd_back_def = Define ‘
val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+ (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
betree_node_apply_messages_to_internal_fwd_back
(msgs : (u64 # betree_message_t) betree_list_t)
(new_msgs : (u64 # betree_message_t) betree_list_t) :
@@ -806,7 +812,7 @@ val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘
val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, betree_internal_flush_fwd_def, betree_internal_flush_back_def] = DefineDiv ‘
- (** [betree_main::betree::Node::{5}::apply_messages] *)
+ (** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
(betree_node_apply_messages_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -861,7 +867,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
od))
/\
- (** [betree_main::betree::Node::{5}::apply_messages] *)
+ (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
(betree_node_apply_messages_back
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -918,7 +924,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
od))
/\
- (** [betree_main::betree::Internal::{4}::flush] *)
+ (** [betree_main::betree::Internal::{4}::flush]: forward function *)
(betree_internal_flush_fwd
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -967,7 +973,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
od)
/\
- (** [betree_main::betree::Internal::{4}::flush] *)
+ (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
betree_internal_flush_back
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
@@ -1016,7 +1022,7 @@ val [betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def, be
val betree_node_apply_fwd_def = Define ‘
- (** [betree_main::betree::Node::{5}::apply] *)
+ (** [betree_main::betree::Node::{5}::apply]: forward function *)
betree_node_apply_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1036,7 +1042,7 @@ val betree_node_apply_fwd_def = Define ‘
val betree_node_apply_back_def = Define ‘
- (** [betree_main::betree::Node::{5}::apply] *)
+ (** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
betree_node_apply_back
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
@@ -1049,7 +1055,7 @@ val betree_node_apply_back_def = Define ‘
val betree_be_tree_new_fwd_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::new] *)
+ (** [betree_main::betree::BeTree::{6}::new]: forward function *)
betree_be_tree_new_fwd
(min_flush_size : u64) (split_size : u64) (st : state) :
(state # betree_be_tree_t) result
@@ -1075,7 +1081,7 @@ val betree_be_tree_new_fwd_def = Define ‘
val betree_be_tree_apply_fwd_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::apply] *)
+ (** [betree_main::betree::BeTree::{6}::apply]: forward function *)
betree_be_tree_apply_fwd
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
:
@@ -1093,7 +1099,7 @@ val betree_be_tree_apply_fwd_def = Define ‘
val betree_be_tree_apply_back_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::apply] *)
+ (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
betree_be_tree_apply_back
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
:
@@ -1113,7 +1119,7 @@ val betree_be_tree_apply_back_def = Define ‘
val betree_be_tree_insert_fwd_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::insert] *)
+ (** [betree_main::betree::BeTree::{6}::insert]: forward function *)
betree_be_tree_insert_fwd
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
(state # unit) result
@@ -1127,7 +1133,7 @@ val betree_be_tree_insert_fwd_def = Define ‘
val betree_be_tree_insert_back_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::insert] *)
+ (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
betree_be_tree_insert_back
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
betree_be_tree_t result
@@ -1136,7 +1142,7 @@ val betree_be_tree_insert_back_def = Define ‘
val betree_be_tree_delete_fwd_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::delete] *)
+ (** [betree_main::betree::BeTree::{6}::delete]: forward function *)
betree_be_tree_delete_fwd
(self : betree_be_tree_t) (key : u64) (st : state) :
(state # unit) result
@@ -1149,7 +1155,7 @@ val betree_be_tree_delete_fwd_def = Define ‘
val betree_be_tree_delete_back_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::delete] *)
+ (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
betree_be_tree_delete_back
(self : betree_be_tree_t) (key : u64) (st : state) :
betree_be_tree_t result
@@ -1158,7 +1164,7 @@ val betree_be_tree_delete_back_def = Define ‘
val betree_be_tree_upsert_fwd_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::upsert] *)
+ (** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
betree_be_tree_upsert_fwd
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
@@ -1172,7 +1178,7 @@ val betree_be_tree_upsert_fwd_def = Define ‘
val betree_be_tree_upsert_back_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::upsert] *)
+ (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
betree_be_tree_upsert_back
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
@@ -1182,7 +1188,7 @@ val betree_be_tree_upsert_back_def = Define ‘
val betree_be_tree_lookup_fwd_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::lookup] *)
+ (** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
betree_be_tree_lookup_fwd
(self : betree_be_tree_t) (key : u64) (st : state) :
(state # u64 option) result
@@ -1191,7 +1197,7 @@ val betree_be_tree_lookup_fwd_def = Define ‘
val betree_be_tree_lookup_back_def = Define ‘
- (** [betree_main::betree::BeTree::{6}::lookup] *)
+ (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
betree_be_tree_lookup_back
(self : betree_be_tree_t) (key : u64) (st : state) :
betree_be_tree_t result
@@ -1203,7 +1209,7 @@ val betree_be_tree_lookup_back_def = Define ‘
val main_fwd_def = Define ‘
- (** [betree_main::main] *)
+ (** [betree_main::main]: forward function *)
main_fwd : unit result =
Return ()
diff --git a/tests/hol4/betree/betreeMain_OpaqueScript.sml b/tests/hol4/betree/betreeMain_OpaqueScript.sml
index a6f0cf15..1d16db4c 100644
--- a/tests/hol4/betree/betreeMain_OpaqueScript.sml
+++ b/tests/hol4/betree/betreeMain_OpaqueScript.sml
@@ -1,26 +1,26 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [betree_main]: opaque function definitions *)
+(** [betree_main]: external function declarations *)
open primitivesLib divDefLib
open betreeMain_TypesTheory
val _ = new_theory "betreeMain_Opaque"
-val _ = new_constant ("betree_utils_load_internal_node_fwd",
+(** [betree_main::betree_utils::load_internal_node]: forward function *)val _ = new_constant ("betree_utils_load_internal_node_fwd",
“:u64 -> state -> (state # (u64 # betree_message_t) betree_list_t)
result”)
-val _ = new_constant ("betree_utils_store_internal_node_fwd",
+(** [betree_main::betree_utils::store_internal_node]: forward function *)val _ = new_constant ("betree_utils_store_internal_node_fwd",
“:u64 -> (u64 # betree_message_t) betree_list_t -> state -> (state # unit)
result”)
-val _ = new_constant ("betree_utils_load_leaf_node_fwd",
+(** [betree_main::betree_utils::load_leaf_node]: forward function *)val _ = new_constant ("betree_utils_load_leaf_node_fwd",
“:u64 -> state -> (state # (u64 # u64) betree_list_t) result”)
-val _ = new_constant ("betree_utils_store_leaf_node_fwd",
+(** [betree_main::betree_utils::store_leaf_node]: forward function *)val _ = new_constant ("betree_utils_store_leaf_node_fwd",
“:u64 -> (u64 # u64) betree_list_t -> state -> (state # unit) result”)
-val _ = new_constant ("core_option_option_unwrap_fwd",
+(** [core::option::Option::{0}::unwrap]: forward function *)val _ = new_constant ("core_option_option_unwrap_fwd",
“:'t option -> state -> (state # 't) result”)
val _ = export_theory ()
diff --git a/tests/hol4/hashmap/hashmap_FunsScript.sml b/tests/hol4/hashmap/hashmap_FunsScript.sml
index 9ad497f5..1ed57080 100644
--- a/tests/hol4/hashmap/hashmap_FunsScript.sml
+++ b/tests/hol4/hashmap/hashmap_FunsScript.sml
@@ -7,13 +7,13 @@ val _ = new_theory "hashmap_Funs"
val hash_key_fwd_def = Define ‘
- (** [hashmap::hash_key] *)
+ (** [hashmap::hash_key]: forward function *)
hash_key_fwd (k : usize) : usize result =
Return k
val [hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::allocate_slots] *)
+ (** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
hash_map_allocate_slots_loop_fwd
(slots : 't list_t vec) (n : usize) : 't list_t vec result =
if usize_gt n (int_to_usize 0)
@@ -27,14 +27,14 @@ val [hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
val hash_map_allocate_slots_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::allocate_slots] *)
+ (** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
hash_map_allocate_slots_fwd
(slots : 't list_t vec) (n : usize) : 't list_t vec result =
hash_map_allocate_slots_loop_fwd slots n
val hash_map_new_with_capacity_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::new_with_capacity] *)
+ (** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
hash_map_new_with_capacity_fwd
(capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) :
't hash_map_t result
@@ -55,14 +55,15 @@ val hash_map_new_with_capacity_fwd_def = Define ‘
val hash_map_new_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::new] *)
+ (** [hashmap::HashMap::{0}::new]: forward function *)
hash_map_new_fwd : 't hash_map_t result =
hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4)
(int_to_usize 5)
val [hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::clear] *)
+ (** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_clear_loop_fwd_back
(slots : 't list_t vec) (i : usize) : 't list_t vec result =
let i0 = vec_len slots in
@@ -77,7 +78,8 @@ val [hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
val hash_map_clear_fwd_back_def = Define ‘
- (** [hashmap::HashMap::{0}::clear] *)
+ (** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_clear_fwd_back (self : 't hash_map_t) : 't hash_map_t result =
do
v <- hash_map_clear_loop_fwd_back self.hash_map_slots (int_to_usize 0);
@@ -91,13 +93,13 @@ val hash_map_clear_fwd_back_def = Define ‘
val hash_map_len_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::len] *)
+ (** [hashmap::HashMap::{0}::len]: forward function *)
hash_map_len_fwd (self : 't hash_map_t) : usize result =
Return self.hash_map_num_entries
val [hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
hash_map_insert_in_list_loop_fwd
(key : usize) (value : 't) (ls : 't list_t) : bool result =
(case ls of
@@ -109,14 +111,14 @@ val [hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
val hash_map_insert_in_list_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
hash_map_insert_in_list_fwd
(key : usize) (value : 't) (ls : 't list_t) : bool result =
hash_map_insert_in_list_loop_fwd key value ls
val [hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
hash_map_insert_in_list_loop_back
(key : usize) (value : 't) (ls : 't list_t) : 't list_t result =
(case ls of
@@ -132,14 +134,15 @@ val [hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
val hash_map_insert_in_list_back_def = Define ‘
- (** [hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
hash_map_insert_in_list_back
(key : usize) (value : 't) (ls : 't list_t) : 't list_t result =
hash_map_insert_in_list_loop_back key value ls
val hash_map_insert_no_resize_fwd_back_def = Define ‘
- (** [hashmap::HashMap::{0}::insert_no_resize] *)
+ (** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_insert_no_resize_fwd_back
(self : 't hash_map_t) (key : usize) (value : 't) : 't hash_map_t result =
do
@@ -176,7 +179,8 @@ Definition core_num_u32_max_c_def:
End
val [hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::move_elements_from_list] *)
+ (** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_move_elements_from_list_loop_fwd_back
(ntable : 't hash_map_t) (ls : 't list_t) : 't hash_map_t result =
(case ls of
@@ -189,14 +193,16 @@ val [hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
val hash_map_move_elements_from_list_fwd_back_def = Define ‘
- (** [hashmap::HashMap::{0}::move_elements_from_list] *)
+ (** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_move_elements_from_list_fwd_back
(ntable : 't hash_map_t) (ls : 't list_t) : 't hash_map_t result =
hash_map_move_elements_from_list_loop_fwd_back ntable ls
val [hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::move_elements] *)
+ (** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_move_elements_loop_fwd_back
(ntable : 't hash_map_t) (slots : 't list_t vec) (i : usize) :
('t hash_map_t # 't list_t vec) result
@@ -221,7 +227,8 @@ val [hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
val hash_map_move_elements_fwd_back_def = Define ‘
- (** [hashmap::HashMap::{0}::move_elements] *)
+ (** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_move_elements_fwd_back
(ntable : 't hash_map_t) (slots : 't list_t vec) (i : usize) :
('t hash_map_t # 't list_t vec) result
@@ -230,7 +237,8 @@ val hash_map_move_elements_fwd_back_def = Define ‘
val hash_map_try_resize_fwd_back_def = Define ‘
- (** [hashmap::HashMap::{0}::try_resize] *)
+ (** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_try_resize_fwd_back (self : 't hash_map_t) : 't hash_map_t result =
do
max_usize <- mk_usize (u32_to_int core_num_u32_max_c);
@@ -263,7 +271,8 @@ val hash_map_try_resize_fwd_back_def = Define ‘
val hash_map_insert_fwd_back_def = Define ‘
- (** [hashmap::HashMap::{0}::insert] *)
+ (** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hash_map_insert_fwd_back
(self : 't hash_map_t) (key : usize) (value : 't) : 't hash_map_t result =
do
@@ -276,7 +285,7 @@ val hash_map_insert_fwd_back_def = Define ‘
val [hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::contains_key_in_list] *)
+ (** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
hash_map_contains_key_in_list_loop_fwd
(key : usize) (ls : 't list_t) : bool result =
(case ls of
@@ -288,14 +297,14 @@ val [hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
val hash_map_contains_key_in_list_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::contains_key_in_list] *)
+ (** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
hash_map_contains_key_in_list_fwd
(key : usize) (ls : 't list_t) : bool result =
hash_map_contains_key_in_list_loop_fwd key ls
val hash_map_contains_key_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::contains_key] *)
+ (** [hashmap::HashMap::{0}::contains_key]: forward function *)
hash_map_contains_key_fwd
(self : 't hash_map_t) (key : usize) : bool result =
do
@@ -310,7 +319,7 @@ val hash_map_contains_key_fwd_def = Define ‘
val [hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::get_in_list] *)
+ (** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
hash_map_get_in_list_loop_fwd (key : usize) (ls : 't list_t) : 't result =
(case ls of
| ListCons ckey cvalue tl =>
@@ -321,13 +330,13 @@ val [hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
val hash_map_get_in_list_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::get_in_list] *)
+ (** [hashmap::HashMap::{0}::get_in_list]: forward function *)
hash_map_get_in_list_fwd (key : usize) (ls : 't list_t) : 't result =
hash_map_get_in_list_loop_fwd key ls
val hash_map_get_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::get] *)
+ (** [hashmap::HashMap::{0}::get]: forward function *)
hash_map_get_fwd (self : 't hash_map_t) (key : usize) : 't result =
do
hash <- hash_key_fwd key;
@@ -341,7 +350,7 @@ val hash_map_get_fwd_def = Define ‘
val [hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
hash_map_get_mut_in_list_loop_fwd
(ls : 't list_t) (key : usize) : 't result =
(case ls of
@@ -353,13 +362,13 @@ val [hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
val hash_map_get_mut_in_list_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
hash_map_get_mut_in_list_fwd (ls : 't list_t) (key : usize) : 't result =
hash_map_get_mut_in_list_loop_fwd ls key
val [hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
hash_map_get_mut_in_list_loop_back
(ls : 't list_t) (key : usize) (ret : 't) : 't list_t result =
(case ls of
@@ -375,14 +384,14 @@ val [hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
val hash_map_get_mut_in_list_back_def = Define ‘
- (** [hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
hash_map_get_mut_in_list_back
(ls : 't list_t) (key : usize) (ret : 't) : 't list_t result =
hash_map_get_mut_in_list_loop_back ls key ret
val hash_map_get_mut_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::get_mut] *)
+ (** [hashmap::HashMap::{0}::get_mut]: forward function *)
hash_map_get_mut_fwd (self : 't hash_map_t) (key : usize) : 't result =
do
hash <- hash_key_fwd key;
@@ -396,7 +405,7 @@ val hash_map_get_mut_fwd_def = Define ‘
val hash_map_get_mut_back_def = Define ‘
- (** [hashmap::HashMap::{0}::get_mut] *)
+ (** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
hash_map_get_mut_back
(self : 't hash_map_t) (key : usize) (ret : 't) : 't hash_map_t result =
do
@@ -413,7 +422,7 @@ val hash_map_get_mut_back_def = Define ‘
val [hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
hash_map_remove_from_list_loop_fwd
(key : usize) (ls : 't list_t) : 't option result =
(case ls of
@@ -429,14 +438,14 @@ val [hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
val hash_map_remove_from_list_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
hash_map_remove_from_list_fwd
(key : usize) (ls : 't list_t) : 't option result =
hash_map_remove_from_list_loop_fwd key ls
val [hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
- (** [hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
hash_map_remove_from_list_loop_back
(key : usize) (ls : 't list_t) : 't list_t result =
(case ls of
@@ -456,14 +465,14 @@ val [hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
val hash_map_remove_from_list_back_def = Define ‘
- (** [hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
hash_map_remove_from_list_back
(key : usize) (ls : 't list_t) : 't list_t result =
hash_map_remove_from_list_loop_back key ls
val hash_map_remove_fwd_def = Define ‘
- (** [hashmap::HashMap::{0}::remove] *)
+ (** [hashmap::HashMap::{0}::remove]: forward function *)
hash_map_remove_fwd (self : 't hash_map_t) (key : usize) : 't option result =
do
hash <- hash_key_fwd key;
@@ -484,7 +493,7 @@ val hash_map_remove_fwd_def = Define ‘
val hash_map_remove_back_def = Define ‘
- (** [hashmap::HashMap::{0}::remove] *)
+ (** [hashmap::HashMap::{0}::remove]: backward function 0 *)
hash_map_remove_back
(self : 't hash_map_t) (key : usize) : 't hash_map_t result =
do
@@ -513,7 +522,7 @@ val hash_map_remove_back_def = Define ‘
val test1_fwd_def = Define ‘
- (** [hashmap::test1] *)
+ (** [hashmap::test1]: forward function *)
test1_fwd : unit result =
do
hm <- hash_map_new_fwd;
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
index 5a8f7ff8..6ec6223d 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
@@ -7,13 +7,13 @@ val _ = new_theory "hashmapMain_Funs"
val hashmap_hash_key_fwd_def = Define ‘
- (** [hashmap_main::hashmap::hash_key] *)
+ (** [hashmap_main::hashmap::hash_key]: forward function *)
hashmap_hash_key_fwd (k : usize) : usize result =
Return k
val [hashmap_hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
hashmap_hash_map_allocate_slots_loop_fwd
(slots : 't hashmap_list_t vec) (n : usize) :
't hashmap_list_t vec result
@@ -29,7 +29,7 @@ val [hashmap_hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘
val hashmap_hash_map_allocate_slots_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
hashmap_hash_map_allocate_slots_fwd
(slots : 't hashmap_list_t vec) (n : usize) :
't hashmap_list_t vec result
@@ -38,7 +38,7 @@ val hashmap_hash_map_allocate_slots_fwd_def = Define ‘
val hashmap_hash_map_new_with_capacity_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
hashmap_hash_map_new_with_capacity_fwd
(capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) :
't hashmap_hash_map_t result
@@ -60,14 +60,15 @@ val hashmap_hash_map_new_with_capacity_fwd_def = Define ‘
val hashmap_hash_map_new_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::new] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
hashmap_hash_map_new_fwd : 't hashmap_hash_map_t result =
hashmap_hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4)
(int_to_usize 5)
val [hashmap_hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_clear_loop_fwd_back
(slots : 't hashmap_list_t vec) (i : usize) :
't hashmap_list_t vec result
@@ -84,7 +85,8 @@ val [hashmap_hash_map_clear_loop_fwd_back_def] = DefineDiv ‘
val hashmap_hash_map_clear_fwd_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::clear] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_clear_fwd_back
(self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result =
do
@@ -102,13 +104,13 @@ val hashmap_hash_map_clear_fwd_back_def = Define ‘
val hashmap_hash_map_len_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::len] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
hashmap_hash_map_len_fwd (self : 't hashmap_hash_map_t) : usize result =
Return self.hashmap_hash_map_num_entries
val [hashmap_hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
hashmap_hash_map_insert_in_list_loop_fwd
(key : usize) (value : 't) (ls : 't hashmap_list_t) : bool result =
(case ls of
@@ -120,14 +122,14 @@ val [hashmap_hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘
val hashmap_hash_map_insert_in_list_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
hashmap_hash_map_insert_in_list_fwd
(key : usize) (value : 't) (ls : 't hashmap_list_t) : bool result =
hashmap_hash_map_insert_in_list_loop_fwd key value ls
val [hashmap_hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
hashmap_hash_map_insert_in_list_loop_back
(key : usize) (value : 't) (ls : 't hashmap_list_t) :
't hashmap_list_t result
@@ -146,7 +148,7 @@ val [hashmap_hash_map_insert_in_list_loop_back_def] = DefineDiv ‘
val hashmap_hash_map_insert_in_list_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
hashmap_hash_map_insert_in_list_back
(key : usize) (value : 't) (ls : 't hashmap_list_t) :
't hashmap_list_t result
@@ -155,7 +157,8 @@ val hashmap_hash_map_insert_in_list_back_def = Define ‘
val hashmap_hash_map_insert_no_resize_fwd_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_insert_no_resize_fwd_back
(self : 't hashmap_hash_map_t) (key : usize) (value : 't) :
't hashmap_hash_map_t result
@@ -199,7 +202,8 @@ Definition core_num_u32_max_c_def:
End
val [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_move_elements_from_list_loop_fwd_back
(ntable : 't hashmap_hash_map_t) (ls : 't hashmap_list_t) :
't hashmap_hash_map_t result
@@ -214,7 +218,8 @@ val [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
val hashmap_hash_map_move_elements_from_list_fwd_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_move_elements_from_list_fwd_back
(ntable : 't hashmap_hash_map_t) (ls : 't hashmap_list_t) :
't hashmap_hash_map_t result
@@ -223,7 +228,8 @@ val hashmap_hash_map_move_elements_from_list_fwd_back_def = Define ‘
val [hashmap_hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_move_elements_loop_fwd_back
(ntable : 't hashmap_hash_map_t) (slots : 't hashmap_list_t vec)
(i : usize) :
@@ -249,7 +255,8 @@ val [hashmap_hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘
val hashmap_hash_map_move_elements_fwd_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::move_elements] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_move_elements_fwd_back
(ntable : 't hashmap_hash_map_t) (slots : 't hashmap_list_t vec)
(i : usize) :
@@ -259,7 +266,8 @@ val hashmap_hash_map_move_elements_fwd_back_def = Define ‘
val hashmap_hash_map_try_resize_fwd_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::try_resize] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_try_resize_fwd_back
(self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result =
do
@@ -293,7 +301,8 @@ val hashmap_hash_map_try_resize_fwd_back_def = Define ‘
val hashmap_hash_map_insert_fwd_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::insert] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
hashmap_hash_map_insert_fwd_back
(self : 't hashmap_hash_map_t) (key : usize) (value : 't) :
't hashmap_hash_map_t result
@@ -308,7 +317,7 @@ val hashmap_hash_map_insert_fwd_back_def = Define ‘
val [hashmap_hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
hashmap_hash_map_contains_key_in_list_loop_fwd
(key : usize) (ls : 't hashmap_list_t) : bool result =
(case ls of
@@ -320,14 +329,14 @@ val [hashmap_hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘
val hashmap_hash_map_contains_key_in_list_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
hashmap_hash_map_contains_key_in_list_fwd
(key : usize) (ls : 't hashmap_list_t) : bool result =
hashmap_hash_map_contains_key_in_list_loop_fwd key ls
val hashmap_hash_map_contains_key_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::contains_key] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
hashmap_hash_map_contains_key_fwd
(self : 't hashmap_hash_map_t) (key : usize) : bool result =
do
@@ -342,7 +351,7 @@ val hashmap_hash_map_contains_key_fwd_def = Define ‘
val [hashmap_hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
hashmap_hash_map_get_in_list_loop_fwd
(key : usize) (ls : 't hashmap_list_t) : 't result =
(case ls of
@@ -354,14 +363,14 @@ val [hashmap_hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘
val hashmap_hash_map_get_in_list_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
hashmap_hash_map_get_in_list_fwd
(key : usize) (ls : 't hashmap_list_t) : 't result =
hashmap_hash_map_get_in_list_loop_fwd key ls
val hashmap_hash_map_get_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
hashmap_hash_map_get_fwd
(self : 't hashmap_hash_map_t) (key : usize) : 't result =
do
@@ -376,7 +385,7 @@ val hashmap_hash_map_get_fwd_def = Define ‘
val [hashmap_hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
hashmap_hash_map_get_mut_in_list_loop_fwd
(ls : 't hashmap_list_t) (key : usize) : 't result =
(case ls of
@@ -388,14 +397,14 @@ val [hashmap_hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘
val hashmap_hash_map_get_mut_in_list_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
hashmap_hash_map_get_mut_in_list_fwd
(ls : 't hashmap_list_t) (key : usize) : 't result =
hashmap_hash_map_get_mut_in_list_loop_fwd ls key
val [hashmap_hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
hashmap_hash_map_get_mut_in_list_loop_back
(ls : 't hashmap_list_t) (key : usize) (ret : 't) :
't hashmap_list_t result
@@ -413,7 +422,7 @@ val [hashmap_hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘
val hashmap_hash_map_get_mut_in_list_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
hashmap_hash_map_get_mut_in_list_back
(ls : 't hashmap_list_t) (key : usize) (ret : 't) :
't hashmap_list_t result
@@ -422,7 +431,7 @@ val hashmap_hash_map_get_mut_in_list_back_def = Define ‘
val hashmap_hash_map_get_mut_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
hashmap_hash_map_get_mut_fwd
(self : 't hashmap_hash_map_t) (key : usize) : 't result =
do
@@ -437,7 +446,7 @@ val hashmap_hash_map_get_mut_fwd_def = Define ‘
val hashmap_hash_map_get_mut_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::get_mut] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
hashmap_hash_map_get_mut_back
(self : 't hashmap_hash_map_t) (key : usize) (ret : 't) :
't hashmap_hash_map_t result
@@ -456,7 +465,7 @@ val hashmap_hash_map_get_mut_back_def = Define ‘
val [hashmap_hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
hashmap_hash_map_remove_from_list_loop_fwd
(key : usize) (ls : 't hashmap_list_t) : 't option result =
(case ls of
@@ -473,14 +482,14 @@ val [hashmap_hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘
val hashmap_hash_map_remove_from_list_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
hashmap_hash_map_remove_from_list_fwd
(key : usize) (ls : 't hashmap_list_t) : 't option result =
hashmap_hash_map_remove_from_list_loop_fwd key ls
val [hashmap_hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
- (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
hashmap_hash_map_remove_from_list_loop_back
(key : usize) (ls : 't hashmap_list_t) : 't hashmap_list_t result =
(case ls of
@@ -501,14 +510,14 @@ val [hashmap_hash_map_remove_from_list_loop_back_def] = DefineDiv ‘
val hashmap_hash_map_remove_from_list_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
hashmap_hash_map_remove_from_list_back
(key : usize) (ls : 't hashmap_list_t) : 't hashmap_list_t result =
hashmap_hash_map_remove_from_list_loop_back key ls
val hashmap_hash_map_remove_fwd_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
hashmap_hash_map_remove_fwd
(self : 't hashmap_hash_map_t) (key : usize) : 't option result =
do
@@ -530,7 +539,7 @@ val hashmap_hash_map_remove_fwd_def = Define ‘
val hashmap_hash_map_remove_back_def = Define ‘
- (** [hashmap_main::hashmap::HashMap::{0}::remove] *)
+ (** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
hashmap_hash_map_remove_back
(self : 't hashmap_hash_map_t) (key : usize) :
't hashmap_hash_map_t result
@@ -566,7 +575,7 @@ val hashmap_hash_map_remove_back_def = Define ‘
val hashmap_test1_fwd_def = Define ‘
- (** [hashmap_main::hashmap::test1] *)
+ (** [hashmap_main::hashmap::test1]: forward function *)
hashmap_test1_fwd : unit result =
do
hm <- hashmap_hash_map_new_fwd;
@@ -623,7 +632,7 @@ val hashmap_test1_fwd_def = Define ‘
val _ = assert_return (“hashmap_test1_fwd”)
val insert_on_disk_fwd_def = Define ‘
- (** [hashmap_main::insert_on_disk] *)
+ (** [hashmap_main::insert_on_disk]: forward function *)
insert_on_disk_fwd
(key : usize) (value : u64) (st : state) : (state # unit) result =
do
@@ -635,7 +644,7 @@ val insert_on_disk_fwd_def = Define ‘
val main_fwd_def = Define ‘
- (** [hashmap_main::main] *)
+ (** [hashmap_main::main]: forward function *)
main_fwd : unit result =
Return ()
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
index 5f6bcbb4..f7221d92 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml
@@ -1,15 +1,15 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap_main]: opaque function definitions *)
+(** [hashmap_main]: external function declarations *)
open primitivesLib divDefLib
open hashmapMain_TypesTheory
val _ = new_theory "hashmapMain_Opaque"
-val _ = new_constant ("hashmap_utils_deserialize_fwd",
+(** [hashmap_main::hashmap_utils::deserialize]: forward function *)val _ = new_constant ("hashmap_utils_deserialize_fwd",
“:state -> (state # u64 hashmap_hash_map_t) result”)
-val _ = new_constant ("hashmap_utils_serialize_fwd",
+(** [hashmap_main::hashmap_utils::serialize]: forward function *)val _ = new_constant ("hashmap_utils_serialize_fwd",
“:u64 hashmap_hash_map_t -> state -> (state # unit) result”)
val _ = export_theory ()
diff --git a/tests/hol4/misc-constants/constantsScript.sml b/tests/hol4/misc-constants/constantsScript.sml
index 324d553d..145c3e0f 100644
--- a/tests/hol4/misc-constants/constantsScript.sml
+++ b/tests/hol4/misc-constants/constantsScript.sml
@@ -38,7 +38,7 @@ Definition x2_c_def:
End
val incr_fwd_def = Define ‘
- (** [constants::incr] *)
+ (** [constants::incr]: forward function *)
incr_fwd (n : u32) : u32 result =
u32_add n (int_to_u32 1)
@@ -52,7 +52,7 @@ Definition x3_c_def:
End
val mk_pair0_fwd_def = Define ‘
- (** [constants::mk_pair0] *)
+ (** [constants::mk_pair0]: forward function *)
mk_pair0_fwd (x : u32) (y : u32) : (u32 # u32) result =
Return (x, y)
@@ -63,7 +63,7 @@ Datatype:
End
val mk_pair1_fwd_def = Define ‘
- (** [constants::mk_pair1] *)
+ (** [constants::mk_pair1]: forward function *)
mk_pair1_fwd (x : u32) (y : u32) : (u32, u32) pair_t result =
Return (<| pair_x := x; pair_y := y |>)
@@ -108,7 +108,7 @@ Datatype:
End
val wrap_new_fwd_def = Define ‘
- (** [constants::Wrap::{0}::new] *)
+ (** [constants::Wrap::{0}::new]: forward function *)
wrap_new_fwd (val : 't) : 't wrap_t result =
Return (<| wrap_val := val |>)
@@ -122,7 +122,7 @@ Definition y_c_def:
End
val unwrap_y_fwd_def = Define ‘
- (** [constants::unwrap_y] *)
+ (** [constants::unwrap_y]: forward function *)
unwrap_y_fwd : i32 result =
Return y_c.wrap_val
@@ -144,13 +144,13 @@ Definition get_z1_z1_c_def:
End
val get_z1_fwd_def = Define ‘
- (** [constants::get_z1] *)
+ (** [constants::get_z1]: forward function *)
get_z1_fwd : i32 result =
Return get_z1_z1_c
val add_fwd_def = Define ‘
- (** [constants::add] *)
+ (** [constants::add]: forward function *)
add_fwd (a : i32) (b : i32) : i32 result =
i32_add a b
@@ -180,7 +180,7 @@ Definition q3_c_def:
End
val get_z2_fwd_def = Define ‘
- (** [constants::get_z2] *)
+ (** [constants::get_z2]: forward function *)
get_z2_fwd : i32 result =
do
i <- get_z1_fwd;
diff --git a/tests/hol4/misc-external/external_FunsScript.sml b/tests/hol4/misc-external/external_FunsScript.sml
index 8172bc1c..f3692ee2 100644
--- a/tests/hol4/misc-external/external_FunsScript.sml
+++ b/tests/hol4/misc-external/external_FunsScript.sml
@@ -7,7 +7,7 @@ val _ = new_theory "external_Funs"
val swap_fwd_def = Define ‘
- (** [external::swap] *)
+ (** [external::swap]: forward function *)
swap_fwd (x : 't) (y : 't) (st : state) : (state # unit) result =
do
(st0, _) <- core_mem_swap_fwd x y st;
@@ -18,7 +18,7 @@ val swap_fwd_def = Define ‘
val swap_back_def = Define ‘
- (** [external::swap] *)
+ (** [external::swap]: backward function 0 *)
swap_back
(x : 't) (y : 't) (st : state) (st0 : state) : (state # ('t # 't)) result =
do
@@ -30,7 +30,7 @@ val swap_back_def = Define ‘
val test_new_non_zero_u32_fwd_def = Define ‘
- (** [external::test_new_non_zero_u32] *)
+ (** [external::test_new_non_zero_u32]: forward function *)
test_new_non_zero_u32_fwd
(x : u32) (st : state) : (state # core_num_nonzero_non_zero_u32_t) result =
do
@@ -40,7 +40,7 @@ val test_new_non_zero_u32_fwd_def = Define ‘
val test_vec_fwd_def = Define ‘
- (** [external::test_vec] *)
+ (** [external::test_vec]: forward function *)
test_vec_fwd : unit result =
let v = vec_new in do
_ <- vec_push_back v (int_to_u32 0);
@@ -52,7 +52,7 @@ val test_vec_fwd_def = Define ‘
val _ = assert_return (“test_vec_fwd”)
val custom_swap_fwd_def = Define ‘
- (** [external::custom_swap] *)
+ (** [external::custom_swap]: forward function *)
custom_swap_fwd (x : 't) (y : 't) (st : state) : (state # 't) result =
do
(st0, _) <- core_mem_swap_fwd x y st;
@@ -63,7 +63,7 @@ val custom_swap_fwd_def = Define ‘
val custom_swap_back_def = Define ‘
- (** [external::custom_swap] *)
+ (** [external::custom_swap]: backward function 0 *)
custom_swap_back
(x : 't) (y : 't) (st : state) (ret : 't) (st0 : state) :
(state # ('t # 't)) result
@@ -77,7 +77,7 @@ val custom_swap_back_def = Define ‘
val test_custom_swap_fwd_def = Define ‘
- (** [external::test_custom_swap] *)
+ (** [external::test_custom_swap]: forward function *)
test_custom_swap_fwd
(x : u32) (y : u32) (st : state) : (state # unit) result =
do
@@ -87,7 +87,7 @@ val test_custom_swap_fwd_def = Define ‘
val test_custom_swap_back_def = Define ‘
- (** [external::test_custom_swap] *)
+ (** [external::test_custom_swap]: backward function 0 *)
test_custom_swap_back
(x : u32) (y : u32) (st : state) (st0 : state) :
(state # (u32 # u32)) result
@@ -96,7 +96,7 @@ val test_custom_swap_back_def = Define ‘
val test_swap_non_zero_fwd_def = Define ‘
- (** [external::test_swap_non_zero] *)
+ (** [external::test_swap_non_zero]: forward function *)
test_swap_non_zero_fwd (x : u32) (st : state) : (state # u32) result =
do
(st0, _) <- swap_fwd x (int_to_u32 0) st;
diff --git a/tests/hol4/misc-external/external_OpaqueScript.sml b/tests/hol4/misc-external/external_OpaqueScript.sml
index e2fd281d..b5a6d91d 100644
--- a/tests/hol4/misc-external/external_OpaqueScript.sml
+++ b/tests/hol4/misc-external/external_OpaqueScript.sml
@@ -1,25 +1,25 @@
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [external]: opaque function definitions *)
+(** [external]: external function declarations *)
open primitivesLib divDefLib
open external_TypesTheory
val _ = new_theory "external_Opaque"
-val _ = new_constant ("core_mem_swap_fwd",
+(** [core::mem::swap]: forward function *)val _ = new_constant ("core_mem_swap_fwd",
“:'t -> 't -> state -> (state # unit) result”)
-val _ = new_constant ("core_mem_swap_back0",
+(** [core::mem::swap]: backward function 0 *)val _ = new_constant ("core_mem_swap_back0",
“:'t -> 't -> state -> state -> (state # 't) result”)
-val _ = new_constant ("core_mem_swap_back1",
+(** [core::mem::swap]: backward function 1 *)val _ = new_constant ("core_mem_swap_back1",
“:'t -> 't -> state -> state -> (state # 't) result”)
-val _ = new_constant ("core_num_nonzero_non_zero_u32_new_fwd",
+(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)val _ = new_constant ("core_num_nonzero_non_zero_u32_new_fwd",
“:u32 -> state -> (state # core_num_nonzero_non_zero_u32_t option)
result”)
-val _ = new_constant ("core_option_option_unwrap_fwd",
+(** [core::option::Option::{0}::unwrap]: forward function *)val _ = new_constant ("core_option_option_unwrap_fwd",
“:'t option -> state -> (state # 't) result”)
val _ = export_theory ()
diff --git a/tests/hol4/misc-loops/loops_FunsScript.sml b/tests/hol4/misc-loops/loops_FunsScript.sml
index f0ef036b..65cf77d4 100644
--- a/tests/hol4/misc-loops/loops_FunsScript.sml
+++ b/tests/hol4/misc-loops/loops_FunsScript.sml
@@ -7,7 +7,7 @@ val _ = new_theory "loops_Funs"
val [sum_loop_fwd_def] = DefineDiv ‘
- (** [loops::sum] *)
+ (** [loops::sum]: loop 0: forward function *)
sum_loop_fwd (max : u32) (i : u32) (s : u32) : u32 result =
if u32_lt i max
then (
@@ -20,13 +20,13 @@ val [sum_loop_fwd_def] = DefineDiv ‘
val sum_fwd_def = Define ‘
- (** [loops::sum] *)
+ (** [loops::sum]: forward function *)
sum_fwd (max : u32) : u32 result =
sum_loop_fwd max (int_to_u32 0) (int_to_u32 0)
val [sum_with_mut_borrows_loop_fwd_def] = DefineDiv ‘
- (** [loops::sum_with_mut_borrows] *)
+ (** [loops::sum_with_mut_borrows]: loop 0: forward function *)
sum_with_mut_borrows_loop_fwd
(max : u32) (mi : u32) (ms : u32) : u32 result =
if u32_lt mi max
@@ -40,13 +40,13 @@ val [sum_with_mut_borrows_loop_fwd_def] = DefineDiv ‘
val sum_with_mut_borrows_fwd_def = Define ‘
- (** [loops::sum_with_mut_borrows] *)
+ (** [loops::sum_with_mut_borrows]: forward function *)
sum_with_mut_borrows_fwd (max : u32) : u32 result =
sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
val [sum_with_shared_borrows_loop_fwd_def] = DefineDiv ‘
- (** [loops::sum_with_shared_borrows] *)
+ (** [loops::sum_with_shared_borrows]: loop 0: forward function *)
sum_with_shared_borrows_loop_fwd
(max : u32) (i : u32) (s : u32) : u32 result =
if u32_lt i max
@@ -60,13 +60,14 @@ val [sum_with_shared_borrows_loop_fwd_def] = DefineDiv ‘
val sum_with_shared_borrows_fwd_def = Define ‘
- (** [loops::sum_with_shared_borrows] *)
+ (** [loops::sum_with_shared_borrows]: forward function *)
sum_with_shared_borrows_fwd (max : u32) : u32 result =
sum_with_shared_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0)
val [clear_loop_fwd_back_def] = DefineDiv ‘
- (** [loops::clear] *)
+ (** [loops::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
clear_loop_fwd_back (v : u32 vec) (i : usize) : u32 vec result =
let i0 = vec_len v in
if usize_lt i i0
@@ -80,13 +81,14 @@ val [clear_loop_fwd_back_def] = DefineDiv ‘
val clear_fwd_back_def = Define ‘
- (** [loops::clear] *)
+ (** [loops::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
clear_fwd_back (v : u32 vec) : u32 vec result =
clear_loop_fwd_back v (int_to_usize 0)
val [list_mem_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_mem] *)
+ (** [loops::list_mem]: loop 0: forward function *)
list_mem_loop_fwd (x : u32) (ls : u32 list_t) : bool result =
(case ls of
| ListCons y tl => if y = x then Return T else list_mem_loop_fwd x tl
@@ -94,13 +96,13 @@ val [list_mem_loop_fwd_def] = DefineDiv ‘
val list_mem_fwd_def = Define ‘
- (** [loops::list_mem] *)
+ (** [loops::list_mem]: forward function *)
list_mem_fwd (x : u32) (ls : u32 list_t) : bool result =
list_mem_loop_fwd x ls
val [list_nth_mut_loop_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop] *)
+ (** [loops::list_nth_mut_loop]: loop 0: forward function *)
list_nth_mut_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result =
(case ls of
| ListCons x tl =>
@@ -115,13 +117,13 @@ val [list_nth_mut_loop_loop_fwd_def] = DefineDiv ‘
val list_nth_mut_loop_fwd_def = Define ‘
- (** [loops::list_nth_mut_loop] *)
+ (** [loops::list_nth_mut_loop]: forward function *)
list_nth_mut_loop_fwd (ls : 't list_t) (i : u32) : 't result =
list_nth_mut_loop_loop_fwd ls i
val [list_nth_mut_loop_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop] *)
+ (** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
list_nth_mut_loop_loop_back
(ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
(case ls of
@@ -138,14 +140,14 @@ val [list_nth_mut_loop_loop_back_def] = DefineDiv ‘
val list_nth_mut_loop_back_def = Define ‘
- (** [loops::list_nth_mut_loop] *)
+ (** [loops::list_nth_mut_loop]: backward function 0 *)
list_nth_mut_loop_back
(ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
list_nth_mut_loop_loop_back ls i ret
val [list_nth_shared_loop_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_shared_loop] *)
+ (** [loops::list_nth_shared_loop]: loop 0: forward function *)
list_nth_shared_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result =
(case ls of
| ListCons x tl =>
@@ -160,13 +162,13 @@ val [list_nth_shared_loop_loop_fwd_def] = DefineDiv ‘
val list_nth_shared_loop_fwd_def = Define ‘
- (** [loops::list_nth_shared_loop] *)
+ (** [loops::list_nth_shared_loop]: forward function *)
list_nth_shared_loop_fwd (ls : 't list_t) (i : u32) : 't result =
list_nth_shared_loop_loop_fwd ls i
val [get_elem_mut_loop_fwd_def] = DefineDiv ‘
- (** [loops::get_elem_mut] *)
+ (** [loops::get_elem_mut]: loop 0: forward function *)
get_elem_mut_loop_fwd (x : usize) (ls : usize list_t) : usize result =
(case ls of
| ListCons y tl => if y = x then Return y else get_elem_mut_loop_fwd x tl
@@ -174,7 +176,7 @@ val [get_elem_mut_loop_fwd_def] = DefineDiv ‘
val get_elem_mut_fwd_def = Define ‘
- (** [loops::get_elem_mut] *)
+ (** [loops::get_elem_mut]: forward function *)
get_elem_mut_fwd (slots : usize list_t vec) (x : usize) : usize result =
do
l <- vec_index_mut_fwd slots (int_to_usize 0);
@@ -183,7 +185,7 @@ val get_elem_mut_fwd_def = Define ‘
val [get_elem_mut_loop_back_def] = DefineDiv ‘
- (** [loops::get_elem_mut] *)
+ (** [loops::get_elem_mut]: loop 0: backward function 0 *)
get_elem_mut_loop_back
(x : usize) (ls : usize list_t) (ret : usize) : usize list_t result =
(case ls of
@@ -199,7 +201,7 @@ val [get_elem_mut_loop_back_def] = DefineDiv ‘
val get_elem_mut_back_def = Define ‘
- (** [loops::get_elem_mut] *)
+ (** [loops::get_elem_mut]: backward function 0 *)
get_elem_mut_back
(slots : usize list_t vec) (x : usize) (ret : usize) :
usize list_t vec result
@@ -212,7 +214,7 @@ val get_elem_mut_back_def = Define ‘
val [get_elem_shared_loop_fwd_def] = DefineDiv ‘
- (** [loops::get_elem_shared] *)
+ (** [loops::get_elem_shared]: loop 0: forward function *)
get_elem_shared_loop_fwd (x : usize) (ls : usize list_t) : usize result =
(case ls of
| ListCons y tl =>
@@ -221,7 +223,7 @@ val [get_elem_shared_loop_fwd_def] = DefineDiv ‘
val get_elem_shared_fwd_def = Define ‘
- (** [loops::get_elem_shared] *)
+ (** [loops::get_elem_shared]: forward function *)
get_elem_shared_fwd (slots : usize list_t vec) (x : usize) : usize result =
do
l <- vec_index_fwd slots (int_to_usize 0);
@@ -230,25 +232,25 @@ val get_elem_shared_fwd_def = Define ‘
val id_mut_fwd_def = Define ‘
- (** [loops::id_mut] *)
+ (** [loops::id_mut]: forward function *)
id_mut_fwd (ls : 't list_t) : 't list_t result =
Return ls
val id_mut_back_def = Define ‘
- (** [loops::id_mut] *)
+ (** [loops::id_mut]: backward function 0 *)
id_mut_back (ls : 't list_t) (ret : 't list_t) : 't list_t result =
Return ret
val id_shared_fwd_def = Define ‘
- (** [loops::id_shared] *)
+ (** [loops::id_shared]: forward function *)
id_shared_fwd (ls : 't list_t) : 't list_t result =
Return ls
val [list_nth_mut_loop_with_id_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_with_id] *)
+ (** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
list_nth_mut_loop_with_id_loop_fwd (i : u32) (ls : 't list_t) : 't result =
(case ls of
| ListCons x tl =>
@@ -263,7 +265,7 @@ val [list_nth_mut_loop_with_id_loop_fwd_def] = DefineDiv ‘
val list_nth_mut_loop_with_id_fwd_def = Define ‘
- (** [loops::list_nth_mut_loop_with_id] *)
+ (** [loops::list_nth_mut_loop_with_id]: forward function *)
list_nth_mut_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result =
do
ls0 <- id_mut_fwd ls;
@@ -272,7 +274,7 @@ val list_nth_mut_loop_with_id_fwd_def = Define ‘
val [list_nth_mut_loop_with_id_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_with_id] *)
+ (** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
list_nth_mut_loop_with_id_loop_back
(i : u32) (ls : 't list_t) (ret : 't) : 't list_t result =
(case ls of
@@ -289,7 +291,7 @@ val [list_nth_mut_loop_with_id_loop_back_def] = DefineDiv ‘
val list_nth_mut_loop_with_id_back_def = Define ‘
- (** [loops::list_nth_mut_loop_with_id] *)
+ (** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
list_nth_mut_loop_with_id_back
(ls : 't list_t) (i : u32) (ret : 't) : 't list_t result =
do
@@ -300,7 +302,7 @@ val list_nth_mut_loop_with_id_back_def = Define ‘
val [list_nth_shared_loop_with_id_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_shared_loop_with_id] *)
+ (** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
list_nth_shared_loop_with_id_loop_fwd
(i : u32) (ls : 't list_t) : 't result =
(case ls of
@@ -316,7 +318,7 @@ val [list_nth_shared_loop_with_id_loop_fwd_def] = DefineDiv ‘
val list_nth_shared_loop_with_id_fwd_def = Define ‘
- (** [loops::list_nth_shared_loop_with_id] *)
+ (** [loops::list_nth_shared_loop_with_id]: forward function *)
list_nth_shared_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result =
do
ls0 <- id_shared_fwd ls;
@@ -325,7 +327,7 @@ val list_nth_shared_loop_with_id_fwd_def = Define ‘
val [list_nth_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_pair] *)
+ (** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
list_nth_mut_loop_pair_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -344,14 +346,14 @@ val [list_nth_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
val list_nth_mut_loop_pair_fwd_def = Define ‘
- (** [loops::list_nth_mut_loop_pair] *)
+ (** [loops::list_nth_mut_loop_pair]: forward function *)
list_nth_mut_loop_pair_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_mut_loop_pair_loop_fwd ls0 ls1 i
val [list_nth_mut_loop_pair_loop_back'a_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_pair] *)
+ (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
list_nth_mut_loop_pair_loop_back'a
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -373,7 +375,7 @@ val [list_nth_mut_loop_pair_loop_back'a_def] = DefineDiv ‘
val list_nth_mut_loop_pair_back'a_def = Define ‘
- (** [loops::list_nth_mut_loop_pair] *)
+ (** [loops::list_nth_mut_loop_pair]: backward function 0 *)
list_nth_mut_loop_pair_back'a
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -382,7 +384,7 @@ val list_nth_mut_loop_pair_back'a_def = Define ‘
val [list_nth_mut_loop_pair_loop_back'b_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_pair] *)
+ (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *)
list_nth_mut_loop_pair_loop_back'b
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -404,7 +406,7 @@ val [list_nth_mut_loop_pair_loop_back'b_def] = DefineDiv ‘
val list_nth_mut_loop_pair_back'b_def = Define ‘
- (** [loops::list_nth_mut_loop_pair] *)
+ (** [loops::list_nth_mut_loop_pair]: backward function 1 *)
list_nth_mut_loop_pair_back'b
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -413,7 +415,7 @@ val list_nth_mut_loop_pair_back'b_def = Define ‘
val [list_nth_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_shared_loop_pair] *)
+ (** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
list_nth_shared_loop_pair_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -432,14 +434,14 @@ val [list_nth_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
val list_nth_shared_loop_pair_fwd_def = Define ‘
- (** [loops::list_nth_shared_loop_pair] *)
+ (** [loops::list_nth_shared_loop_pair]: forward function *)
list_nth_shared_loop_pair_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_shared_loop_pair_loop_fwd ls0 ls1 i
val [list_nth_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_pair_merge] *)
+ (** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
list_nth_mut_loop_pair_merge_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -458,14 +460,14 @@ val [list_nth_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
val list_nth_mut_loop_pair_merge_fwd_def = Define ‘
- (** [loops::list_nth_mut_loop_pair_merge] *)
+ (** [loops::list_nth_mut_loop_pair_merge]: forward function *)
list_nth_mut_loop_pair_merge_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i
val [list_nth_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_mut_loop_pair_merge] *)
+ (** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
list_nth_mut_loop_pair_merge_loop_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) :
('t list_t # 't list_t) result
@@ -488,7 +490,7 @@ val [list_nth_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
val list_nth_mut_loop_pair_merge_back_def = Define ‘
- (** [loops::list_nth_mut_loop_pair_merge] *)
+ (** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
list_nth_mut_loop_pair_merge_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) :
('t list_t # 't list_t) result
@@ -497,7 +499,7 @@ val list_nth_mut_loop_pair_merge_back_def = Define ‘
val [list_nth_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_shared_loop_pair_merge] *)
+ (** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
list_nth_shared_loop_pair_merge_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -516,14 +518,14 @@ val [list_nth_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
val list_nth_shared_loop_pair_merge_fwd_def = Define ‘
- (** [loops::list_nth_shared_loop_pair_merge] *)
+ (** [loops::list_nth_shared_loop_pair_merge]: forward function *)
list_nth_shared_loop_pair_merge_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i
val [list_nth_mut_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_mut_shared_loop_pair] *)
+ (** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
list_nth_mut_shared_loop_pair_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -542,14 +544,14 @@ val [list_nth_mut_shared_loop_pair_loop_fwd_def] = DefineDiv ‘
val list_nth_mut_shared_loop_pair_fwd_def = Define ‘
- (** [loops::list_nth_mut_shared_loop_pair] *)
+ (** [loops::list_nth_mut_shared_loop_pair]: forward function *)
list_nth_mut_shared_loop_pair_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i
val [list_nth_mut_shared_loop_pair_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_mut_shared_loop_pair] *)
+ (** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
list_nth_mut_shared_loop_pair_loop_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -571,7 +573,7 @@ val [list_nth_mut_shared_loop_pair_loop_back_def] = DefineDiv ‘
val list_nth_mut_shared_loop_pair_back_def = Define ‘
- (** [loops::list_nth_mut_shared_loop_pair] *)
+ (** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
list_nth_mut_shared_loop_pair_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -580,7 +582,7 @@ val list_nth_mut_shared_loop_pair_back_def = Define ‘
val [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
list_nth_mut_shared_loop_pair_merge_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -599,14 +601,14 @@ val [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
val list_nth_mut_shared_loop_pair_merge_fwd_def = Define ‘
- (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
list_nth_mut_shared_loop_pair_merge_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i
val [list_nth_mut_shared_loop_pair_merge_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
list_nth_mut_shared_loop_pair_merge_loop_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -628,7 +630,7 @@ val [list_nth_mut_shared_loop_pair_merge_loop_back_def] = DefineDiv ‘
val list_nth_mut_shared_loop_pair_merge_back_def = Define ‘
- (** [loops::list_nth_mut_shared_loop_pair_merge] *)
+ (** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
list_nth_mut_shared_loop_pair_merge_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -637,7 +639,7 @@ val list_nth_mut_shared_loop_pair_merge_back_def = Define ‘
val [list_nth_shared_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_shared_mut_loop_pair] *)
+ (** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
list_nth_shared_mut_loop_pair_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -656,14 +658,14 @@ val [list_nth_shared_mut_loop_pair_loop_fwd_def] = DefineDiv ‘
val list_nth_shared_mut_loop_pair_fwd_def = Define ‘
- (** [loops::list_nth_shared_mut_loop_pair] *)
+ (** [loops::list_nth_shared_mut_loop_pair]: forward function *)
list_nth_shared_mut_loop_pair_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i
val [list_nth_shared_mut_loop_pair_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_shared_mut_loop_pair] *)
+ (** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
list_nth_shared_mut_loop_pair_loop_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -685,7 +687,7 @@ val [list_nth_shared_mut_loop_pair_loop_back_def] = DefineDiv ‘
val list_nth_shared_mut_loop_pair_back_def = Define ‘
- (** [loops::list_nth_shared_mut_loop_pair] *)
+ (** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
list_nth_shared_mut_loop_pair_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -694,7 +696,7 @@ val list_nth_shared_mut_loop_pair_back_def = Define ‘
val [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
- (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
list_nth_shared_mut_loop_pair_merge_loop_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
(case ls0 of
@@ -713,14 +715,14 @@ val [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘
val list_nth_shared_mut_loop_pair_merge_fwd_def = Define ‘
- (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
list_nth_shared_mut_loop_pair_merge_fwd
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result =
list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i
val [list_nth_shared_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
- (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
list_nth_shared_mut_loop_pair_merge_loop_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
@@ -742,7 +744,7 @@ val [list_nth_shared_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘
val list_nth_shared_mut_loop_pair_merge_back_def = Define ‘
- (** [loops::list_nth_shared_mut_loop_pair_merge] *)
+ (** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
list_nth_shared_mut_loop_pair_merge_back
(ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) :
't list_t result
diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
index c8b106cd..66614c3f 100644
--- a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
+++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml
@@ -38,49 +38,49 @@ Datatype:
End
val neg_test_fwd_def = Define ‘
- (** [no_nested_borrows::neg_test] *)
+ (** [no_nested_borrows::neg_test]: forward function *)
neg_test_fwd (x : i32) : i32 result =
i32_neg x
val add_test_fwd_def = Define ‘
- (** [no_nested_borrows::add_test] *)
+ (** [no_nested_borrows::add_test]: forward function *)
add_test_fwd (x : u32) (y : u32) : u32 result =
u32_add x y
val subs_test_fwd_def = Define ‘
- (** [no_nested_borrows::subs_test] *)
+ (** [no_nested_borrows::subs_test]: forward function *)
subs_test_fwd (x : u32) (y : u32) : u32 result =
u32_sub x y
val div_test_fwd_def = Define ‘
- (** [no_nested_borrows::div_test] *)
+ (** [no_nested_borrows::div_test]: forward function *)
div_test_fwd (x : u32) (y : u32) : u32 result =
u32_div x y
val div_test1_fwd_def = Define ‘
- (** [no_nested_borrows::div_test1] *)
+ (** [no_nested_borrows::div_test1]: forward function *)
div_test1_fwd (x : u32) : u32 result =
u32_div x (int_to_u32 2)
val rem_test_fwd_def = Define ‘
- (** [no_nested_borrows::rem_test] *)
+ (** [no_nested_borrows::rem_test]: forward function *)
rem_test_fwd (x : u32) (y : u32) : u32 result =
u32_rem x y
val cast_test_fwd_def = Define ‘
- (** [no_nested_borrows::cast_test] *)
+ (** [no_nested_borrows::cast_test]: forward function *)
cast_test_fwd (x : u32) : i32 result =
mk_i32 (u32_to_int x)
val test2_fwd_def = Define ‘
- (** [no_nested_borrows::test2] *)
+ (** [no_nested_borrows::test2]: forward function *)
test2_fwd : unit result =
do
_ <- u32_add (int_to_u32 23) (int_to_u32 44);
@@ -92,13 +92,13 @@ val test2_fwd_def = Define ‘
val _ = assert_return (“test2_fwd”)
val get_max_fwd_def = Define ‘
- (** [no_nested_borrows::get_max] *)
+ (** [no_nested_borrows::get_max]: forward function *)
get_max_fwd (x : u32) (y : u32) : u32 result =
if u32_ge x y then Return x else Return y
val test3_fwd_def = Define ‘
- (** [no_nested_borrows::test3] *)
+ (** [no_nested_borrows::test3]: forward function *)
test3_fwd : unit result =
do
x <- get_max_fwd (int_to_u32 4) (int_to_u32 3);
@@ -112,7 +112,7 @@ val test3_fwd_def = Define ‘
val _ = assert_return (“test3_fwd”)
val test_neg1_fwd_def = Define ‘
- (** [no_nested_borrows::test_neg1] *)
+ (** [no_nested_borrows::test_neg1]: forward function *)
test_neg1_fwd : unit result =
do
y <- i32_neg (int_to_i32 3);
@@ -124,7 +124,7 @@ val test_neg1_fwd_def = Define ‘
val _ = assert_return (“test_neg1_fwd”)
val refs_test1_fwd_def = Define ‘
- (** [no_nested_borrows::refs_test1] *)
+ (** [no_nested_borrows::refs_test1]: forward function *)
refs_test1_fwd : unit result =
if ~ (int_to_i32 1 = int_to_i32 1) then Fail Failure else Return ()
@@ -133,7 +133,7 @@ val refs_test1_fwd_def = Define ‘
val _ = assert_return (“refs_test1_fwd”)
val refs_test2_fwd_def = Define ‘
- (** [no_nested_borrows::refs_test2] *)
+ (** [no_nested_borrows::refs_test2]: forward function *)
refs_test2_fwd : unit result =
if ~ (int_to_i32 2 = int_to_i32 2)
then Fail Failure
@@ -151,7 +151,7 @@ val refs_test2_fwd_def = Define ‘
val _ = assert_return (“refs_test2_fwd”)
val test_list1_fwd_def = Define ‘
- (** [no_nested_borrows::test_list1] *)
+ (** [no_nested_borrows::test_list1]: forward function *)
test_list1_fwd : unit result =
Return ()
@@ -160,7 +160,7 @@ val test_list1_fwd_def = Define ‘
val _ = assert_return (“test_list1_fwd”)
val test_box1_fwd_def = Define ‘
- (** [no_nested_borrows::test_box1] *)
+ (** [no_nested_borrows::test_box1]: forward function *)
test_box1_fwd : unit result =
let b = int_to_i32 1 in
let x = b in
@@ -171,25 +171,25 @@ val test_box1_fwd_def = Define ‘
val _ = assert_return (“test_box1_fwd”)
val copy_int_fwd_def = Define ‘
- (** [no_nested_borrows::copy_int] *)
+ (** [no_nested_borrows::copy_int]: forward function *)
copy_int_fwd (x : i32) : i32 result =
Return x
val test_unreachable_fwd_def = Define ‘
- (** [no_nested_borrows::test_unreachable] *)
+ (** [no_nested_borrows::test_unreachable]: forward function *)
test_unreachable_fwd (b : bool) : unit result =
if b then Fail Failure else Return ()
val test_panic_fwd_def = Define ‘
- (** [no_nested_borrows::test_panic] *)
+ (** [no_nested_borrows::test_panic]: forward function *)
test_panic_fwd (b : bool) : unit result =
if b then Fail Failure else Return ()
val test_copy_int_fwd_def = Define ‘
- (** [no_nested_borrows::test_copy_int] *)
+ (** [no_nested_borrows::test_copy_int]: forward function *)
test_copy_int_fwd : unit result =
do
y <- copy_int_fwd (int_to_i32 0);
@@ -201,13 +201,13 @@ val test_copy_int_fwd_def = Define ‘
val _ = assert_return (“test_copy_int_fwd”)
val is_cons_fwd_def = Define ‘
- (** [no_nested_borrows::is_cons] *)
+ (** [no_nested_borrows::is_cons]: forward function *)
is_cons_fwd (l : 't list_t) : bool result =
(case l of | ListCons t l0 => Return T | ListNil => Return F)
val test_is_cons_fwd_def = Define ‘
- (** [no_nested_borrows::test_is_cons] *)
+ (** [no_nested_borrows::test_is_cons]: forward function *)
test_is_cons_fwd : unit result =
let l = ListNil in
do
@@ -220,13 +220,13 @@ val test_is_cons_fwd_def = Define ‘
val _ = assert_return (“test_is_cons_fwd”)
val split_list_fwd_def = Define ‘
- (** [no_nested_borrows::split_list] *)
+ (** [no_nested_borrows::split_list]: forward function *)
split_list_fwd (l : 't list_t) : ('t # 't list_t) result =
(case l of | ListCons hd tl => Return (hd, tl) | ListNil => Fail Failure)
val test_split_list_fwd_def = Define ‘
- (** [no_nested_borrows::test_split_list] *)
+ (** [no_nested_borrows::test_split_list]: forward function *)
test_split_list_fwd : unit result =
let l = ListNil in
do
@@ -240,19 +240,19 @@ val test_split_list_fwd_def = Define ‘
val _ = assert_return (“test_split_list_fwd”)
val choose_fwd_def = Define ‘
- (** [no_nested_borrows::choose] *)
+ (** [no_nested_borrows::choose]: forward function *)
choose_fwd (b : bool) (x : 't) (y : 't) : 't result =
if b then Return x else Return y
val choose_back_def = Define ‘
- (** [no_nested_borrows::choose] *)
+ (** [no_nested_borrows::choose]: backward function 0 *)
choose_back (b : bool) (x : 't) (y : 't) (ret : 't) : ('t # 't) result =
if b then Return (ret, y) else Return (x, ret)
val choose_test_fwd_def = Define ‘
- (** [no_nested_borrows::choose_test] *)
+ (** [no_nested_borrows::choose_test]: forward function *)
choose_test_fwd : unit result =
do
z <- choose_fwd T (int_to_i32 0) (int_to_i32 0);
@@ -273,7 +273,7 @@ val choose_test_fwd_def = Define ‘
val _ = assert_return (“choose_test_fwd”)
val test_char_fwd_def = Define ‘
- (** [no_nested_borrows::test_char] *)
+ (** [no_nested_borrows::test_char]: forward function *)
test_char_fwd : char result =
Return #"a"
@@ -287,7 +287,7 @@ Datatype:
End
val [list_length_fwd_def] = DefineDiv ‘
- (** [no_nested_borrows::list_length] *)
+ (** [no_nested_borrows::list_length]: forward function *)
list_length_fwd (l : 't list_t) : u32 result =
(case l of
| ListCons t l1 => do
@@ -298,7 +298,7 @@ val [list_length_fwd_def] = DefineDiv ‘
val [list_nth_shared_fwd_def] = DefineDiv ‘
- (** [no_nested_borrows::list_nth_shared] *)
+ (** [no_nested_borrows::list_nth_shared]: forward function *)
list_nth_shared_fwd (l : 't list_t) (i : u32) : 't result =
(case l of
| ListCons x tl =>
@@ -312,7 +312,7 @@ val [list_nth_shared_fwd_def] = DefineDiv ‘
val [list_nth_mut_fwd_def] = DefineDiv ‘
- (** [no_nested_borrows::list_nth_mut] *)
+ (** [no_nested_borrows::list_nth_mut]: forward function *)
list_nth_mut_fwd (l : 't list_t) (i : u32) : 't result =
(case l of
| ListCons x tl =>
@@ -326,7 +326,7 @@ val [list_nth_mut_fwd_def] = DefineDiv ‘
val [list_nth_mut_back_def] = DefineDiv ‘
- (** [no_nested_borrows::list_nth_mut] *)
+ (** [no_nested_borrows::list_nth_mut]: backward function 0 *)
list_nth_mut_back (l : 't list_t) (i : u32) (ret : 't) : 't list_t result =
(case l of
| ListCons x tl =>
@@ -342,7 +342,7 @@ val [list_nth_mut_back_def] = DefineDiv ‘
val [list_rev_aux_fwd_def] = DefineDiv ‘
- (** [no_nested_borrows::list_rev_aux] *)
+ (** [no_nested_borrows::list_rev_aux]: forward function *)
list_rev_aux_fwd (li : 't list_t) (lo : 't list_t) : 't list_t result =
(case li of
| ListCons hd tl => list_rev_aux_fwd tl (ListCons hd lo)
@@ -350,13 +350,14 @@ val [list_rev_aux_fwd_def] = DefineDiv ‘
val list_rev_fwd_back_def = Define ‘
- (** [no_nested_borrows::list_rev] *)
+ (** [no_nested_borrows::list_rev]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
list_rev_fwd_back (l : 't list_t) : 't list_t result =
let li = mem_replace_fwd l ListNil in list_rev_aux_fwd li ListNil
val test_list_functions_fwd_def = Define ‘
- (** [no_nested_borrows::test_list_functions] *)
+ (** [no_nested_borrows::test_list_functions]: forward function *)
test_list_functions_fwd : unit result =
let l = ListNil in
let l0 = ListCons (int_to_i32 2) l in
@@ -411,63 +412,63 @@ val test_list_functions_fwd_def = Define ‘
val _ = assert_return (“test_list_functions_fwd”)
val id_mut_pair1_fwd_def = Define ‘
- (** [no_nested_borrows::id_mut_pair1] *)
+ (** [no_nested_borrows::id_mut_pair1]: forward function *)
id_mut_pair1_fwd (x : 't1) (y : 't2) : ('t1 # 't2) result =
Return (x, y)
val id_mut_pair1_back_def = Define ‘
- (** [no_nested_borrows::id_mut_pair1] *)
+ (** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
id_mut_pair1_back
(x : 't1) (y : 't2) (ret : ('t1 # 't2)) : ('t1 # 't2) result =
let (t, t0) = ret in Return (t, t0)
val id_mut_pair2_fwd_def = Define ‘
- (** [no_nested_borrows::id_mut_pair2] *)
+ (** [no_nested_borrows::id_mut_pair2]: forward function *)
id_mut_pair2_fwd (p : ('t1 # 't2)) : ('t1 # 't2) result =
let (t, t0) = p in Return (t, t0)
val id_mut_pair2_back_def = Define ‘
- (** [no_nested_borrows::id_mut_pair2] *)
+ (** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
id_mut_pair2_back
(p : ('t1 # 't2)) (ret : ('t1 # 't2)) : ('t1 # 't2) result =
let (t, t0) = ret in Return (t, t0)
val id_mut_pair3_fwd_def = Define ‘
- (** [no_nested_borrows::id_mut_pair3] *)
+ (** [no_nested_borrows::id_mut_pair3]: forward function *)
id_mut_pair3_fwd (x : 't1) (y : 't2) : ('t1 # 't2) result =
Return (x, y)
val id_mut_pair3_back'a_def = Define ‘
- (** [no_nested_borrows::id_mut_pair3] *)
+ (** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
id_mut_pair3_back'a (x : 't1) (y : 't2) (ret : 't1) : 't1 result =
Return ret
val id_mut_pair3_back'b_def = Define ‘
- (** [no_nested_borrows::id_mut_pair3] *)
+ (** [no_nested_borrows::id_mut_pair3]: backward function 1 *)
id_mut_pair3_back'b (x : 't1) (y : 't2) (ret : 't2) : 't2 result =
Return ret
val id_mut_pair4_fwd_def = Define ‘
- (** [no_nested_borrows::id_mut_pair4] *)
+ (** [no_nested_borrows::id_mut_pair4]: forward function *)
id_mut_pair4_fwd (p : ('t1 # 't2)) : ('t1 # 't2) result =
let (t, t0) = p in Return (t, t0)
val id_mut_pair4_back'a_def = Define ‘
- (** [no_nested_borrows::id_mut_pair4] *)
+ (** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
id_mut_pair4_back'a (p : ('t1 # 't2)) (ret : 't1) : 't1 result =
Return ret
val id_mut_pair4_back'b_def = Define ‘
- (** [no_nested_borrows::id_mut_pair4] *)
+ (** [no_nested_borrows::id_mut_pair4]: backward function 1 *)
id_mut_pair4_back'b (p : ('t1 # 't2)) (ret : 't2) : 't2 result =
Return ret
@@ -478,19 +479,19 @@ Datatype:
End
val new_tuple1_fwd_def = Define ‘
- (** [no_nested_borrows::new_tuple1] *)
+ (** [no_nested_borrows::new_tuple1]: forward function *)
new_tuple1_fwd : (u32, u32) struct_with_tuple_t result =
Return (<| struct_with_tuple_p := (int_to_u32 1, int_to_u32 2) |>)
val new_tuple2_fwd_def = Define ‘
- (** [no_nested_borrows::new_tuple2] *)
+ (** [no_nested_borrows::new_tuple2]: forward function *)
new_tuple2_fwd : (i16, i16) struct_with_tuple_t result =
Return (<| struct_with_tuple_p := (int_to_i16 1, int_to_i16 2) |>)
val new_tuple3_fwd_def = Define ‘
- (** [no_nested_borrows::new_tuple3] *)
+ (** [no_nested_borrows::new_tuple3]: forward function *)
new_tuple3_fwd : (u64, i64) struct_with_tuple_t result =
Return (<| struct_with_tuple_p := (int_to_u64 1, int_to_i64 2) |>)
@@ -501,7 +502,7 @@ Datatype:
End
val new_pair1_fwd_def = Define ‘
- (** [no_nested_borrows::new_pair1] *)
+ (** [no_nested_borrows::new_pair1]: forward function *)
new_pair1_fwd : (u32, u32) struct_with_pair_t result =
Return
(<|
@@ -511,7 +512,7 @@ val new_pair1_fwd_def = Define ‘
val test_constants_fwd_def = Define ‘
- (** [no_nested_borrows::test_constants] *)
+ (** [no_nested_borrows::test_constants]: forward function *)
test_constants_fwd : unit result =
do
swt <- new_tuple1_fwd;
@@ -546,7 +547,7 @@ val test_constants_fwd_def = Define ‘
val _ = assert_return (“test_constants_fwd”)
val test_weird_borrows1_fwd_def = Define ‘
- (** [no_nested_borrows::test_weird_borrows1] *)
+ (** [no_nested_borrows::test_weird_borrows1]: forward function *)
test_weird_borrows1_fwd : unit result =
Return ()
@@ -555,26 +556,27 @@ val test_weird_borrows1_fwd_def = Define ‘
val _ = assert_return (“test_weird_borrows1_fwd”)
val test_mem_replace_fwd_back_def = Define ‘
- (** [no_nested_borrows::test_mem_replace] *)
+ (** [no_nested_borrows::test_mem_replace]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
test_mem_replace_fwd_back (px : u32) : u32 result =
let y = mem_replace_fwd px (int_to_u32 1) in
if ~ (y = int_to_u32 0) then Fail Failure else Return (int_to_u32 2)
val test_shared_borrow_bool1_fwd_def = Define ‘
- (** [no_nested_borrows::test_shared_borrow_bool1] *)
+ (** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
test_shared_borrow_bool1_fwd (b : bool) : u32 result =
if b then Return (int_to_u32 0) else Return (int_to_u32 1)
val test_shared_borrow_bool2_fwd_def = Define ‘
- (** [no_nested_borrows::test_shared_borrow_bool2] *)
+ (** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
test_shared_borrow_bool2_fwd : u32 result =
Return (int_to_u32 0)
val test_shared_borrow_enum1_fwd_def = Define ‘
- (** [no_nested_borrows::test_shared_borrow_enum1] *)
+ (** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
test_shared_borrow_enum1_fwd (l : u32 list_t) : u32 result =
(case l of
| ListCons i l0 => Return (int_to_u32 1)
@@ -582,7 +584,7 @@ val test_shared_borrow_enum1_fwd_def = Define ‘
val test_shared_borrow_enum2_fwd_def = Define ‘
- (** [no_nested_borrows::test_shared_borrow_enum2] *)
+ (** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
test_shared_borrow_enum2_fwd : u32 result =
Return (int_to_u32 0)
diff --git a/tests/hol4/misc-paper/paperScript.sml b/tests/hol4/misc-paper/paperScript.sml
index 4d6e99ba..3ac5b6ca 100644
--- a/tests/hol4/misc-paper/paperScript.sml
+++ b/tests/hol4/misc-paper/paperScript.sml
@@ -6,13 +6,14 @@ val _ = new_theory "paper"
val ref_incr_fwd_back_def = Define ‘
- (** [paper::ref_incr] *)
+ (** [paper::ref_incr]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
ref_incr_fwd_back (x : i32) : i32 result =
i32_add x (int_to_i32 1)
val test_incr_fwd_def = Define ‘
- (** [paper::test_incr] *)
+ (** [paper::test_incr]: forward function *)
test_incr_fwd : unit result =
do
x <- ref_incr_fwd_back (int_to_i32 0);
@@ -24,19 +25,19 @@ val test_incr_fwd_def = Define ‘
val _ = assert_return (“test_incr_fwd”)
val choose_fwd_def = Define ‘
- (** [paper::choose] *)
+ (** [paper::choose]: forward function *)
choose_fwd (b : bool) (x : 't) (y : 't) : 't result =
if b then Return x else Return y
val choose_back_def = Define ‘
- (** [paper::choose] *)
+ (** [paper::choose]: backward function 0 *)
choose_back (b : bool) (x : 't) (y : 't) (ret : 't) : ('t # 't) result =
if b then Return (ret, y) else Return (x, ret)
val test_choose_fwd_def = Define ‘
- (** [paper::test_choose] *)
+ (** [paper::test_choose]: forward function *)
test_choose_fwd : unit result =
do
z <- choose_fwd T (int_to_i32 0) (int_to_i32 0);
@@ -62,7 +63,7 @@ Datatype:
End
val [list_nth_mut_fwd_def] = DefineDiv ‘
- (** [paper::list_nth_mut] *)
+ (** [paper::list_nth_mut]: forward function *)
list_nth_mut_fwd (l : 't list_t) (i : u32) : 't result =
(case l of
| ListCons x tl =>
@@ -76,7 +77,7 @@ val [list_nth_mut_fwd_def] = DefineDiv ‘
val [list_nth_mut_back_def] = DefineDiv ‘
- (** [paper::list_nth_mut] *)
+ (** [paper::list_nth_mut]: backward function 0 *)
list_nth_mut_back (l : 't list_t) (i : u32) (ret : 't) : 't list_t result =
(case l of
| ListCons x tl =>
@@ -92,7 +93,7 @@ val [list_nth_mut_back_def] = DefineDiv ‘
val [sum_fwd_def] = DefineDiv ‘
- (** [paper::sum] *)
+ (** [paper::sum]: forward function *)
sum_fwd (l : i32 list_t) : i32 result =
(case l of
| ListCons x tl => do
@@ -103,7 +104,7 @@ val [sum_fwd_def] = DefineDiv ‘
val test_nth_fwd_def = Define ‘
- (** [paper::test_nth] *)
+ (** [paper::test_nth]: forward function *)
test_nth_fwd : unit result =
let l = ListNil in
let l0 = ListCons (int_to_i32 3) l in
@@ -121,7 +122,7 @@ val test_nth_fwd_def = Define ‘
val _ = assert_return (“test_nth_fwd”)
val call_choose_fwd_def = Define ‘
- (** [paper::call_choose] *)
+ (** [paper::call_choose]: forward function *)
call_choose_fwd (p : (u32 # u32)) : u32 result =
let (px, py) = p in
do
diff --git a/tests/hol4/misc-polonius_list/poloniusListScript.sml b/tests/hol4/misc-polonius_list/poloniusListScript.sml
index dd631169..06876ed4 100644
--- a/tests/hol4/misc-polonius_list/poloniusListScript.sml
+++ b/tests/hol4/misc-polonius_list/poloniusListScript.sml
@@ -11,7 +11,7 @@ Datatype:
End
val [get_list_at_x_fwd_def] = DefineDiv ‘
- (** [polonius_list::get_list_at_x] *)
+ (** [polonius_list::get_list_at_x]: forward function *)
get_list_at_x_fwd (ls : u32 list_t) (x : u32) : u32 list_t result =
(case ls of
| ListCons hd tl =>
@@ -20,7 +20,7 @@ val [get_list_at_x_fwd_def] = DefineDiv ‘
val [get_list_at_x_back_def] = DefineDiv ‘
- (** [polonius_list::get_list_at_x] *)
+ (** [polonius_list::get_list_at_x]: backward function 0 *)
get_list_at_x_back
(ls : u32 list_t) (x : u32) (ret : u32 list_t) : u32 list_t result =
(case ls of
diff --git a/tests/lean/.gitignore b/tests/lean/.gitignore
index e74f9899..4d1c5853 100644
--- a/tests/lean/.gitignore
+++ b/tests/lean/.gitignore
@@ -1,2 +1,2 @@
-*/lake-packages/
-*/build/ \ No newline at end of file
+lake-packages
+build \ No newline at end of file
diff --git a/tests/lean/BetreeMain.lean b/tests/lean/BetreeMain.lean
new file mode 100644
index 00000000..5f307877
--- /dev/null
+++ b/tests/lean/BetreeMain.lean
@@ -0,0 +1 @@
+import BetreeMain.Funs
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
new file mode 100644
index 00000000..142adf08
--- /dev/null
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -0,0 +1,1023 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: function definitions
+import Base
+import BetreeMain.Types
+import BetreeMain.FunsExternal
+open Primitives
+namespace betree_main
+
+/- [betree_main::betree::load_internal_node]: forward function -/
+def betree.load_internal_node
+ (id : U64) (st : State) :
+ Result (State × (betree.List (U64 × betree.Message)))
+ :=
+ betree_utils.load_internal_node id st
+
+/- [betree_main::betree::store_internal_node]: forward function -/
+def betree.store_internal_node
+ (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) :
+ Result (State × Unit)
+ :=
+ do
+ let (st0, _) ← betree_utils.store_internal_node id content st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::load_leaf_node]: forward function -/
+def betree.load_leaf_node
+ (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) :=
+ betree_utils.load_leaf_node id st
+
+/- [betree_main::betree::store_leaf_node]: forward function -/
+def betree.store_leaf_node
+ (id : U64) (content : betree.List (U64 × U64)) (st : State) :
+ Result (State × Unit)
+ :=
+ do
+ let (st0, _) ← betree_utils.store_leaf_node id content st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::fresh_node_id]: forward function -/
+def betree.fresh_node_id (counter : U64) : Result U64 :=
+ do
+ let _ ← counter + (U64.ofInt 1)
+ Result.ret counter
+
+/- [betree_main::betree::fresh_node_id]: backward function 0 -/
+def betree.fresh_node_id_back (counter : U64) : Result U64 :=
+ counter + (U64.ofInt 1)
+
+/- [betree_main::betree::NodeIdCounter::{0}::new]: forward function -/
+def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
+ Result.ret { next_node_id := (U64.ofInt 0) }
+
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function -/
+def betree.NodeIdCounter.fresh_id (self : betree.NodeIdCounter) : Result U64 :=
+ do
+ let _ ← self.next_node_id + (U64.ofInt 1)
+ Result.ret self.next_node_id
+
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 -/
+def betree.NodeIdCounter.fresh_id_back
+ (self : betree.NodeIdCounter) : Result betree.NodeIdCounter :=
+ do
+ let i ← self.next_node_id + (U64.ofInt 1)
+ Result.ret { next_node_id := i }
+
+/- [core::num::u64::{10}::MAX] -/
+def core_num_u64_max_body : Result U64 :=
+ Result.ret (U64.ofInt 18446744073709551615)
+def core_num_u64_max_c : U64 := eval_global core_num_u64_max_body (by simp)
+
+/- [betree_main::betree::upsert_update]: forward function -/
+def betree.upsert_update
+ (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
+ match prev with
+ | Option.none =>
+ match st with
+ | betree.UpsertFunState.Add v => Result.ret v
+ | betree.UpsertFunState.Sub i => Result.ret (U64.ofInt 0)
+ | Option.some prev0 =>
+ match st with
+ | betree.UpsertFunState.Add v =>
+ do
+ let margin ← core_num_u64_max_c - prev0
+ if margin >= v
+ then prev0 + v
+ else Result.ret core_num_u64_max_c
+ | betree.UpsertFunState.Sub v =>
+ if prev0 >= v
+ then prev0 - v
+ else Result.ret (U64.ofInt 0)
+
+/- [betree_main::betree::List::{1}::len]: forward function -/
+divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 :=
+ match self with
+ | betree.List.Cons t tl =>
+ do
+ let i ← betree.List.len T tl
+ (U64.ofInt 1) + i
+ | betree.List.Nil => Result.ret (U64.ofInt 0)
+
+/- [betree_main::betree::List::{1}::split_at]: forward function -/
+divergent def betree.List.split_at
+ (T : Type) (self : betree.List T) (n : U64) :
+ Result ((betree.List T) × (betree.List T))
+ :=
+ if n = (U64.ofInt 0)
+ then Result.ret (betree.List.Nil, self)
+ else
+ match self with
+ | betree.List.Cons hd tl =>
+ do
+ let i ← n - (U64.ofInt 1)
+ let p ← betree.List.split_at T tl i
+ let (ls0, ls1) := p
+ let l := ls0
+ Result.ret (betree.List.Cons hd l, ls1)
+ | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def betree.List.push_front
+ (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
+ let tl := mem.replace (betree.List T) self betree.List.Nil
+ let l := tl
+ Result.ret (betree.List.Cons x l)
+
+/- [betree_main::betree::List::{1}::pop_front]: forward function -/
+def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
+ let ls := mem.replace (betree.List T) self betree.List.Nil
+ match ls with
+ | betree.List.Cons x tl => Result.ret x
+ | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::pop_front]: backward function 0 -/
+def betree.List.pop_front_back
+ (T : Type) (self : betree.List T) : Result (betree.List T) :=
+ let ls := mem.replace (betree.List T) self betree.List.Nil
+ match ls with
+ | betree.List.Cons x tl => Result.ret tl
+ | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::hd]: forward function -/
+def betree.List.hd (T : Type) (self : betree.List T) : Result T :=
+ match self with
+ | betree.List.Cons hd l => Result.ret hd
+ | betree.List.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{2}::head_has_key]: forward function -/
+def betree.List.head_has_key
+ (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool :=
+ match self with
+ | betree.List.Cons hd l => let (i, _) := hd
+ Result.ret (i = key)
+ | betree.List.Nil => Result.ret false
+
+/- [betree_main::betree::List::{2}::partition_at_pivot]: forward function -/
+divergent def betree.List.partition_at_pivot
+ (T : Type) (self : betree.List (U64 × T)) (pivot : U64) :
+ Result ((betree.List (U64 × T)) × (betree.List (U64 × T)))
+ :=
+ match self with
+ | betree.List.Cons hd tl =>
+ let (i, t) := hd
+ if i >= pivot
+ then Result.ret (betree.List.Nil, betree.List.Cons (i, t) tl)
+ else
+ do
+ let p ← betree.List.partition_at_pivot T tl pivot
+ let (ls0, ls1) := p
+ let l := ls0
+ Result.ret (betree.List.Cons (i, t) l, ls1)
+ | betree.List.Nil => Result.ret (betree.List.Nil, betree.List.Nil)
+
+/- [betree_main::betree::Leaf::{3}::split]: forward function -/
+def betree.Leaf.split
+ (self : betree.Leaf) (content : betree.List (U64 × U64))
+ (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
+ Result (State × betree.Internal)
+ :=
+ do
+ let p ← betree.List.split_at (U64 × U64) content params.split_size
+ let (content0, content1) := p
+ let p0 ← betree.List.hd (U64 × U64) content1
+ let (pivot, _) := p0
+ let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
+ let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+ let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
+ let (st0, _) ← betree.store_leaf_node id0 content0 st
+ let (st1, _) ← betree.store_leaf_node id1 content1 st0
+ let n := betree.Node.Leaf { id := id0, size := params.split_size }
+ let n0 := betree.Node.Leaf { id := id1, size := params.split_size }
+ Result.ret (st1, betree.Internal.mk self.id pivot n n0)
+
+/- [betree_main::betree::Leaf::{3}::split]: backward function 2 -/
+def betree.Leaf.split_back
+ (self : betree.Leaf) (content : betree.List (U64 × U64))
+ (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
+ Result betree.NodeIdCounter
+ :=
+ do
+ let p ← betree.List.split_at (U64 × U64) content params.split_size
+ let (content0, content1) := p
+ let _ ← betree.List.hd (U64 × U64) content1
+ let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
+ let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+ let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
+ let (st0, _) ← betree.store_leaf_node id0 content0 st
+ let _ ← betree.store_leaf_node id1 content1 st0
+ betree.NodeIdCounter.fresh_id_back node_id_cnt0
+
+/- [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function -/
+divergent def betree.Node.lookup_in_bindings
+ (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) :=
+ match bindings with
+ | betree.List.Cons hd tl =>
+ let (i, i0) := hd
+ if i = key
+ then Result.ret (Option.some i0)
+ else
+ if i > key
+ then Result.ret Option.none
+ else betree.Node.lookup_in_bindings key tl
+ | betree.List.Nil => Result.ret Option.none
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function -/
+divergent def betree.Node.lookup_first_message_for_key
+ (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ match msgs with
+ | betree.List.Cons x next_msgs =>
+ let (i, m) := x
+ if i >= key
+ then Result.ret (betree.List.Cons (i, m) next_msgs)
+ else betree.Node.lookup_first_message_for_key key next_msgs
+ | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 -/
+divergent def betree.Node.lookup_first_message_for_key_back
+ (key : U64) (msgs : betree.List (U64 × betree.Message))
+ (ret0 : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ match msgs with
+ | betree.List.Cons x next_msgs =>
+ let (i, m) := x
+ if i >= key
+ then Result.ret ret0
+ else
+ do
+ let next_msgs0 ←
+ betree.Node.lookup_first_message_for_key_back key next_msgs ret0
+ Result.ret (betree.List.Cons (i, m) next_msgs0)
+ | betree.List.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_upserts]: forward function -/
+divergent def betree.Node.apply_upserts
+ (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
+ (st : State) :
+ Result (State × U64)
+ :=
+ do
+ let b ← betree.List.head_has_key betree.Message msgs key
+ if b
+ then
+ do
+ let msg ← betree.List.pop_front (U64 × betree.Message) msgs
+ let (_, m) := msg
+ match m with
+ | betree.Message.Insert i => Result.fail Error.panic
+ | betree.Message.Delete => Result.fail Error.panic
+ | betree.Message.Upsert s =>
+ do
+ let v ← betree.upsert_update prev s
+ let msgs0 ←
+ betree.List.pop_front_back (U64 × betree.Message) msgs
+ betree.Node.apply_upserts msgs0 (Option.some v) key st
+ else
+ do
+ let (st0, v) ← core.option.Option.unwrap U64 prev st
+ let _ ←
+ betree.List.push_front (U64 × betree.Message) msgs (key,
+ betree.Message.Insert v)
+ Result.ret (st0, v)
+
+/- [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 -/
+divergent def betree.Node.apply_upserts_back
+ (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
+ (st : State) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ do
+ let b ← betree.List.head_has_key betree.Message msgs key
+ if b
+ then
+ do
+ let msg ← betree.List.pop_front (U64 × betree.Message) msgs
+ let (_, m) := msg
+ match m with
+ | betree.Message.Insert i => Result.fail Error.panic
+ | betree.Message.Delete => Result.fail Error.panic
+ | betree.Message.Upsert s =>
+ do
+ let v ← betree.upsert_update prev s
+ let msgs0 ←
+ betree.List.pop_front_back (U64 × betree.Message) msgs
+ betree.Node.apply_upserts_back msgs0 (Option.some v) key st
+ else
+ do
+ let (_, v) ← core.option.Option.unwrap U64 prev st
+ betree.List.push_front (U64 × betree.Message) msgs (key,
+ betree.Message.Insert v)
+
+/- [betree_main::betree::Node::{5}::lookup]: forward function -/
+mutual divergent def betree.Node.lookup
+ (self : betree.Node) (key : U64) (st : State) :
+ Result (State × (Option U64))
+ :=
+ match self with
+ | betree.Node.Internal node =>
+ do
+ let ⟨ i, i0, n, n0 ⟩ := node
+ let (st0, msgs) ← betree.load_internal_node i st
+ let pending ← betree.Node.lookup_first_message_for_key key msgs
+ match pending with
+ | betree.List.Cons p l =>
+ let (k, msg) := p
+ if k != key
+ then
+ do
+ let (st1, opt) ←
+ betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
+ key st0
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ (betree.List.Cons (k, msg) l)
+ Result.ret (st1, opt)
+ else
+ match msg with
+ | betree.Message.Insert v =>
+ do
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ (betree.List.Cons (k, betree.Message.Insert v) l)
+ Result.ret (st0, Option.some v)
+ | betree.Message.Delete =>
+ do
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ (betree.List.Cons (k, betree.Message.Delete) l)
+ Result.ret (st0, Option.none)
+ | betree.Message.Upsert ufs =>
+ do
+ let (st1, v) ←
+ betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
+ n0) key st0
+ let (st2, v0) ←
+ betree.Node.apply_upserts (betree.List.Cons (k,
+ betree.Message.Upsert ufs) l) v key st1
+ let node0 ←
+ betree.Internal.lookup_in_children_back (betree.Internal.mk i
+ i0 n n0) key st0
+ let ⟨ i1, _, _, _ ⟩ := node0
+ let pending0 ←
+ betree.Node.apply_upserts_back (betree.List.Cons (k,
+ betree.Message.Upsert ufs) l) v key st1
+ let msgs0 ←
+ betree.Node.lookup_first_message_for_key_back key msgs pending0
+ let (st3, _) ← betree.store_internal_node i1 msgs0 st2
+ Result.ret (st3, Option.some v0)
+ | betree.List.Nil =>
+ do
+ let (st1, opt) ←
+ betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
+ key st0
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ betree.List.Nil
+ Result.ret (st1, opt)
+ | betree.Node.Leaf node =>
+ do
+ let (st0, bindings) ← betree.load_leaf_node node.id st
+ let opt ← betree.Node.lookup_in_bindings key bindings
+ Result.ret (st0, opt)
+
+/- [betree_main::betree::Node::{5}::lookup]: backward function 0 -/
+divergent def betree.Node.lookup_back
+ (self : betree.Node) (key : U64) (st : State) : Result betree.Node :=
+ match self with
+ | betree.Node.Internal node =>
+ do
+ let ⟨ i, i0, n, n0 ⟩ := node
+ let (st0, msgs) ← betree.load_internal_node i st
+ let pending ← betree.Node.lookup_first_message_for_key key msgs
+ match pending with
+ | betree.List.Cons p l =>
+ let (k, msg) := p
+ if k != key
+ then
+ do
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ (betree.List.Cons (k, msg) l)
+ let node0 ←
+ betree.Internal.lookup_in_children_back (betree.Internal.mk i i0
+ n n0) key st0
+ Result.ret (betree.Node.Internal node0)
+ else
+ match msg with
+ | betree.Message.Insert v =>
+ do
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ (betree.List.Cons (k, betree.Message.Insert v) l)
+ Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
+ | betree.Message.Delete =>
+ do
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ (betree.List.Cons (k, betree.Message.Delete) l)
+ Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
+ | betree.Message.Upsert ufs =>
+ do
+ let (st1, v) ←
+ betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
+ n0) key st0
+ let (st2, _) ←
+ betree.Node.apply_upserts (betree.List.Cons (k,
+ betree.Message.Upsert ufs) l) v key st1
+ let node0 ←
+ betree.Internal.lookup_in_children_back (betree.Internal.mk i
+ i0 n n0) key st0
+ let ⟨ i1, i2, n1, n2 ⟩ := node0
+ let pending0 ←
+ betree.Node.apply_upserts_back (betree.List.Cons (k,
+ betree.Message.Upsert ufs) l) v key st1
+ let msgs0 ←
+ betree.Node.lookup_first_message_for_key_back key msgs pending0
+ let _ ← betree.store_internal_node i1 msgs0 st2
+ Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1
+ n2))
+ | betree.List.Nil =>
+ do
+ let _ ←
+ betree.Node.lookup_first_message_for_key_back key msgs
+ betree.List.Nil
+ let node0 ←
+ betree.Internal.lookup_in_children_back (betree.Internal.mk i i0 n
+ n0) key st0
+ Result.ret (betree.Node.Internal node0)
+ | betree.Node.Leaf node =>
+ do
+ let (_, bindings) ← betree.load_leaf_node node.id st
+ let _ ← betree.Node.lookup_in_bindings key bindings
+ Result.ret (betree.Node.Leaf node)
+
+/- [betree_main::betree::Internal::{4}::lookup_in_children]: forward function -/
+divergent def betree.Internal.lookup_in_children
+ (self : betree.Internal) (key : U64) (st : State) :
+ Result (State × (Option U64))
+ :=
+ let ⟨ _, i, n, n0 ⟩ := self
+ if key < i
+ then betree.Node.lookup n key st
+ else betree.Node.lookup n0 key st
+
+/- [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 -/
+divergent def betree.Internal.lookup_in_children_back
+ (self : betree.Internal) (key : U64) (st : State) : Result betree.Internal :=
+ let ⟨ i, i0, n, n0 ⟩ := self
+ if key < i0
+ then
+ do
+ let n1 ← betree.Node.lookup_back n key st
+ Result.ret (betree.Internal.mk i i0 n1 n0)
+ else
+ do
+ let n1 ← betree.Node.lookup_back n0 key st
+ Result.ret (betree.Internal.mk i i0 n n1)
+
+end
+
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function -/
+divergent def betree.Node.lookup_mut_in_bindings
+ (key : U64) (bindings : betree.List (U64 × U64)) :
+ Result (betree.List (U64 × U64))
+ :=
+ match bindings with
+ | betree.List.Cons hd tl =>
+ let (i, i0) := hd
+ if i >= key
+ then Result.ret (betree.List.Cons (i, i0) tl)
+ else betree.Node.lookup_mut_in_bindings key tl
+ | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 -/
+divergent def betree.Node.lookup_mut_in_bindings_back
+ (key : U64) (bindings : betree.List (U64 × U64))
+ (ret0 : betree.List (U64 × U64)) :
+ Result (betree.List (U64 × U64))
+ :=
+ match bindings with
+ | betree.List.Cons hd tl =>
+ let (i, i0) := hd
+ if i >= key
+ then Result.ret ret0
+ else
+ do
+ let tl0 ← betree.Node.lookup_mut_in_bindings_back key tl ret0
+ Result.ret (betree.List.Cons (i, i0) tl0)
+ | betree.List.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def betree.Node.apply_to_leaf
+ (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message)
+ :
+ Result (betree.List (U64 × U64))
+ :=
+ do
+ let bindings0 ← betree.Node.lookup_mut_in_bindings key bindings
+ let b ← betree.List.head_has_key U64 bindings0 key
+ if b
+ then
+ do
+ let hd ← betree.List.pop_front (U64 × U64) bindings0
+ match new_msg with
+ | betree.Message.Insert v =>
+ do
+ let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+ let bindings2 ←
+ betree.List.push_front (U64 × U64) bindings1 (key, v)
+ betree.Node.lookup_mut_in_bindings_back key bindings bindings2
+ | betree.Message.Delete =>
+ do
+ let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+ betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+ | betree.Message.Upsert s =>
+ do
+ let (_, i) := hd
+ let v ← betree.upsert_update (Option.some i) s
+ let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
+ let bindings2 ←
+ betree.List.push_front (U64 × U64) bindings1 (key, v)
+ betree.Node.lookup_mut_in_bindings_back key bindings bindings2
+ else
+ match new_msg with
+ | betree.Message.Insert v =>
+ do
+ let bindings1 ←
+ betree.List.push_front (U64 × U64) bindings0 (key, v)
+ betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+ | betree.Message.Delete =>
+ betree.Node.lookup_mut_in_bindings_back key bindings bindings0
+ | betree.Message.Upsert s =>
+ do
+ let v ← betree.upsert_update Option.none s
+ let bindings1 ←
+ betree.List.push_front (U64 × U64) bindings0 (key, v)
+ betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+
+/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.apply_messages_to_leaf
+ (bindings : betree.List (U64 × U64))
+ (new_msgs : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × U64))
+ :=
+ match new_msgs with
+ | betree.List.Cons new_msg new_msgs_tl =>
+ do
+ let (i, m) := new_msg
+ let bindings0 ← betree.Node.apply_to_leaf bindings i m
+ betree.Node.apply_messages_to_leaf bindings0 new_msgs_tl
+ | betree.List.Nil => Result.ret bindings
+
+/- [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.filter_messages_for_key
+ (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ match msgs with
+ | betree.List.Cons p l =>
+ let (k, m) := p
+ if k = key
+ then
+ do
+ let msgs0 ←
+ betree.List.pop_front_back (U64 × betree.Message) (betree.List.Cons
+ (k, m) l)
+ betree.Node.filter_messages_for_key key msgs0
+ else Result.ret (betree.List.Cons (k, m) l)
+ | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function -/
+divergent def betree.Node.lookup_first_message_after_key
+ (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ match msgs with
+ | betree.List.Cons p next_msgs =>
+ let (k, m) := p
+ if k = key
+ then betree.Node.lookup_first_message_after_key key next_msgs
+ else Result.ret (betree.List.Cons (k, m) next_msgs)
+ | betree.List.Nil => Result.ret betree.List.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 -/
+divergent def betree.Node.lookup_first_message_after_key_back
+ (key : U64) (msgs : betree.List (U64 × betree.Message))
+ (ret0 : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ match msgs with
+ | betree.List.Cons p next_msgs =>
+ let (k, m) := p
+ if k = key
+ then
+ do
+ let next_msgs0 ←
+ betree.Node.lookup_first_message_after_key_back key next_msgs ret0
+ Result.ret (betree.List.Cons (k, m) next_msgs0)
+ else Result.ret ret0
+ | betree.List.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def betree.Node.apply_to_internal
+ (msgs : betree.List (U64 × betree.Message)) (key : U64)
+ (new_msg : betree.Message) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ do
+ let msgs0 ← betree.Node.lookup_first_message_for_key key msgs
+ let b ← betree.List.head_has_key betree.Message msgs0 key
+ if b
+ then
+ match new_msg with
+ | betree.Message.Insert i =>
+ do
+ let msgs1 ← betree.Node.filter_messages_for_key key msgs0
+ let msgs2 ←
+ betree.List.push_front (U64 × betree.Message) msgs1 (key,
+ betree.Message.Insert i)
+ betree.Node.lookup_first_message_for_key_back key msgs msgs2
+ | betree.Message.Delete =>
+ do
+ let msgs1 ← betree.Node.filter_messages_for_key key msgs0
+ let msgs2 ←
+ betree.List.push_front (U64 × betree.Message) msgs1 (key,
+ betree.Message.Delete)
+ betree.Node.lookup_first_message_for_key_back key msgs msgs2
+ | betree.Message.Upsert s =>
+ do
+ let p ← betree.List.hd (U64 × betree.Message) msgs0
+ let (_, m) := p
+ match m with
+ | betree.Message.Insert prev =>
+ do
+ let v ← betree.upsert_update (Option.some prev) s
+ let msgs1 ←
+ betree.List.pop_front_back (U64 × betree.Message) msgs0
+ let msgs2 ←
+ betree.List.push_front (U64 × betree.Message) msgs1 (key,
+ betree.Message.Insert v)
+ betree.Node.lookup_first_message_for_key_back key msgs msgs2
+ | betree.Message.Delete =>
+ do
+ let v ← betree.upsert_update Option.none s
+ let msgs1 ←
+ betree.List.pop_front_back (U64 × betree.Message) msgs0
+ let msgs2 ←
+ betree.List.push_front (U64 × betree.Message) msgs1 (key,
+ betree.Message.Insert v)
+ betree.Node.lookup_first_message_for_key_back key msgs msgs2
+ | betree.Message.Upsert ufs =>
+ do
+ let msgs1 ←
+ betree.Node.lookup_first_message_after_key key msgs0
+ let msgs2 ←
+ betree.List.push_front (U64 × betree.Message) msgs1 (key,
+ betree.Message.Upsert s)
+ let msgs3 ←
+ betree.Node.lookup_first_message_after_key_back key msgs0 msgs2
+ betree.Node.lookup_first_message_for_key_back key msgs msgs3
+ else
+ do
+ let msgs1 ←
+ betree.List.push_front (U64 × betree.Message) msgs0 (key, new_msg)
+ betree.Node.lookup_first_message_for_key_back key msgs msgs1
+
+/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.apply_messages_to_internal
+ (msgs : betree.List (U64 × betree.Message))
+ (new_msgs : betree.List (U64 × betree.Message)) :
+ Result (betree.List (U64 × betree.Message))
+ :=
+ match new_msgs with
+ | betree.List.Cons new_msg new_msgs_tl =>
+ do
+ let (i, m) := new_msg
+ let msgs0 ← betree.Node.apply_to_internal msgs i m
+ betree.Node.apply_messages_to_internal msgs0 new_msgs_tl
+ | betree.List.Nil => Result.ret msgs
+
+/- [betree_main::betree::Node::{5}::apply_messages]: forward function -/
+mutual divergent def betree.Node.apply_messages
+ (self : betree.Node) (params : betree.Params)
+ (node_id_cnt : betree.NodeIdCounter)
+ (msgs : betree.List (U64 × betree.Message)) (st : State) :
+ Result (State × Unit)
+ :=
+ match self with
+ | betree.Node.Internal node =>
+ do
+ let ⟨ i, i0, n, n0 ⟩ := node
+ let (st0, content) ← betree.load_internal_node i st
+ let content0 ← betree.Node.apply_messages_to_internal content msgs
+ let num_msgs ← betree.List.len (U64 × betree.Message) content0
+ if num_msgs >= params.min_flush_size
+ then
+ do
+ let (st1, content1) ←
+ betree.Internal.flush (betree.Internal.mk i i0 n n0) params
+ node_id_cnt content0 st0
+ let (node0, _) ←
+ betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
+ node_id_cnt content0 st0
+ let ⟨ i1, _, _, _ ⟩ := node0
+ let (st2, _) ← betree.store_internal_node i1 content1 st1
+ Result.ret (st2, ())
+ else
+ do
+ let (st1, _) ← betree.store_internal_node i content0 st0
+ Result.ret (st1, ())
+ | betree.Node.Leaf node =>
+ do
+ let (st0, content) ← betree.load_leaf_node node.id st
+ let content0 ← betree.Node.apply_messages_to_leaf content msgs
+ let len ← betree.List.len (U64 × U64) content0
+ let i ← (U64.ofInt 2) * params.split_size
+ if len >= i
+ then
+ do
+ let (st1, _) ←
+ betree.Leaf.split node content0 params node_id_cnt st0
+ let (st2, _) ← betree.store_leaf_node node.id betree.List.Nil st1
+ Result.ret (st2, ())
+ else
+ do
+ let (st1, _) ← betree.store_leaf_node node.id content0 st0
+ Result.ret (st1, ())
+
+/- [betree_main::betree::Node::{5}::apply_messages]: backward function 0 -/
+divergent def betree.Node.apply_messages_back
+ (self : betree.Node) (params : betree.Params)
+ (node_id_cnt : betree.NodeIdCounter)
+ (msgs : betree.List (U64 × betree.Message)) (st : State) :
+ Result (betree.Node × betree.NodeIdCounter)
+ :=
+ match self with
+ | betree.Node.Internal node =>
+ do
+ let ⟨ i, i0, n, n0 ⟩ := node
+ let (st0, content) ← betree.load_internal_node i st
+ let content0 ← betree.Node.apply_messages_to_internal content msgs
+ let num_msgs ← betree.List.len (U64 × betree.Message) content0
+ if num_msgs >= params.min_flush_size
+ then
+ do
+ let (st1, content1) ←
+ betree.Internal.flush (betree.Internal.mk i i0 n n0) params
+ node_id_cnt content0 st0
+ let (node0, node_id_cnt0) ←
+ betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
+ node_id_cnt content0 st0
+ let ⟨ i1, i2, n1, n2 ⟩ := node0
+ let _ ← betree.store_internal_node i1 content1 st1
+ Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1 n2),
+ node_id_cnt0)
+ else
+ do
+ let _ ← betree.store_internal_node i content0 st0
+ Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0),
+ node_id_cnt)
+ | betree.Node.Leaf node =>
+ do
+ let (st0, content) ← betree.load_leaf_node node.id st
+ let content0 ← betree.Node.apply_messages_to_leaf content msgs
+ let len ← betree.List.len (U64 × U64) content0
+ let i ← (U64.ofInt 2) * params.split_size
+ if len >= i
+ then
+ do
+ let (st1, new_node) ←
+ betree.Leaf.split node content0 params node_id_cnt st0
+ let _ ← betree.store_leaf_node node.id betree.List.Nil st1
+ let node_id_cnt0 ←
+ betree.Leaf.split_back node content0 params node_id_cnt st0
+ Result.ret (betree.Node.Internal new_node, node_id_cnt0)
+ else
+ do
+ let _ ← betree.store_leaf_node node.id content0 st0
+ Result.ret (betree.Node.Leaf { node with size := len }, node_id_cnt)
+
+/- [betree_main::betree::Internal::{4}::flush]: forward function -/
+divergent def betree.Internal.flush
+ (self : betree.Internal) (params : betree.Params)
+ (node_id_cnt : betree.NodeIdCounter)
+ (content : betree.List (U64 × betree.Message)) (st : State) :
+ Result (State × (betree.List (U64 × betree.Message)))
+ :=
+ do
+ let ⟨ _, i, n, n0 ⟩ := self
+ let p ← betree.List.partition_at_pivot betree.Message content i
+ let (msgs_left, msgs_right) := p
+ let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+ if len_left >= params.min_flush_size
+ then
+ do
+ let (st0, _) ←
+ betree.Node.apply_messages n params node_id_cnt msgs_left st
+ let (_, node_id_cnt0) ←
+ betree.Node.apply_messages_back n params node_id_cnt msgs_left st
+ let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+ if len_right >= params.min_flush_size
+ then
+ do
+ let (st1, _) ←
+ betree.Node.apply_messages n0 params node_id_cnt0 msgs_right st0
+ let _ ←
+ betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
+ st0
+ Result.ret (st1, betree.List.Nil)
+ else Result.ret (st0, msgs_right)
+ else
+ do
+ let (st0, _) ←
+ betree.Node.apply_messages n0 params node_id_cnt msgs_right st
+ let _ ←
+ betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
+ Result.ret (st0, msgs_left)
+
+/- [betree_main::betree::Internal::{4}::flush]: backward function 0 -/
+divergent def betree.Internal.flush_back
+ (self : betree.Internal) (params : betree.Params)
+ (node_id_cnt : betree.NodeIdCounter)
+ (content : betree.List (U64 × betree.Message)) (st : State) :
+ Result (betree.Internal × betree.NodeIdCounter)
+ :=
+ do
+ let ⟨ i, i0, n, n0 ⟩ := self
+ let p ← betree.List.partition_at_pivot betree.Message content i0
+ let (msgs_left, msgs_right) := p
+ let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+ if len_left >= params.min_flush_size
+ then
+ do
+ let (st0, _) ←
+ betree.Node.apply_messages n params node_id_cnt msgs_left st
+ let (n1, node_id_cnt0) ←
+ betree.Node.apply_messages_back n params node_id_cnt msgs_left st
+ let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+ if len_right >= params.min_flush_size
+ then
+ do
+ let (n2, node_id_cnt1) ←
+ betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
+ st0
+ Result.ret (betree.Internal.mk i i0 n1 n2, node_id_cnt1)
+ else Result.ret (betree.Internal.mk i i0 n1 n0, node_id_cnt0)
+ else
+ do
+ let (n1, node_id_cnt0) ←
+ betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
+ Result.ret (betree.Internal.mk i i0 n n1, node_id_cnt0)
+
+end
+
+/- [betree_main::betree::Node::{5}::apply]: forward function -/
+def betree.Node.apply
+ (self : betree.Node) (params : betree.Params)
+ (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
+ (st : State) :
+ Result (State × Unit)
+ :=
+ do
+ let l := betree.List.Nil
+ let (st0, _) ←
+ betree.Node.apply_messages self params node_id_cnt (betree.List.Cons
+ (key, new_msg) l) st
+ let _ ←
+ betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
+ (key, new_msg) l) st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::Node::{5}::apply]: backward function 0 -/
+def betree.Node.apply_back
+ (self : betree.Node) (params : betree.Params)
+ (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
+ (st : State) :
+ Result (betree.Node × betree.NodeIdCounter)
+ :=
+ let l := betree.List.Nil
+ betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
+ (key, new_msg) l) st
+
+/- [betree_main::betree::BeTree::{6}::new]: forward function -/
+def betree.BeTree.new
+ (min_flush_size : U64) (split_size : U64) (st : State) :
+ Result (State × betree.BeTree)
+ :=
+ do
+ let node_id_cnt ← betree.NodeIdCounter.new
+ let id ← betree.NodeIdCounter.fresh_id node_id_cnt
+ let (st0, _) ← betree.store_leaf_node id betree.List.Nil st
+ let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
+ Result.ret (st0,
+ {
+ params :=
+ { min_flush_size := min_flush_size, split_size := split_size },
+ node_id_cnt := node_id_cnt0,
+ root := (betree.Node.Leaf { id := id, size := (U64.ofInt 0) })
+ })
+
+/- [betree_main::betree::BeTree::{6}::apply]: forward function -/
+def betree.BeTree.apply
+ (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
+ Result (State × Unit)
+ :=
+ do
+ let (st0, _) ←
+ betree.Node.apply self.root self.params self.node_id_cnt key msg st
+ let _ ←
+ betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::apply]: backward function 0 -/
+def betree.BeTree.apply_back
+ (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
+ Result betree.BeTree
+ :=
+ do
+ let (n, nic) ←
+ betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
+ Result.ret { self with node_id_cnt := nic, root := n }
+
+/- [betree_main::betree::BeTree::{6}::insert]: forward function -/
+def betree.BeTree.insert
+ (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
+ Result (State × Unit)
+ :=
+ do
+ let (st0, _) ←
+ betree.BeTree.apply self key (betree.Message.Insert value) st
+ let _ ←
+ betree.BeTree.apply_back self key (betree.Message.Insert value) st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::insert]: backward function 0 -/
+def betree.BeTree.insert_back
+ (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
+ Result betree.BeTree
+ :=
+ betree.BeTree.apply_back self key (betree.Message.Insert value) st
+
+/- [betree_main::betree::BeTree::{6}::delete]: forward function -/
+def betree.BeTree.delete
+ (self : betree.BeTree) (key : U64) (st : State) : Result (State × Unit) :=
+ do
+ let (st0, _) ← betree.BeTree.apply self key betree.Message.Delete st
+ let _ ← betree.BeTree.apply_back self key betree.Message.Delete st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::delete]: backward function 0 -/
+def betree.BeTree.delete_back
+ (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
+ betree.BeTree.apply_back self key betree.Message.Delete st
+
+/- [betree_main::betree::BeTree::{6}::upsert]: forward function -/
+def betree.BeTree.upsert
+ (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
+ :
+ Result (State × Unit)
+ :=
+ do
+ let (st0, _) ←
+ betree.BeTree.apply self key (betree.Message.Upsert upd) st
+ let _ ← betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
+ Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::upsert]: backward function 0 -/
+def betree.BeTree.upsert_back
+ (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
+ :
+ Result betree.BeTree
+ :=
+ betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
+
+/- [betree_main::betree::BeTree::{6}::lookup]: forward function -/
+def betree.BeTree.lookup
+ (self : betree.BeTree) (key : U64) (st : State) :
+ Result (State × (Option U64))
+ :=
+ betree.Node.lookup self.root key st
+
+/- [betree_main::betree::BeTree::{6}::lookup]: backward function 0 -/
+def betree.BeTree.lookup_back
+ (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
+ do
+ let n ← betree.Node.lookup_back self.root key st
+ Result.ret { self with root := n }
+
+/- [betree_main::main]: forward function -/
+def main : Result Unit :=
+ Result.ret ()
+
+/- Unit test for [betree_main::main] -/
+#assert (main == .ret ())
+
+end betree_main
diff --git a/tests/lean/BetreeMain/FunsExternal.lean b/tests/lean/BetreeMain/FunsExternal.lean
new file mode 100644
index 00000000..71d26da4
--- /dev/null
+++ b/tests/lean/BetreeMain/FunsExternal.lean
@@ -0,0 +1,35 @@
+-- [betree_main]: external functions.
+import Base
+import BetreeMain.Types
+open Primitives
+open betree_main
+
+-- TODO: fill those bodies
+
+/- [betree_main::betree_utils::load_internal_node] -/
+def betree_utils.load_internal_node
+ :
+ U64 → State → Result (State × (betree.List (U64 × betree.Message))) :=
+ fun _ _ => .fail .panic
+
+/- [betree_main::betree_utils::store_internal_node] -/
+def betree_utils.store_internal_node
+ :
+ U64 → betree.List (U64 × betree.Message) → State → Result (State
+ × Unit) :=
+ fun _ _ _ => .fail .panic
+
+/- [betree_main::betree_utils::load_leaf_node] -/
+def betree_utils.load_leaf_node
+ : U64 → State → Result (State × (betree.List (U64 × U64))) :=
+ fun _ _ => .fail .panic
+
+/- [betree_main::betree_utils::store_leaf_node] -/
+def betree_utils.store_leaf_node
+ : U64 → betree.List (U64 × U64) → State → Result (State × Unit) :=
+ fun _ _ _ => .fail .panic
+
+/- [core::option::Option::{0}::unwrap] -/
+def core.option.Option.unwrap
+ (T : Type) : Option T → State → Result (State × T) :=
+ fun _ _ => .fail .panic
diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean
new file mode 100644
index 00000000..430d2dda
--- /dev/null
+++ b/tests/lean/BetreeMain/FunsExternal_Template.lean
@@ -0,0 +1,30 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import BetreeMain.Types
+open Primitives
+open betree_main
+
+/- [betree_main::betree_utils::load_internal_node]: forward function -/
+axiom betree_utils.load_internal_node
+ : U64 → State → Result (State × (betree.List (U64 × betree.Message)))
+
+/- [betree_main::betree_utils::store_internal_node]: forward function -/
+axiom betree_utils.store_internal_node
+ :
+ U64 → betree.List (U64 × betree.Message) → State → Result (State ×
+ Unit)
+
+/- [betree_main::betree_utils::load_leaf_node]: forward function -/
+axiom betree_utils.load_leaf_node
+ : U64 → State → Result (State × (betree.List (U64 × U64)))
+
+/- [betree_main::betree_utils::store_leaf_node]: forward function -/
+axiom betree_utils.store_leaf_node
+ : U64 → betree.List (U64 × U64) → State → Result (State × Unit)
+
+/- [core::option::Option::{0}::unwrap]: forward function -/
+axiom core.option.Option.unwrap
+ (T : Type) : Option T → State → Result (State × T)
+
diff --git a/tests/lean/BetreeMain/Types.lean b/tests/lean/BetreeMain/Types.lean
new file mode 100644
index 00000000..783ade64
--- /dev/null
+++ b/tests/lean/BetreeMain/Types.lean
@@ -0,0 +1,59 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: type definitions
+import Base
+open Primitives
+namespace betree_main
+
+/- [betree_main::betree::List] -/
+inductive betree.List (T : Type) :=
+| Cons : T → betree.List T → betree.List T
+| Nil : betree.List T
+
+/- [betree_main::betree::UpsertFunState] -/
+inductive betree.UpsertFunState :=
+| Add : U64 → betree.UpsertFunState
+| Sub : U64 → betree.UpsertFunState
+
+/- [betree_main::betree::Message] -/
+inductive betree.Message :=
+| Insert : U64 → betree.Message
+| Delete : betree.Message
+| Upsert : betree.UpsertFunState → betree.Message
+
+/- [betree_main::betree::Leaf] -/
+structure betree.Leaf where
+ id : U64
+ size : U64
+
+mutual
+
+/- [betree_main::betree::Node] -/
+inductive betree.Node :=
+| Internal : betree.Internal → betree.Node
+| Leaf : betree.Leaf → betree.Node
+
+/- [betree_main::betree::Internal] -/
+inductive betree.Internal :=
+| mk : U64 → U64 → betree.Node → betree.Node → betree.Internal
+
+end
+
+/- [betree_main::betree::Params] -/
+structure betree.Params where
+ min_flush_size : U64
+ split_size : U64
+
+/- [betree_main::betree::NodeIdCounter] -/
+structure betree.NodeIdCounter where
+ next_node_id : U64
+
+/- [betree_main::betree::BeTree] -/
+structure betree.BeTree where
+ params : betree.Params
+ node_id_cnt : betree.NodeIdCounter
+ root : betree.Node
+
+/- The state type used in the state-error monad -/
+axiom State : Type
+
+end betree_main
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
new file mode 100644
index 00000000..4a5a7b8f
--- /dev/null
+++ b/tests/lean/Constants.lean
@@ -0,0 +1,128 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [constants]
+import Base
+open Primitives
+namespace constants
+
+/- [constants::X0] -/
+def x0_body : Result U32 := Result.ret (U32.ofInt 0)
+def x0_c : U32 := eval_global x0_body (by simp)
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
+def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
+
+/- [constants::X1] -/
+def x1_body : Result U32 := Result.ret core_num_u32_max_c
+def x1_c : U32 := eval_global x1_body (by simp)
+
+/- [constants::X2] -/
+def x2_body : Result U32 := Result.ret (U32.ofInt 3)
+def x2_c : U32 := eval_global x2_body (by simp)
+
+/- [constants::incr]: forward function -/
+def incr (n : U32) : Result U32 :=
+ n + (U32.ofInt 1)
+
+/- [constants::X3] -/
+def x3_body : Result U32 := incr (U32.ofInt 32)
+def x3_c : U32 := eval_global x3_body (by simp)
+
+/- [constants::mk_pair0]: forward function -/
+def mk_pair0 (x : U32) (y : U32) : Result (U32 × U32) :=
+ Result.ret (x, y)
+
+/- [constants::Pair] -/
+structure Pair (T1 T2 : Type) where
+ x : T1
+ y : T2
+
+/- [constants::mk_pair1]: forward function -/
+def mk_pair1 (x : U32) (y : U32) : Result (Pair U32 U32) :=
+ Result.ret { x := x, y := y }
+
+/- [constants::P0] -/
+def p0_body : Result (U32 × U32) := mk_pair0 (U32.ofInt 0) (U32.ofInt 1)
+def p0_c : (U32 × U32) := eval_global p0_body (by simp)
+
+/- [constants::P1] -/
+def p1_body : Result (Pair U32 U32) := mk_pair1 (U32.ofInt 0) (U32.ofInt 1)
+def p1_c : Pair U32 U32 := eval_global p1_body (by simp)
+
+/- [constants::P2] -/
+def p2_body : Result (U32 × U32) := Result.ret ((U32.ofInt 0), (U32.ofInt 1))
+def p2_c : (U32 × U32) := eval_global p2_body (by simp)
+
+/- [constants::P3] -/
+def p3_body : Result (Pair U32 U32) :=
+ Result.ret { x := (U32.ofInt 0), y := (U32.ofInt 1) }
+def p3_c : Pair U32 U32 := eval_global p3_body (by simp)
+
+/- [constants::Wrap] -/
+structure Wrap (T : Type) where
+ val : T
+
+/- [constants::Wrap::{0}::new]: forward function -/
+def Wrap.new (T : Type) (val : T) : Result (Wrap T) :=
+ Result.ret { val := val }
+
+/- [constants::Y] -/
+def y_body : Result (Wrap I32) := Wrap.new I32 (I32.ofInt 2)
+def y_c : Wrap I32 := eval_global y_body (by simp)
+
+/- [constants::unwrap_y]: forward function -/
+def unwrap_y : Result I32 :=
+ Result.ret y_c.val
+
+/- [constants::YVAL] -/
+def yval_body : Result I32 := unwrap_y
+def yval_c : I32 := eval_global yval_body (by simp)
+
+/- [constants::get_z1::Z1] -/
+def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3)
+def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
+
+/- [constants::get_z1]: forward function -/
+def get_z1 : Result I32 :=
+ Result.ret get_z1_z1_c
+
+/- [constants::add]: forward function -/
+def add (a : I32) (b : I32) : Result I32 :=
+ a + b
+
+/- [constants::Q1] -/
+def q1_body : Result I32 := Result.ret (I32.ofInt 5)
+def q1_c : I32 := eval_global q1_body (by simp)
+
+/- [constants::Q2] -/
+def q2_body : Result I32 := Result.ret q1_c
+def q2_c : I32 := eval_global q2_body (by simp)
+
+/- [constants::Q3] -/
+def q3_body : Result I32 := add q2_c (I32.ofInt 3)
+def q3_c : I32 := eval_global q3_body (by simp)
+
+/- [constants::get_z2]: forward function -/
+def get_z2 : Result I32 :=
+ do
+ let i ← get_z1
+ let i0 ← add i q3_c
+ add q1_c i0
+
+/- [constants::S1] -/
+def s1_body : Result U32 := Result.ret (U32.ofInt 6)
+def s1_c : U32 := eval_global s1_body (by simp)
+
+/- [constants::S2] -/
+def s2_body : Result U32 := incr s1_c
+def s2_c : U32 := eval_global s2_body (by simp)
+
+/- [constants::S3] -/
+def s3_body : Result (Pair U32 U32) := Result.ret p3_c
+def s3_c : Pair U32 U32 := eval_global s3_body (by simp)
+
+/- [constants::S4] -/
+def s4_body : Result (Pair U32 U32) := mk_pair1 (U32.ofInt 7) (U32.ofInt 8)
+def s4_c : Pair U32 U32 := eval_global s4_body (by simp)
+
+end constants
diff --git a/tests/lean/misc-external/External.lean b/tests/lean/External.lean
index b95db309..b95db309 100644
--- a/tests/lean/misc-external/External.lean
+++ b/tests/lean/External.lean
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
new file mode 100644
index 00000000..674aaebd
--- /dev/null
+++ b/tests/lean/External/Funs.lean
@@ -0,0 +1,88 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: function definitions
+import Base
+import External.Types
+import External.FunsExternal
+open Primitives
+namespace external
+
+/- [external::swap]: forward function -/
+def swap (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
+ do
+ let (st0, _) ← core.mem.swap T x y st
+ let (st1, _) ← core.mem.swap_back0 T x y st st0
+ let (st2, _) ← core.mem.swap_back1 T x y st st1
+ Result.ret (st2, ())
+
+/- [external::swap]: backward function 0 -/
+def swap_back
+ (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
+ Result (State × (T × T))
+ :=
+ do
+ let (st1, _) ← core.mem.swap T x y st
+ let (st2, x0) ← core.mem.swap_back0 T x y st st1
+ let (_, y0) ← core.mem.swap_back1 T x y st st2
+ Result.ret (st0, (x0, y0))
+
+/- [external::test_new_non_zero_u32]: forward function -/
+def test_new_non_zero_u32
+ (x : U32) (st : State) : Result (State × core.num.nonzero.NonZeroU32) :=
+ do
+ let (st0, opt) ← core.num.nonzero.NonZeroU32.new x st
+ core.option.Option.unwrap core.num.nonzero.NonZeroU32 opt st0
+
+/- [external::test_vec]: forward function -/
+def test_vec : Result Unit :=
+ do
+ let v := Vec.new U32
+ let _ ← Vec.push U32 v (U32.ofInt 0)
+ Result.ret ()
+
+/- Unit test for [external::test_vec] -/
+#assert (test_vec == .ret ())
+
+/- [external::custom_swap]: forward function -/
+def custom_swap
+ (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
+ do
+ let (st0, _) ← core.mem.swap T x y st
+ let (st1, x0) ← core.mem.swap_back0 T x y st st0
+ let (st2, _) ← core.mem.swap_back1 T x y st st1
+ Result.ret (st2, x0)
+
+/- [external::custom_swap]: backward function 0 -/
+def custom_swap_back
+ (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) :
+ Result (State × (T × T))
+ :=
+ do
+ let (st1, _) ← core.mem.swap T x y st
+ let (st2, _) ← core.mem.swap_back0 T x y st st1
+ let (_, y0) ← core.mem.swap_back1 T x y st st2
+ Result.ret (st0, (ret0, y0))
+
+/- [external::test_custom_swap]: forward function -/
+def test_custom_swap
+ (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
+ do
+ let (st0, _) ← custom_swap U32 x y st
+ Result.ret (st0, ())
+
+/- [external::test_custom_swap]: backward function 0 -/
+def test_custom_swap_back
+ (x : U32) (y : U32) (st : State) (st0 : State) :
+ Result (State × (U32 × U32))
+ :=
+ custom_swap_back U32 x y st (U32.ofInt 1) st0
+
+/- [external::test_swap_non_zero]: forward function -/
+def test_swap_non_zero (x : U32) (st : State) : Result (State × U32) :=
+ do
+ let (st0, _) ← swap U32 x (U32.ofInt 0) st
+ let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0) st st0
+ if x0 = (U32.ofInt 0)
+ then Result.fail Error.panic
+ else Result.ret (st1, x0)
+
+end external
diff --git a/tests/lean/External/FunsExternal.lean b/tests/lean/External/FunsExternal.lean
new file mode 100644
index 00000000..aae11ba1
--- /dev/null
+++ b/tests/lean/External/FunsExternal.lean
@@ -0,0 +1,33 @@
+-- [external]: templates for the external functions.
+import Base
+import External.Types
+open Primitives
+open external
+
+-- TODO: fill those bodies
+
+/- [core::mem::swap] -/
+def core.mem.swap
+ (T : Type) : T → T → State → Result (State × Unit) :=
+ fun _x _y s => .ret (s, ())
+
+/- [core::mem::swap] -/
+def core.mem.swap_back0
+ (T : Type) : T → T → State → State → Result (State × T) :=
+ fun _x y _s0 s1 => .ret (s1, y)
+
+/- [core::mem::swap] -/
+def core.mem.swap_back1
+ (T : Type) : T → T → State → State → Result (State × T) :=
+ fun x _y _s0 s1 => .ret (s1, x)
+
+/- [core::num::nonzero::NonZeroU32::{14}::new] -/
+def core.num.nonzero.NonZeroU32.new
+ :
+ U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t)) :=
+ fun _ _ => .fail .panic
+
+/- [core::option::Option::{0}::unwrap] -/
+def core.option.Option.unwrap
+ (T : Type) : Option T → State → Result (State × T) :=
+ fun _ _ => .fail .panic
diff --git a/tests/lean/External/FunsExternal_Template.lean b/tests/lean/External/FunsExternal_Template.lean
new file mode 100644
index 00000000..c8bc397f
--- /dev/null
+++ b/tests/lean/External/FunsExternal_Template.lean
@@ -0,0 +1,27 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import External.Types
+open Primitives
+open external
+
+/- [core::mem::swap]: forward function -/
+axiom core.mem.swap (T : Type) : T → T → State → Result (State × Unit)
+
+/- [core::mem::swap]: backward function 0 -/
+axiom core.mem.swap_back0
+ (T : Type) : T → T → State → State → Result (State × T)
+
+/- [core::mem::swap]: backward function 1 -/
+axiom core.mem.swap_back1
+ (T : Type) : T → T → State → State → Result (State × T)
+
+/- [core::num::nonzero::NonZeroU32::{14}::new]: forward function -/
+axiom core.num.nonzero.NonZeroU32.new
+ : U32 → State → Result (State × (Option core.num.nonzero.NonZeroU32))
+
+/- [core::option::Option::{0}::unwrap]: forward function -/
+axiom core.option.Option.unwrap
+ (T : Type) : Option T → State → Result (State × T)
+
diff --git a/tests/lean/External/Opaque.lean b/tests/lean/External/Opaque.lean
new file mode 100644
index 00000000..d0297523
--- /dev/null
+++ b/tests/lean/External/Opaque.lean
@@ -0,0 +1,32 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: opaque function definitions
+import Base
+import External.Types
+open Primitives
+
+namespace external
+
+structure OpaqueDefs where
+
+ /- [core::mem::swap] -/
+ core.mem.swap_fwd (T : Type) : T → T → State → Result (State × Unit)
+
+ /- [core::mem::swap] -/
+ core.mem.swap_back0
+ (T : Type) : T → T → State → State → Result (State × T)
+
+ /- [core::mem::swap] -/
+ core.mem.swap_back1
+ (T : Type) : T → T → State → State → Result (State × T)
+
+ /- [core::num::nonzero::NonZeroU32::{14}::new] -/
+ core.num.nonzero.NonZeroU32.new_fwd
+ :
+ U32 → State → Result (State × (Option
+ core_num_nonzero_non_zero_u32_t))
+
+ /- [core::option::Option::{0}::unwrap] -/
+ core.option.Option.unwrap_fwd
+ (T : Type) : Option T → State → Result (State × T)
+
+end external
diff --git a/tests/lean/misc-external/External/Types.lean b/tests/lean/External/Types.lean
index ed1842be..ba984e2a 100644
--- a/tests/lean/misc-external/External/Types.lean
+++ b/tests/lean/External/Types.lean
@@ -1,10 +1,13 @@
-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
-- [external]: type definitions
-import Base.Primitives
+import Base
+open Primitives
+namespace external
/- [core::num::nonzero::NonZeroU32] -/
-axiom core_num_nonzero_non_zero_u32_t : Type
+axiom core.num.nonzero.NonZeroU32 : Type
/- The state type used in the state-error monad -/
axiom State : Type
+end external
diff --git a/tests/lean/Hashmap.lean b/tests/lean/Hashmap.lean
new file mode 100644
index 00000000..35034754
--- /dev/null
+++ b/tests/lean/Hashmap.lean
@@ -0,0 +1,2 @@
+import Hashmap.Funs
+import Hashmap.Properties
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
new file mode 100644
index 00000000..870693b5
--- /dev/null
+++ b/tests/lean/Hashmap/Funs.lean
@@ -0,0 +1,449 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: function definitions
+import Base
+import Hashmap.Types
+open Primitives
+namespace hashmap
+
+/- [hashmap::hash_key]: forward function -/
+def hash_key (k : Usize) : Result Usize :=
+ Result.ret k
+
+/- [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
+divergent def HashMap.allocate_slots_loop
+ (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
+ if n > (Usize.ofInt 0)
+ then
+ do
+ let slots0 ← Vec.push (List T) slots List.Nil
+ let n0 ← n - (Usize.ofInt 1)
+ HashMap.allocate_slots_loop T slots0 n0
+ else Result.ret slots
+
+/- [hashmap::HashMap::{0}::allocate_slots]: forward function -/
+def HashMap.allocate_slots
+ (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
+ HashMap.allocate_slots_loop T slots n
+
+/- [hashmap::HashMap::{0}::new_with_capacity]: forward function -/
+def HashMap.new_with_capacity
+ (T : Type) (capacity : Usize) (max_load_dividend : Usize)
+ (max_load_divisor : Usize) :
+ Result (HashMap T)
+ :=
+ do
+ let v := Vec.new (List T)
+ let slots ← HashMap.allocate_slots T v capacity
+ let i ← capacity * max_load_dividend
+ let i0 ← i / max_load_divisor
+ Result.ret
+ {
+ num_entries := (Usize.ofInt 0),
+ max_load_factor := (max_load_dividend, max_load_divisor),
+ max_load := i0,
+ slots := slots
+ }
+
+/- [hashmap::HashMap::{0}::new]: forward function -/
+def HashMap.new (T : Type) : Result (HashMap T) :=
+ HashMap.new_with_capacity T (Usize.ofInt 32) (Usize.ofInt 4) (Usize.ofInt 5)
+
+/- [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.clear_loop
+ (T : Type) (slots : Vec (List T)) (i : Usize) : Result (Vec (List T)) :=
+ let i0 := Vec.len (List T) slots
+ if i < i0
+ then
+ do
+ let i1 ← i + (Usize.ofInt 1)
+ let slots0 ← Vec.index_mut_back (List T) slots i List.Nil
+ HashMap.clear_loop T slots0 i1
+ else Result.ret slots
+
+/- [hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) :=
+ do
+ let v ← HashMap.clear_loop T self.slots (Usize.ofInt 0)
+ Result.ret { self with num_entries := (Usize.ofInt 0), slots := v }
+
+/- [hashmap::HashMap::{0}::len]: forward function -/
+def HashMap.len (T : Type) (self : HashMap T) : Result Usize :=
+ Result.ret self.num_entries
+
+/- [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function -/
+divergent def HashMap.insert_in_list_loop
+ (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
+ match ls with
+ | List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret false
+ else HashMap.insert_in_list_loop T key value tl
+ | List.Nil => Result.ret true
+
+/- [hashmap::HashMap::{0}::insert_in_list]: forward function -/
+def HashMap.insert_in_list
+ (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
+ HashMap.insert_in_list_loop T key value ls
+
+/- [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 -/
+divergent def HashMap.insert_in_list_loop_back
+ (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
+ match ls with
+ | List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret (List.Cons ckey value tl)
+ else
+ do
+ let tl0 ← HashMap.insert_in_list_loop_back T key value tl
+ Result.ret (List.Cons ckey cvalue tl0)
+ | List.Nil => let l := List.Nil
+ Result.ret (List.Cons key value l)
+
+/- [hashmap::HashMap::{0}::insert_in_list]: backward function 0 -/
+def HashMap.insert_in_list_back
+ (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
+ HashMap.insert_in_list_loop_back T key value ls
+
+/- [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def HashMap.insert_no_resize
+ (T : Type) (self : HashMap T) (key : Usize) (value : T) :
+ Result (HashMap T)
+ :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (List T) self.slots hash_mod
+ let inserted ← HashMap.insert_in_list T key value l
+ if inserted
+ then
+ do
+ let i0 ← self.num_entries + (Usize.ofInt 1)
+ let l0 ← HashMap.insert_in_list_back T key value l
+ let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+ Result.ret { self with num_entries := i0, slots := v }
+ else
+ do
+ let l0 ← HashMap.insert_in_list_back T key value l
+ let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+ Result.ret { self with slots := v }
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
+def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
+
+/- [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.move_elements_from_list_loop
+ (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
+ match ls with
+ | List.Cons k v tl =>
+ do
+ let ntable0 ← HashMap.insert_no_resize T ntable k v
+ HashMap.move_elements_from_list_loop T ntable0 tl
+ | List.Nil => Result.ret ntable
+
+/- [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def HashMap.move_elements_from_list
+ (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
+ HashMap.move_elements_from_list_loop T ntable ls
+
+/- [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.move_elements_loop
+ (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
+ Result ((HashMap T) × (Vec (List T)))
+ :=
+ let i0 := Vec.len (List T) slots
+ if i < i0
+ then
+ do
+ let l ← Vec.index_mut (List T) slots i
+ let ls := mem.replace (List T) l List.Nil
+ let ntable0 ← HashMap.move_elements_from_list T ntable ls
+ let i1 ← i + (Usize.ofInt 1)
+ let l0 := mem.replace_back (List T) l List.Nil
+ let slots0 ← Vec.index_mut_back (List T) slots i l0
+ HashMap.move_elements_loop T ntable0 slots0 i1
+ else Result.ret (ntable, slots)
+
+/- [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def HashMap.move_elements
+ (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
+ Result ((HashMap T) × (Vec (List T)))
+ :=
+ HashMap.move_elements_loop T ntable slots i
+
+/- [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) :=
+ do
+ let max_usize ← Scalar.cast .Usize core_num_u32_max_c
+ let capacity := Vec.len (List T) self.slots
+ let n1 ← max_usize / (Usize.ofInt 2)
+ let (i, i0) := self.max_load_factor
+ let i1 ← n1 / i
+ if capacity <= i1
+ then
+ do
+ let i2 ← capacity * (Usize.ofInt 2)
+ let ntable ← HashMap.new_with_capacity T i2 i i0
+ let (ntable0, _) ←
+ HashMap.move_elements T ntable self.slots (Usize.ofInt 0)
+ Result.ret
+ {
+ ntable0
+ with
+ num_entries := self.num_entries, max_load_factor := (i, i0)
+ }
+ else Result.ret { self with max_load_factor := (i, i0) }
+
+/- [hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def HashMap.insert
+ (T : Type) (self : HashMap T) (key : Usize) (value : T) :
+ Result (HashMap T)
+ :=
+ do
+ let self0 ← HashMap.insert_no_resize T self key value
+ let i ← HashMap.len T self0
+ if i > self0.max_load
+ then HashMap.try_resize T self0
+ else Result.ret self0
+
+/- [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function -/
+divergent def HashMap.contains_key_in_list_loop
+ (T : Type) (key : Usize) (ls : List T) : Result Bool :=
+ match ls with
+ | List.Cons ckey t tl =>
+ if ckey = key
+ then Result.ret true
+ else HashMap.contains_key_in_list_loop T key tl
+ | List.Nil => Result.ret false
+
+/- [hashmap::HashMap::{0}::contains_key_in_list]: forward function -/
+def HashMap.contains_key_in_list
+ (T : Type) (key : Usize) (ls : List T) : Result Bool :=
+ HashMap.contains_key_in_list_loop T key ls
+
+/- [hashmap::HashMap::{0}::contains_key]: forward function -/
+def HashMap.contains_key
+ (T : Type) (self : HashMap T) (key : Usize) : Result Bool :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index (List T) self.slots hash_mod
+ HashMap.contains_key_in_list T key l
+
+/- [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
+divergent def HashMap.get_in_list_loop
+ (T : Type) (key : Usize) (ls : List T) : Result T :=
+ match ls with
+ | List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret cvalue
+ else HashMap.get_in_list_loop T key tl
+ | List.Nil => Result.fail Error.panic
+
+/- [hashmap::HashMap::{0}::get_in_list]: forward function -/
+def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T :=
+ HashMap.get_in_list_loop T key ls
+
+/- [hashmap::HashMap::{0}::get]: forward function -/
+def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index (List T) self.slots hash_mod
+ HashMap.get_in_list T key l
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
+divergent def HashMap.get_mut_in_list_loop
+ (T : Type) (ls : List T) (key : Usize) : Result T :=
+ match ls with
+ | List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret cvalue
+ else HashMap.get_mut_in_list_loop T tl key
+ | List.Nil => Result.fail Error.panic
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: forward function -/
+def HashMap.get_mut_in_list
+ (T : Type) (ls : List T) (key : Usize) : Result T :=
+ HashMap.get_mut_in_list_loop T ls key
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 -/
+divergent def HashMap.get_mut_in_list_loop_back
+ (T : Type) (ls : List T) (key : Usize) (ret0 : T) : Result (List T) :=
+ match ls with
+ | List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret (List.Cons ckey ret0 tl)
+ else
+ do
+ let tl0 ← HashMap.get_mut_in_list_loop_back T tl key ret0
+ Result.ret (List.Cons ckey cvalue tl0)
+ | List.Nil => Result.fail Error.panic
+
+/- [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 -/
+def HashMap.get_mut_in_list_back
+ (T : Type) (ls : List T) (key : Usize) (ret0 : T) : Result (List T) :=
+ HashMap.get_mut_in_list_loop_back T ls key ret0
+
+/- [hashmap::HashMap::{0}::get_mut]: forward function -/
+def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (List T) self.slots hash_mod
+ HashMap.get_mut_in_list T l key
+
+/- [hashmap::HashMap::{0}::get_mut]: backward function 0 -/
+def HashMap.get_mut_back
+ (T : Type) (self : HashMap T) (key : Usize) (ret0 : T) :
+ Result (HashMap T)
+ :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (List T) self.slots hash_mod
+ let l0 ← HashMap.get_mut_in_list_back T l key ret0
+ let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+ Result.ret { self with slots := v }
+
+/- [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
+divergent def HashMap.remove_from_list_loop
+ (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
+ match ls with
+ | List.Cons ckey t tl =>
+ if ckey = key
+ then
+ let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
+ match mv_ls with
+ | List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
+ | List.Nil => Result.fail Error.panic
+ else HashMap.remove_from_list_loop T key tl
+ | List.Nil => Result.ret Option.none
+
+/- [hashmap::HashMap::{0}::remove_from_list]: forward function -/
+def HashMap.remove_from_list
+ (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
+ HashMap.remove_from_list_loop T key ls
+
+/- [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 -/
+divergent def HashMap.remove_from_list_loop_back
+ (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
+ match ls with
+ | List.Cons ckey t tl =>
+ if ckey = key
+ then
+ let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
+ match mv_ls with
+ | List.Cons i cvalue tl0 => Result.ret tl0
+ | List.Nil => Result.fail Error.panic
+ else
+ do
+ let tl0 ← HashMap.remove_from_list_loop_back T key tl
+ Result.ret (List.Cons ckey t tl0)
+ | List.Nil => Result.ret List.Nil
+
+/- [hashmap::HashMap::{0}::remove_from_list]: backward function 1 -/
+def HashMap.remove_from_list_back
+ (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
+ HashMap.remove_from_list_loop_back T key ls
+
+/- [hashmap::HashMap::{0}::remove]: forward function -/
+def HashMap.remove
+ (T : Type) (self : HashMap T) (key : Usize) : Result (Option T) :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (List T) self.slots hash_mod
+ let x ← HashMap.remove_from_list T key l
+ match x with
+ | Option.none => Result.ret Option.none
+ | Option.some x0 =>
+ do
+ let _ ← self.num_entries - (Usize.ofInt 1)
+ Result.ret (Option.some x0)
+
+/- [hashmap::HashMap::{0}::remove]: backward function 0 -/
+def HashMap.remove_back
+ (T : Type) (self : HashMap T) (key : Usize) : Result (HashMap T) :=
+ do
+ let hash ← hash_key key
+ let i := Vec.len (List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (List T) self.slots hash_mod
+ let x ← HashMap.remove_from_list T key l
+ match x with
+ | Option.none =>
+ do
+ let l0 ← HashMap.remove_from_list_back T key l
+ let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+ Result.ret { self with slots := v }
+ | Option.some x0 =>
+ do
+ let i0 ← self.num_entries - (Usize.ofInt 1)
+ let l0 ← HashMap.remove_from_list_back T key l
+ let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+ Result.ret { self with num_entries := i0, slots := v }
+
+/- [hashmap::test1]: forward function -/
+def test1 : Result Unit :=
+ do
+ let hm ← HashMap.new U64
+ let hm0 ← HashMap.insert U64 hm (Usize.ofInt 0) (U64.ofInt 42)
+ let hm1 ← HashMap.insert U64 hm0 (Usize.ofInt 128) (U64.ofInt 18)
+ let hm2 ← HashMap.insert U64 hm1 (Usize.ofInt 1024) (U64.ofInt 138)
+ let hm3 ← HashMap.insert U64 hm2 (Usize.ofInt 1056) (U64.ofInt 256)
+ let i ← HashMap.get U64 hm3 (Usize.ofInt 128)
+ if not (i = (U64.ofInt 18))
+ then Result.fail Error.panic
+ else
+ do
+ let hm4 ←
+ HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024) (U64.ofInt 56)
+ let i0 ← HashMap.get U64 hm4 (Usize.ofInt 1024)
+ if not (i0 = (U64.ofInt 56))
+ then Result.fail Error.panic
+ else
+ do
+ let x ← HashMap.remove U64 hm4 (Usize.ofInt 1024)
+ match x with
+ | Option.none => Result.fail Error.panic
+ | Option.some x0 =>
+ if not (x0 = (U64.ofInt 56))
+ then Result.fail Error.panic
+ else
+ do
+ let hm5 ← HashMap.remove_back U64 hm4 (Usize.ofInt 1024)
+ let i1 ← HashMap.get U64 hm5 (Usize.ofInt 0)
+ if not (i1 = (U64.ofInt 42))
+ then Result.fail Error.panic
+ else
+ do
+ let i2 ← HashMap.get U64 hm5 (Usize.ofInt 128)
+ if not (i2 = (U64.ofInt 18))
+ then Result.fail Error.panic
+ else
+ do
+ let i3 ← HashMap.get U64 hm5 (Usize.ofInt 1056)
+ if not (i3 = (U64.ofInt 256))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [hashmap::test1] -/
+#assert (test1 == .ret ())
+
+end hashmap
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
new file mode 100644
index 00000000..3652f608
--- /dev/null
+++ b/tests/lean/Hashmap/Properties.lean
@@ -0,0 +1,439 @@
+import Hashmap.Funs
+
+open Primitives
+open Result
+
+namespace List
+
+-- TODO: we don't want to use the original List.lookup because it uses BEq
+-- TODO: rewrite rule: match x == y with ... -> if x = y then ... else ... ? (actually doesn't work because of sugar)
+-- TODO: move?
+@[simp]
+def lookup' {α : Type} (ls: _root_.List (Usize × α)) (key: Usize) : Option α :=
+ match ls with
+ | [] => none
+ | (k, x) :: tl => if k = key then some x else lookup' tl key
+
+end List
+
+namespace hashmap
+
+namespace List
+
+def v {α : Type} (ls: List α) : _root_.List (Usize × α) :=
+ match ls with
+ | Nil => []
+ | Cons k x tl => (k, x) :: v tl
+
+@[simp] theorem v_nil (α : Type) : (Nil : List α).v = [] := by rfl
+@[simp] theorem v_cons {α : Type} k x (tl: List α) : (Cons k x tl).v = (k, x) :: v tl := by rfl
+
+@[simp]
+abbrev lookup {α : Type} (ls: List α) (key: Usize) : Option α :=
+ ls.v.lookup' key
+
+@[simp]
+abbrev len {α : Type} (ls : List α) : Int := ls.v.len
+
+end List
+
+namespace HashMap
+
+abbrev Core.List := _root_.List
+
+namespace List
+
+end List
+
+-- TODO: move
+@[simp] theorem neq_imp_nbeq [BEq α] [LawfulBEq α] (x y : α) (heq : ¬ x = y) : ¬ x == y := by simp [*]
+@[simp] theorem neq_imp_nbeq_rev [BEq α] [LawfulBEq α] (x y : α) (heq : ¬ x = y) : ¬ y == x := by simp [*]
+
+-- TODO: move
+-- TODO: this doesn't work because of sugar
+theorem match_lawful_beq [BEq α] [LawfulBEq α] [DecidableEq α] (x y : α) :
+ (x == y) = (if x = y then true else false) := by
+ split <;> simp_all
+
+@[pspec]
+theorem insert_in_list_spec0 {α : Type} (key: Usize) (value: α) (ls: List α) :
+ ∃ b,
+ insert_in_list α key value ls = ret b ∧
+ (b ↔ ls.lookup key = none)
+ := match ls with
+ | .Nil => by simp [insert_in_list, insert_in_list_loop]
+ | .Cons k v tl =>
+ if h: k = key then -- TODO: The order of k/key matters
+ by
+ simp [insert_in_list]
+ rw [insert_in_list_loop]
+ simp [h]
+ else
+ have ⟨ b, hi ⟩ := insert_in_list_spec0 key value tl
+ by
+ exists b
+ simp [insert_in_list]
+ rw [insert_in_list_loop] -- TODO: Using simp leads to infinite recursion
+ simp only [insert_in_list] at hi
+ simp [*]
+
+-- Variation: use progress
+theorem insert_in_list_spec1 {α : Type} (key: Usize) (value: α) (ls: List α) :
+ ∃ b,
+ insert_in_list α key value ls = ret b ∧
+ (b ↔ ls.lookup key = none)
+ := match ls with
+ | .Nil => by simp [insert_in_list, insert_in_list_loop]
+ | .Cons k v tl =>
+ if h: k = key then -- TODO: The order of k/key matters
+ by
+ simp [insert_in_list]
+ rw [insert_in_list_loop]
+ simp [h]
+ else
+ by
+ simp only [insert_in_list]
+ rw [insert_in_list_loop]
+ conv => rhs; ext; simp [*]
+ progress keep heq as ⟨ b, hi ⟩
+ simp only [insert_in_list] at heq
+ exists b
+
+-- Variation: use tactics from the beginning
+theorem insert_in_list_spec2 {α : Type} (key: Usize) (value: α) (ls: List α) :
+ ∃ b,
+ insert_in_list α key value ls = ret b ∧
+ (b ↔ (ls.lookup key = none))
+ := by
+ induction ls
+ case Nil => simp [insert_in_list, insert_in_list_loop]
+ case Cons k v tl ih =>
+ simp only [insert_in_list]
+ rw [insert_in_list_loop]
+ simp only
+ if h: k = key then
+ simp [h]
+ else
+ conv => rhs; ext; left; simp [h] -- TODO: Simplify
+ simp only [insert_in_list] at ih;
+ -- TODO: give the possibility of using underscores
+ progress as ⟨ b, h ⟩
+ simp [*]
+
+def distinct_keys (ls : Core.List (Usize × α)) := ls.pairwise_rel (λ x y => x.fst ≠ y.fst)
+
+def hash_mod_key (k : Usize) (l : Int) : Int :=
+ match hash_key k with
+ | .ret k => k.val % l
+ | _ => 0
+
+@[simp]
+theorem hash_mod_key_eq : hash_mod_key k l = k.val % l := by
+ simp [hash_mod_key, hash_key]
+
+def slot_s_inv_hash (l i : Int) (ls : Core.List (Usize × α)) : Prop :=
+ ls.allP (λ (k, _) => hash_mod_key k l = i)
+
+@[simp]
+def slot_s_inv (l i : Int) (ls : Core.List (Usize × α)) : Prop :=
+ distinct_keys ls ∧
+ slot_s_inv_hash l i ls
+
+def slot_t_inv (l i : Int) (s : List α) : Prop := slot_s_inv l i s.v
+
+-- Interpret the hashmap as a list of lists
+def v (hm : HashMap α) : Core.List (Core.List (Usize × α)) :=
+ hm.slots.val.map List.v
+
+-- Interpret the hashmap as an associative list
+def al_v (hm : HashMap α) : Core.List (Usize × α) :=
+ hm.v.flatten
+
+-- TODO: automatic derivation
+instance : Inhabited (List α) where
+ default := .Nil
+
+@[simp]
+def slots_s_inv (s : Core.List (List α)) : Prop :=
+ ∀ (i : Int), 0 ≤ i → i < s.len → slot_t_inv s.len i (s.index i)
+
+def slots_t_inv (s : Vec (List α)) : Prop :=
+ slots_s_inv s.v
+
+@[simp]
+def base_inv (hm : HashMap α) : Prop :=
+ -- [num_entries] correctly tracks the number of entries
+ hm.num_entries.val = hm.al_v.len ∧
+ -- Slots invariant
+ slots_t_inv hm.slots ∧
+ -- The capacity must be > 0 (otherwise we can't resize)
+ 0 < hm.slots.length
+ -- TODO: load computation
+
+def inv (hm : HashMap α) : Prop :=
+ -- Base invariant
+ base_inv hm
+ -- TODO: either the hashmap is not overloaded, or we can't resize it
+
+theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+ (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
+ (hdk : distinct_keys l0.v) :
+ ∃ l1,
+ insert_in_list_back α key value l0 = ret l1 ∧
+ -- We update the binding
+ l1.lookup key = value ∧
+ (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
+ -- We preserve part of the key invariant
+ slot_s_inv_hash l (hash_mod_key key l) l1.v ∧
+ -- Reasoning about the length
+ (match l0.lookup key with
+ | none => l1.len = l0.len + 1
+ | some _ => l1.len = l0.len) ∧
+ -- The keys are distinct
+ distinct_keys l1.v ∧
+ -- We need this auxiliary property to prove that the keys distinct properties is preserved
+ (∀ k, k ≠ key → l0.v.allP (λ (k1, _) => k ≠ k1) → l1.v.allP (λ (k1, _) => k ≠ k1))
+ := match l0 with
+ | .Nil => by checkpoint
+ simp (config := {contextual := true})
+ [insert_in_list_back, insert_in_list_loop_back,
+ List.v, slot_s_inv_hash, distinct_keys, List.pairwise_rel]
+ | .Cons k v tl0 =>
+ if h: k = key then by checkpoint
+ simp [insert_in_list_back]
+ rw [insert_in_list_loop_back]
+ simp [h]
+ split_conjs
+ . intros; simp [*]
+ . simp [List.v, slot_s_inv_hash] at *
+ simp [*]
+ . simp [*, distinct_keys] at *
+ apply hdk
+ . tauto
+ else by checkpoint
+ simp [insert_in_list_back]
+ rw [insert_in_list_loop_back]
+ simp [h]
+ have : slot_s_inv_hash l (hash_mod_key key l) (List.v tl0) := by checkpoint
+ simp_all [List.v, slot_s_inv_hash]
+ have : distinct_keys (List.v tl0) := by checkpoint
+ simp [distinct_keys] at hdk
+ simp [hdk, distinct_keys]
+ progress keep heq as ⟨ tl1 .. ⟩
+ simp only [insert_in_list_back] at heq
+ have : slot_s_inv_hash l (hash_mod_key key l) (List.v (List.Cons k v tl1)) := by checkpoint
+ simp [List.v, slot_s_inv_hash] at *
+ simp [*]
+ have : distinct_keys ((k, v) :: List.v tl1) := by checkpoint
+ simp [distinct_keys] at *
+ simp [*]
+ -- TODO: canonize addition by default?
+ simp_all [Int.add_assoc, Int.add_comm, Int.add_left_comm]
+
+@[pspec]
+theorem insert_in_list_back_spec {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+ (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
+ (hdk : distinct_keys l0.v) :
+ ∃ l1,
+ insert_in_list_back α key value l0 = ret l1 ∧
+ -- We update the binding
+ l1.lookup key = value ∧
+ (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
+ -- We preserve part of the key invariant
+ slot_s_inv_hash l (hash_mod_key key l) l1.v ∧
+ -- Reasoning about the length
+ (match l0.lookup key with
+ | none => l1.len = l0.len + 1
+ | some _ => l1.len = l0.len) ∧
+ -- The keys are distinct
+ distinct_keys l1.v
+ := by
+ progress with insert_in_list_back_spec_aux as ⟨ l1 .. ⟩
+ exists l1
+
+@[simp]
+def slots_t_lookup (s : Core.List (List α)) (k : Usize) : Option α :=
+ let i := hash_mod_key k s.len
+ let slot := s.index i
+ slot.lookup k
+
+def lookup (hm : HashMap α) (k : Usize) : Option α :=
+ slots_t_lookup hm.slots.val k
+
+@[simp]
+abbrev len_s (hm : HashMap α) : Int := hm.al_v.len
+
+-- Remark: α and β must live in the same universe, otherwise the
+-- bind doesn't work
+theorem if_update_eq
+ {α β : Type u} (b : Bool) (y : α) (e : Result α) (f : α → Result β) :
+ (if b then Bind.bind e f else f y) = Bind.bind (if b then e else pure y) f
+ := by
+ split <;> simp [Pure.pure]
+
+-- Small helper
+-- TODO: move, and introduce a better solution with nice syntax
+def mk_opaque {α : Sort u} (x : α) : { y : α // y = x} :=
+ ⟨ x, by simp ⟩
+
+--set_option profiler true
+--set_option profiler.threshold 10
+--set_option trace.profiler true
+
+-- For pretty printing (useful when copy-pasting goals)
+attribute [pp_dot] List.length -- use the dot notation when printing
+set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse)
+
+theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value : α)
+ (hinv : hm.inv) (hnsat : hm.lookup key = none → hm.len_s < Usize.max) :
+ ∃ nhm, hm.insert_no_resize α key value = ret nhm ∧
+ -- We preserve the invariant
+ nhm.inv ∧
+ -- We updated the binding for key
+ nhm.lookup key = some value ∧
+ -- We left the other bindings unchanged
+ (∀ k, ¬ k = key → nhm.lookup k = hm.lookup k) ∧
+ -- Reasoning about the length
+ (match hm.lookup key with
+ | none => nhm.len_s = hm.len_s + 1
+ | some _ => nhm.len_s = hm.len_s) := by
+ rw [insert_no_resize]
+ simp only [hash_key, bind_tc_ret] -- TODO: annoying
+ have _ : (Vec.len (List α) hm.slots).val ≠ 0 := by checkpoint
+ intro
+ simp_all [inv]
+ progress keep _ as ⟨ hash_mod, hhm ⟩
+ have _ : 0 ≤ hash_mod.val := by checkpoint scalar_tac
+ have _ : hash_mod.val < Vec.length hm.slots := by
+ have : 0 < hm.slots.val.len := by
+ simp [inv] at hinv
+ simp [hinv]
+ -- TODO: we want to automate that
+ simp [*, Int.emod_lt_of_pos]
+ -- TODO: change the spec of Vec.index_mut to introduce a let-binding.
+ -- or: make progress introduce the let-binding by itself (this is clearer)
+ progress as ⟨ l, h_leq ⟩
+ -- TODO: make progress use the names written in the goal
+ progress as ⟨ inserted ⟩
+ rw [if_update_eq] -- TODO: necessary because we don't have a join
+ -- TODO: progress to ...
+ have hipost :
+ ∃ i0, (if inserted = true then hm.num_entries + Usize.ofInt 1 else pure hm.num_entries) = ret i0 ∧
+ i0.val = if inserted then hm.num_entries.val + 1 else hm.num_entries.val
+ := by
+ if inserted then
+ simp [*]
+ have hbounds : hm.num_entries.val + (Usize.ofInt 1).val ≤ Usize.max := by
+ simp [lookup] at hnsat
+ simp_all
+ simp [inv] at hinv
+ int_tac
+ -- TODO: progress fails in command line mode with "index out of bounds"
+ -- and I have no idea how to fix this. The error happens after progress
+ -- introduced the new goals. It must be when we exit the "withApp", etc.
+ -- helpers.
+ -- progress as ⟨ z, hp ⟩
+ have ⟨ z, hp ⟩ := Usize.add_spec hbounds
+ simp [hp]
+ else
+ simp [*, Pure.pure]
+ progress as ⟨ i0 ⟩
+ have h_slot : slot_s_inv_hash hm.slots.length (hash_mod_key key hm.slots.length) l.v
+ := by
+ simp [inv] at hinv
+ have h := (hinv.right.left hash_mod.val (by assumption) (by assumption)).right
+ simp [slot_t_inv, hhm] at h
+ simp [h, hhm, h_leq]
+ have hd : distinct_keys l.v := by checkpoint
+ simp [inv, slots_t_inv, slot_t_inv] at hinv
+ have h := hinv.right.left hash_mod.val (by assumption) (by assumption)
+ simp [h, h_leq]
+ -- TODO: hide the variables and only keep the props
+ -- TODO: allow providing terms to progress to instantiate the meta variables
+ -- which are not propositions
+ progress as ⟨ l0, _, _, _, hlen .. ⟩
+ progress keep hv as ⟨ v, h_veq ⟩
+ -- TODO: update progress to automate that
+ -- TODO: later I don't want to inline nhm - we need to control simp: deactivate
+ -- zeta reduction? For now I have to do this peculiar manipulation
+ have ⟨ nhm, nhm_eq ⟩ := @mk_opaque (HashMap α) { num_entries := i0, max_load_factor := hm.max_load_factor, max_load := hm.max_load, slots := v }
+ exists nhm
+ have hupdt : lookup nhm key = some value := by checkpoint
+ simp [lookup, List.lookup] at *
+ simp_all
+ have hlkp : ∀ k, ¬ k = key → nhm.lookup k = hm.lookup k := by
+ simp [lookup, List.lookup] at *
+ intro k hk
+ -- We have to make a case disjunction: either the hashes are different,
+ -- in which case we don't even lookup the same slots, or the hashes
+ -- are the same, in which case we have to reason about what happens
+ -- in one slot
+ let k_hash_mod := k.val % v.val.len
+ have : 0 < hm.slots.val.len := by simp_all [inv]
+ have hvpos : 0 < v.val.len := by simp_all
+ have hvnz: v.val.len ≠ 0 := by
+ simp_all
+ have _ : 0 ≤ k_hash_mod := by
+ -- TODO: we want to automate this
+ simp
+ apply Int.emod_nonneg k.val hvnz
+ have _ : k_hash_mod < Vec.length hm.slots := by
+ -- TODO: we want to automate this
+ simp
+ have h := Int.emod_lt_of_pos k.val hvpos
+ simp_all
+ if h_hm : k_hash_mod = hash_mod.val then
+ simp_all
+ else
+ simp_all
+ have _ :
+ match hm.lookup key with
+ | none => nhm.len_s = hm.len_s + 1
+ | some _ => nhm.len_s = hm.len_s := by checkpoint
+ simp only [lookup, List.lookup, len_s, al_v, HashMap.v, slots_t_lookup] at *
+ -- We have to do a case disjunction
+ simp_all
+ simp [_root_.List.update_map_eq]
+ -- TODO: dependent rewrites
+ have _ : key.val % hm.slots.val.len < (List.map List.v hm.slots.val).len := by
+ simp [*]
+ simp [_root_.List.len_flatten_update_eq, *]
+ split <;>
+ rename_i heq <;>
+ simp [heq] at hlen <;>
+ -- TODO: canonize addition by default? We need a tactic to simplify arithmetic equalities
+ -- with addition and substractions ((ℤ, +) is a group or something - there should exist a tactic
+ -- somewhere in mathlib?)
+ simp [Int.add_assoc, Int.add_comm, Int.add_left_comm] <;>
+ int_tac
+ have hinv : inv nhm := by
+ simp [inv] at *
+ split_conjs
+ . match h: lookup hm key with
+ | none =>
+ simp [h, lookup] at *
+ simp_all
+ | some _ =>
+ simp_all [lookup]
+ . simp [slots_t_inv, slot_t_inv] at *
+ intro i hipos _
+ have _ := hinv.right.left i hipos (by simp_all)
+ simp [hhm, h_veq, nhm_eq] at * -- TODO: annoying, we do that because simp_all fails below
+ -- We need a case disjunction
+ if h_ieq : i = key.val % _root_.List.len hm.slots.val then
+ -- TODO: simp_all fails: "(deterministic) timeout at 'whnf'"
+ -- Also, it is annoying to do this kind
+ -- of rewritings by hand. We could have a different simp
+ -- which safely substitutes variables when we have an
+ -- equality `x = ...` and `x` doesn't appear in the rhs
+ simp [h_ieq] at *
+ simp [*]
+ else
+ simp [*]
+ . -- TODO: simp[*] fails: "(deterministic) timeout at 'whnf'"
+ simp [hinv, h_veq, nhm_eq]
+ simp_all
+
+end HashMap
+
+end hashmap
diff --git a/tests/lean/Hashmap/Types.lean b/tests/lean/Hashmap/Types.lean
new file mode 100644
index 00000000..6606cf9e
--- /dev/null
+++ b/tests/lean/Hashmap/Types.lean
@@ -0,0 +1,19 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap]: type definitions
+import Base
+open Primitives
+namespace hashmap
+
+/- [hashmap::List] -/
+inductive List (T : Type) :=
+| Cons : Usize → T → List T → List T
+| Nil : List T
+
+/- [hashmap::HashMap] -/
+structure HashMap (T : Type) where
+ num_entries : Usize
+ max_load_factor : (Usize × Usize)
+ max_load : Usize
+ slots : Vec (List T)
+
+end hashmap
diff --git a/tests/lean/hashmap_on_disk/HashmapMain.lean b/tests/lean/HashmapMain.lean
index 1a4e7f82..1a4e7f82 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain.lean
+++ b/tests/lean/HashmapMain.lean
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
new file mode 100644
index 00000000..610bae46
--- /dev/null
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -0,0 +1,505 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: function definitions
+import Base
+import HashmapMain.Types
+import HashmapMain.FunsExternal
+open Primitives
+namespace hashmap_main
+
+/- [hashmap_main::hashmap::hash_key]: forward function -/
+def hashmap.hash_key (k : Usize) : Result Usize :=
+ Result.ret k
+
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
+divergent def hashmap.HashMap.allocate_slots_loop
+ (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
+ Result (Vec (hashmap.List T))
+ :=
+ if n > (Usize.ofInt 0)
+ then
+ do
+ let slots0 ← Vec.push (hashmap.List T) slots hashmap.List.Nil
+ let n0 ← n - (Usize.ofInt 1)
+ hashmap.HashMap.allocate_slots_loop T slots0 n0
+ else Result.ret slots
+
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function -/
+def hashmap.HashMap.allocate_slots
+ (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
+ Result (Vec (hashmap.List T))
+ :=
+ hashmap.HashMap.allocate_slots_loop T slots n
+
+/- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function -/
+def hashmap.HashMap.new_with_capacity
+ (T : Type) (capacity : Usize) (max_load_dividend : Usize)
+ (max_load_divisor : Usize) :
+ Result (hashmap.HashMap T)
+ :=
+ do
+ let v := Vec.new (hashmap.List T)
+ let slots ← hashmap.HashMap.allocate_slots T v capacity
+ let i ← capacity * max_load_dividend
+ let i0 ← i / max_load_divisor
+ Result.ret
+ {
+ num_entries := (Usize.ofInt 0),
+ max_load_factor := (max_load_dividend, max_load_divisor),
+ max_load := i0,
+ slots := slots
+ }
+
+/- [hashmap_main::hashmap::HashMap::{0}::new]: forward function -/
+def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) :=
+ hashmap.HashMap.new_with_capacity T (Usize.ofInt 32) (Usize.ofInt 4)
+ (Usize.ofInt 5)
+
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.clear_loop
+ (T : Type) (slots : Vec (hashmap.List T)) (i : Usize) :
+ Result (Vec (hashmap.List T))
+ :=
+ let i0 := Vec.len (hashmap.List T) slots
+ if i < i0
+ then
+ do
+ let i1 ← i + (Usize.ofInt 1)
+ let slots0 ←
+ Vec.index_mut_back (hashmap.List T) slots i hashmap.List.Nil
+ hashmap.HashMap.clear_loop T slots0 i1
+ else Result.ret slots
+
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.clear
+ (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
+ do
+ let v ← hashmap.HashMap.clear_loop T self.slots (Usize.ofInt 0)
+ Result.ret { self with num_entries := (Usize.ofInt 0), slots := v }
+
+/- [hashmap_main::hashmap::HashMap::{0}::len]: forward function -/
+def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize :=
+ Result.ret self.num_entries
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.insert_in_list_loop
+ (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
+ match ls with
+ | hashmap.List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret false
+ else hashmap.HashMap.insert_in_list_loop T key value tl
+ | hashmap.List.Nil => Result.ret true
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function -/
+def hashmap.HashMap.insert_in_list
+ (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
+ hashmap.HashMap.insert_in_list_loop T key value ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 -/
+divergent def hashmap.HashMap.insert_in_list_loop_back
+ (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
+ Result (hashmap.List T)
+ :=
+ match ls with
+ | hashmap.List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret (hashmap.List.Cons ckey value tl)
+ else
+ do
+ let tl0 ← hashmap.HashMap.insert_in_list_loop_back T key value tl
+ Result.ret (hashmap.List.Cons ckey cvalue tl0)
+ | hashmap.List.Nil =>
+ let l := hashmap.List.Nil
+ Result.ret (hashmap.List.Cons key value l)
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 -/
+def hashmap.HashMap.insert_in_list_back
+ (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
+ Result (hashmap.List T)
+ :=
+ hashmap.HashMap.insert_in_list_loop_back T key value ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.insert_no_resize
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
+ Result (hashmap.HashMap T)
+ :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+ let inserted ← hashmap.HashMap.insert_in_list T key value l
+ if inserted
+ then
+ do
+ let i0 ← self.num_entries + (Usize.ofInt 1)
+ let l0 ← hashmap.HashMap.insert_in_list_back T key value l
+ let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+ Result.ret { self with num_entries := i0, slots := v }
+ else
+ do
+ let l0 ← hashmap.HashMap.insert_in_list_back T key value l
+ let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+ Result.ret { self with slots := v }
+
+/- [core::num::u32::{9}::MAX] -/
+def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
+def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.move_elements_from_list_loop
+ (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
+ Result (hashmap.HashMap T)
+ :=
+ match ls with
+ | hashmap.List.Cons k v tl =>
+ do
+ let ntable0 ← hashmap.HashMap.insert_no_resize T ntable k v
+ hashmap.HashMap.move_elements_from_list_loop T ntable0 tl
+ | hashmap.List.Nil => Result.ret ntable
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.move_elements_from_list
+ (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
+ Result (hashmap.HashMap T)
+ :=
+ hashmap.HashMap.move_elements_from_list_loop T ntable ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.move_elements_loop
+ (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
+ (i : Usize) :
+ Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
+ :=
+ let i0 := Vec.len (hashmap.List T) slots
+ if i < i0
+ then
+ do
+ let l ← Vec.index_mut (hashmap.List T) slots i
+ let ls := mem.replace (hashmap.List T) l hashmap.List.Nil
+ let ntable0 ← hashmap.HashMap.move_elements_from_list T ntable ls
+ let i1 ← i + (Usize.ofInt 1)
+ let l0 := mem.replace_back (hashmap.List T) l hashmap.List.Nil
+ let slots0 ← Vec.index_mut_back (hashmap.List T) slots i l0
+ hashmap.HashMap.move_elements_loop T ntable0 slots0 i1
+ else Result.ret (ntable, slots)
+
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.move_elements
+ (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
+ (i : Usize) :
+ Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
+ :=
+ hashmap.HashMap.move_elements_loop T ntable slots i
+
+/- [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.try_resize
+ (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
+ do
+ let max_usize ← Scalar.cast .Usize core_num_u32_max_c
+ let capacity := Vec.len (hashmap.List T) self.slots
+ let n1 ← max_usize / (Usize.ofInt 2)
+ let (i, i0) := self.max_load_factor
+ let i1 ← n1 / i
+ if capacity <= i1
+ then
+ do
+ let i2 ← capacity * (Usize.ofInt 2)
+ let ntable ← hashmap.HashMap.new_with_capacity T i2 i i0
+ let (ntable0, _) ←
+ hashmap.HashMap.move_elements T ntable self.slots (Usize.ofInt 0)
+ Result.ret
+ {
+ ntable0
+ with
+ num_entries := self.num_entries, max_load_factor := (i, i0)
+ }
+ else Result.ret { self with max_load_factor := (i, i0) }
+
+/- [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.insert
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
+ Result (hashmap.HashMap T)
+ :=
+ do
+ let self0 ← hashmap.HashMap.insert_no_resize T self key value
+ let i ← hashmap.HashMap.len T self0
+ if i > self0.max_load
+ then hashmap.HashMap.try_resize T self0
+ else Result.ret self0
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.contains_key_in_list_loop
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
+ match ls with
+ | hashmap.List.Cons ckey t tl =>
+ if ckey = key
+ then Result.ret true
+ else hashmap.HashMap.contains_key_in_list_loop T key tl
+ | hashmap.List.Nil => Result.ret false
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function -/
+def hashmap.HashMap.contains_key_in_list
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
+ hashmap.HashMap.contains_key_in_list_loop T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function -/
+def hashmap.HashMap.contains_key
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index (hashmap.List T) self.slots hash_mod
+ hashmap.HashMap.contains_key_in_list T key l
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.get_in_list_loop
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
+ match ls with
+ | hashmap.List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret cvalue
+ else hashmap.HashMap.get_in_list_loop T key tl
+ | hashmap.List.Nil => Result.fail Error.panic
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function -/
+def hashmap.HashMap.get_in_list
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
+ hashmap.HashMap.get_in_list_loop T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::get]: forward function -/
+def hashmap.HashMap.get
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index (hashmap.List T) self.slots hash_mod
+ hashmap.HashMap.get_in_list T key l
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.get_mut_in_list_loop
+ (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
+ match ls with
+ | hashmap.List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret cvalue
+ else hashmap.HashMap.get_mut_in_list_loop T tl key
+ | hashmap.List.Nil => Result.fail Error.panic
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function -/
+def hashmap.HashMap.get_mut_in_list
+ (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
+ hashmap.HashMap.get_mut_in_list_loop T ls key
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 -/
+divergent def hashmap.HashMap.get_mut_in_list_loop_back
+ (T : Type) (ls : hashmap.List T) (key : Usize) (ret0 : T) :
+ Result (hashmap.List T)
+ :=
+ match ls with
+ | hashmap.List.Cons ckey cvalue tl =>
+ if ckey = key
+ then Result.ret (hashmap.List.Cons ckey ret0 tl)
+ else
+ do
+ let tl0 ← hashmap.HashMap.get_mut_in_list_loop_back T tl key ret0
+ Result.ret (hashmap.List.Cons ckey cvalue tl0)
+ | hashmap.List.Nil => Result.fail Error.panic
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 -/
+def hashmap.HashMap.get_mut_in_list_back
+ (T : Type) (ls : hashmap.List T) (key : Usize) (ret0 : T) :
+ Result (hashmap.List T)
+ :=
+ hashmap.HashMap.get_mut_in_list_loop_back T ls key ret0
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function -/
+def hashmap.HashMap.get_mut
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+ hashmap.HashMap.get_mut_in_list T l key
+
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 -/
+def hashmap.HashMap.get_mut_back
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) (ret0 : T) :
+ Result (hashmap.HashMap T)
+ :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+ let l0 ← hashmap.HashMap.get_mut_in_list_back T l key ret0
+ let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+ Result.ret { self with slots := v }
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.remove_from_list_loop
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
+ match ls with
+ | hashmap.List.Cons ckey t tl =>
+ if ckey = key
+ then
+ let mv_ls :=
+ mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
+ hashmap.List.Nil
+ match mv_ls with
+ | hashmap.List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
+ | hashmap.List.Nil => Result.fail Error.panic
+ else hashmap.HashMap.remove_from_list_loop T key tl
+ | hashmap.List.Nil => Result.ret Option.none
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function -/
+def hashmap.HashMap.remove_from_list
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
+ hashmap.HashMap.remove_from_list_loop T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 -/
+divergent def hashmap.HashMap.remove_from_list_loop_back
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
+ match ls with
+ | hashmap.List.Cons ckey t tl =>
+ if ckey = key
+ then
+ let mv_ls :=
+ mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
+ hashmap.List.Nil
+ match mv_ls with
+ | hashmap.List.Cons i cvalue tl0 => Result.ret tl0
+ | hashmap.List.Nil => Result.fail Error.panic
+ else
+ do
+ let tl0 ← hashmap.HashMap.remove_from_list_loop_back T key tl
+ Result.ret (hashmap.List.Cons ckey t tl0)
+ | hashmap.List.Nil => Result.ret hashmap.List.Nil
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 -/
+def hashmap.HashMap.remove_from_list_back
+ (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
+ hashmap.HashMap.remove_from_list_loop_back T key ls
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove]: forward function -/
+def hashmap.HashMap.remove
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result (Option T) :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+ let x ← hashmap.HashMap.remove_from_list T key l
+ match x with
+ | Option.none => Result.ret Option.none
+ | Option.some x0 =>
+ do
+ let _ ← self.num_entries - (Usize.ofInt 1)
+ Result.ret (Option.some x0)
+
+/- [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 -/
+def hashmap.HashMap.remove_back
+ (T : Type) (self : hashmap.HashMap T) (key : Usize) :
+ Result (hashmap.HashMap T)
+ :=
+ do
+ let hash ← hashmap.hash_key key
+ let i := Vec.len (hashmap.List T) self.slots
+ let hash_mod ← hash % i
+ let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+ let x ← hashmap.HashMap.remove_from_list T key l
+ match x with
+ | Option.none =>
+ do
+ let l0 ← hashmap.HashMap.remove_from_list_back T key l
+ let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+ Result.ret { self with slots := v }
+ | Option.some x0 =>
+ do
+ let i0 ← self.num_entries - (Usize.ofInt 1)
+ let l0 ← hashmap.HashMap.remove_from_list_back T key l
+ let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+ Result.ret { self with num_entries := i0, slots := v }
+
+/- [hashmap_main::hashmap::test1]: forward function -/
+def hashmap.test1 : Result Unit :=
+ do
+ let hm ← hashmap.HashMap.new U64
+ let hm0 ← hashmap.HashMap.insert U64 hm (Usize.ofInt 0) (U64.ofInt 42)
+ let hm1 ← hashmap.HashMap.insert U64 hm0 (Usize.ofInt 128) (U64.ofInt 18)
+ let hm2 ←
+ hashmap.HashMap.insert U64 hm1 (Usize.ofInt 1024) (U64.ofInt 138)
+ let hm3 ←
+ hashmap.HashMap.insert U64 hm2 (Usize.ofInt 1056) (U64.ofInt 256)
+ let i ← hashmap.HashMap.get U64 hm3 (Usize.ofInt 128)
+ if not (i = (U64.ofInt 18))
+ then Result.fail Error.panic
+ else
+ do
+ let hm4 ←
+ hashmap.HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024)
+ (U64.ofInt 56)
+ let i0 ← hashmap.HashMap.get U64 hm4 (Usize.ofInt 1024)
+ if not (i0 = (U64.ofInt 56))
+ then Result.fail Error.panic
+ else
+ do
+ let x ← hashmap.HashMap.remove U64 hm4 (Usize.ofInt 1024)
+ match x with
+ | Option.none => Result.fail Error.panic
+ | Option.some x0 =>
+ if not (x0 = (U64.ofInt 56))
+ then Result.fail Error.panic
+ else
+ do
+ let hm5 ←
+ hashmap.HashMap.remove_back U64 hm4 (Usize.ofInt 1024)
+ let i1 ← hashmap.HashMap.get U64 hm5 (Usize.ofInt 0)
+ if not (i1 = (U64.ofInt 42))
+ then Result.fail Error.panic
+ else
+ do
+ let i2 ← hashmap.HashMap.get U64 hm5 (Usize.ofInt 128)
+ if not (i2 = (U64.ofInt 18))
+ then Result.fail Error.panic
+ else
+ do
+ let i3 ←
+ hashmap.HashMap.get U64 hm5 (Usize.ofInt 1056)
+ if not (i3 = (U64.ofInt 256))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [hashmap_main::hashmap::test1] -/
+#assert (hashmap.test1 == .ret ())
+
+/- [hashmap_main::insert_on_disk]: forward function -/
+def insert_on_disk
+ (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
+ do
+ let (st0, hm) ← hashmap_utils.deserialize st
+ let hm0 ← hashmap.HashMap.insert U64 hm key value
+ let (st1, _) ← hashmap_utils.serialize hm0 st0
+ Result.ret (st1, ())
+
+/- [hashmap_main::main]: forward function -/
+def main : Result Unit :=
+ Result.ret ()
+
+/- Unit test for [hashmap_main::main] -/
+#assert (main == .ret ())
+
+end hashmap_main
diff --git a/tests/lean/HashmapMain/FunsExternal.lean b/tests/lean/HashmapMain/FunsExternal.lean
new file mode 100644
index 00000000..b394b32b
--- /dev/null
+++ b/tests/lean/HashmapMain/FunsExternal.lean
@@ -0,0 +1,17 @@
+-- [hashmap_main]: templates for the external functions.
+import Base
+import HashmapMain.Types
+open Primitives
+open hashmap_main
+
+-- TODO: fill those bodies
+
+/- [hashmap_main::hashmap_utils::deserialize] -/
+def hashmap_utils.deserialize
+ : State → Result (State × (hashmap.HashMap U64)) :=
+ fun _ => .fail .panic
+
+/- [hashmap_main::hashmap_utils::serialize] -/
+def hashmap_utils.serialize
+ : hashmap.HashMap U64 → State → Result (State × Unit) :=
+ fun _ _ => .fail .panic
diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean
new file mode 100644
index 00000000..f537fc8f
--- /dev/null
+++ b/tests/lean/HashmapMain/FunsExternal_Template.lean
@@ -0,0 +1,16 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: external functions.
+-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
+import Base
+import HashmapMain.Types
+open Primitives
+open hashmap_main
+
+/- [hashmap_main::hashmap_utils::deserialize]: forward function -/
+axiom hashmap_utils.deserialize
+ : State → Result (State × (hashmap.HashMap U64))
+
+/- [hashmap_main::hashmap_utils::serialize]: forward function -/
+axiom hashmap_utils.serialize
+ : hashmap.HashMap U64 → State → Result (State × Unit)
+
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean b/tests/lean/HashmapMain/Opaque.lean
index d98f431a..abf04c94 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean
+++ b/tests/lean/HashmapMain/Opaque.lean
@@ -1,15 +1,19 @@
-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
-- [hashmap_main]: opaque function definitions
-import Base.Primitives
+import Base
import HashmapMain.Types
+open Primitives
+
+namespace hashmap_main
structure OpaqueDefs where
/- [hashmap_main::hashmap_utils::deserialize] -/
- hashmap_utils_deserialize_fwd
- : State -> Result (State × (hashmap_hash_map_t U64))
+ hashmap_utils.deserialize_fwd
+ : State → Result (State × (hashmap_hash_map_t U64))
/- [hashmap_main::hashmap_utils::serialize] -/
- hashmap_utils_serialize_fwd
- : hashmap_hash_map_t U64 -> State -> Result (State × Unit)
+ hashmap_utils.serialize_fwd
+ : hashmap_hash_map_t U64 → State → Result (State × Unit)
+end hashmap_main
diff --git a/tests/lean/HashmapMain/Types.lean b/tests/lean/HashmapMain/Types.lean
new file mode 100644
index 00000000..3b3d0d7c
--- /dev/null
+++ b/tests/lean/HashmapMain/Types.lean
@@ -0,0 +1,22 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [hashmap_main]: type definitions
+import Base
+open Primitives
+namespace hashmap_main
+
+/- [hashmap_main::hashmap::List] -/
+inductive hashmap.List (T : Type) :=
+| Cons : Usize → T → hashmap.List T → hashmap.List T
+| Nil : hashmap.List T
+
+/- [hashmap_main::hashmap::HashMap] -/
+structure hashmap.HashMap (T : Type) where
+ num_entries : Usize
+ max_load_factor : (Usize × Usize)
+ max_load : Usize
+ slots : Vec (hashmap.List T)
+
+/- The state type used in the state-error monad -/
+axiom State : Type
+
+end hashmap_main
diff --git a/tests/lean/misc-loops/Loops.lean b/tests/lean/Loops.lean
index 60c73776..60c73776 100644
--- a/tests/lean/misc-loops/Loops.lean
+++ b/tests/lean/Loops.lean
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
new file mode 100644
index 00000000..f7e6603d
--- /dev/null
+++ b/tests/lean/Loops/Funs.lean
@@ -0,0 +1,611 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: function definitions
+import Base
+import Loops.Types
+open Primitives
+namespace loops
+
+/- [loops::sum]: loop 0: forward function -/
+divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
+ if i < max
+ then do
+ let s0 ← s + i
+ let i0 ← i + (U32.ofInt 1)
+ sum_loop max i0 s0
+ else s * (U32.ofInt 2)
+
+/- [loops::sum]: forward function -/
+def sum (max : U32) : Result U32 :=
+ sum_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [loops::sum_with_mut_borrows]: loop 0: forward function -/
+divergent def sum_with_mut_borrows_loop
+ (max : U32) (mi : U32) (ms : U32) : Result U32 :=
+ if mi < max
+ then
+ do
+ let ms0 ← ms + mi
+ let mi0 ← mi + (U32.ofInt 1)
+ sum_with_mut_borrows_loop max mi0 ms0
+ else ms * (U32.ofInt 2)
+
+/- [loops::sum_with_mut_borrows]: forward function -/
+def sum_with_mut_borrows (max : U32) : Result U32 :=
+ sum_with_mut_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [loops::sum_with_shared_borrows]: loop 0: forward function -/
+divergent def sum_with_shared_borrows_loop
+ (max : U32) (i : U32) (s : U32) : Result U32 :=
+ if i < max
+ then
+ do
+ let i0 ← i + (U32.ofInt 1)
+ let s0 ← s + i0
+ sum_with_shared_borrows_loop max i0 s0
+ else s * (U32.ofInt 2)
+
+/- [loops::sum_with_shared_borrows]: forward function -/
+def sum_with_shared_borrows (max : U32) : Result U32 :=
+ sum_with_shared_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [loops::clear]: loop 0: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+divergent def clear_loop (v : Vec U32) (i : Usize) : Result (Vec U32) :=
+ let i0 := Vec.len U32 v
+ if i < i0
+ then
+ do
+ let i1 ← i + (Usize.ofInt 1)
+ let v0 ← Vec.index_mut_back U32 v i (U32.ofInt 0)
+ clear_loop v0 i1
+ else Result.ret v
+
+/- [loops::clear]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def clear (v : Vec U32) : Result (Vec U32) :=
+ clear_loop v (Usize.ofInt 0)
+
+/- [loops::list_mem]: loop 0: forward function -/
+divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
+ match ls with
+ | List.Cons y tl => if y = x
+ then Result.ret true
+ else list_mem_loop x tl
+ | List.Nil => Result.ret false
+
+/- [loops::list_mem]: forward function -/
+def list_mem (x : U32) (ls : List U32) : Result Bool :=
+ list_mem_loop x ls
+
+/- [loops::list_nth_mut_loop]: loop 0: forward function -/
+divergent def list_nth_mut_loop_loop
+ (T : Type) (ls : List T) (i : U32) : Result T :=
+ match ls with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut_loop_loop T tl i0
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop]: forward function -/
+def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+ list_nth_mut_loop_loop T ls i
+
+/- [loops::list_nth_mut_loop]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_loop_back
+ (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+ match ls with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+ Result.ret (List.Cons x tl0)
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop]: backward function 0 -/
+def list_nth_mut_loop_back
+ (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+ list_nth_mut_loop_loop_back T ls i ret0
+
+/- [loops::list_nth_shared_loop]: loop 0: forward function -/
+divergent def list_nth_shared_loop_loop
+ (T : Type) (ls : List T) (i : U32) : Result T :=
+ match ls with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared_loop_loop T tl i0
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop]: forward function -/
+def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+ list_nth_shared_loop_loop T ls i
+
+/- [loops::get_elem_mut]: loop 0: forward function -/
+divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
+ match ls with
+ | List.Cons y tl => if y = x
+ then Result.ret y
+ else get_elem_mut_loop x tl
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: forward function -/
+def get_elem_mut (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
+ do
+ let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
+ get_elem_mut_loop x l
+
+/- [loops::get_elem_mut]: loop 0: backward function 0 -/
+divergent def get_elem_mut_loop_back
+ (x : Usize) (ls : List Usize) (ret0 : Usize) : Result (List Usize) :=
+ match ls with
+ | List.Cons y tl =>
+ if y = x
+ then Result.ret (List.Cons ret0 tl)
+ else
+ do
+ let tl0 ← get_elem_mut_loop_back x tl ret0
+ Result.ret (List.Cons y tl0)
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: backward function 0 -/
+def get_elem_mut_back
+ (slots : Vec (List Usize)) (x : Usize) (ret0 : Usize) :
+ Result (Vec (List Usize))
+ :=
+ do
+ let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
+ let l0 ← get_elem_mut_loop_back x l ret0
+ Vec.index_mut_back (List Usize) slots (Usize.ofInt 0) l0
+
+/- [loops::get_elem_shared]: loop 0: forward function -/
+divergent def get_elem_shared_loop
+ (x : Usize) (ls : List Usize) : Result Usize :=
+ match ls with
+ | List.Cons y tl => if y = x
+ then Result.ret y
+ else get_elem_shared_loop x tl
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_shared]: forward function -/
+def get_elem_shared (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
+ do
+ let l ← Vec.index (List Usize) slots (Usize.ofInt 0)
+ get_elem_shared_loop x l
+
+/- [loops::id_mut]: forward function -/
+def id_mut (T : Type) (ls : List T) : Result (List T) :=
+ Result.ret ls
+
+/- [loops::id_mut]: backward function 0 -/
+def id_mut_back (T : Type) (ls : List T) (ret0 : List T) : Result (List T) :=
+ Result.ret ret0
+
+/- [loops::id_shared]: forward function -/
+def id_shared (T : Type) (ls : List T) : Result (List T) :=
+ Result.ret ls
+
+/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_mut_loop_with_id_loop
+ (T : Type) (i : U32) (ls : List T) : Result T :=
+ match ls with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut_loop_with_id_loop T i0 tl
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id]: forward function -/
+def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
+ do
+ let ls0 ← id_mut T ls
+ list_nth_mut_loop_with_id_loop T i ls0
+
+/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_with_id_loop_back
+ (T : Type) (i : U32) (ls : List T) (ret0 : T) : Result (List T) :=
+ match ls with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+ Result.ret (List.Cons x tl0)
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id]: backward function 0 -/
+def list_nth_mut_loop_with_id_back
+ (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+ do
+ let ls0 ← id_mut T ls
+ let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+ id_mut_back T ls l
+
+/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_shared_loop_with_id_loop
+ (T : Type) (i : U32) (ls : List T) : Result T :=
+ match ls with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared_loop_with_id_loop T i0 tl
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_with_id]: forward function -/
+def list_nth_shared_loop_with_id
+ (T : Type) (ls : List T) (i : U32) : Result T :=
+ do
+ let ls0 ← id_shared T ls
+ list_nth_shared_loop_with_id_loop T i ls0
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut_loop_pair_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: forward function -/
+def list_nth_mut_loop_pair
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_mut_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_pair_loop_back'a
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl0)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x0 tl00)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: backward function 0 -/
+def list_nth_mut_loop_pair_back'a
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 -/
+divergent def list_nth_mut_loop_pair_loop_back'b
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x1 tl10)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: backward function 1 -/
+def list_nth_mut_loop_pair_back'b
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared_loop_pair_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair]: forward function -/
+def list_nth_shared_loop_pair
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_shared_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_merge_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge]: forward function -/
+def list_nth_mut_loop_pair_merge
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_pair_merge_loop_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
+ Result ((List T) × (List T))
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then let (t, t0) := ret0
+ Result.ret (List.Cons t tl0, List.Cons t0 tl1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let (tl00, tl10) ←
+ list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge]: backward function 0 -/
+def list_nth_mut_loop_pair_merge_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
+ Result ((List T) × (List T))
+ :=
+ list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_merge_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair_merge]: forward function -/
+def list_nth_shared_loop_pair_merge
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair]: forward function -/
+def list_nth_mut_shared_loop_pair
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 -/
+divergent def list_nth_mut_shared_loop_pair_loop_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl0)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl00 ←
+ list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x0 tl00)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair]: backward function 0 -/
+def list_nth_mut_shared_loop_pair_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function -/
+def list_nth_mut_shared_loop_pair_merge
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl0)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl00 ←
+ list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x0 tl00)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 -/
+def list_nth_mut_shared_loop_pair_merge_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair]: forward function -/
+def list_nth_shared_mut_loop_pair
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 -/
+divergent def list_nth_shared_mut_loop_pair_loop_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl10 ←
+ list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x1 tl10)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair]: backward function 1 -/
+def list_nth_shared_mut_loop_pair_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (x0, x1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function -/
+def list_nth_shared_mut_loop_pair_merge
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+ list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ match ls0 with
+ | List.Cons x0 tl0 =>
+ match ls1 with
+ | List.Cons x1 tl1 =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl1)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl10 ←
+ list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+ Result.ret (List.Cons x1 tl10)
+ | List.Nil => Result.fail Error.panic
+ | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 -/
+def list_nth_shared_mut_loop_pair_merge_back
+ (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+ Result (List T)
+ :=
+ list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+end loops
diff --git a/tests/lean/Loops/Types.lean b/tests/lean/Loops/Types.lean
new file mode 100644
index 00000000..f8bc193b
--- /dev/null
+++ b/tests/lean/Loops/Types.lean
@@ -0,0 +1,12 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: type definitions
+import Base
+open Primitives
+namespace loops
+
+/- [loops::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+end loops
diff --git a/tests/lean/Makefile b/tests/lean/Makefile
index ed3b3e3b..3ccfbec2 100644
--- a/tests/lean/Makefile
+++ b/tests/lean/Makefile
@@ -1,40 +1,35 @@
ALL_DIRS ?= $(filter-out %~ lean-toolchain% Makefile%, $(wildcard *))
+# TODO: remove
UPDATE_DIRS = $(addprefix update-,$(ALL_DIRS))
+# TODO: remove
VERIFY_DIRS = $(addprefix verif-,$(ALL_DIRS))
+# TODO: remove
CLEAN_DIRS = $(addprefix clean-,$(ALL_DIRS))
+# TODO: remove
COPY_LEAN_TOOLCHAIN = $(addprefix copy-lean-toolchain-,$(ALL_DIRS))
.PHONY: all
all: prepare-projects verify
.PHONY: prepare-projects
-prepare-projects: $(COPY_LEAN_TOOLCHAIN)
+prepare-projects: copy-lean-toolchain
.PHONY: prepare-projects
-copy-lean-toolchain-%:
- cp lean-toolchain $*
+copy-lean-toolchain:
+ cp ../../backends/lean/lean-toolchain .
.PHONY: update
-update: $(UPDATE_DIRS)
-
-.PHONY: update-%
-update-%:
- cd $* && lake update
+update:
+ lake update
.PHONY: verify
-verify: $(VERIFY_DIRS)
-
-.PHONY: verif-%
-verif-%:
- cd $* && lake build
+verify:
+ lake build
.PHONY: clean
-clean: $(CLEAN_DIRS)
-
-.PHONY: clean-%
-clean-%:
- cd $* && lake clean
+clean:
+ lake clean
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
new file mode 100644
index 00000000..bc707fd9
--- /dev/null
+++ b/tests/lean/NoNestedBorrows.lean
@@ -0,0 +1,511 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [no_nested_borrows]
+import Base
+open Primitives
+namespace no_nested_borrows
+
+/- [no_nested_borrows::Pair] -/
+structure Pair (T1 T2 : Type) where
+ x : T1
+ y : T2
+
+/- [no_nested_borrows::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [no_nested_borrows::One] -/
+inductive One (T1 : Type) :=
+| One : T1 → One T1
+
+/- [no_nested_borrows::EmptyEnum] -/
+inductive EmptyEnum :=
+| Empty : EmptyEnum
+
+/- [no_nested_borrows::Enum] -/
+inductive Enum :=
+| Variant1 : Enum
+| Variant2 : Enum
+
+/- [no_nested_borrows::EmptyStruct] -/
+structure EmptyStruct where
+
+/- [no_nested_borrows::Sum] -/
+inductive Sum (T1 T2 : Type) :=
+| Left : T1 → Sum T1 T2
+| Right : T2 → Sum T1 T2
+
+/- [no_nested_borrows::neg_test]: forward function -/
+def neg_test (x : I32) : Result I32 :=
+ - x
+
+/- [no_nested_borrows::add_test]: forward function -/
+def add_test (x : U32) (y : U32) : Result U32 :=
+ x + y
+
+/- [no_nested_borrows::subs_test]: forward function -/
+def subs_test (x : U32) (y : U32) : Result U32 :=
+ x - y
+
+/- [no_nested_borrows::div_test]: forward function -/
+def div_test (x : U32) (y : U32) : Result U32 :=
+ x / y
+
+/- [no_nested_borrows::div_test1]: forward function -/
+def div_test1 (x : U32) : Result U32 :=
+ x / (U32.ofInt 2)
+
+/- [no_nested_borrows::rem_test]: forward function -/
+def rem_test (x : U32) (y : U32) : Result U32 :=
+ x % y
+
+/- [no_nested_borrows::cast_test]: forward function -/
+def cast_test (x : U32) : Result I32 :=
+ Scalar.cast .I32 x
+
+/- [no_nested_borrows::test2]: forward function -/
+def test2 : Result Unit :=
+ do
+ let _ ← (U32.ofInt 23) + (U32.ofInt 44)
+ Result.ret ()
+
+/- Unit test for [no_nested_borrows::test2] -/
+#assert (test2 == .ret ())
+
+/- [no_nested_borrows::get_max]: forward function -/
+def get_max (x : U32) (y : U32) : Result U32 :=
+ if x >= y
+ then Result.ret x
+ else Result.ret y
+
+/- [no_nested_borrows::test3]: forward function -/
+def test3 : Result Unit :=
+ do
+ let x ← get_max (U32.ofInt 4) (U32.ofInt 3)
+ let y ← get_max (U32.ofInt 10) (U32.ofInt 11)
+ let z ← x + y
+ if not (z = (U32.ofInt 15))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test3] -/
+#assert (test3 == .ret ())
+
+/- [no_nested_borrows::test_neg1]: forward function -/
+def test_neg1 : Result Unit :=
+ do
+ let y ← - (I32.ofInt 3)
+ if not (y = (I32.ofInt (-(3:Int))))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_neg1] -/
+#assert (test_neg1 == .ret ())
+
+/- [no_nested_borrows::refs_test1]: forward function -/
+def refs_test1 : Result Unit :=
+ if not ((I32.ofInt 1) = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::refs_test1] -/
+#assert (refs_test1 == .ret ())
+
+/- [no_nested_borrows::refs_test2]: forward function -/
+def refs_test2 : Result Unit :=
+ if not ((I32.ofInt 2) = (I32.ofInt 2))
+ then Result.fail Error.panic
+ else
+ if not ((I32.ofInt 0) = (I32.ofInt 0))
+ then Result.fail Error.panic
+ else
+ if not ((I32.ofInt 2) = (I32.ofInt 2))
+ then Result.fail Error.panic
+ else
+ if not ((I32.ofInt 2) = (I32.ofInt 2))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::refs_test2] -/
+#assert (refs_test2 == .ret ())
+
+/- [no_nested_borrows::test_list1]: forward function -/
+def test_list1 : Result Unit :=
+ Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_list1] -/
+#assert (test_list1 == .ret ())
+
+/- [no_nested_borrows::test_box1]: forward function -/
+def test_box1 : Result Unit :=
+ let b := (I32.ofInt 1)
+ let x := b
+ if not (x = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_box1] -/
+#assert (test_box1 == .ret ())
+
+/- [no_nested_borrows::copy_int]: forward function -/
+def copy_int (x : I32) : Result I32 :=
+ Result.ret x
+
+/- [no_nested_borrows::test_unreachable]: forward function -/
+def test_unreachable (b : Bool) : Result Unit :=
+ if b
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- [no_nested_borrows::test_panic]: forward function -/
+def test_panic (b : Bool) : Result Unit :=
+ if b
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- [no_nested_borrows::test_copy_int]: forward function -/
+def test_copy_int : Result Unit :=
+ do
+ let y ← copy_int (I32.ofInt 0)
+ if not ((I32.ofInt 0) = y)
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_copy_int] -/
+#assert (test_copy_int == .ret ())
+
+/- [no_nested_borrows::is_cons]: forward function -/
+def is_cons (T : Type) (l : List T) : Result Bool :=
+ match l with
+ | List.Cons t l0 => Result.ret true
+ | List.Nil => Result.ret false
+
+/- [no_nested_borrows::test_is_cons]: forward function -/
+def test_is_cons : Result Unit :=
+ do
+ let l := List.Nil
+ let b ← is_cons I32 (List.Cons (I32.ofInt 0) l)
+ if not b
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_is_cons] -/
+#assert (test_is_cons == .ret ())
+
+/- [no_nested_borrows::split_list]: forward function -/
+def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
+ match l with
+ | List.Cons hd tl => Result.ret (hd, tl)
+ | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::test_split_list]: forward function -/
+def test_split_list : Result Unit :=
+ do
+ let l := List.Nil
+ let p ← split_list I32 (List.Cons (I32.ofInt 0) l)
+ let (hd, _) := p
+ if not (hd = (I32.ofInt 0))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_split_list] -/
+#assert (test_split_list == .ret ())
+
+/- [no_nested_borrows::choose]: forward function -/
+def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+ if b
+ then Result.ret x
+ else Result.ret y
+
+/- [no_nested_borrows::choose]: backward function 0 -/
+def choose_back
+ (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
+ if b
+ then Result.ret (ret0, y)
+ else Result.ret (x, ret0)
+
+/- [no_nested_borrows::choose_test]: forward function -/
+def choose_test : Result Unit :=
+ do
+ let z ← choose I32 true (I32.ofInt 0) (I32.ofInt 0)
+ let z0 ← z + (I32.ofInt 1)
+ if not (z0 = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else
+ do
+ let (x, y) ← choose_back I32 true (I32.ofInt 0) (I32.ofInt 0) z0
+ if not (x = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else
+ if not (y = (I32.ofInt 0))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::choose_test] -/
+#assert (choose_test == .ret ())
+
+/- [no_nested_borrows::test_char]: forward function -/
+def test_char : Result Char :=
+ Result.ret 'a'
+
+mutual
+
+/- [no_nested_borrows::NodeElem] -/
+inductive NodeElem (T : Type) :=
+| Cons : Tree T → NodeElem T → NodeElem T
+| Nil : NodeElem T
+
+/- [no_nested_borrows::Tree] -/
+inductive Tree (T : Type) :=
+| Leaf : T → Tree T
+| Node : T → NodeElem T → Tree T → Tree T
+
+end
+
+/- [no_nested_borrows::list_length]: forward function -/
+divergent def list_length (T : Type) (l : List T) : Result U32 :=
+ match l with
+ | List.Cons t l1 => do
+ let i ← list_length T l1
+ (U32.ofInt 1) + i
+ | List.Nil => Result.ret (U32.ofInt 0)
+
+/- [no_nested_borrows::list_nth_shared]: forward function -/
+divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
+ match l with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_shared T tl i0
+ | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::list_nth_mut]: forward function -/
+divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+ match l with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut T tl i0
+ | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::list_nth_mut]: backward function 0 -/
+divergent def list_nth_mut_back
+ (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
+ match l with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl0 ← list_nth_mut_back T tl i0 ret0
+ Result.ret (List.Cons x tl0)
+ | List.Nil => Result.fail Error.panic
+
+/- [no_nested_borrows::list_rev_aux]: forward function -/
+divergent def list_rev_aux
+ (T : Type) (li : List T) (lo : List T) : Result (List T) :=
+ match li with
+ | List.Cons hd tl => list_rev_aux T tl (List.Cons hd lo)
+ | List.Nil => Result.ret lo
+
+/- [no_nested_borrows::list_rev]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def list_rev (T : Type) (l : List T) : Result (List T) :=
+ let li := mem.replace (List T) l List.Nil
+ list_rev_aux T li List.Nil
+
+/- [no_nested_borrows::test_list_functions]: forward function -/
+def test_list_functions : Result Unit :=
+ do
+ let l := List.Nil
+ let l0 := List.Cons (I32.ofInt 2) l
+ let l1 := List.Cons (I32.ofInt 1) l0
+ let i ← list_length I32 (List.Cons (I32.ofInt 0) l1)
+ if not (i = (U32.ofInt 3))
+ then Result.fail Error.panic
+ else
+ do
+ let i0 ←
+ list_nth_shared I32 (List.Cons (I32.ofInt 0) l1) (U32.ofInt 0)
+ if not (i0 = (I32.ofInt 0))
+ then Result.fail Error.panic
+ else
+ do
+ let i1 ←
+ list_nth_shared I32 (List.Cons (I32.ofInt 0) l1) (U32.ofInt 1)
+ if not (i1 = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else
+ do
+ let i2 ←
+ list_nth_shared I32 (List.Cons (I32.ofInt 0) l1)
+ (U32.ofInt 2)
+ if not (i2 = (I32.ofInt 2))
+ then Result.fail Error.panic
+ else
+ do
+ let ls ←
+ list_nth_mut_back I32 (List.Cons (I32.ofInt 0) l1)
+ (U32.ofInt 1) (I32.ofInt 3)
+ let i3 ← list_nth_shared I32 ls (U32.ofInt 0)
+ if not (i3 = (I32.ofInt 0))
+ then Result.fail Error.panic
+ else
+ do
+ let i4 ← list_nth_shared I32 ls (U32.ofInt 1)
+ if not (i4 = (I32.ofInt 3))
+ then Result.fail Error.panic
+ else
+ do
+ let i5 ← list_nth_shared I32 ls (U32.ofInt 2)
+ if not (i5 = (I32.ofInt 2))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_list_functions] -/
+#assert (test_list_functions == .ret ())
+
+/- [no_nested_borrows::id_mut_pair1]: forward function -/
+def id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
+ Result.ret (x, y)
+
+/- [no_nested_borrows::id_mut_pair1]: backward function 0 -/
+def id_mut_pair1_back
+ (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
+ let (t, t0) := ret0
+ Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair2]: forward function -/
+def id_mut_pair2 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
+ let (t, t0) := p
+ Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair2]: backward function 0 -/
+def id_mut_pair2_back
+ (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
+ let (t, t0) := ret0
+ Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair3]: forward function -/
+def id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
+ Result.ret (x, y)
+
+/- [no_nested_borrows::id_mut_pair3]: backward function 0 -/
+def id_mut_pair3_back'a
+ (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 :=
+ Result.ret ret0
+
+/- [no_nested_borrows::id_mut_pair3]: backward function 1 -/
+def id_mut_pair3_back'b
+ (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 :=
+ Result.ret ret0
+
+/- [no_nested_borrows::id_mut_pair4]: forward function -/
+def id_mut_pair4 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
+ let (t, t0) := p
+ Result.ret (t, t0)
+
+/- [no_nested_borrows::id_mut_pair4]: backward function 0 -/
+def id_mut_pair4_back'a
+ (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 :=
+ Result.ret ret0
+
+/- [no_nested_borrows::id_mut_pair4]: backward function 1 -/
+def id_mut_pair4_back'b
+ (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 :=
+ Result.ret ret0
+
+/- [no_nested_borrows::StructWithTuple] -/
+structure StructWithTuple (T1 T2 : Type) where
+ p : (T1 × T2)
+
+/- [no_nested_borrows::new_tuple1]: forward function -/
+def new_tuple1 : Result (StructWithTuple U32 U32) :=
+ Result.ret { p := ((U32.ofInt 1), (U32.ofInt 2)) }
+
+/- [no_nested_borrows::new_tuple2]: forward function -/
+def new_tuple2 : Result (StructWithTuple I16 I16) :=
+ Result.ret { p := ((I16.ofInt 1), (I16.ofInt 2)) }
+
+/- [no_nested_borrows::new_tuple3]: forward function -/
+def new_tuple3 : Result (StructWithTuple U64 I64) :=
+ Result.ret { p := ((U64.ofInt 1), (I64.ofInt 2)) }
+
+/- [no_nested_borrows::StructWithPair] -/
+structure StructWithPair (T1 T2 : Type) where
+ p : Pair T1 T2
+
+/- [no_nested_borrows::new_pair1]: forward function -/
+def new_pair1 : Result (StructWithPair U32 U32) :=
+ Result.ret { p := { x := (U32.ofInt 1), y := (U32.ofInt 2) } }
+
+/- [no_nested_borrows::test_constants]: forward function -/
+def test_constants : Result Unit :=
+ do
+ let swt ← new_tuple1
+ let (i, _) := swt.p
+ if not (i = (U32.ofInt 1))
+ then Result.fail Error.panic
+ else
+ do
+ let swt0 ← new_tuple2
+ let (i0, _) := swt0.p
+ if not (i0 = (I16.ofInt 1))
+ then Result.fail Error.panic
+ else
+ do
+ let swt1 ← new_tuple3
+ let (i1, _) := swt1.p
+ if not (i1 = (U64.ofInt 1))
+ then Result.fail Error.panic
+ else
+ do
+ let swp ← new_pair1
+ if not (swp.p.x = (U32.ofInt 1))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_constants] -/
+#assert (test_constants == .ret ())
+
+/- [no_nested_borrows::test_weird_borrows1]: forward function -/
+def test_weird_borrows1 : Result Unit :=
+ Result.ret ()
+
+/- Unit test for [no_nested_borrows::test_weird_borrows1] -/
+#assert (test_weird_borrows1 == .ret ())
+
+/- [no_nested_borrows::test_mem_replace]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def test_mem_replace (px : U32) : Result U32 :=
+ let y := mem.replace U32 px (U32.ofInt 1)
+ if not (y = (U32.ofInt 0))
+ then Result.fail Error.panic
+ else Result.ret (U32.ofInt 2)
+
+/- [no_nested_borrows::test_shared_borrow_bool1]: forward function -/
+def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
+ if b
+ then Result.ret (U32.ofInt 0)
+ else Result.ret (U32.ofInt 1)
+
+/- [no_nested_borrows::test_shared_borrow_bool2]: forward function -/
+def test_shared_borrow_bool2 : Result U32 :=
+ Result.ret (U32.ofInt 0)
+
+/- [no_nested_borrows::test_shared_borrow_enum1]: forward function -/
+def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
+ match l with
+ | List.Cons i l0 => Result.ret (U32.ofInt 1)
+ | List.Nil => Result.ret (U32.ofInt 0)
+
+/- [no_nested_borrows::test_shared_borrow_enum2]: forward function -/
+def test_shared_borrow_enum2 : Result U32 :=
+ Result.ret (U32.ofInt 0)
+
+end no_nested_borrows
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
new file mode 100644
index 00000000..cee7128a
--- /dev/null
+++ b/tests/lean/Paper.lean
@@ -0,0 +1,121 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [paper]
+import Base
+open Primitives
+namespace paper
+
+/- [paper::ref_incr]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) -/
+def ref_incr (x : I32) : Result I32 :=
+ x + (I32.ofInt 1)
+
+/- [paper::test_incr]: forward function -/
+def test_incr : Result Unit :=
+ do
+ let x ← ref_incr (I32.ofInt 0)
+ if not (x = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [paper::test_incr] -/
+#assert (test_incr == .ret ())
+
+/- [paper::choose]: forward function -/
+def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+ if b
+ then Result.ret x
+ else Result.ret y
+
+/- [paper::choose]: backward function 0 -/
+def choose_back
+ (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
+ if b
+ then Result.ret (ret0, y)
+ else Result.ret (x, ret0)
+
+/- [paper::test_choose]: forward function -/
+def test_choose : Result Unit :=
+ do
+ let z ← choose I32 true (I32.ofInt 0) (I32.ofInt 0)
+ let z0 ← z + (I32.ofInt 1)
+ if not (z0 = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else
+ do
+ let (x, y) ← choose_back I32 true (I32.ofInt 0) (I32.ofInt 0) z0
+ if not (x = (I32.ofInt 1))
+ then Result.fail Error.panic
+ else
+ if not (y = (I32.ofInt 0))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [paper::test_choose] -/
+#assert (test_choose == .ret ())
+
+/- [paper::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [paper::list_nth_mut]: forward function -/
+divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+ match l with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret x
+ else do
+ let i0 ← i - (U32.ofInt 1)
+ list_nth_mut T tl i0
+ | List.Nil => Result.fail Error.panic
+
+/- [paper::list_nth_mut]: backward function 0 -/
+divergent def list_nth_mut_back
+ (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
+ match l with
+ | List.Cons x tl =>
+ if i = (U32.ofInt 0)
+ then Result.ret (List.Cons ret0 tl)
+ else
+ do
+ let i0 ← i - (U32.ofInt 1)
+ let tl0 ← list_nth_mut_back T tl i0 ret0
+ Result.ret (List.Cons x tl0)
+ | List.Nil => Result.fail Error.panic
+
+/- [paper::sum]: forward function -/
+divergent def sum (l : List I32) : Result I32 :=
+ match l with
+ | List.Cons x tl => do
+ let i ← sum tl
+ x + i
+ | List.Nil => Result.ret (I32.ofInt 0)
+
+/- [paper::test_nth]: forward function -/
+def test_nth : Result Unit :=
+ do
+ let l := List.Nil
+ let l0 := List.Cons (I32.ofInt 3) l
+ let l1 := List.Cons (I32.ofInt 2) l0
+ let x ← list_nth_mut I32 (List.Cons (I32.ofInt 1) l1) (U32.ofInt 2)
+ let x0 ← x + (I32.ofInt 1)
+ let l2 ←
+ list_nth_mut_back I32 (List.Cons (I32.ofInt 1) l1) (U32.ofInt 2) x0
+ let i ← sum l2
+ if not (i = (I32.ofInt 7))
+ then Result.fail Error.panic
+ else Result.ret ()
+
+/- Unit test for [paper::test_nth] -/
+#assert (test_nth == .ret ())
+
+/- [paper::call_choose]: forward function -/
+def call_choose (p : (U32 × U32)) : Result U32 :=
+ do
+ let (px, py) := p
+ let pz ← choose U32 true px py
+ let pz0 ← pz + (U32.ofInt 1)
+ let (px0, _) ← choose_back U32 true px py pz0
+ Result.ret px0
+
+end paper
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
new file mode 100644
index 00000000..1453c275
--- /dev/null
+++ b/tests/lean/PoloniusList.lean
@@ -0,0 +1,34 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [polonius_list]
+import Base
+open Primitives
+namespace polonius_list
+
+/- [polonius_list::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [polonius_list::get_list_at_x]: forward function -/
+divergent def get_list_at_x (ls : List U32) (x : U32) : Result (List U32) :=
+ match ls with
+ | List.Cons hd tl =>
+ if hd = x
+ then Result.ret (List.Cons hd tl)
+ else get_list_at_x tl x
+ | List.Nil => Result.ret List.Nil
+
+/- [polonius_list::get_list_at_x]: backward function 0 -/
+divergent def get_list_at_x_back
+ (ls : List U32) (x : U32) (ret0 : List U32) : Result (List U32) :=
+ match ls with
+ | List.Cons hd tl =>
+ if hd = x
+ then Result.ret ret0
+ else
+ do
+ let tl0 ← get_list_at_x_back tl x ret0
+ Result.ret (List.Cons hd tl0)
+ | List.Nil => Result.ret ret0
+
+end polonius_list
diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/hashmap/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/hashmap/Hashmap.lean b/tests/lean/hashmap/Hashmap.lean
deleted file mode 100644
index 41630205..00000000
--- a/tests/lean/hashmap/Hashmap.lean
+++ /dev/null
@@ -1 +0,0 @@
-import Hashmap.Funs
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean b/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
deleted file mode 100644
index 197b0a6a..00000000
--- a/tests/lean/hashmap/Hashmap/Clauses/Clauses.lean
+++ /dev/null
@@ -1,107 +0,0 @@
--- [hashmap]: templates for the decreases clauses
-import Base.Primitives
-import Hashmap.Types
-
-/- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T))
- (n : Usize) :=
- (slots, n)
-
-/- [hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_allocate_slots_loop_decreases $slots $n) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T))
- (i : Usize) :=
- (slots, i)
-
-/- [hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
- (value : T) (ls : list_t T) :=
- (key, value, ls)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_insert_in_list_loop_decreases $key $value $ls) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hash_map_move_elements_from_list_loop_terminates (T : Type)
- (ntable : hash_map_t T) (ls : list_t T) :=
- (ntable, ls)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T)
- (slots : Vec (list_t T)) (i : Usize) :=
- (ntable, slots, i)
-
-/- [hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_loop_decreases $ntable $slots $i) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : Usize)
- (ls : list_t T) :=
- (key, ls)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_contains_key_in_list_loop_decreases $key $ls) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
- (ls : list_t T) :=
- (key, ls)
-
-/- [hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T)
- (key : Usize) :=
- (ls, key)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_mut_in_list_loop_decreases $ls $key) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
- (ls : list_t T) :=
- (key, ls)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_remove_from_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Template.lean b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
deleted file mode 100644
index 560592c8..00000000
--- a/tests/lean/hashmap/Hashmap/Clauses/Template.lean
+++ /dev/null
@@ -1,108 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap]: templates for the decreases clauses
-import Base.Primitives
-import Hashmap.Types
-
-/- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T))
- (n : Usize) :=
- (slots, n)
-
-/- [hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_allocate_slots_loop_decreases $slots $n) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T))
- (i : Usize) :=
- (slots, i)
-
-/- [hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
- (value : T) (ls : list_t T) :=
- (key, value, ls)
-
-/- [hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_insert_in_list_loop_decreases $key $value $ls) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hash_map_move_elements_from_list_loop_terminates (T : Type)
- (ntable : hash_map_t T) (ls : list_t T) :=
- (ntable, ls)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_from_list_loop_decreases $ntable $ls) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T)
- (slots : Vec (list_t T)) (i : Usize) :=
- (ntable, slots, i)
-
-/- [hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_move_elements_loop_decreases $ntable $slots $i) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hash_map_contains_key_in_list_loop_terminates (T : Type) (key : Usize)
- (ls : list_t T) :=
- (key, ls)
-
-/- [hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_contains_key_in_list_loop_decreases $key $ls) =>
- `(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
- (ls : list_t T) :=
- (key, ls)
-
-/- [hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hash_map_get_mut_in_list_loop_terminates (T : Type) (ls : list_t T)
- (key : Usize) :=
- (ls, key)
-
-/- [hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_get_mut_in_list_loop_decreases $ls $key) =>`(tactic| sorry)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
- (ls : list_t T) :=
- (key, ls)
-
-/- [hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hash_map_remove_from_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
diff --git a/tests/lean/hashmap/Hashmap/Funs.lean b/tests/lean/hashmap/Hashmap/Funs.lean
deleted file mode 100644
index 77b1a157..00000000
--- a/tests/lean/hashmap/Hashmap/Funs.lean
+++ /dev/null
@@ -1,513 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap]: function definitions
-import Base.Primitives
-import Hashmap.Types
-import Hashmap.Clauses.Clauses
-
-/- [hashmap::hash_key] -/
-def hash_key_fwd (k : Usize) : Result Usize :=
- Result.ret k
-
-/- [hashmap::HashMap::{0}::allocate_slots] -/
-def hash_map_allocate_slots_loop_fwd
- (T : Type) (slots : Vec (list_t T)) (n : Usize) :
- (Result (Vec (list_t T)))
- :=
- if h: n > (Usize.ofInt 0 (by intlit))
- then
- do
- let slots0 ← vec_push_back (list_t T) slots list_t.Nil
- let n0 ← n - (Usize.ofInt 1 (by intlit))
- hash_map_allocate_slots_loop_fwd T slots0 n0
- else Result.ret slots
-termination_by hash_map_allocate_slots_loop_fwd slots n =>
- hash_map_allocate_slots_loop_terminates T slots n
-decreasing_by hash_map_allocate_slots_loop_decreases slots n
-
-/- [hashmap::HashMap::{0}::allocate_slots] -/
-def hash_map_allocate_slots_fwd
- (T : Type) (slots : Vec (list_t T)) (n : Usize) : Result (Vec (list_t T)) :=
- hash_map_allocate_slots_loop_fwd T slots n
-
-/- [hashmap::HashMap::{0}::new_with_capacity] -/
-def hash_map_new_with_capacity_fwd
- (T : Type) (capacity : Usize) (max_load_dividend : Usize)
- (max_load_divisor : Usize) :
- Result (hash_map_t T)
- :=
- do
- let v := vec_new (list_t T)
- let slots ← hash_map_allocate_slots_fwd T v capacity
- let i ← capacity * max_load_dividend
- let i0 ← i / max_load_divisor
- Result.ret
- {
- hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
- hash_map_max_load_factor := (max_load_dividend, max_load_divisor),
- hash_map_max_load := i0,
- hash_map_slots := slots
- }
-
-/- [hashmap::HashMap::{0}::new] -/
-def hash_map_new_fwd (T : Type) : Result (hash_map_t T) :=
- hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
- (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
-
-/- [hashmap::HashMap::{0}::clear] -/
-def hash_map_clear_loop_fwd_back
- (T : Type) (slots : Vec (list_t T)) (i : Usize) :
- (Result (Vec (list_t T)))
- :=
- let i0 := vec_len (list_t T) slots
- if h: i < i0
- then
- do
- let i1 ← i + (Usize.ofInt 1 (by intlit))
- let slots0 ← vec_index_mut_back (list_t T) slots i list_t.Nil
- hash_map_clear_loop_fwd_back T slots0 i1
- else Result.ret slots
-termination_by hash_map_clear_loop_fwd_back slots i =>
- hash_map_clear_loop_terminates T slots i
-decreasing_by hash_map_clear_loop_decreases slots i
-
-/- [hashmap::HashMap::{0}::clear] -/
-def hash_map_clear_fwd_back
- (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
- do
- let v ←
- hash_map_clear_loop_fwd_back T self.hash_map_slots
- (Usize.ofInt 0 (by intlit))
- Result.ret
- {
- self
- with
- hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
- hash_map_slots := v
- }
-
-/- [hashmap::HashMap::{0}::len] -/
-def hash_map_len_fwd (T : Type) (self : hash_map_t T) : Result Usize :=
- Result.ret self.hash_map_num_entries
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_loop_fwd
- (T : Type) (key : Usize) (value : T) (ls : list_t T) : (Result Bool) :=
- match h: ls with
- | list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret false
- else hash_map_insert_in_list_loop_fwd T key value tl
- | list_t.Nil => Result.ret true
-termination_by hash_map_insert_in_list_loop_fwd key value ls =>
- hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_fwd
- (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result Bool :=
- hash_map_insert_in_list_loop_fwd T key value ls
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_loop_back
- (T : Type) (key : Usize) (value : T) (ls : list_t T) : (Result (list_t T)) :=
- match h: ls with
- | list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret (list_t.Cons ckey value tl)
- else
- do
- let tl0 ← hash_map_insert_in_list_loop_back T key value tl
- Result.ret (list_t.Cons ckey cvalue tl0)
- | list_t.Nil => let l := list_t.Nil
- Result.ret (list_t.Cons key value l)
-termination_by hash_map_insert_in_list_loop_back key value ls =>
- hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def hash_map_insert_in_list_back
- (T : Type) (key : Usize) (value : T) (ls : list_t T) : Result (list_t T) :=
- hash_map_insert_in_list_loop_back T key value ls
-
-/- [hashmap::HashMap::{0}::insert_no_resize] -/
-def hash_map_insert_no_resize_fwd_back
- (T : Type) (self : hash_map_t T) (key : Usize) (value : T) :
- Result (hash_map_t T)
- :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
- let inserted ← hash_map_insert_in_list_fwd T key value l
- if h: inserted
- then
- do
- let i0 ← self.hash_map_num_entries + (Usize.ofInt 1 (by intlit))
- let l0 ← hash_map_insert_in_list_back T key value l
- let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
- Result.ret
- { self with hash_map_num_entries := i0, hash_map_slots := v }
- else
- do
- let l0 ← hash_map_insert_in_list_back T key value l
- let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
- Result.ret { self with hash_map_slots := v }
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
- Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [hashmap::HashMap::{0}::move_elements_from_list] -/
-def hash_map_move_elements_from_list_loop_fwd_back
- (T : Type) (ntable : hash_map_t T) (ls : list_t T) :
- (Result (hash_map_t T))
- :=
- match h: ls with
- | list_t.Cons k v tl =>
- do
- let ntable0 ← hash_map_insert_no_resize_fwd_back T ntable k v
- hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
- | list_t.Nil => Result.ret ntable
-termination_by hash_map_move_elements_from_list_loop_fwd_back ntable ls =>
- hash_map_move_elements_from_list_loop_terminates T ntable ls
-decreasing_by hash_map_move_elements_from_list_loop_decreases ntable ls
-
-/- [hashmap::HashMap::{0}::move_elements_from_list] -/
-def hash_map_move_elements_from_list_fwd_back
- (T : Type) (ntable : hash_map_t T) (ls : list_t T) : Result (hash_map_t T) :=
- hash_map_move_elements_from_list_loop_fwd_back T ntable ls
-
-/- [hashmap::HashMap::{0}::move_elements] -/
-def hash_map_move_elements_loop_fwd_back
- (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) :
- (Result ((hash_map_t T) × (Vec (list_t T))))
- :=
- let i0 := vec_len (list_t T) slots
- if h: i < i0
- then
- do
- let l ← vec_index_mut_fwd (list_t T) slots i
- let ls := mem_replace_fwd (list_t T) l list_t.Nil
- let ntable0 ← hash_map_move_elements_from_list_fwd_back T ntable ls
- let i1 ← i + (Usize.ofInt 1 (by intlit))
- let l0 := mem_replace_back (list_t T) l list_t.Nil
- let slots0 ← vec_index_mut_back (list_t T) slots i l0
- hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
- else Result.ret (ntable, slots)
-termination_by hash_map_move_elements_loop_fwd_back ntable slots i =>
- hash_map_move_elements_loop_terminates T ntable slots i
-decreasing_by hash_map_move_elements_loop_decreases ntable slots i
-
-/- [hashmap::HashMap::{0}::move_elements] -/
-def hash_map_move_elements_fwd_back
- (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : Usize) :
- Result ((hash_map_t T) × (Vec (list_t T)))
- :=
- hash_map_move_elements_loop_fwd_back T ntable slots i
-
-/- [hashmap::HashMap::{0}::try_resize] -/
-def hash_map_try_resize_fwd_back
- (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
- do
- let max_usize ← Scalar.cast .Usize core_num_u32_max_c
- let capacity := vec_len (list_t T) self.hash_map_slots
- let n1 ← max_usize / (Usize.ofInt 2 (by intlit))
- let (i, i0) := self.hash_map_max_load_factor
- let i1 ← n1 / i
- if h: capacity <= i1
- then
- do
- let i2 ← capacity * (Usize.ofInt 2 (by intlit))
- let ntable ← hash_map_new_with_capacity_fwd T i2 i i0
- let (ntable0, _) ←
- hash_map_move_elements_fwd_back T ntable self.hash_map_slots
- (Usize.ofInt 0 (by intlit))
- Result.ret
- {
- ntable0
- with
- hash_map_num_entries := self.hash_map_num_entries,
- hash_map_max_load_factor := (i, i0)
- }
- else Result.ret { self with hash_map_max_load_factor := (i, i0) }
-
-/- [hashmap::HashMap::{0}::insert] -/
-def hash_map_insert_fwd_back
- (T : Type) (self : hash_map_t T) (key : Usize) (value : T) :
- Result (hash_map_t T)
- :=
- do
- let self0 ← hash_map_insert_no_resize_fwd_back T self key value
- let i ← hash_map_len_fwd T self0
- if h: i > self0.hash_map_max_load
- then hash_map_try_resize_fwd_back T self0
- else Result.ret self0
-
-/- [hashmap::HashMap::{0}::contains_key_in_list] -/
-def hash_map_contains_key_in_list_loop_fwd
- (T : Type) (key : Usize) (ls : list_t T) : (Result Bool) :=
- match h: ls with
- | list_t.Cons ckey t tl =>
- if h: ckey = key
- then Result.ret true
- else hash_map_contains_key_in_list_loop_fwd T key tl
- | list_t.Nil => Result.ret false
-termination_by hash_map_contains_key_in_list_loop_fwd key ls =>
- hash_map_contains_key_in_list_loop_terminates T key ls
-decreasing_by hash_map_contains_key_in_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::contains_key_in_list] -/
-def hash_map_contains_key_in_list_fwd
- (T : Type) (key : Usize) (ls : list_t T) : Result Bool :=
- hash_map_contains_key_in_list_loop_fwd T key ls
-
-/- [hashmap::HashMap::{0}::contains_key] -/
-def hash_map_contains_key_fwd
- (T : Type) (self : hash_map_t T) (key : Usize) : Result Bool :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod
- hash_map_contains_key_in_list_fwd T key l
-
-/- [hashmap::HashMap::{0}::get_in_list] -/
-def hash_map_get_in_list_loop_fwd
- (T : Type) (key : Usize) (ls : list_t T) : (Result T) :=
- match h: ls with
- | list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret cvalue
- else hash_map_get_in_list_loop_fwd T key tl
- | list_t.Nil => Result.fail Error.panic
-termination_by hash_map_get_in_list_loop_fwd key ls =>
- hash_map_get_in_list_loop_terminates T key ls
-decreasing_by hash_map_get_in_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::get_in_list] -/
-def hash_map_get_in_list_fwd
- (T : Type) (key : Usize) (ls : list_t T) : Result T :=
- hash_map_get_in_list_loop_fwd T key ls
-
-/- [hashmap::HashMap::{0}::get] -/
-def hash_map_get_fwd
- (T : Type) (self : hash_map_t T) (key : Usize) : Result T :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod
- hash_map_get_in_list_fwd T key l
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_loop_fwd
- (T : Type) (ls : list_t T) (key : Usize) : (Result T) :=
- match h: ls with
- | list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret cvalue
- else hash_map_get_mut_in_list_loop_fwd T tl key
- | list_t.Nil => Result.fail Error.panic
-termination_by hash_map_get_mut_in_list_loop_fwd ls key =>
- hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_fwd
- (T : Type) (ls : list_t T) (key : Usize) : Result T :=
- hash_map_get_mut_in_list_loop_fwd T ls key
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_loop_back
- (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : (Result (list_t T)) :=
- match h: ls with
- | list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret (list_t.Cons ckey ret0 tl)
- else
- do
- let tl0 ← hash_map_get_mut_in_list_loop_back T tl key ret0
- Result.ret (list_t.Cons ckey cvalue tl0)
- | list_t.Nil => Result.fail Error.panic
-termination_by hash_map_get_mut_in_list_loop_back ls key ret0 =>
- hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def hash_map_get_mut_in_list_back
- (T : Type) (ls : list_t T) (key : Usize) (ret0 : T) : Result (list_t T) :=
- hash_map_get_mut_in_list_loop_back T ls key ret0
-
-/- [hashmap::HashMap::{0}::get_mut] -/
-def hash_map_get_mut_fwd
- (T : Type) (self : hash_map_t T) (key : Usize) : Result T :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
- hash_map_get_mut_in_list_fwd T l key
-
-/- [hashmap::HashMap::{0}::get_mut] -/
-def hash_map_get_mut_back
- (T : Type) (self : hash_map_t T) (key : Usize) (ret0 : T) :
- Result (hash_map_t T)
- :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
- let l0 ← hash_map_get_mut_in_list_back T l key ret0
- let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
- Result.ret { self with hash_map_slots := v }
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_loop_fwd
- (T : Type) (key : Usize) (ls : list_t T) : (Result (Option T)) :=
- match h: ls with
- | list_t.Cons ckey t tl =>
- if h: ckey = key
- then
- let mv_ls :=
- mem_replace_fwd (list_t T) (list_t.Cons ckey t tl) list_t.Nil
- match h: mv_ls with
- | list_t.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
- | list_t.Nil => Result.fail Error.panic
- else hash_map_remove_from_list_loop_fwd T key tl
- | list_t.Nil => Result.ret Option.none
-termination_by hash_map_remove_from_list_loop_fwd key ls =>
- hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_fwd
- (T : Type) (key : Usize) (ls : list_t T) : Result (Option T) :=
- hash_map_remove_from_list_loop_fwd T key ls
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_loop_back
- (T : Type) (key : Usize) (ls : list_t T) : (Result (list_t T)) :=
- match h: ls with
- | list_t.Cons ckey t tl =>
- if h: ckey = key
- then
- let mv_ls :=
- mem_replace_fwd (list_t T) (list_t.Cons ckey t tl) list_t.Nil
- match h: mv_ls with
- | list_t.Cons i cvalue tl0 => Result.ret tl0
- | list_t.Nil => Result.fail Error.panic
- else
- do
- let tl0 ← hash_map_remove_from_list_loop_back T key tl
- Result.ret (list_t.Cons ckey t tl0)
- | list_t.Nil => Result.ret list_t.Nil
-termination_by hash_map_remove_from_list_loop_back key ls =>
- hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def hash_map_remove_from_list_back
- (T : Type) (key : Usize) (ls : list_t T) : Result (list_t T) :=
- hash_map_remove_from_list_loop_back T key ls
-
-/- [hashmap::HashMap::{0}::remove] -/
-def hash_map_remove_fwd
- (T : Type) (self : hash_map_t T) (key : Usize) : Result (Option T) :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
- let x ← hash_map_remove_from_list_fwd T key l
- match h: x with
- | Option.none => Result.ret Option.none
- | Option.some x0 =>
- do
- let _ ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit))
- Result.ret (Option.some x0)
-
-/- [hashmap::HashMap::{0}::remove] -/
-def hash_map_remove_back
- (T : Type) (self : hash_map_t T) (key : Usize) : Result (hash_map_t T) :=
- do
- let hash ← hash_key_fwd key
- let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod ← hash % i
- let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
- let x ← hash_map_remove_from_list_fwd T key l
- match h: x with
- | Option.none =>
- do
- let l0 ← hash_map_remove_from_list_back T key l
- let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
- Result.ret { self with hash_map_slots := v }
- | Option.some x0 =>
- do
- let i0 ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit))
- let l0 ← hash_map_remove_from_list_back T key l
- let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0
- Result.ret
- { self with hash_map_num_entries := i0, hash_map_slots := v }
-
-/- [hashmap::test1] -/
-def test1_fwd : Result Unit :=
- do
- let hm ← hash_map_new_fwd U64
- let hm0 ←
- hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
- (U64.ofInt 42 (by intlit))
- let hm1 ←
- hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
- (U64.ofInt 18 (by intlit))
- let hm2 ←
- hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
- (U64.ofInt 138 (by intlit))
- let hm3 ←
- hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
- (U64.ofInt 256 (by intlit))
- let i ← hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
- if h: not (i = (U64.ofInt 18 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let hm4 ←
- hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
- (U64.ofInt 56 (by intlit))
- let i0 ← hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
- if h: not (i0 = (U64.ofInt 56 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let x ←
- hash_map_remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
- match h: x with
- | Option.none => Result.fail Error.panic
- | Option.some x0 =>
- if h: not (x0 = (U64.ofInt 56 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let hm5 ←
- hash_map_remove_back U64 hm4 (Usize.ofInt 1024 (by intlit))
- let i1 ←
- hash_map_get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
- if h: not (i1 = (U64.ofInt 42 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i2 ←
- hash_map_get_fwd U64 hm5 (Usize.ofInt 128 (by intlit))
- if h: not (i2 = (U64.ofInt 18 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i3 ←
- hash_map_get_fwd U64 hm5
- (Usize.ofInt 1056 (by intlit))
- if h: not (i3 = (U64.ofInt 256 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean
deleted file mode 100644
index 6eabf7da..00000000
--- a/tests/lean/hashmap/Hashmap/Types.lean
+++ /dev/null
@@ -1,16 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap]: type definitions
-import Base.Primitives
-
-/- [hashmap::List] -/
-inductive list_t (T : Type) :=
-| Cons : Usize -> T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [hashmap::HashMap] -/
-structure hash_map_t (T : Type) where
- hash_map_num_entries : Usize
- hash_map_max_load_factor : (Usize × Usize)
- hash_map_max_load : Usize
- hash_map_slots : Vec (list_t T)
-
diff --git a/tests/lean/hashmap/lake-manifest.json b/tests/lean/hashmap/lake-manifest.json
deleted file mode 100644
index 88e446e5..00000000
--- a/tests/lean/hashmap/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "1c5ed7840906e29e1f8ca7dbf088cf155e5397e9",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/hashmap/lakefile.lean b/tests/lean/hashmap/lakefile.lean
deleted file mode 100644
index 713785f6..00000000
--- a/tests/lean/hashmap/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «hashmap» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Hashmap» {}
diff --git a/tests/lean/hashmap/lean-toolchain b/tests/lean/hashmap/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/hashmap/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/hashmap_on_disk/.gitignore b/tests/lean/hashmap_on_disk/.gitignore
deleted file mode 100644
index a1735e7c..00000000
--- a/tests/lean/hashmap_on_disk/.gitignore
+++ /dev/null
@@ -1,5 +0,0 @@
-/build
-/lean_packages/*
-!/lean_packages/manifest.json
-/build
-/lake-packages/*
diff --git a/tests/lean/hashmap_on_disk/Base/Primitives.lean b/tests/lean/hashmap_on_disk/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/hashmap_on_disk/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
deleted file mode 100644
index a4dc996a..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Clauses.lean
+++ /dev/null
@@ -1,110 +0,0 @@
-import Base.Primitives
-import HashmapMain.Types
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hashmap_hash_map_allocate_slots_loop_terminates (T : Type)
- (slots : Vec (hashmap_list_t T)) (n : Usize) :=
- (slots, n)
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hashmap_hash_map_clear_loop_terminates (T : Type)
- (slots : Vec (hashmap_list_t T)) (i : Usize) :=
- (slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
- (value : T) (ls : hashmap_list_t T) :=
- (key, value, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_insert_in_list_loop_decreases $key $value $ls) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_from_list_loop_terminates (T : Type)
- (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :=
- (ntable, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_from_list_loop_decreases $ntable
-$ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_loop_terminates (T : Type)
- (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : Usize)
- :=
- (ntable, slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_loop_decreases $ntable $slots $i) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type)
- (key : Usize) (ls : hashmap_list_t T) :=
- (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_contains_key_in_list_loop_decreases $key $ls) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
- (ls : hashmap_list_t T) :=
- (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type)
- (ls : hashmap_list_t T) (key : Usize) :=
- (ls, key)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_mut_in_list_loop_decreases $ls $key) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
- (ls : hashmap_list_t T) :=
- (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_remove_from_list_loop_decreases $key $ls) =>
- `(tactic| sorry)
-
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
deleted file mode 100644
index 33802597..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
+++ /dev/null
@@ -1,112 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap_main]: templates for the decreases clauses
-import Base.Primitives
-import HashmapMain.Types
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/
-@[simp]
-def hashmap_hash_map_allocate_slots_loop_terminates (T : Type)
- (slots : Vec (hashmap_list_t T)) (n : Usize) :=
- (slots, n)
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases_by tactic -/
-syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
-@[simp]
-def hashmap_hash_map_clear_loop_terminates (T : Type)
- (slots : Vec (hashmap_list_t T)) (i : Usize) :=
- (slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: decreases_by tactic -/
-syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_insert_in_list_loop_terminates (T : Type) (key : Usize)
- (value : T) (ls : hashmap_list_t T) :=
- (key, value, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_insert_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_insert_in_list_loop_decreases $key $value $ls) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_from_list_loop_terminates (T : Type)
- (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :=
- (ntable, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_from_list_loop_decreases $ntable
-$ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/
-@[simp]
-def hashmap_hash_map_move_elements_loop_terminates (T : Type)
- (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : Usize)
- :=
- (ntable, slots, i)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: decreases_by tactic -/
-syntax "hashmap_hash_map_move_elements_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_move_elements_loop_decreases $ntable $slots $i) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_contains_key_in_list_loop_terminates (T : Type)
- (key : Usize) (ls : hashmap_list_t T) :=
- (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_contains_key_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_contains_key_in_list_loop_decreases $key $ls) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_in_list_loop_terminates (T : Type) (key : Usize)
- (ls : hashmap_list_t T) :=
- (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_in_list_loop_decreases $key $ls) =>`(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_get_mut_in_list_loop_terminates (T : Type)
- (ls : hashmap_list_t T) (key : Usize) :=
- (ls, key)
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_get_mut_in_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_get_mut_in_list_loop_decreases $ls $key) =>
- `(tactic| sorry)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: termination measure -/
-@[simp]
-def hashmap_hash_map_remove_from_list_loop_terminates (T : Type) (key : Usize)
- (ls : hashmap_list_t T) :=
- (key, ls)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: decreases_by tactic -/
-syntax "hashmap_hash_map_remove_from_list_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| hashmap_hash_map_remove_from_list_loop_decreases $key $ls) =>
- `(tactic| sorry)
-
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean b/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean
deleted file mode 100644
index a5103acc..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/ExternalFuns.lean
+++ /dev/null
@@ -1,5 +0,0 @@
-import Base.Primitives
-import HashmapMain.Types
-import HashmapMain.Opaque
-
-def opaque_defs : OpaqueDefs := by sorry
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
deleted file mode 100644
index 342c3833..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
+++ /dev/null
@@ -1,590 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap_main]: function definitions
-import Base.Primitives
-import HashmapMain.Types
-import HashmapMain.ExternalFuns
-import HashmapMain.Clauses.Clauses
-
-/- [hashmap_main::hashmap::hash_key] -/
-def hashmap_hash_key_fwd (k : Usize) : Result Usize :=
- Result.ret k
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-def hashmap_hash_map_allocate_slots_loop_fwd
- (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) :
- (Result (Vec (hashmap_list_t T)))
- :=
- if h: n > (Usize.ofInt 0 (by intlit))
- then
- do
- let slots0 ← vec_push_back (hashmap_list_t T) slots hashmap_list_t.Nil
- let n0 ← n - (Usize.ofInt 1 (by intlit))
- hashmap_hash_map_allocate_slots_loop_fwd T slots0 n0
- else Result.ret slots
-termination_by hashmap_hash_map_allocate_slots_loop_fwd slots n =>
- hashmap_hash_map_allocate_slots_loop_terminates T slots n
-decreasing_by hashmap_hash_map_allocate_slots_loop_decreases slots n
-
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-def hashmap_hash_map_allocate_slots_fwd
- (T : Type) (slots : Vec (hashmap_list_t T)) (n : Usize) :
- Result (Vec (hashmap_list_t T))
- :=
- hashmap_hash_map_allocate_slots_loop_fwd T slots n
-
-/- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] -/
-def hashmap_hash_map_new_with_capacity_fwd
- (T : Type) (capacity : Usize) (max_load_dividend : Usize)
- (max_load_divisor : Usize) :
- Result (hashmap_hash_map_t T)
- :=
- do
- let v := vec_new (hashmap_list_t T)
- let slots ← hashmap_hash_map_allocate_slots_fwd T v capacity
- let i ← capacity * max_load_dividend
- let i0 ← i / max_load_divisor
- Result.ret
- {
- hashmap_hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
- hashmap_hash_map_max_load_factor :=
- (max_load_dividend, max_load_divisor),
- hashmap_hash_map_max_load := i0,
- hashmap_hash_map_slots := slots
- }
-
-/- [hashmap_main::hashmap::HashMap::{0}::new] -/
-def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) :=
- hashmap_hash_map_new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
- (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap_hash_map_clear_loop_fwd_back
- (T : Type) (slots : Vec (hashmap_list_t T)) (i : Usize) :
- (Result (Vec (hashmap_list_t T)))
- :=
- let i0 := vec_len (hashmap_list_t T) slots
- if h: i < i0
- then
- do
- let i1 ← i + (Usize.ofInt 1 (by intlit))
- let slots0 ←
- vec_index_mut_back (hashmap_list_t T) slots i hashmap_list_t.Nil
- hashmap_hash_map_clear_loop_fwd_back T slots0 i1
- else Result.ret slots
-termination_by hashmap_hash_map_clear_loop_fwd_back slots i =>
- hashmap_hash_map_clear_loop_terminates T slots i
-decreasing_by hashmap_hash_map_clear_loop_decreases slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap_hash_map_clear_fwd_back
- (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
- do
- let v ←
- hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
- (Usize.ofInt 0 (by intlit))
- Result.ret
- {
- self
- with
- hashmap_hash_map_num_entries := (Usize.ofInt 0 (by intlit)),
- hashmap_hash_map_slots := v
- }
-
-/- [hashmap_main::hashmap::HashMap::{0}::len] -/
-def hashmap_hash_map_len_fwd
- (T : Type) (self : hashmap_hash_map_t T) : Result Usize :=
- Result.ret self.hashmap_hash_map_num_entries
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_loop_fwd
- (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
- (Result Bool)
- :=
- match h: ls with
- | hashmap_list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret false
- else hashmap_hash_map_insert_in_list_loop_fwd T key value tl
- | hashmap_list_t.Nil => Result.ret true
-termination_by hashmap_hash_map_insert_in_list_loop_fwd key value ls =>
- hashmap_hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_fwd
- (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) : Result Bool :=
- hashmap_hash_map_insert_in_list_loop_fwd T key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_loop_back
- (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
- (Result (hashmap_list_t T))
- :=
- match h: ls with
- | hashmap_list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret (hashmap_list_t.Cons ckey value tl)
- else
- do
- let tl0 ← hashmap_hash_map_insert_in_list_loop_back T key value tl
- Result.ret (hashmap_list_t.Cons ckey cvalue tl0)
- | hashmap_list_t.Nil =>
- let l := hashmap_list_t.Nil
- Result.ret (hashmap_list_t.Cons key value l)
-termination_by hashmap_hash_map_insert_in_list_loop_back key value ls =>
- hashmap_hash_map_insert_in_list_loop_terminates T key value ls
-decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap_hash_map_insert_in_list_back
- (T : Type) (key : Usize) (value : T) (ls : hashmap_list_t T) :
- Result (hashmap_list_t T)
- :=
- hashmap_hash_map_insert_in_list_loop_back T key value ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] -/
-def hashmap_hash_map_insert_no_resize_fwd_back
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) :
- Result (hashmap_hash_map_t T)
- :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- let inserted ← hashmap_hash_map_insert_in_list_fwd T key value l
- if h: inserted
- then
- do
- let i0 ← self.hashmap_hash_map_num_entries +
- (Usize.ofInt 1 (by intlit))
- let l0 ← hashmap_hash_map_insert_in_list_back T key value l
- let v ←
- vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
- hash_mod l0
- Result.ret
- {
- self
- with
- hashmap_hash_map_num_entries := i0, hashmap_hash_map_slots := v
- }
- else
- do
- let l0 ← hashmap_hash_map_insert_in_list_back T key value l
- let v ←
- vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
- hash_mod l0
- Result.ret { self with hashmap_hash_map_slots := v }
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
- Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-def hashmap_hash_map_move_elements_from_list_loop_fwd_back
- (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
- (Result (hashmap_hash_map_t T))
- :=
- match h: ls with
- | hashmap_list_t.Cons k v tl =>
- do
- let ntable0 ← hashmap_hash_map_insert_no_resize_fwd_back T ntable k v
- hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
- | hashmap_list_t.Nil => Result.ret ntable
-termination_by hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls
- =>
- hashmap_hash_map_move_elements_from_list_loop_terminates T ntable ls
-decreasing_by hashmap_hash_map_move_elements_from_list_loop_decreases ntable ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-def hashmap_hash_map_move_elements_from_list_fwd_back
- (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
- Result (hashmap_hash_map_t T)
- :=
- hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-def hashmap_hash_map_move_elements_loop_fwd_back
- (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
- (i : Usize) :
- (Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T))))
- :=
- let i0 := vec_len (hashmap_list_t T) slots
- if h: i < i0
- then
- do
- let l ← vec_index_mut_fwd (hashmap_list_t T) slots i
- let ls := mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.Nil
- let ntable0 ←
- hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls
- let i1 ← i + (Usize.ofInt 1 (by intlit))
- let l0 := mem_replace_back (hashmap_list_t T) l hashmap_list_t.Nil
- let slots0 ← vec_index_mut_back (hashmap_list_t T) slots i l0
- hashmap_hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
- else Result.ret (ntable, slots)
-termination_by hashmap_hash_map_move_elements_loop_fwd_back ntable slots i =>
- hashmap_hash_map_move_elements_loop_terminates T ntable slots i
-decreasing_by hashmap_hash_map_move_elements_loop_decreases ntable slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-def hashmap_hash_map_move_elements_fwd_back
- (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
- (i : Usize) :
- Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T)))
- :=
- hashmap_hash_map_move_elements_loop_fwd_back T ntable slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::try_resize] -/
-def hashmap_hash_map_try_resize_fwd_back
- (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
- do
- let max_usize ← Scalar.cast .Usize core_num_u32_max_c
- let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let n1 ← max_usize / (Usize.ofInt 2 (by intlit))
- let (i, i0) := self.hashmap_hash_map_max_load_factor
- let i1 ← n1 / i
- if h: capacity <= i1
- then
- do
- let i2 ← capacity * (Usize.ofInt 2 (by intlit))
- let ntable ← hashmap_hash_map_new_with_capacity_fwd T i2 i i0
- let (ntable0, _) ←
- hashmap_hash_map_move_elements_fwd_back T ntable
- self.hashmap_hash_map_slots (Usize.ofInt 0 (by intlit))
- Result.ret
- {
- ntable0
- with
- hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
- hashmap_hash_map_max_load_factor := (i, i0)
- }
- else Result.ret { self with hashmap_hash_map_max_load_factor := (i, i0) }
-
-/- [hashmap_main::hashmap::HashMap::{0}::insert] -/
-def hashmap_hash_map_insert_fwd_back
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (value : T) :
- Result (hashmap_hash_map_t T)
- :=
- do
- let self0 ← hashmap_hash_map_insert_no_resize_fwd_back T self key value
- let i ← hashmap_hash_map_len_fwd T self0
- if h: i > self0.hashmap_hash_map_max_load
- then hashmap_hash_map_try_resize_fwd_back T self0
- else Result.ret self0
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-def hashmap_hash_map_contains_key_in_list_loop_fwd
- (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result Bool) :=
- match h: ls with
- | hashmap_list_t.Cons ckey t tl =>
- if h: ckey = key
- then Result.ret true
- else hashmap_hash_map_contains_key_in_list_loop_fwd T key tl
- | hashmap_list_t.Nil => Result.ret false
-termination_by hashmap_hash_map_contains_key_in_list_loop_fwd key ls =>
- hashmap_hash_map_contains_key_in_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_contains_key_in_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-def hashmap_hash_map_contains_key_in_list_fwd
- (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result Bool :=
- hashmap_hash_map_contains_key_in_list_loop_fwd T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key] -/
-def hashmap_hash_map_contains_key_fwd
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result Bool :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- hashmap_hash_map_contains_key_in_list_fwd T key l
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-def hashmap_hash_map_get_in_list_loop_fwd
- (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result T) :=
- match h: ls with
- | hashmap_list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret cvalue
- else hashmap_hash_map_get_in_list_loop_fwd T key tl
- | hashmap_list_t.Nil => Result.fail Error.panic
-termination_by hashmap_hash_map_get_in_list_loop_fwd key ls =>
- hashmap_hash_map_get_in_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_get_in_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-def hashmap_hash_map_get_in_list_fwd
- (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result T :=
- hashmap_hash_map_get_in_list_loop_fwd T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::get] -/
-def hashmap_hash_map_get_fwd
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- hashmap_hash_map_get_in_list_fwd T key l
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_loop_fwd
- (T : Type) (ls : hashmap_list_t T) (key : Usize) : (Result T) :=
- match h: ls with
- | hashmap_list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret cvalue
- else hashmap_hash_map_get_mut_in_list_loop_fwd T tl key
- | hashmap_list_t.Nil => Result.fail Error.panic
-termination_by hashmap_hash_map_get_mut_in_list_loop_fwd ls key =>
- hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_fwd
- (T : Type) (ls : hashmap_list_t T) (key : Usize) : Result T :=
- hashmap_hash_map_get_mut_in_list_loop_fwd T ls key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_loop_back
- (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) :
- (Result (hashmap_list_t T))
- :=
- match h: ls with
- | hashmap_list_t.Cons ckey cvalue tl =>
- if h: ckey = key
- then Result.ret (hashmap_list_t.Cons ckey ret0 tl)
- else
- do
- let tl0 ← hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0
- Result.ret (hashmap_list_t.Cons ckey cvalue tl0)
- | hashmap_list_t.Nil => Result.fail Error.panic
-termination_by hashmap_hash_map_get_mut_in_list_loop_back ls key ret0 =>
- hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
-decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap_hash_map_get_mut_in_list_back
- (T : Type) (ls : hashmap_list_t T) (key : Usize) (ret0 : T) :
- Result (hashmap_list_t T)
- :=
- hashmap_hash_map_get_mut_in_list_loop_back T ls key ret0
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap_hash_map_get_mut_fwd
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result T :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- hashmap_hash_map_get_mut_in_list_fwd T l key
-
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap_hash_map_get_mut_back
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) (ret0 : T) :
- Result (hashmap_hash_map_t T)
- :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- let l0 ← hashmap_hash_map_get_mut_in_list_back T l key ret0
- let v ←
- vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
- hash_mod l0
- Result.ret { self with hashmap_hash_map_slots := v }
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_loop_fwd
- (T : Type) (key : Usize) (ls : hashmap_list_t T) : (Result (Option T)) :=
- match h: ls with
- | hashmap_list_t.Cons ckey t tl =>
- if h: ckey = key
- then
- let mv_ls :=
- mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.Cons ckey t tl)
- hashmap_list_t.Nil
- match h: mv_ls with
- | hashmap_list_t.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
- | hashmap_list_t.Nil => Result.fail Error.panic
- else hashmap_hash_map_remove_from_list_loop_fwd T key tl
- | hashmap_list_t.Nil => Result.ret Option.none
-termination_by hashmap_hash_map_remove_from_list_loop_fwd key ls =>
- hashmap_hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_fwd
- (T : Type) (key : Usize) (ls : hashmap_list_t T) : Result (Option T) :=
- hashmap_hash_map_remove_from_list_loop_fwd T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_loop_back
- (T : Type) (key : Usize) (ls : hashmap_list_t T) :
- (Result (hashmap_list_t T))
- :=
- match h: ls with
- | hashmap_list_t.Cons ckey t tl =>
- if h: ckey = key
- then
- let mv_ls :=
- mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.Cons ckey t tl)
- hashmap_list_t.Nil
- match h: mv_ls with
- | hashmap_list_t.Cons i cvalue tl0 => Result.ret tl0
- | hashmap_list_t.Nil => Result.fail Error.panic
- else
- do
- let tl0 ← hashmap_hash_map_remove_from_list_loop_back T key tl
- Result.ret (hashmap_list_t.Cons ckey t tl0)
- | hashmap_list_t.Nil => Result.ret hashmap_list_t.Nil
-termination_by hashmap_hash_map_remove_from_list_loop_back key ls =>
- hashmap_hash_map_remove_from_list_loop_terminates T key ls
-decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap_hash_map_remove_from_list_back
- (T : Type) (key : Usize) (ls : hashmap_list_t T) :
- Result (hashmap_list_t T)
- :=
- hashmap_hash_map_remove_from_list_loop_back T key ls
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap_hash_map_remove_fwd
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) : Result (Option T) :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- let x ← hashmap_hash_map_remove_from_list_fwd T key l
- match h: x with
- | Option.none => Result.ret Option.none
- | Option.some x0 =>
- do
- let _ ← self.hashmap_hash_map_num_entries -
- (Usize.ofInt 1 (by intlit))
- Result.ret (Option.some x0)
-
-/- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap_hash_map_remove_back
- (T : Type) (self : hashmap_hash_map_t T) (key : Usize) :
- Result (hashmap_hash_map_t T)
- :=
- do
- let hash ← hashmap_hash_key_fwd key
- let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
- let hash_mod ← hash % i
- let l ←
- vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
- let x ← hashmap_hash_map_remove_from_list_fwd T key l
- match h: x with
- | Option.none =>
- do
- let l0 ← hashmap_hash_map_remove_from_list_back T key l
- let v ←
- vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
- hash_mod l0
- Result.ret { self with hashmap_hash_map_slots := v }
- | Option.some x0 =>
- do
- let i0 ← self.hashmap_hash_map_num_entries -
- (Usize.ofInt 1 (by intlit))
- let l0 ← hashmap_hash_map_remove_from_list_back T key l
- let v ←
- vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
- hash_mod l0
- Result.ret
- {
- self
- with
- hashmap_hash_map_num_entries := i0, hashmap_hash_map_slots := v
- }
-
-/- [hashmap_main::hashmap::test1] -/
-def hashmap_test1_fwd : Result Unit :=
- do
- let hm ← hashmap_hash_map_new_fwd U64
- let hm0 ←
- hashmap_hash_map_insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
- (U64.ofInt 42 (by intlit))
- let hm1 ←
- hashmap_hash_map_insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
- (U64.ofInt 18 (by intlit))
- let hm2 ←
- hashmap_hash_map_insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
- (U64.ofInt 138 (by intlit))
- let hm3 ←
- hashmap_hash_map_insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
- (U64.ofInt 256 (by intlit))
- let i ← hashmap_hash_map_get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
- if h: not (i = (U64.ofInt 18 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let hm4 ←
- hashmap_hash_map_get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
- (U64.ofInt 56 (by intlit))
- let i0 ←
- hashmap_hash_map_get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
- if h: not (i0 = (U64.ofInt 56 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let x ←
- hashmap_hash_map_remove_fwd U64 hm4
- (Usize.ofInt 1024 (by intlit))
- match h: x with
- | Option.none => Result.fail Error.panic
- | Option.some x0 =>
- if h: not (x0 = (U64.ofInt 56 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let hm5 ←
- hashmap_hash_map_remove_back U64 hm4
- (Usize.ofInt 1024 (by intlit))
- let i1 ←
- hashmap_hash_map_get_fwd U64 hm5
- (Usize.ofInt 0 (by intlit))
- if h: not (i1 = (U64.ofInt 42 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i2 ←
- hashmap_hash_map_get_fwd U64 hm5
- (Usize.ofInt 128 (by intlit))
- if h: not (i2 = (U64.ofInt 18 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i3 ←
- hashmap_hash_map_get_fwd U64 hm5
- (Usize.ofInt 1056 (by intlit))
- if h: not (i3 = (U64.ofInt 256 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- [hashmap_main::insert_on_disk] -/
-def insert_on_disk_fwd
- (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
- do
- let (st0, hm) ← opaque_defs.hashmap_utils_deserialize_fwd st
- let hm0 ← hashmap_hash_map_insert_fwd_back U64 hm key value
- let (st1, _) ← opaque_defs.hashmap_utils_serialize_fwd hm0 st0
- Result.ret (st1, ())
-
-/- [hashmap_main::main] -/
-def main_fwd : Result Unit :=
- Result.ret ()
-
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean b/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
deleted file mode 100644
index 0509fbbd..00000000
--- a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
+++ /dev/null
@@ -1,19 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [hashmap_main]: type definitions
-import Base.Primitives
-
-/- [hashmap_main::hashmap::List] -/
-inductive hashmap_list_t (T : Type) :=
-| Cons : Usize -> T -> hashmap_list_t T -> hashmap_list_t T
-| Nil : hashmap_list_t T
-
-/- [hashmap_main::hashmap::HashMap] -/
-structure hashmap_hash_map_t (T : Type) where
- hashmap_hash_map_num_entries : Usize
- hashmap_hash_map_max_load_factor : (Usize × Usize)
- hashmap_hash_map_max_load : Usize
- hashmap_hash_map_slots : Vec (hashmap_list_t T)
-
-/- The state type used in the state-error monad -/
-axiom State : Type
-
diff --git a/tests/lean/hashmap_on_disk/lake-manifest.json b/tests/lean/hashmap_on_disk/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/hashmap_on_disk/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/hashmap_on_disk/lakefile.lean b/tests/lean/hashmap_on_disk/lakefile.lean
deleted file mode 100644
index 70daf427..00000000
--- a/tests/lean/hashmap_on_disk/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «hashmap_main» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «HashmapMain» {}
diff --git a/tests/lean/hashmap_on_disk/lean-toolchain b/tests/lean/hashmap_on_disk/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/hashmap_on_disk/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/lake-manifest.json b/tests/lean/lake-manifest.json
new file mode 100644
index 00000000..94030cb6
--- /dev/null
+++ b/tests/lean/lake-manifest.json
@@ -0,0 +1,40 @@
+{"version": 4,
+ "packagesDir": "lake-packages",
+ "packages":
+ [{"git":
+ {"url": "https://github.com/EdAyers/ProofWidgets4",
+ "subDir?": null,
+ "rev": "c43db94a8f495dad37829e9d7ad65483d68c86b8",
+ "name": "proofwidgets",
+ "inputRev?": "v0.0.11"}},
+ {"path": {"name": "Base", "dir": "./../../backends/lean"}},
+ {"git":
+ {"url": "https://github.com/mhuisi/lean4-cli.git",
+ "subDir?": null,
+ "rev": "5a858c32963b6b19be0d477a30a1f4b6c120be7e",
+ "name": "Cli",
+ "inputRev?": "nightly"}},
+ {"git":
+ {"url": "https://github.com/leanprover-community/mathlib4.git",
+ "subDir?": null,
+ "rev": "fa05951a270fef2873666c46f138e90338cd48d6",
+ "name": "mathlib",
+ "inputRev?": null}},
+ {"git":
+ {"url": "https://github.com/gebner/quote4",
+ "subDir?": null,
+ "rev": "c0d9516f44d07feee01c1103c8f2f7c24a822b55",
+ "name": "Qq",
+ "inputRev?": "master"}},
+ {"git":
+ {"url": "https://github.com/JLimperg/aesop",
+ "subDir?": null,
+ "rev": "f04538ab6ad07642368cf11d2702acc0a9b4bcee",
+ "name": "aesop",
+ "inputRev?": "master"}},
+ {"git":
+ {"url": "https://github.com/leanprover/std4",
+ "subDir?": null,
+ "rev": "dff883c55395438ae2a5c65ad5ddba084b600feb",
+ "name": "std",
+ "inputRev?": "main"}}]}
diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean
new file mode 100644
index 00000000..ae63b129
--- /dev/null
+++ b/tests/lean/lakefile.lean
@@ -0,0 +1,19 @@
+import Lake
+open Lake DSL
+
+require mathlib from git
+ "https://github.com/leanprover-community/mathlib4.git"
+
+require Base from "../../backends/lean"
+
+package «tests» {}
+
+@[default_target] lean_lib betreeMain
+@[default_target] lean_lib constants
+@[default_target] lean_lib external
+@[default_target] lean_lib hashmap
+@[default_target] lean_lib hashmapMain
+@[default_target] lean_lib loops
+@[default_target] lean_lib noNestedBorrows
+@[default_target] lean_lib paper
+@[default_target] lean_lib poloniusList
diff --git a/tests/lean/lean-toolchain b/tests/lean/lean-toolchain
index bbf57f10..334c5053 100644
--- a/tests/lean/lean-toolchain
+++ b/tests/lean/lean-toolchain
@@ -1 +1 @@
-leanprover/lean4:nightly-2023-01-21
+leanprover/lean4:nightly-2023-07-12 \ No newline at end of file
diff --git a/tests/lean/misc-constants/Base/Primitives.lean b/tests/lean/misc-constants/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-constants/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-constants/Constants.lean b/tests/lean/misc-constants/Constants.lean
deleted file mode 100644
index 8306ed85..00000000
--- a/tests/lean/misc-constants/Constants.lean
+++ /dev/null
@@ -1,131 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [constants]
-import Base.Primitives
-
-/- [constants::X0] -/
-def x0_body : Result U32 := Result.ret (U32.ofInt 0 (by intlit))
-def x0_c : U32 := eval_global x0_body (by simp)
-
-/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : Result U32 :=
- Result.ret (U32.ofInt 4294967295 (by intlit))
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
-/- [constants::X1] -/
-def x1_body : Result U32 := Result.ret core_num_u32_max_c
-def x1_c : U32 := eval_global x1_body (by simp)
-
-/- [constants::X2] -/
-def x2_body : Result U32 := Result.ret (U32.ofInt 3 (by intlit))
-def x2_c : U32 := eval_global x2_body (by simp)
-
-/- [constants::incr] -/
-def incr_fwd (n : U32) : Result U32 :=
- n + (U32.ofInt 1 (by intlit))
-
-/- [constants::X3] -/
-def x3_body : Result U32 := incr_fwd (U32.ofInt 32 (by intlit))
-def x3_c : U32 := eval_global x3_body (by simp)
-
-/- [constants::mk_pair0] -/
-def mk_pair0_fwd (x : U32) (y : U32) : Result (U32 × U32) :=
- Result.ret (x, y)
-
-/- [constants::Pair] -/
-structure pair_t (T1 T2 : Type) where
- pair_x : T1
- pair_y : T2
-
-/- [constants::mk_pair1] -/
-def mk_pair1_fwd (x : U32) (y : U32) : Result (pair_t U32 U32) :=
- Result.ret { pair_x := x, pair_y := y }
-
-/- [constants::P0] -/
-def p0_body : Result (U32 × U32) :=
- mk_pair0_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
-def p0_c : (U32 × U32) := eval_global p0_body (by simp)
-
-/- [constants::P1] -/
-def p1_body : Result (pair_t U32 U32) :=
- mk_pair1_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
-def p1_c : pair_t U32 U32 := eval_global p1_body (by simp)
-
-/- [constants::P2] -/
-def p2_body : Result (U32 × U32) :=
- Result.ret ((U32.ofInt 0 (by intlit)), (U32.ofInt 1 (by intlit)))
-def p2_c : (U32 × U32) := eval_global p2_body (by simp)
-
-/- [constants::P3] -/
-def p3_body : Result (pair_t U32 U32) :=
- Result.ret
- { pair_x := (U32.ofInt 0 (by intlit)), pair_y := (U32.ofInt 1 (by intlit)) }
-def p3_c : pair_t U32 U32 := eval_global p3_body (by simp)
-
-/- [constants::Wrap] -/
-structure wrap_t (T : Type) where
- wrap_val : T
-
-/- [constants::Wrap::{0}::new] -/
-def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) :=
- Result.ret { wrap_val := val }
-
-/- [constants::Y] -/
-def y_body : Result (wrap_t I32) := wrap_new_fwd I32 (I32.ofInt 2 (by intlit))
-def y_c : wrap_t I32 := eval_global y_body (by simp)
-
-/- [constants::unwrap_y] -/
-def unwrap_y_fwd : Result I32 :=
- Result.ret y_c.wrap_val
-
-/- [constants::YVAL] -/
-def yval_body : Result I32 := unwrap_y_fwd
-def yval_c : I32 := eval_global yval_body (by simp)
-
-/- [constants::get_z1::Z1] -/
-def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3 (by intlit))
-def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
-
-/- [constants::get_z1] -/
-def get_z1_fwd : Result I32 :=
- Result.ret get_z1_z1_c
-
-/- [constants::add] -/
-def add_fwd (a : I32) (b : I32) : Result I32 :=
- a + b
-
-/- [constants::Q1] -/
-def q1_body : Result I32 := Result.ret (I32.ofInt 5 (by intlit))
-def q1_c : I32 := eval_global q1_body (by simp)
-
-/- [constants::Q2] -/
-def q2_body : Result I32 := Result.ret q1_c
-def q2_c : I32 := eval_global q2_body (by simp)
-
-/- [constants::Q3] -/
-def q3_body : Result I32 := add_fwd q2_c (I32.ofInt 3 (by intlit))
-def q3_c : I32 := eval_global q3_body (by simp)
-
-/- [constants::get_z2] -/
-def get_z2_fwd : Result I32 :=
- do
- let i ← get_z1_fwd
- let i0 ← add_fwd i q3_c
- add_fwd q1_c i0
-
-/- [constants::S1] -/
-def s1_body : Result U32 := Result.ret (U32.ofInt 6 (by intlit))
-def s1_c : U32 := eval_global s1_body (by simp)
-
-/- [constants::S2] -/
-def s2_body : Result U32 := incr_fwd s1_c
-def s2_c : U32 := eval_global s2_body (by simp)
-
-/- [constants::S3] -/
-def s3_body : Result (pair_t U32 U32) := Result.ret p3_c
-def s3_c : pair_t U32 U32 := eval_global s3_body (by simp)
-
-/- [constants::S4] -/
-def s4_body : Result (pair_t U32 U32) :=
- mk_pair1_fwd (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit))
-def s4_c : pair_t U32 U32 := eval_global s4_body (by simp)
-
diff --git a/tests/lean/misc-constants/lake-manifest.json b/tests/lean/misc-constants/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-constants/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-constants/lakefile.lean b/tests/lean/misc-constants/lakefile.lean
deleted file mode 100644
index 01aacb90..00000000
--- a/tests/lean/misc-constants/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «constants» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Constants» {}
diff --git a/tests/lean/misc-constants/lean-toolchain b/tests/lean/misc-constants/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-constants/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-external/Base/Primitives.lean b/tests/lean/misc-external/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-external/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-external/External/ExternalFuns.lean b/tests/lean/misc-external/External/ExternalFuns.lean
deleted file mode 100644
index 6bd4f4a9..00000000
--- a/tests/lean/misc-external/External/ExternalFuns.lean
+++ /dev/null
@@ -1,5 +0,0 @@
-import Base.Primitives
-import External.Types
-import External.Opaque
-
-def opaque_defs : OpaqueDefs := sorry
diff --git a/tests/lean/misc-external/External/Funs.lean b/tests/lean/misc-external/External/Funs.lean
deleted file mode 100644
index eeb83989..00000000
--- a/tests/lean/misc-external/External/Funs.lean
+++ /dev/null
@@ -1,84 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [external]: function definitions
-import Base.Primitives
-import External.Types
-import External.ExternalFuns
-
-/- [external::swap] -/
-def swap_fwd
- (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
- do
- let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
- let (st1, _) ← opaque_defs.core_mem_swap_back0 T x y st st0
- let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
- Result.ret (st2, ())
-
-/- [external::swap] -/
-def swap_back
- (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
- Result (State × (T × T))
- :=
- do
- let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
- let (st2, x0) ← opaque_defs.core_mem_swap_back0 T x y st st1
- let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
- Result.ret (st0, (x0, y0))
-
-/- [external::test_new_non_zero_u32] -/
-def test_new_non_zero_u32_fwd
- (x : U32) (st : State) : Result (State × core_num_nonzero_non_zero_u32_t) :=
- do
- let (st0, opt) ← opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st
- opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t
- opt st0
-
-/- [external::test_vec] -/
-def test_vec_fwd : Result Unit :=
- do
- let v := vec_new U32
- let _ ← vec_push_back U32 v (U32.ofInt 0 (by intlit))
- Result.ret ()
-
-/- [external::custom_swap] -/
-def custom_swap_fwd
- (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
- do
- let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st
- let (st1, x0) ← opaque_defs.core_mem_swap_back0 T x y st st0
- let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1
- Result.ret (st2, x0)
-
-/- [external::custom_swap] -/
-def custom_swap_back
- (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) :
- Result (State × (T × T))
- :=
- do
- let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st
- let (st2, _) ← opaque_defs.core_mem_swap_back0 T x y st st1
- let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2
- Result.ret (st0, (ret0, y0))
-
-/- [external::test_custom_swap] -/
-def test_custom_swap_fwd
- (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
- do
- let (st0, _) ← custom_swap_fwd U32 x y st
- Result.ret (st0, ())
-
-/- [external::test_custom_swap] -/
-def test_custom_swap_back
- (x : U32) (y : U32) (st : State) (st0 : State) :
- Result (State × (U32 × U32))
- :=
- custom_swap_back U32 x y st (U32.ofInt 1 (by intlit)) st0
-
-/- [external::test_swap_non_zero] -/
-def test_swap_non_zero_fwd (x : U32) (st : State) : Result (State × U32) :=
- do
- let (st0, _) ← swap_fwd U32 x (U32.ofInt 0 (by intlit)) st
- let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0 (by intlit)) st st0
- if h: x0 = (U32.ofInt 0 (by intlit))
- then Result.fail Error.panic
- else Result.ret (st1, x0)
-
diff --git a/tests/lean/misc-external/External/Opaque.lean b/tests/lean/misc-external/External/Opaque.lean
deleted file mode 100644
index d641912b..00000000
--- a/tests/lean/misc-external/External/Opaque.lean
+++ /dev/null
@@ -1,27 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [external]: opaque function definitions
-import Base.Primitives
-import External.Types
-
-structure OpaqueDefs where
-
- /- [core::mem::swap] -/
- core_mem_swap_fwd (T : Type) : T -> T -> State -> Result (State × Unit)
-
- /- [core::mem::swap] -/
- core_mem_swap_back0
- (T : Type) : T -> T -> State -> State -> Result (State × T)
-
- /- [core::mem::swap] -/
- core_mem_swap_back1
- (T : Type) : T -> T -> State -> State -> Result (State × T)
-
- /- [core::num::nonzero::NonZeroU32::{14}::new] -/
- core_num_nonzero_non_zero_u32_new_fwd
- :
- U32 -> State -> Result (State × (Option core_num_nonzero_non_zero_u32_t))
-
- /- [core::option::Option::{0}::unwrap] -/
- core_option_option_unwrap_fwd
- (T : Type) : Option T -> State -> Result (State × T)
-
diff --git a/tests/lean/misc-external/lake-manifest.json b/tests/lean/misc-external/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-external/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-external/lakefile.lean b/tests/lean/misc-external/lakefile.lean
deleted file mode 100644
index 6cc4aae4..00000000
--- a/tests/lean/misc-external/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «external» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «External» {}
diff --git a/tests/lean/misc-external/lean-toolchain b/tests/lean/misc-external/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-external/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-loops/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
deleted file mode 100644
index 89a7ce34..00000000
--- a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean
+++ /dev/null
@@ -1,205 +0,0 @@
--- [loops]: decreases clauses
-import Base.Primitives
-import Loops.Types
-
-/- [loops::sum]: termination measure -/
-@[simp]
-def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s)
-
-syntax "sum_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::sum_with_mut_borrows]: termination measure -/
-@[simp]
-def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) :=
- (max, mi, ms)
-
-syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
-
-/- [loops::sum_with_shared_borrows]: termination measure -/
-@[simp]
-def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) :=
- (max, i, s)
-
-syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i)
-
-syntax "clear_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
-
-/- [loops::list_mem]: termination measure -/
-@[simp]
-def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls)
-
-syntax "list_mem_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop]: termination measure -/
-@[simp]
-def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
- (ls, i)
-
-syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop]: termination measure -/
-@[simp]
-def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
- (ls, i)
-
-syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::get_elem_mut]: termination measure -/
-@[simp]
-def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-syntax "get_elem_mut_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::get_elem_shared]: termination measure -/
-@[simp]
-def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-syntax "get_elem_shared_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32)
- (ls : list_t T) :=
- (i, ls)
-
-syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32)
- (ls : list_t T) :=
- (i, ls)
-
-syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
- (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
- (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
-
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean
deleted file mode 100644
index 2e28a6c0..00000000
--- a/tests/lean/misc-loops/Loops/Clauses/Template.lean
+++ /dev/null
@@ -1,205 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: templates for the decreases clauses
-import Base.Primitives
-import Loops.Types
-
-/- [loops::sum]: termination measure -/
-@[simp] def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s)
-
-/- [loops::sum]: decreases_by tactic -/
-syntax "sum_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::sum_with_mut_borrows]: termination measure -/
-@[simp]
-def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) :=
- (max, mi, ms)
-
-/- [loops::sum_with_mut_borrows]: decreases_by tactic -/
-syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
-
-/- [loops::sum_with_shared_borrows]: termination measure -/
-@[simp]
-def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) :=
- (max, i, s)
-
-/- [loops::sum_with_shared_borrows]: decreases_by tactic -/
-syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
-
-/- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : Vec U32) (i : Usize) := (v, i)
-
-/- [loops::clear]: decreases_by tactic -/
-syntax "clear_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
-
-/- [loops::list_mem]: termination measure -/
-@[simp] def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls)
-
-/- [loops::list_mem]: decreases_by tactic -/
-syntax "list_mem_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop]: termination measure -/
-@[simp]
-def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) :=
- (ls, i)
-
-/- [loops::list_nth_mut_loop]: decreases_by tactic -/
-syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop]: termination measure -/
-@[simp]
-def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32)
- :=
- (ls, i)
-
-/- [loops::list_nth_shared_loop]: decreases_by tactic -/
-syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
-
-/- [loops::get_elem_mut]: termination measure -/
-@[simp]
-def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-/- [loops::get_elem_mut]: decreases_by tactic -/
-syntax "get_elem_mut_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::get_elem_shared]: termination measure -/
-@[simp]
-def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls)
-
-/- [loops::get_elem_shared]: decreases_by tactic -/
-syntax "get_elem_shared_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32)
- (ls : list_t T) :=
- (i, ls)
-
-/- [loops::list_nth_mut_loop_with_id]: decreases_by tactic -/
-syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_with_id]: termination measure -/
-@[simp]
-def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32)
- (ls : list_t T) :=
- (i, ls)
-
-/- [loops::list_nth_shared_loop_with_id]: decreases_by tactic -/
-syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/
-syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/
-syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/
-syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
- (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
- (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/
-syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
-@[simp]
-def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
- (ls0 : list_t T) (ls1 : list_t T) (i : U32) :=
- (ls0, ls1, i)
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/
-syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
-macro_rules
-| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
- `(tactic| sorry)
-
diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean
deleted file mode 100644
index fd8d62d7..00000000
--- a/tests/lean/misc-loops/Loops/Funs.lean
+++ /dev/null
@@ -1,705 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: function definitions
-import Base.Primitives
-import Loops.Types
-import Loops.Clauses.Clauses
-
-/- [loops::sum] -/
-def sum_loop_fwd (max : U32) (i : U32) (s : U32) : (Result U32) :=
- if h: i < max
- then
- do
- let s0 ← s + i
- let i0 ← i + (U32.ofInt 1 (by intlit))
- sum_loop_fwd max i0 s0
- else s * (U32.ofInt 2 (by intlit))
-termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
-decreasing_by sum_loop_decreases max i s
-
-/- [loops::sum] -/
-def sum_fwd (max : U32) : Result U32 :=
- sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit))
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_loop_fwd
- (max : U32) (mi : U32) (ms : U32) : (Result U32) :=
- if h: mi < max
- then
- do
- let ms0 ← ms + mi
- let mi0 ← mi + (U32.ofInt 1 (by intlit))
- sum_with_mut_borrows_loop_fwd max mi0 ms0
- else ms * (U32.ofInt 2 (by intlit))
-termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
- sum_with_mut_borrows_loop_terminates max mi ms
-decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
-
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_fwd (max : U32) : Result U32 :=
- sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
- (U32.ofInt 0 (by intlit))
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_loop_fwd
- (max : U32) (i : U32) (s : U32) : (Result U32) :=
- if h: i < max
- then
- do
- let i0 ← i + (U32.ofInt 1 (by intlit))
- let s0 ← s + i0
- sum_with_shared_borrows_loop_fwd max i0 s0
- else s * (U32.ofInt 2 (by intlit))
-termination_by sum_with_shared_borrows_loop_fwd max i s =>
- sum_with_shared_borrows_loop_terminates max i s
-decreasing_by sum_with_shared_borrows_loop_decreases max i s
-
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_fwd (max : U32) : Result U32 :=
- sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
- (U32.ofInt 0 (by intlit))
-
-/- [loops::clear] -/
-def clear_loop_fwd_back (v : Vec U32) (i : Usize) : (Result (Vec U32)) :=
- let i0 := vec_len U32 v
- if h: i < i0
- then
- do
- let i1 ← i + (Usize.ofInt 1 (by intlit))
- let v0 ← vec_index_mut_back U32 v i (U32.ofInt 0 (by intlit))
- clear_loop_fwd_back v0 i1
- else Result.ret v
-termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
-decreasing_by clear_loop_decreases v i
-
-/- [loops::clear] -/
-def clear_fwd_back (v : Vec U32) : Result (Vec U32) :=
- clear_loop_fwd_back v (Usize.ofInt 0 (by intlit))
-
-/- [loops::list_mem] -/
-def list_mem_loop_fwd (x : U32) (ls : list_t U32) : (Result Bool) :=
- match h: ls with
- | list_t.Cons y tl =>
- if h: y = x
- then Result.ret true
- else list_mem_loop_fwd x tl
- | list_t.Nil => Result.ret false
-termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
-decreasing_by list_mem_loop_decreases x ls
-
-/- [loops::list_mem] -/
-def list_mem_fwd (x : U32) (ls : list_t U32) : Result Bool :=
- list_mem_loop_fwd x ls
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_loop_fwd
- (T : Type) (ls : list_t T) (i : U32) : (Result T) :=
- match h: ls with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_loop_loop_fwd T tl i0
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_loop_fwd ls i =>
- list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
- list_nth_mut_loop_loop_fwd T ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_loop_back
- (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) :=
- match h: ls with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
- Result.ret (list_t.Cons x tl0)
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_loop_back ls i ret0 =>
- list_nth_mut_loop_loop_terminates T ls i
-decreasing_by list_nth_mut_loop_loop_decreases ls i
-
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_back
- (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
- list_nth_mut_loop_loop_back T ls i ret0
-
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_loop_fwd
- (T : Type) (ls : list_t T) (i : U32) : (Result T) :=
- match h: ls with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_loop_loop_fwd T tl i0
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_loop_fwd ls i =>
- list_nth_shared_loop_loop_terminates T ls i
-decreasing_by list_nth_shared_loop_loop_decreases ls i
-
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_fwd (T : Type) (ls : list_t T) (i : U32) : Result T :=
- list_nth_shared_loop_loop_fwd T ls i
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_loop_fwd (x : Usize) (ls : list_t Usize) : (Result Usize) :=
- match h: ls with
- | list_t.Cons y tl =>
- if h: y = x
- then Result.ret y
- else get_elem_mut_loop_fwd x tl
- | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_fwd (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
- do
- let l ←
- vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
- get_elem_mut_loop_fwd x l
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_loop_back
- (x : Usize) (ls : list_t Usize) (ret0 : Usize) : (Result (list_t Usize)) :=
- match h: ls with
- | list_t.Cons y tl =>
- if h: y = x
- then Result.ret (list_t.Cons ret0 tl)
- else
- do
- let tl0 ← get_elem_mut_loop_back x tl ret0
- Result.ret (list_t.Cons y tl0)
- | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_mut_loop_back x ls ret0 =>
- get_elem_mut_loop_terminates x ls
-decreasing_by get_elem_mut_loop_decreases x ls
-
-/- [loops::get_elem_mut] -/
-def get_elem_mut_back
- (slots : Vec (list_t Usize)) (x : Usize) (ret0 : Usize) :
- Result (Vec (list_t Usize))
- :=
- do
- let l ←
- vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
- let l0 ← get_elem_mut_loop_back x l ret0
- vec_index_mut_back (list_t Usize) slots (Usize.ofInt 0 (by intlit)) l0
-
-/- [loops::get_elem_shared] -/
-def get_elem_shared_loop_fwd
- (x : Usize) (ls : list_t Usize) : (Result Usize) :=
- match h: ls with
- | list_t.Cons y tl =>
- if h: y = x
- then Result.ret y
- else get_elem_shared_loop_fwd x tl
- | list_t.Nil => Result.fail Error.panic
-termination_by get_elem_shared_loop_fwd x ls =>
- get_elem_shared_loop_terminates x ls
-decreasing_by get_elem_shared_loop_decreases x ls
-
-/- [loops::get_elem_shared] -/
-def get_elem_shared_fwd
- (slots : Vec (list_t Usize)) (x : Usize) : Result Usize :=
- do
- let l ← vec_index_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit))
- get_elem_shared_loop_fwd x l
-
-/- [loops::id_mut] -/
-def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
- Result.ret ls
-
-/- [loops::id_mut] -/
-def id_mut_back
- (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) :=
- Result.ret ret0
-
-/- [loops::id_shared] -/
-def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
- Result.ret ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_loop_fwd
- (T : Type) (i : U32) (ls : list_t T) : (Result T) :=
- match h: ls with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_loop_with_id_loop_fwd T i0 tl
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
- list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_fwd
- (T : Type) (ls : list_t T) (i : U32) : Result T :=
- do
- let ls0 ← id_mut_fwd T ls
- list_nth_mut_loop_with_id_loop_fwd T i ls0
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_loop_back
- (T : Type) (i : U32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) :=
- match h: ls with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
- Result.ret (list_t.Cons x tl0)
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
- list_nth_mut_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_back
- (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
- do
- let ls0 ← id_mut_fwd T ls
- let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
- id_mut_back T ls l
-
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_loop_fwd
- (T : Type) (i : U32) (ls : list_t T) : (Result T) :=
- match h: ls with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_loop_with_id_loop_fwd T i0 tl
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
- list_nth_shared_loop_with_id_loop_terminates T i ls
-decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
-
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_fwd
- (T : Type) (ls : list_t T) (i : U32) : Result T :=
- do
- let ls0 ← id_shared_fwd T ls
- list_nth_shared_loop_with_id_loop_fwd T i ls0
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
- list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_back'a
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- (Result (list_t T))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl0)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x0 tl00)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
- list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_back'a
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- Result (list_t T)
- :=
- list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_loop_back'b
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- (Result (list_t T))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x1 tl10)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
- list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_back'b
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- Result (list_t T)
- :=
- list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
- list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
- list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_loop_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
- (Result ((list_t T) × (list_t T)))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then
- let (t, t0) := ret0
- Result.ret (list_t.Cons t tl0, list_t.Cons t0 tl1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let (tl00, tl10) ←
- list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x0 tl00, list_t.Cons x1 tl10)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
- list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) :
- Result ((list_t T) × (list_t T))
- :=
- list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
- list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
- list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_loop_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- (Result (list_t T))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl0)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl00 ←
- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x0 tl00)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
- list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- Result (list_t T)
- :=
- list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
- list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_loop_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- (Result (list_t T))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl0)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl00 ←
- list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x0 tl00)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
- list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- Result (list_t T)
- :=
- list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
- list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_loop_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- (Result (list_t T))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl10 ←
- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x1 tl10)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
- list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- Result (list_t T)
- :=
- list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_loop_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (x0, x1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
- list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_fwd
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : Result (T × T) :=
- list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_loop_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- (Result (list_t T))
- :=
- match h: ls0 with
- | list_t.Cons x0 tl0 =>
- match h: ls1 with
- | list_t.Cons x1 tl1 =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl1)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl10 ←
- list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
- Result.ret (list_t.Cons x1 tl10)
- | list_t.Nil => Result.fail Error.panic
- | list_t.Nil => Result.fail Error.panic
-termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
- list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
-decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_back
- (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) :
- Result (list_t T)
- :=
- list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
diff --git a/tests/lean/misc-loops/Loops/Types.lean b/tests/lean/misc-loops/Loops/Types.lean
deleted file mode 100644
index ca43f4c8..00000000
--- a/tests/lean/misc-loops/Loops/Types.lean
+++ /dev/null
@@ -1,9 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: type definitions
-import Base.Primitives
-
-/- [loops::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
diff --git a/tests/lean/misc-loops/lake-manifest.json b/tests/lean/misc-loops/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-loops/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-loops/lakefile.lean b/tests/lean/misc-loops/lakefile.lean
deleted file mode 100644
index 097c0a7d..00000000
--- a/tests/lean/misc-loops/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «loops» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Loops» {}
diff --git a/tests/lean/misc-loops/lean-toolchain b/tests/lean/misc-loops/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-loops/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean b/tests/lean/misc-no_nested_borrows/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-no_nested_borrows/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
deleted file mode 100644
index 12c7d8f7..00000000
--- a/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
+++ /dev/null
@@ -1,538 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [no_nested_borrows]
-import Base.Primitives
-
-/- [no_nested_borrows::Pair] -/
-structure pair_t (T1 T2 : Type) where
- pair_x : T1
- pair_y : T2
-
-/- [no_nested_borrows::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [no_nested_borrows::One] -/
-inductive one_t (T1 : Type) :=
-| One : T1 -> one_t T1
-
-/- [no_nested_borrows::EmptyEnum] -/
-inductive empty_enum_t :=
-| Empty : empty_enum_t
-
-/- [no_nested_borrows::Enum] -/
-inductive enum_t :=
-| Variant1 : enum_t
-| Variant2 : enum_t
-
-/- [no_nested_borrows::EmptyStruct] -/
-structure empty_struct_t where
-
-/- [no_nested_borrows::Sum] -/
-inductive sum_t (T1 T2 : Type) :=
-| Left : T1 -> sum_t T1 T2
-| Right : T2 -> sum_t T1 T2
-
-/- [no_nested_borrows::neg_test] -/
-def neg_test_fwd (x : I32) : Result I32 :=
- - x
-
-/- [no_nested_borrows::add_test] -/
-def add_test_fwd (x : U32) (y : U32) : Result U32 :=
- x + y
-
-/- [no_nested_borrows::subs_test] -/
-def subs_test_fwd (x : U32) (y : U32) : Result U32 :=
- x - y
-
-/- [no_nested_borrows::div_test] -/
-def div_test_fwd (x : U32) (y : U32) : Result U32 :=
- x / y
-
-/- [no_nested_borrows::div_test1] -/
-def div_test1_fwd (x : U32) : Result U32 :=
- x / (U32.ofInt 2 (by intlit))
-
-/- [no_nested_borrows::rem_test] -/
-def rem_test_fwd (x : U32) (y : U32) : Result U32 :=
- x % y
-
-/- [no_nested_borrows::cast_test] -/
-def cast_test_fwd (x : U32) : Result I32 :=
- Scalar.cast .I32 x
-
-/- [no_nested_borrows::test2] -/
-def test2_fwd : Result Unit :=
- do
- let _ ← (U32.ofInt 23 (by intlit)) + (U32.ofInt 44 (by intlit))
- Result.ret ()
-
-/- Unit test for [no_nested_borrows::test2] -/
-#assert (test2_fwd == .ret ())
-
-/- [no_nested_borrows::get_max] -/
-def get_max_fwd (x : U32) (y : U32) : Result U32 :=
- if h: x >= y
- then Result.ret x
- else Result.ret y
-
-/- [no_nested_borrows::test3] -/
-def test3_fwd : Result Unit :=
- do
- let x ← get_max_fwd (U32.ofInt 4 (by intlit)) (U32.ofInt 3 (by intlit))
- let y ← get_max_fwd (U32.ofInt 10 (by intlit)) (U32.ofInt 11 (by intlit))
- let z ← x + y
- if h: not (z = (U32.ofInt 15 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test3] -/
-#assert (test3_fwd == .ret ())
-
-/- [no_nested_borrows::test_neg1] -/
-def test_neg1_fwd : Result Unit :=
- do
- let y ← - (I32.ofInt 3 (by intlit))
- if h: not (y = (I32.ofInt (-(3:Int)) (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_neg1] -/
-#assert (test_neg1_fwd == .ret ())
-
-/- [no_nested_borrows::refs_test1] -/
-def refs_test1_fwd : Result Unit :=
- if h: not ((I32.ofInt 1 (by intlit)) = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::refs_test1] -/
-#assert (refs_test1_fwd == .ret ())
-
-/- [no_nested_borrows::refs_test2] -/
-def refs_test2_fwd : Result Unit :=
- if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
- then Result.fail Error.panic
- else
- if h: not ((I32.ofInt 0 (by intlit)) = (I32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else
- if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
- then Result.fail Error.panic
- else
- if h: not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::refs_test2] -/
-#assert (refs_test2_fwd == .ret ())
-
-/- [no_nested_borrows::test_list1] -/
-def test_list1_fwd : Result Unit :=
- Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_list1] -/
-#assert (test_list1_fwd == .ret ())
-
-/- [no_nested_borrows::test_box1] -/
-def test_box1_fwd : Result Unit :=
- let b := (I32.ofInt 1 (by intlit))
- let x := b
- if h: not (x = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_box1] -/
-#assert (test_box1_fwd == .ret ())
-
-/- [no_nested_borrows::copy_int] -/
-def copy_int_fwd (x : I32) : Result I32 :=
- Result.ret x
-
-/- [no_nested_borrows::test_unreachable] -/
-def test_unreachable_fwd (b : Bool) : Result Unit :=
- if h: b
- then Result.fail Error.panic
- else Result.ret ()
-
-/- [no_nested_borrows::test_panic] -/
-def test_panic_fwd (b : Bool) : Result Unit :=
- if h: b
- then Result.fail Error.panic
- else Result.ret ()
-
-/- [no_nested_borrows::test_copy_int] -/
-def test_copy_int_fwd : Result Unit :=
- do
- let y ← copy_int_fwd (I32.ofInt 0 (by intlit))
- if h: not ((I32.ofInt 0 (by intlit)) = y)
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_copy_int] -/
-#assert (test_copy_int_fwd == .ret ())
-
-/- [no_nested_borrows::is_cons] -/
-def is_cons_fwd (T : Type) (l : list_t T) : Result Bool :=
- match h: l with
- | list_t.Cons t l0 => Result.ret true
- | list_t.Nil => Result.ret false
-
-/- [no_nested_borrows::test_is_cons] -/
-def test_is_cons_fwd : Result Unit :=
- do
- let l := list_t.Nil
- let b ← is_cons_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l)
- if h: not b
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_is_cons] -/
-#assert (test_is_cons_fwd == .ret ())
-
-/- [no_nested_borrows::split_list] -/
-def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) :=
- match h: l with
- | list_t.Cons hd tl => Result.ret (hd, tl)
- | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::test_split_list] -/
-def test_split_list_fwd : Result Unit :=
- do
- let l := list_t.Nil
- let p ← split_list_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l)
- let (hd, _) := p
- if h: not (hd = (I32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_split_list] -/
-#assert (test_split_list_fwd == .ret ())
-
-/- [no_nested_borrows::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
- if h: b
- then Result.ret x
- else Result.ret y
-
-/- [no_nested_borrows::choose] -/
-def choose_back
- (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
- if h: b
- then Result.ret (ret0, y)
- else Result.ret (x, ret0)
-
-/- [no_nested_borrows::choose_test] -/
-def choose_test_fwd : Result Unit :=
- do
- let z ←
- choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
- let z0 ← z + (I32.ofInt 1 (by intlit))
- if h: not (z0 = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let (x, y) ←
- choose_back I32 true (I32.ofInt 0 (by intlit))
- (I32.ofInt 0 (by intlit)) z0
- if h: not (x = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- if h: not (y = (I32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::choose_test] -/
-#assert (choose_test_fwd == .ret ())
-
-/- [no_nested_borrows::test_char] -/
-def test_char_fwd : Result Char :=
- Result.ret 'a'
-
-mutual
-
-/- [no_nested_borrows::NodeElem] -/
-inductive node_elem_t (T : Type) :=
-| Cons : tree_t T -> node_elem_t T -> node_elem_t T
-| Nil : node_elem_t T
-
-/- [no_nested_borrows::Tree] -/
-inductive tree_t (T : Type) :=
-| Leaf : T -> tree_t T
-| Node : T -> node_elem_t T -> tree_t T -> tree_t T
-
-end
-
-/- [no_nested_borrows::list_length] -/
-def list_length_fwd (T : Type) (l : list_t T) : Result U32 :=
- match h: l with
- | list_t.Cons t l1 =>
- do
- let i ← list_length_fwd T l1
- (U32.ofInt 1 (by intlit)) + i
- | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::list_nth_shared] -/
-def list_nth_shared_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
- match h: l with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_shared_fwd T tl i0
- | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_nth_mut] -/
-def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
- match h: l with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_fwd T tl i0
- | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_nth_mut] -/
-def list_nth_mut_back
- (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
- match h: l with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl0 ← list_nth_mut_back T tl i0 ret0
- Result.ret (list_t.Cons x tl0)
- | list_t.Nil => Result.fail Error.panic
-
-/- [no_nested_borrows::list_rev_aux] -/
-def list_rev_aux_fwd
- (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) :=
- match h: li with
- | list_t.Cons hd tl => list_rev_aux_fwd T tl (list_t.Cons hd lo)
- | list_t.Nil => Result.ret lo
-
-/- [no_nested_borrows::list_rev] -/
-def list_rev_fwd_back (T : Type) (l : list_t T) : Result (list_t T) :=
- let li := mem_replace_fwd (list_t T) l list_t.Nil
- list_rev_aux_fwd T li list_t.Nil
-
-/- [no_nested_borrows::test_list_functions] -/
-def test_list_functions_fwd : Result Unit :=
- do
- let l := list_t.Nil
- let l0 := list_t.Cons (I32.ofInt 2 (by intlit)) l
- let l1 := list_t.Cons (I32.ofInt 1 (by intlit)) l0
- let i ← list_length_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1)
- if h: not (i = (U32.ofInt 3 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i0 ←
- list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit)) l1)
- (U32.ofInt 0 (by intlit))
- if h: not (i0 = (I32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i1 ←
- list_nth_shared_fwd I32 (list_t.Cons (I32.ofInt 0 (by intlit))
- l1) (U32.ofInt 1 (by intlit))
- if h: not (i1 = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i2 ←
- list_nth_shared_fwd I32 (list_t.Cons
- (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 2 (by intlit))
- if h: not (i2 = (I32.ofInt 2 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let ls ←
- list_nth_mut_back I32 (list_t.Cons
- (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 1 (by intlit))
- (I32.ofInt 3 (by intlit))
- let i3 ←
- list_nth_shared_fwd I32 ls (U32.ofInt 0 (by intlit))
- if h: not (i3 = (I32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i4 ←
- list_nth_shared_fwd I32 ls (U32.ofInt 1 (by intlit))
- if h: not (i4 = (I32.ofInt 3 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let i5 ←
- list_nth_shared_fwd I32 ls
- (U32.ofInt 2 (by intlit))
- if h: not (i5 = (I32.ofInt 2 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_list_functions] -/
-#assert (test_list_functions_fwd == .ret ())
-
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
- Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_back
- (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
- let (t, t0) := ret0
- Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
- let (t, t0) := p
- Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_back
- (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
- let (t, t0) := ret0
- Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
- Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_back'a
- (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 :=
- Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_back'b
- (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 :=
- Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
- let (t, t0) := p
- Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_back'a
- (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 :=
- Result.ret ret0
-
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_back'b
- (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 :=
- Result.ret ret0
-
-/- [no_nested_borrows::StructWithTuple] -/
-structure struct_with_tuple_t (T1 T2 : Type) where
- struct_with_tuple_p : (T1 × T2)
-
-/- [no_nested_borrows::new_tuple1] -/
-def new_tuple1_fwd : Result (struct_with_tuple_t U32 U32) :=
- Result.ret
- {
- struct_with_tuple_p :=
- ((U32.ofInt 1 (by intlit)), (U32.ofInt 2 (by intlit)))
- }
-
-/- [no_nested_borrows::new_tuple2] -/
-def new_tuple2_fwd : Result (struct_with_tuple_t I16 I16) :=
- Result.ret
- {
- struct_with_tuple_p :=
- ((I16.ofInt 1 (by intlit)), (I16.ofInt 2 (by intlit)))
- }
-
-/- [no_nested_borrows::new_tuple3] -/
-def new_tuple3_fwd : Result (struct_with_tuple_t U64 I64) :=
- Result.ret
- {
- struct_with_tuple_p :=
- ((U64.ofInt 1 (by intlit)), (I64.ofInt 2 (by intlit)))
- }
-
-/- [no_nested_borrows::StructWithPair] -/
-structure struct_with_pair_t (T1 T2 : Type) where
- struct_with_pair_p : pair_t T1 T2
-
-/- [no_nested_borrows::new_pair1] -/
-def new_pair1_fwd : Result (struct_with_pair_t U32 U32) :=
- Result.ret
- {
- struct_with_pair_p :=
- {
- pair_x := (U32.ofInt 1 (by intlit)),
- pair_y := (U32.ofInt 2 (by intlit))
- }
- }
-
-/- [no_nested_borrows::test_constants] -/
-def test_constants_fwd : Result Unit :=
- do
- let swt ← new_tuple1_fwd
- let (i, _) := swt.struct_with_tuple_p
- if h: not (i = (U32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let swt0 ← new_tuple2_fwd
- let (i0, _) := swt0.struct_with_tuple_p
- if h: not (i0 = (I16.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let swt1 ← new_tuple3_fwd
- let (i1, _) := swt1.struct_with_tuple_p
- if h: not (i1 = (U64.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let swp ← new_pair1_fwd
- if h: not (swp.struct_with_pair_p.pair_x =
- (U32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_constants] -/
-#assert (test_constants_fwd == .ret ())
-
-/- [no_nested_borrows::test_weird_borrows1] -/
-def test_weird_borrows1_fwd : Result Unit :=
- Result.ret ()
-
-/- Unit test for [no_nested_borrows::test_weird_borrows1] -/
-#assert (test_weird_borrows1_fwd == .ret ())
-
-/- [no_nested_borrows::test_mem_replace] -/
-def test_mem_replace_fwd_back (px : U32) : Result U32 :=
- let y := mem_replace_fwd U32 px (U32.ofInt 1 (by intlit))
- if h: not (y = (U32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else Result.ret (U32.ofInt 2 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_bool1] -/
-def test_shared_borrow_bool1_fwd (b : Bool) : Result U32 :=
- if h: b
- then Result.ret (U32.ofInt 0 (by intlit))
- else Result.ret (U32.ofInt 1 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_bool2] -/
-def test_shared_borrow_bool2_fwd : Result U32 :=
- Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_enum1] -/
-def test_shared_borrow_enum1_fwd (l : list_t U32) : Result U32 :=
- match h: l with
- | list_t.Cons i l0 => Result.ret (U32.ofInt 1 (by intlit))
- | list_t.Nil => Result.ret (U32.ofInt 0 (by intlit))
-
-/- [no_nested_borrows::test_shared_borrow_enum2] -/
-def test_shared_borrow_enum2_fwd : Result U32 :=
- Result.ret (U32.ofInt 0 (by intlit))
-
diff --git a/tests/lean/misc-no_nested_borrows/lake-manifest.json b/tests/lean/misc-no_nested_borrows/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-no_nested_borrows/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-no_nested_borrows/lakefile.lean b/tests/lean/misc-no_nested_borrows/lakefile.lean
deleted file mode 100644
index 58619110..00000000
--- a/tests/lean/misc-no_nested_borrows/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «no_nested_borrows» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «NoNestedBorrows» {}
diff --git a/tests/lean/misc-no_nested_borrows/lean-toolchain b/tests/lean/misc-no_nested_borrows/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-no_nested_borrows/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-paper/Base/Primitives.lean b/tests/lean/misc-paper/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-paper/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-paper/Paper.lean b/tests/lean/misc-paper/Paper.lean
deleted file mode 100644
index 0b16fb8e..00000000
--- a/tests/lean/misc-paper/Paper.lean
+++ /dev/null
@@ -1,123 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [paper]
-import Base.Primitives
-
-/- [paper::ref_incr] -/
-def ref_incr_fwd_back (x : I32) : Result I32 :=
- x + (I32.ofInt 1 (by intlit))
-
-/- [paper::test_incr] -/
-def test_incr_fwd : Result Unit :=
- do
- let x ← ref_incr_fwd_back (I32.ofInt 0 (by intlit))
- if h: not (x = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [paper::test_incr] -/
-#assert (test_incr_fwd == .ret ())
-
-/- [paper::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
- if h: b
- then Result.ret x
- else Result.ret y
-
-/- [paper::choose] -/
-def choose_back
- (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
- if h: b
- then Result.ret (ret0, y)
- else Result.ret (x, ret0)
-
-/- [paper::test_choose] -/
-def test_choose_fwd : Result Unit :=
- do
- let z ←
- choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
- let z0 ← z + (I32.ofInt 1 (by intlit))
- if h: not (z0 = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- do
- let (x, y) ←
- choose_back I32 true (I32.ofInt 0 (by intlit))
- (I32.ofInt 0 (by intlit)) z0
- if h: not (x = (I32.ofInt 1 (by intlit)))
- then Result.fail Error.panic
- else
- if h: not (y = (I32.ofInt 0 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [paper::test_choose] -/
-#assert (test_choose_fwd == .ret ())
-
-/- [paper::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [paper::list_nth_mut] -/
-def list_nth_mut_fwd (T : Type) (l : list_t T) (i : U32) : Result T :=
- match h: l with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret x
- else do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- list_nth_mut_fwd T tl i0
- | list_t.Nil => Result.fail Error.panic
-
-/- [paper::list_nth_mut] -/
-def list_nth_mut_back
- (T : Type) (l : list_t T) (i : U32) (ret0 : T) : Result (list_t T) :=
- match h: l with
- | list_t.Cons x tl =>
- if h: i = (U32.ofInt 0 (by intlit))
- then Result.ret (list_t.Cons ret0 tl)
- else
- do
- let i0 ← i - (U32.ofInt 1 (by intlit))
- let tl0 ← list_nth_mut_back T tl i0 ret0
- Result.ret (list_t.Cons x tl0)
- | list_t.Nil => Result.fail Error.panic
-
-/- [paper::sum] -/
-def sum_fwd (l : list_t I32) : Result I32 :=
- match h: l with
- | list_t.Cons x tl => do
- let i ← sum_fwd tl
- x + i
- | list_t.Nil => Result.ret (I32.ofInt 0 (by intlit))
-
-/- [paper::test_nth] -/
-def test_nth_fwd : Result Unit :=
- do
- let l := list_t.Nil
- let l0 := list_t.Cons (I32.ofInt 3 (by intlit)) l
- let l1 := list_t.Cons (I32.ofInt 2 (by intlit)) l0
- let x ←
- list_nth_mut_fwd I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1)
- (U32.ofInt 2 (by intlit))
- let x0 ← x + (I32.ofInt 1 (by intlit))
- let l2 ←
- list_nth_mut_back I32 (list_t.Cons (I32.ofInt 1 (by intlit)) l1)
- (U32.ofInt 2 (by intlit)) x0
- let i ← sum_fwd l2
- if h: not (i = (I32.ofInt 7 (by intlit)))
- then Result.fail Error.panic
- else Result.ret ()
-
-/- Unit test for [paper::test_nth] -/
-#assert (test_nth_fwd == .ret ())
-
-/- [paper::call_choose] -/
-def call_choose_fwd (p : (U32 × U32)) : Result U32 :=
- do
- let (px, py) := p
- let pz ← choose_fwd U32 true px py
- let pz0 ← pz + (U32.ofInt 1 (by intlit))
- let (px0, _) ← choose_back U32 true px py pz0
- Result.ret px0
-
diff --git a/tests/lean/misc-paper/lake-manifest.json b/tests/lean/misc-paper/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-paper/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-paper/lakefile.lean b/tests/lean/misc-paper/lakefile.lean
deleted file mode 100644
index 75d7208e..00000000
--- a/tests/lean/misc-paper/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «paper» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «Paper» {}
diff --git a/tests/lean/misc-paper/lean-toolchain b/tests/lean/misc-paper/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-paper/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21
diff --git a/tests/lean/misc-polonius_list/Base/Primitives.lean b/tests/lean/misc-polonius_list/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-polonius_list/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
- runTermElabM (fun _ => do
- let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
- if not r then
- logInfo "Assertion failed for: "
- logInfo _stx[1]
- logError "Expression reduced to false"
- pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
- | assertionFailure: Error
- | integerOverflow: Error
- | divisionByZero: Error
- | arrayOutOfBounds: Error
- | maximumSizeExceeded: Error
- | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
- | ret (v: α): Result α
- | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
- Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
- match r with
- | Result.ret _ => true
- | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
- if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
- match x with
- | Result.fail _ => by contradiction
- | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
- match x with
- | ret v => f v
- | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
- bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
- pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
- match o with
- | .ret x => .ret ⟨x, rfl⟩
- | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
- let y <-- .ret (0: Nat)
- let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
- let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
- .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min : Int := 0
-@[simp] def U8.max : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min : Int := 0
-@[simp] def U16.max : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min : Int := 0
-@[simp] def U32.max : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min : Int := 0
-@[simp] def U64.max : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min : Int := 0
-@[simp] def U128.max : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min == -128)
-#assert (I8.max == 127)
-#assert (I16.min == -32768)
-#assert (I16.max == 32767)
-#assert (I32.min == -2147483648)
-#assert (I32.max == 2147483647)
-#assert (I64.min == -9223372036854775808)
-#assert (I64.max == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min == 0)
-#assert (U8.max == 255)
-#assert (U16.min == 0)
-#assert (U16.max == 65535)
-#assert (U32.min == 0)
-#assert (U32.max == 4294967295)
-#assert (U64.min == 0)
-#assert (U64.max == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.min
- | .I8 => I8.min
- | .I16 => I16.min
- | .I32 => I32.min
- | .I64 => I64.min
- | .I128 => I128.min
- | .Usize => Usize.min
- | .U8 => U8.min
- | .U16 => U16.min
- | .U32 => U32.min
- | .U64 => U64.min
- | .U128 => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => Isize.max
- | .I8 => I8.max
- | .I16 => I16.max
- | .I32 => I32.max
- | .I64 => I64.max
- | .I128 => I128.max
- | .Usize => Usize.max
- | .U8 => U8.max
- | .U16 => U16.max
- | .U32 => U32.max
- | .U64 => U64.max
- | .U128 => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.min
- | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
- match ty with
- | .Isize => I32.max
- | .Usize => U32.max
- | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
- val : Int
- hmin : Scalar.min ty <= val
- hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
- Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
- (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
- := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
- (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
- { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
- (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
- -- TODO: write this with only one if then else
- if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
- if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
- let hmin: Scalar.min ty <= x := by sorry
- let hmax: x <= Scalar.max ty := by sorry
- return Scalar.ofIntCore x hmin hmax
- else fail integerOverflow
- else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
- Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
- Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8 := Scalar .I8
-@[reducible] def I16 := Scalar .I16
-@[reducible] def I32 := Scalar .I32
-@[reducible] def I64 := Scalar .I64
-@[reducible] def I128 := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8 := Scalar .U8
-@[reducible] def U16 := Scalar .U16
-@[reducible] def U32 := Scalar .U32
-@[reducible] def U64 := Scalar .U64
-@[reducible] def U128 := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
- /-- `- a` computes the negation of `a`.
- The meaning of this notation is type-dependent. -/
- hNeg : α → β
-
-prefix:75 "-" => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
- hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore := @Scalar.ofIntCore .I8
-def I16.ofIntCore := @Scalar.ofIntCore .I16
-def I32.ofIntCore := @Scalar.ofIntCore .I32
-def I64.ofIntCore := @Scalar.ofIntCore .I64
-def I128.ofIntCore := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore := @Scalar.ofIntCore .U8
-def U16.ofIntCore := @Scalar.ofIntCore .U16
-def U32.ofIntCore := @Scalar.ofIntCore .U32
-def U64.ofIntCore := @Scalar.ofIntCore .U64
-def U128.ofIntCore := @Scalar.ofIntCore .U128
-
--- ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt := @Scalar.ofInt .I8
-def I16.ofInt := @Scalar.ofInt .I16
-def I32.ofInt := @Scalar.ofInt .I32
-def I64.ofInt := @Scalar.ofInt .I64
-def I128.ofInt := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt := @Scalar.ofInt .U8
-def U16.ofInt := @Scalar.ofInt .U16
-def U32.ofInt := @Scalar.ofInt .U32
-def U64.ofInt := @Scalar.ofInt .U64
-def U128.ofInt := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
- lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
- | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
- h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
- fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
- fun i j =>
- match decEq i.val j.val with
- | isTrue h => isTrue (Scalar.eq_of_val_eq h)
- | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
- | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
--- size: Nat
--- val: t -> Fin size
--- ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
--- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
--- Lean.Elab.Command.elabCommand (← `(
--- namespace $typeName
--- instance: MachineInteger $typeName where
--- size := size
--- val := val
--- ofNatCore := ofNatCore
--- end $typeName
--- ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
--- if h: MachineInteger.val x < MachineInteger.size dst then
--- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
--- else
--- .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
- let ⟨ v, l ⟩ := v
- Usize.ofIntCore (List.length v) (by sorry) l
-
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
- :=
- if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
- return ⟨ List.concat v.val x, by sorry ⟩
- else
- fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- -- TODO: maybe we should redefine a list library which uses integers
- -- (instead of natural numbers)
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
- if i.val < List.length v.val then
- .ret ()
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- let h: i < List.length v.val := by sorry
- .ret (List.get v.val ⟨i.val, h⟩)
- else
- .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
- if i.val < List.length v.val then
- let i : Nat :=
- match i.val with
- | .ofNat n => n
- | .negSucc n => by sorry -- TODO: we can't get here
- let isLt: i < USize.size := by sorry
- let i : Fin USize.size := { val := i, isLt := isLt }
- .ret ⟨ List.set v.val i.val x, by
- have h: List.length v.val <= Usize.max := v.property
- rewrite [ List.length_set v.val i.val x ]
- assumption
- ⟩
- else
- .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
- x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
- y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
diff --git a/tests/lean/misc-polonius_list/PoloniusList.lean b/tests/lean/misc-polonius_list/PoloniusList.lean
deleted file mode 100644
index 79696996..00000000
--- a/tests/lean/misc-polonius_list/PoloniusList.lean
+++ /dev/null
@@ -1,31 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [polonius_list]
-import Base.Primitives
-
-/- [polonius_list::List] -/
-inductive list_t (T : Type) :=
-| Cons : T -> list_t T -> list_t T
-| Nil : list_t T
-
-/- [polonius_list::get_list_at_x] -/
-def get_list_at_x_fwd (ls : list_t U32) (x : U32) : Result (list_t U32) :=
- match h: ls with
- | list_t.Cons hd tl =>
- if h: hd = x
- then Result.ret (list_t.Cons hd tl)
- else get_list_at_x_fwd tl x
- | list_t.Nil => Result.ret list_t.Nil
-
-/- [polonius_list::get_list_at_x] -/
-def get_list_at_x_back
- (ls : list_t U32) (x : U32) (ret0 : list_t U32) : Result (list_t U32) :=
- match h: ls with
- | list_t.Cons hd tl =>
- if h: hd = x
- then Result.ret ret0
- else
- do
- let tl0 ← get_list_at_x_back tl x ret0
- Result.ret (list_t.Cons hd tl0)
- | list_t.Nil => Result.ret ret0
-
diff --git a/tests/lean/misc-polonius_list/lake-manifest.json b/tests/lean/misc-polonius_list/lake-manifest.json
deleted file mode 100644
index 57b071ca..00000000
--- a/tests/lean/misc-polonius_list/lake-manifest.json
+++ /dev/null
@@ -1,27 +0,0 @@
-{"version": 4,
- "packagesDir": "./lake-packages",
- "packages":
- [{"git":
- {"url": "https://github.com/leanprover-community/mathlib4.git",
- "subDir?": null,
- "rev": "4037792ead804d7bfa8868e2c4684d4223c15ece",
- "name": "mathlib",
- "inputRev?": null}},
- {"git":
- {"url": "https://github.com/gebner/quote4",
- "subDir?": null,
- "rev": "2412c4fdf4a8b689f4467618e5e7b371ae5014aa",
- "name": "Qq",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/JLimperg/aesop",
- "subDir?": null,
- "rev": "7fe9ecd9339b0e1796e89d243b776849c305c690",
- "name": "aesop",
- "inputRev?": "master"}},
- {"git":
- {"url": "https://github.com/leanprover/std4",
- "subDir?": null,
- "rev": "24897887905b3a1254b244369f5dd2cf6174b0ee",
- "name": "std",
- "inputRev?": "main"}}]}
diff --git a/tests/lean/misc-polonius_list/lakefile.lean b/tests/lean/misc-polonius_list/lakefile.lean
deleted file mode 100644
index e89d4259..00000000
--- a/tests/lean/misc-polonius_list/lakefile.lean
+++ /dev/null
@@ -1,12 +0,0 @@
-import Lake
-open Lake DSL
-
-require mathlib from git
- "https://github.com/leanprover-community/mathlib4.git"
-
-package «polonius_list» {}
-
-lean_lib «Base» {}
-
-@[default_target]
-lean_lib «PoloniusList» {}
diff --git a/tests/lean/misc-polonius_list/lean-toolchain b/tests/lean/misc-polonius_list/lean-toolchain
deleted file mode 100644
index bbf57f10..00000000
--- a/tests/lean/misc-polonius_list/lean-toolchain
+++ /dev/null
@@ -1 +0,0 @@
-leanprover/lean4:nightly-2023-01-21