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authorSon Ho2023-03-07 08:41:57 +0100
committerSon HO2023-06-04 21:44:33 +0200
commitfeb60683216a6d9193d6353605560c6c80a1ab41 (patch)
tree222f61e4c5cbcd166e81d82350afc54b002774df
parentb4bad8df4eabb17c71dfa7b24d79d62fc06d0a70 (diff)
Make minor modifications and regenerate the Lean files
-rw-r--r--backends/lean/Primitives.lean2
-rw-r--r--tests/lean/hashmap/Base/Primitives.lean231
-rw-r--r--tests/lean/hashmap/Hashmap/Clauses/Template.lean6
-rw-r--r--tests/lean/hashmap/Hashmap/Funs.lean400
-rw-r--r--tests/lean/hashmap/Hashmap/Types.lean2
-rw-r--r--tests/lean/hashmap_on_disk/Base/Primitives.lean2
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean9
-rw-r--r--tests/lean/hashmap_on_disk/HashmapMain/Funs.lean23
-rw-r--r--tests/lean/misc/constants/Base/Primitives.lean231
-rw-r--r--tests/lean/misc/constants/Constants.lean76
-rw-r--r--tests/lean/misc/external/Base/Primitives.lean231
-rw-r--r--tests/lean/misc/external/External/Funs.lean80
-rw-r--r--tests/lean/misc/external/External/Opaque.lean10
-rw-r--r--tests/lean/misc/external/External/Types.lean2
-rw-r--r--tests/lean/misc/loops/Base/Primitives.lean231
-rw-r--r--tests/lean/misc/loops/Loops/Clauses/Template.lean2
-rw-r--r--tests/lean/misc/loops/Loops/Funs.lean517
-rw-r--r--tests/lean/misc/no_nested_borrows/Base/Primitives.lean231
-rw-r--r--tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean454
-rw-r--r--tests/lean/misc/paper/Base/Primitives.lean231
-rw-r--r--tests/lean/misc/paper/Paper.lean118
21 files changed, 1600 insertions, 1489 deletions
diff --git a/backends/lean/Primitives.lean b/backends/lean/Primitives.lean
index e558e476..346e4b89 100644
--- a/backends/lean/Primitives.lean
+++ b/backends/lean/Primitives.lean
@@ -21,7 +21,7 @@ open Error
inductive Result (α : Type u) where
| ret (v: α): Result α
- | fail (e: Error): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
open Result
diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/hashmap/Base/Primitives.lean
+++ b/tests/lean/hashmap/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
-- Results & monadic combinators
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
- | assertionFailure: error
- | integerOverflow: error
- | arrayOutOfBounds: error
- | maximumSizeExceeded: error
- | panic: error
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
deriving Repr, BEq
-open error
+open Error
-inductive result (α : Type u) where
- | ret (v: α): result α
- | fail (e: error): result α
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
-open result
+open Result
/- HELPERS -/
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
match r with
- | result.ret _ => true
- | result.fail _ => false
+ | Result.ret _ => true
+ | Result.fail _ => false
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
if b then .ret () else fail assertionFailure
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
match x with
- | result.fail _ => by contradiction
- | result.ret x => x
+ | Result.fail _ => by contradiction
+ | Result.ret x => x
/- DO-DSL SUPPORT -/
-def bind (x: result α) (f: α -> result β) : result β :=
+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
+-- Allows using Result in do-blocks
+instance : Bind Result where
bind := bind
-- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
pure := fun x => ret x
/- CUSTOM-DSL SUPPORT -/
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- 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 : (o : result α) → result { x : α // o = ret x }
+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
+ | .fail e => .fail e
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+ `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$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 h: y <-- .ret (0: Nat)
- let _: y = 0 := by cases h; decide
+ 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
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-- MACHINE INTEGERS --
----------------------
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: 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." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- 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.
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
syntax "intlit" : tactic
@@ -129,12 +125,21 @@ macro_rules
-- Also works for other integer types (at the expense of a needless disjunction)
#eval UInt32.ofNatCore 0 (by intlit)
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
-- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
if n >= m then
let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
else
fail integerOverflow
-def USize.checked_add (n: USize) (m: USize): result USize :=
- if h: n.val.val + m.val.val <= 4294967295 then
- .ret ⟨ n.val.val + m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+ | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+ if h: n.val + m.val < USize.size then
.ret ⟨ n.val + m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
if h: m > 0 then
.ret ⟨ n.val % m.val, by
have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
-def USize.checked_mul (n: USize) (m: USize): result USize :=
- if h: n.val.val * m.val.val <= 4294967295 then
- .ret ⟨ n.val.val * m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+ if h: n.val * m.val < USize.size then
.ret ⟨ n.val * m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
if m > 0 then
.ret ⟨ n.val / m.val, by
have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- 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
@@ -209,30 +223,24 @@ run_cmd
end $typeName
))
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- 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
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
-------------
-- VECTORS --
-------------
-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
-- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
match USize.size, usize_size_eq with
| _, Or.inl rfl => simp
| _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
#check vec_new
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
let ⟨ v, l ⟩ := v
USize.ofNatCore (List.length v) l
#eval vec_len Nat (vec_new Nat)
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
-- make the proof work in that case? Probably need to import tactics from
-- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
:=
if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec
-- annotate `x`, which relieves us of having to write `.val` on the right-hand
-- side of the monadic let.
let v := vec_new Nat
- let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+ let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-- TODO: strengthen post-condition above and do a demo to show that we can
-- safely eliminate the `fail` case
return (vec_len Nat x)
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
if h : List.length v.val + 1 <= 4294967295 then
return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
else
fail maximumSizeExceeded
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
else
.fail arrayOutOfBounds
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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 :=
+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 :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
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
+
--------------------
-- ASSERT COMMAND --
--------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
syntax (name := assert) "#assert" term: command
@[command_elab assert]
+unsafe
def assertImpl : CommandElab := fun (_stx: Syntax) => do
- logInfo "Reducing and asserting: "
- logInfo _stx[1]
runTermElabM (fun _ => do
- let e ← Term.elabTerm _stx[1] none
- logInfo (Expr.dbgToString e)
- -- How to evaluate the term and compare the result to true?
+ 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 ())
- -- logInfo (Expr.dbgToString (``true))
- -- throwError "TODO: assert"
#eval 2 == 2
#assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/hashmap/Hashmap/Clauses/Template.lean b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
index 2bc92153..b767a0eb 100644
--- a/tests/lean/hashmap/Hashmap/Clauses/Template.lean
+++ b/tests/lean/hashmap/Hashmap/Clauses/Template.lean
@@ -5,7 +5,7 @@ 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))
+def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T))
(n : USize) :=
(slots, n)
@@ -16,7 +16,7 @@ macro_rules
/- [hashmap::HashMap::{0}::clear]: termination measure -/
@[simp]
-def hash_map_clear_loop_terminates (T : Type) (slots : vec (list_t T))
+def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T))
(i : USize) :=
(slots, i)
@@ -52,7 +52,7 @@ macro_rules
/- [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) :=
+ (slots : Vec (list_t T)) (i : USize) :=
(ntable, slots, i)
syntax "hash_map_move_elements_loop_decreases" term+ : tactic
diff --git a/tests/lean/hashmap/Hashmap/Funs.lean b/tests/lean/hashmap/Hashmap/Funs.lean
index 3bdd9dd2..0b3708fa 100644
--- a/tests/lean/hashmap/Hashmap/Funs.lean
+++ b/tests/lean/hashmap/Hashmap/Funs.lean
@@ -5,42 +5,42 @@ import Hashmap.Types
import Hashmap.Clauses.Clauses
/- [hashmap::hash_key] -/
-def hash_key_fwd (k : USize) : result USize :=
- result.ret k
+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)))
+ (T : Type) (slots : Vec (list_t T)) (n : USize) :
+ (Result (Vec (list_t T)))
:=
- if n > (USize.ofNatCore 0 (by intlit))
+ if h: n > (USize.ofNatCore 0 (by intlit))
then
do
- let slots0 <- vec_push_back (list_t T) slots list_t.ListNil
- let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit))
+ let slots0 ← vec_push_back (list_t T) slots list_t.ListNil
+ let n0 ← USize.checked_sub n (USize.ofNatCore 1 (by intlit))
hash_map_allocate_slots_loop_fwd T slots0 n0
- else result.ret slots
+ 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)) :=
+ (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)
+ 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 <- USize.checked_mul capacity max_load_dividend
- let i0 <- USize.checked_div i max_load_divisor
- result.ret
+ let slots ← hash_map_allocate_slots_fwd T v capacity
+ let i ← USize.checked_mul capacity max_load_dividend
+ let i0 ← USize.checked_div i max_load_divisor
+ Result.ret
{
hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
hash_map_max_load_factor := (max_load_dividend, max_load_divisor),
@@ -49,35 +49,35 @@ def hash_map_new_with_capacity_fwd
}
/- [hashmap::HashMap::{0}::new] -/
-def hash_map_new_fwd (T : Type) : result (hash_map_t T) :=
+def hash_map_new_fwd (T : Type) : Result (hash_map_t T) :=
hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit))
(USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 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)))
+ (T : Type) (slots : Vec (list_t T)) (i : USize) :
+ (Result (Vec (list_t T)))
:=
let i0 := vec_len (list_t T) slots
- if i < i0
+ if h: i < i0
then
do
- let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
- let slots0 <- vec_index_mut_back (list_t T) slots i list_t.ListNil
+ let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit))
+ let slots0 ← vec_index_mut_back (list_t T) slots i list_t.ListNil
hash_map_clear_loop_fwd_back T slots0 i1
- else result.ret slots
+ 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) :=
+ (T : Type) (self : hash_map_t T) : Result (hash_map_t T) :=
do
- let v <-
+ let v ←
hash_map_clear_loop_fwd_back T self.hash_map_slots
(USize.ofNatCore 0 (by intlit))
- result.ret
+ Result.ret
{
hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
hash_map_max_load_factor := self.hash_map_max_load_factor,
@@ -86,69 +86,69 @@ def hash_map_clear_fwd_back
}
/- [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
+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 ls with
+ (T : Type) (key : USize) (value : T) (ls : list_t T) : (Result Bool) :=
+ match h: ls with
| list_t.ListCons ckey cvalue tl =>
- if ckey = key
- then result.ret false
+ if h: ckey = key
+ then Result.ret false
else hash_map_insert_in_list_loop_fwd T key value tl
- | list_t.ListNil => result.ret true
+ | list_t.ListNil => 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 :=
+ (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 ls with
+ (T : Type) (key : USize) (value : T) (ls : list_t T) : (Result (list_t T)) :=
+ match h: ls with
| list_t.ListCons ckey cvalue tl =>
- if ckey = key
- then result.ret (list_t.ListCons ckey value tl)
+ if h: ckey = key
+ then Result.ret (list_t.ListCons ckey value tl)
else
do
- let tl0 <- hash_map_insert_in_list_loop_back T key value tl
- result.ret (list_t.ListCons ckey cvalue tl0)
+ let tl0 ← hash_map_insert_in_list_loop_back T key value tl
+ Result.ret (list_t.ListCons ckey cvalue tl0)
| list_t.ListNil =>
let l := list_t.ListNil
- result.ret (list_t.ListCons key value l)
+ Result.ret (list_t.ListCons 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) :=
+ (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)
+ Result (hash_map_t T)
:=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem 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 inserted
+ let hash_mod ← USize.checked_rem 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 <- USize.checked_add self.hash_map_num_entries
+ let i0 ← USize.checked_add self.hash_map_num_entries
(USize.ofNatCore 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
+ 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
{
hash_map_num_entries := i0,
hash_map_max_load_factor := self.hash_map_max_load_factor,
@@ -157,9 +157,9 @@ def hash_map_insert_no_resize_fwd_back
}
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
+ 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
{
hash_map_num_entries := self.hash_map_num_entries,
hash_map_max_load_factor := self.hash_map_max_load_factor,
@@ -168,76 +168,76 @@ def hash_map_insert_no_resize_fwd_back
}
/- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : result UInt32 :=
- result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+def core_num_u32_max_body : Result UInt32 :=
+ Result.ret (UInt32.ofNatCore 4294967295 (by intlit))
def core_num_u32_max_c : UInt32 := 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))
+ (Result (hash_map_t T))
:=
- match ls with
+ match h: ls with
| list_t.ListCons k v tl =>
do
- let ntable0 <- hash_map_insert_no_resize_fwd_back T ntable k v
+ 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.ListNil => result.ret ntable
+ | list_t.ListNil => 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) :=
+ (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))))
+ (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 i < i0
+ if h: i < i0
then
do
- let l <- vec_index_mut_fwd (list_t T) slots i
+ let l ← vec_index_mut_fwd (list_t T) slots i
let ls := mem_replace_fwd (list_t T) l list_t.ListNil
- let ntable0 <- hash_map_move_elements_from_list_fwd_back T ntable ls
- let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+ let ntable0 ← hash_map_move_elements_from_list_fwd_back T ntable ls
+ let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit))
let l0 := mem_replace_back (list_t T) l list_t.ListNil
- let slots0 <- vec_index_mut_back (list_t T) slots i l0
+ 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)
+ 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)))
+ (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) :=
+ (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 max_usize ← scalar_cast USize core_num_u32_max_c
let capacity := vec_len (list_t T) self.hash_map_slots
- let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
+ let n1 ← USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
let (i, i0) := self.hash_map_max_load_factor
- let i1 <- USize.checked_div n1 i
- if capacity <= i1
+ let i1 ← USize.checked_div n1 i
+ if h: capacity <= i1
then
do
- let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit))
- let ntable <- hash_map_new_with_capacity_fwd T i2 i i0
- let (ntable0, _) <-
+ let i2 ← USize.checked_mul capacity (USize.ofNatCore 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.ofNatCore 0 (by intlit))
- result.ret
+ Result.ret
{
hash_map_num_entries := self.hash_map_num_entries,
hash_map_max_load_factor := (i, i0),
@@ -245,7 +245,7 @@ def hash_map_try_resize_fwd_back
hash_map_slots := ntable0.hash_map_slots
}
else
- result.ret
+ Result.ret
{
hash_map_num_entries := self.hash_map_num_entries,
hash_map_max_load_factor := (i, i0),
@@ -256,133 +256,133 @@ def hash_map_try_resize_fwd_back
/- [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)
+ 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 i > self0.hash_map_max_load
+ 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
+ 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 ls with
+ (T : Type) (key : USize) (ls : list_t T) : (Result Bool) :=
+ match h: ls with
| list_t.ListCons ckey t tl =>
- if ckey = key
- then result.ret true
+ if h: ckey = key
+ then Result.ret true
else hash_map_contains_key_in_list_loop_fwd T key tl
- | list_t.ListNil => result.ret false
+ | list_t.ListNil => 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 :=
+ (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 :=
+ (T : Type) (self : hash_map_t T) (key : USize) : Result Bool :=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem hash i
- let l <- vec_index_fwd (list_t T) self.hash_map_slots hash_mod
+ let hash_mod ← USize.checked_rem 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 ls with
+ (T : Type) (key : USize) (ls : list_t T) : (Result T) :=
+ match h: ls with
| list_t.ListCons ckey cvalue tl =>
- if ckey = key
- then result.ret cvalue
+ if h: ckey = key
+ then Result.ret cvalue
else hash_map_get_in_list_loop_fwd T key tl
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 :=
+ (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 :=
+ (T : Type) (self : hash_map_t T) (key : USize) : Result T :=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem hash i
- let l <- vec_index_fwd (list_t T) self.hash_map_slots hash_mod
+ let hash_mod ← USize.checked_rem 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 ls with
+ (T : Type) (ls : list_t T) (key : USize) : (Result T) :=
+ match h: ls with
| list_t.ListCons ckey cvalue tl =>
- if ckey = key
- then result.ret cvalue
+ if h: ckey = key
+ then Result.ret cvalue
else hash_map_get_mut_in_list_loop_fwd T tl key
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 :=
+ (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 ls with
+ (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : (Result (list_t T)) :=
+ match h: ls with
| list_t.ListCons ckey cvalue tl =>
- if ckey = key
- then result.ret (list_t.ListCons ckey ret0 tl)
+ if h: ckey = key
+ then Result.ret (list_t.ListCons ckey ret0 tl)
else
do
- let tl0 <- hash_map_get_mut_in_list_loop_back T tl key ret0
- result.ret (list_t.ListCons ckey cvalue tl0)
- | list_t.ListNil => result.fail error.panic
+ let tl0 ← hash_map_get_mut_in_list_loop_back T tl key ret0
+ Result.ret (list_t.ListCons ckey cvalue tl0)
+ | list_t.ListNil => 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) :=
+ (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 :=
+ (T : Type) (self : hash_map_t T) (key : USize) : Result T :=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem hash i
- let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod
+ let hash_mod ← USize.checked_rem 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)
+ Result (hash_map_t T)
:=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem 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
+ let hash_mod ← USize.checked_rem 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
{
hash_map_num_entries := self.hash_map_num_entries,
hash_map_max_load_factor := self.hash_map_max_load_factor,
@@ -392,85 +392,85 @@ def hash_map_get_mut_back
/- [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 ls with
+ (T : Type) (key : USize) (ls : list_t T) : (Result (Option T)) :=
+ match h: ls with
| list_t.ListCons ckey t tl =>
- if ckey = key
+ if h: ckey = key
then
let mv_ls :=
mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil
- match mv_ls with
- | list_t.ListCons i cvalue tl0 => result.ret (Option.some cvalue)
- | list_t.ListNil => result.fail error.panic
+ match h: mv_ls with
+ | list_t.ListCons i cvalue tl0 => Result.ret (Option.some cvalue)
+ | list_t.ListNil => Result.fail Error.panic
else hash_map_remove_from_list_loop_fwd T key tl
- | list_t.ListNil => result.ret Option.none
+ | list_t.ListNil => 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) :=
+ (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 ls with
+ (T : Type) (key : USize) (ls : list_t T) : (Result (list_t T)) :=
+ match h: ls with
| list_t.ListCons ckey t tl =>
- if ckey = key
+ if h: ckey = key
then
let mv_ls :=
mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil
- match mv_ls with
- | list_t.ListCons i cvalue tl0 => result.ret tl0
- | list_t.ListNil => result.fail error.panic
+ match h: mv_ls with
+ | list_t.ListCons i cvalue tl0 => Result.ret tl0
+ | list_t.ListNil => Result.fail Error.panic
else
do
- let tl0 <- hash_map_remove_from_list_loop_back T key tl
- result.ret (list_t.ListCons ckey t tl0)
- | list_t.ListNil => result.ret list_t.ListNil
+ let tl0 ← hash_map_remove_from_list_loop_back T key tl
+ Result.ret (list_t.ListCons ckey t tl0)
+ | list_t.ListNil => Result.ret list_t.ListNil
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) :=
+ (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) :=
+ (T : Type) (self : hash_map_t T) (key : USize) : Result (Option T) :=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem 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 x with
- | Option.none => result.ret Option.none
+ let hash_mod ← USize.checked_rem 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 _ <- USize.checked_sub self.hash_map_num_entries
+ let _ ← USize.checked_sub self.hash_map_num_entries
(USize.ofNatCore 1 (by intlit))
- result.ret (Option.some x0)
+ 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) :=
+ (T : Type) (self : hash_map_t T) (key : USize) : Result (hash_map_t T) :=
do
- let hash <- hash_key_fwd key
+ let hash ← hash_key_fwd key
let i := vec_len (list_t T) self.hash_map_slots
- let hash_mod <- USize.checked_rem 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 x with
+ let hash_mod ← USize.checked_rem 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
+ 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
{
hash_map_num_entries := self.hash_map_num_entries,
hash_map_max_load_factor := self.hash_map_max_load_factor,
@@ -479,11 +479,11 @@ def hash_map_remove_back
}
| Option.some x0 =>
do
- let i0 <- USize.checked_sub self.hash_map_num_entries
+ let i0 ← USize.checked_sub self.hash_map_num_entries
(USize.ofNatCore 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
+ 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
{
hash_map_num_entries := i0,
hash_map_max_load_factor := self.hash_map_max_load_factor,
@@ -492,67 +492,67 @@ def hash_map_remove_back
}
/- [hashmap::test1] -/
-def test1_fwd : result Unit :=
+def test1_fwd : Result Unit :=
do
- let hm <- hash_map_new_fwd UInt64
- let hm0 <-
+ let hm ← hash_map_new_fwd UInt64
+ let hm0 ←
hash_map_insert_fwd_back UInt64 hm (USize.ofNatCore 0 (by intlit))
(UInt64.ofNatCore 42 (by intlit))
- let hm1 <-
+ let hm1 ←
hash_map_insert_fwd_back UInt64 hm0 (USize.ofNatCore 128 (by intlit))
(UInt64.ofNatCore 18 (by intlit))
- let hm2 <-
+ let hm2 ←
hash_map_insert_fwd_back UInt64 hm1 (USize.ofNatCore 1024 (by intlit))
(UInt64.ofNatCore 138 (by intlit))
- let hm3 <-
+ let hm3 ←
hash_map_insert_fwd_back UInt64 hm2 (USize.ofNatCore 1056 (by intlit))
(UInt64.ofNatCore 256 (by intlit))
- let i <- hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
- if not (i = (UInt64.ofNatCore 18 (by intlit)))
- then result.fail error.panic
+ let i ← hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
+ if h: not (i = (UInt64.ofNatCore 18 (by intlit)))
+ then Result.fail Error.panic
else
do
- let hm4 <-
+ let hm4 ←
hash_map_get_mut_back UInt64 hm3 (USize.ofNatCore 1024 (by intlit))
(UInt64.ofNatCore 56 (by intlit))
- let i0 <-
+ let i0 ←
hash_map_get_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit))
- if not (i0 = (UInt64.ofNatCore 56 (by intlit)))
- then result.fail error.panic
+ if h: not (i0 = (UInt64.ofNatCore 56 (by intlit)))
+ then Result.fail Error.panic
else
do
- let x <-
+ let x ←
hash_map_remove_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit))
- match x with
- | Option.none => result.fail error.panic
+ match h: x with
+ | Option.none => Result.fail Error.panic
| Option.some x0 =>
- if not (x0 = (UInt64.ofNatCore 56 (by intlit)))
- then result.fail error.panic
+ if h: not (x0 = (UInt64.ofNatCore 56 (by intlit)))
+ then Result.fail Error.panic
else
do
- let hm5 <-
+ let hm5 ←
hash_map_remove_back UInt64 hm4
(USize.ofNatCore 1024 (by intlit))
- let i1 <-
+ let i1 ←
hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 0 (by intlit))
- if not (i1 = (UInt64.ofNatCore 42 (by intlit)))
- then result.fail error.panic
+ if h: not (i1 = (UInt64.ofNatCore 42 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i2 <-
+ let i2 ←
hash_map_get_fwd UInt64 hm5
(USize.ofNatCore 128 (by intlit))
- if not (i2 = (UInt64.ofNatCore 18 (by intlit)))
- then result.fail error.panic
+ if h: not (i2 = (UInt64.ofNatCore 18 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i3 <-
+ let i3 ←
hash_map_get_fwd UInt64 hm5
(USize.ofNatCore 1056 (by intlit))
- if not (i3 = (UInt64.ofNatCore 256 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ if h: not (i3 = (UInt64.ofNatCore 256 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [hashmap::test1] -/
-#assert (test1_fwd = .ret ())
+#assert (test1_fwd == .ret ())
diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean
index 9f08bd60..750bf6de 100644
--- a/tests/lean/hashmap/Hashmap/Types.lean
+++ b/tests/lean/hashmap/Hashmap/Types.lean
@@ -13,6 +13,6 @@ 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)
+ hash_map_slots : Vec (list_t T)
diff --git a/tests/lean/hashmap_on_disk/Base/Primitives.lean b/tests/lean/hashmap_on_disk/Base/Primitives.lean
index e230dcab..5b64e908 100644
--- a/tests/lean/hashmap_on_disk/Base/Primitives.lean
+++ b/tests/lean/hashmap_on_disk/Base/Primitives.lean
@@ -21,7 +21,7 @@ open Error
inductive Result (α : Type u) where
| ret (v: α): Result α
- | fail (e: Error): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
open Result
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
index a514c58a..e64419a6 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
@@ -15,17 +15,16 @@ macro_rules
| `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
`(tactic| sorry)
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots]: termination measure -/
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
@[simp]
-def hashmap_hash_map_clear_slots_loop_terminates (T : Type)
+def hashmap_hash_map_clear_loop_terminates (T : Type)
(slots : Vec (hashmap_list_t T)) (i : USize) :=
(slots, i)
-syntax "hashmap_hash_map_clear_slots_loop_decreases" term+ : tactic
+syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
macro_rules
-| `(tactic| hashmap_hash_map_clear_slots_loop_decreases $slots $i) =>
- `(tactic| sorry)
+| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
@[simp]
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
index 392c8816..c85d14f4 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
@@ -60,8 +60,8 @@ def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) :=
hashmap_hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit))
(USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit))
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
-def hashmap_hash_map_clear_slots_loop_fwd_back
+/- [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)))
:=
@@ -73,26 +73,19 @@ def hashmap_hash_map_clear_slots_loop_fwd_back
let slots0 ←
vec_index_mut_back (hashmap_list_t T) slots i
hashmap_list_t.HashmapListNil
- hashmap_hash_map_clear_slots_loop_fwd_back T slots0 i1
+ hashmap_hash_map_clear_loop_fwd_back T slots0 i1
else Result.ret slots
-termination_by hashmap_hash_map_clear_slots_loop_fwd_back slots i =>
- hashmap_hash_map_clear_slots_loop_terminates T slots i
-decreasing_by hashmap_hash_map_clear_slots_loop_decreases slots i
-
-/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
-def hashmap_hash_map_clear_slots_fwd_back
- (T : Type) (slots : Vec (hashmap_list_t T)) :
- Result (Vec (hashmap_list_t T))
- :=
- hashmap_hash_map_clear_slots_loop_fwd_back T slots
- (USize.ofNatCore 0 (by intlit))
+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_slots_fwd_back T self.hashmap_hash_map_slots
+ hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
+ (USize.ofNatCore 0 (by intlit))
Result.ret
{
hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/misc/constants/Base/Primitives.lean
+++ b/tests/lean/misc/constants/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
-- Results & monadic combinators
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
- | assertionFailure: error
- | integerOverflow: error
- | arrayOutOfBounds: error
- | maximumSizeExceeded: error
- | panic: error
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
deriving Repr, BEq
-open error
+open Error
-inductive result (α : Type u) where
- | ret (v: α): result α
- | fail (e: error): result α
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
-open result
+open Result
/- HELPERS -/
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
match r with
- | result.ret _ => true
- | result.fail _ => false
+ | Result.ret _ => true
+ | Result.fail _ => false
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
if b then .ret () else fail assertionFailure
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
match x with
- | result.fail _ => by contradiction
- | result.ret x => x
+ | Result.fail _ => by contradiction
+ | Result.ret x => x
/- DO-DSL SUPPORT -/
-def bind (x: result α) (f: α -> result β) : result β :=
+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
+-- Allows using Result in do-blocks
+instance : Bind Result where
bind := bind
-- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
pure := fun x => ret x
/- CUSTOM-DSL SUPPORT -/
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- 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 : (o : result α) → result { x : α // o = ret x }
+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
+ | .fail e => .fail e
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+ `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$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 h: y <-- .ret (0: Nat)
- let _: y = 0 := by cases h; decide
+ 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
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-- MACHINE INTEGERS --
----------------------
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: 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." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- 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.
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
syntax "intlit" : tactic
@@ -129,12 +125,21 @@ macro_rules
-- Also works for other integer types (at the expense of a needless disjunction)
#eval UInt32.ofNatCore 0 (by intlit)
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
-- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
if n >= m then
let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
else
fail integerOverflow
-def USize.checked_add (n: USize) (m: USize): result USize :=
- if h: n.val.val + m.val.val <= 4294967295 then
- .ret ⟨ n.val.val + m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+ | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+ if h: n.val + m.val < USize.size then
.ret ⟨ n.val + m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
if h: m > 0 then
.ret ⟨ n.val % m.val, by
have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
-def USize.checked_mul (n: USize) (m: USize): result USize :=
- if h: n.val.val * m.val.val <= 4294967295 then
- .ret ⟨ n.val.val * m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+ if h: n.val * m.val < USize.size then
.ret ⟨ n.val * m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
if m > 0 then
.ret ⟨ n.val / m.val, by
have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- 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
@@ -209,30 +223,24 @@ run_cmd
end $typeName
))
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- 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
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
-------------
-- VECTORS --
-------------
-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
-- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
match USize.size, usize_size_eq with
| _, Or.inl rfl => simp
| _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
#check vec_new
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
let ⟨ v, l ⟩ := v
USize.ofNatCore (List.length v) l
#eval vec_len Nat (vec_new Nat)
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
-- make the proof work in that case? Probably need to import tactics from
-- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
:=
if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec
-- annotate `x`, which relieves us of having to write `.val` on the right-hand
-- side of the monadic let.
let v := vec_new Nat
- let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+ let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-- TODO: strengthen post-condition above and do a demo to show that we can
-- safely eliminate the `fail` case
return (vec_len Nat x)
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
if h : List.length v.val + 1 <= 4294967295 then
return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
else
fail maximumSizeExceeded
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
else
.fail arrayOutOfBounds
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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 :=
+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 :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
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
+
--------------------
-- ASSERT COMMAND --
--------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
syntax (name := assert) "#assert" term: command
@[command_elab assert]
+unsafe
def assertImpl : CommandElab := fun (_stx: Syntax) => do
- logInfo "Reducing and asserting: "
- logInfo _stx[1]
runTermElabM (fun _ => do
- let e ← Term.elabTerm _stx[1] none
- logInfo (Expr.dbgToString e)
- -- How to evaluate the term and compare the result to true?
+ 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 ())
- -- logInfo (Expr.dbgToString (``true))
- -- throwError "TODO: assert"
#eval 2 == 2
#assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/misc/constants/Constants.lean b/tests/lean/misc/constants/Constants.lean
index 9ef9ca44..57f6e403 100644
--- a/tests/lean/misc/constants/Constants.lean
+++ b/tests/lean/misc/constants/Constants.lean
@@ -5,64 +5,64 @@ import Base.Primitives
structure OpaqueDefs where
/- [constants::X0] -/
- def x0_body : result UInt32 := result.ret (UInt32.ofNatCore 0 (by intlit))
+ def x0_body : Result UInt32 := Result.ret (UInt32.ofNatCore 0 (by intlit))
def x0_c : UInt32 := eval_global x0_body (by simp)
/- [core::num::u32::{9}::MAX] -/
- def core_num_u32_max_body : result UInt32 :=
- result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+ def core_num_u32_max_body : Result UInt32 :=
+ Result.ret (UInt32.ofNatCore 4294967295 (by intlit))
def core_num_u32_max_c : UInt32 :=
eval_global core_num_u32_max_body (by simp)
/- [constants::X1] -/
- def x1_body : result UInt32 := result.ret core_num_u32_max_c
+ def x1_body : Result UInt32 := Result.ret core_num_u32_max_c
def x1_c : UInt32 := eval_global x1_body (by simp)
/- [constants::X2] -/
- def x2_body : result UInt32 := result.ret (UInt32.ofNatCore 3 (by intlit))
+ def x2_body : Result UInt32 := Result.ret (UInt32.ofNatCore 3 (by intlit))
def x2_c : UInt32 := eval_global x2_body (by simp)
/- [constants::incr] -/
- def incr_fwd (n : UInt32) : result UInt32 :=
+ def incr_fwd (n : UInt32) : Result UInt32 :=
UInt32.checked_add n (UInt32.ofNatCore 1 (by intlit))
/- [constants::X3] -/
- def x3_body : result UInt32 := incr_fwd (UInt32.ofNatCore 32 (by intlit))
+ def x3_body : Result UInt32 := incr_fwd (UInt32.ofNatCore 32 (by intlit))
def x3_c : UInt32 := eval_global x3_body (by simp)
/- [constants::mk_pair0] -/
- def mk_pair0_fwd (x : UInt32) (y : UInt32) : result (UInt32 × UInt32) :=
- result.ret (x, y)
+ def mk_pair0_fwd (x : UInt32) (y : UInt32) : Result (UInt32 × UInt32) :=
+ 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 : UInt32) (y : UInt32) : result (pair_t UInt32 UInt32) :=
- result.ret { pair_x := x, pair_y := y }
+ def mk_pair1_fwd (x : UInt32) (y : UInt32) : Result (pair_t UInt32 UInt32) :=
+ Result.ret { pair_x := x, pair_y := y }
/- [constants::P0] -/
- def p0_body : result (UInt32 × UInt32) :=
+ def p0_body : Result (UInt32 × UInt32) :=
mk_pair0_fwd (UInt32.ofNatCore 0 (by intlit))
(UInt32.ofNatCore 1 (by intlit))
def p0_c : (UInt32 × UInt32) := eval_global p0_body (by simp)
/- [constants::P1] -/
- def p1_body : result (pair_t UInt32 UInt32) :=
+ def p1_body : Result (pair_t UInt32 UInt32) :=
mk_pair1_fwd (UInt32.ofNatCore 0 (by intlit))
(UInt32.ofNatCore 1 (by intlit))
def p1_c : pair_t UInt32 UInt32 := eval_global p1_body (by simp)
/- [constants::P2] -/
- def p2_body : result (UInt32 × UInt32) :=
- result.ret
+ def p2_body : Result (UInt32 × UInt32) :=
+ Result.ret
((UInt32.ofNatCore 0 (by intlit)),
(UInt32.ofNatCore 1 (by intlit)))
def p2_c : (UInt32 × UInt32) := eval_global p2_body (by simp)
/- [constants::P3] -/
- def p3_body : result (pair_t UInt32 UInt32) :=
- result.ret
+ def p3_body : Result (pair_t UInt32 UInt32) :=
+ Result.ret
{
pair_x := (UInt32.ofNatCore 0 (by intlit)),
pair_y := (UInt32.ofNatCore 1 (by intlit))
@@ -73,68 +73,68 @@ structure OpaqueDefs where
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 }
+ 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 Int32) :=
+ def y_body : Result (wrap_t Int32) :=
wrap_new_fwd Int32 (Int32.ofNatCore 2 (by intlit))
def y_c : wrap_t Int32 := eval_global y_body (by simp)
/- [constants::unwrap_y] -/
- def unwrap_y_fwd : result Int32 :=
- result.ret y_c.wrap_val
+ def unwrap_y_fwd : Result Int32 :=
+ Result.ret y_c.wrap_val
/- [constants::YVAL] -/
- def yval_body : result Int32 := unwrap_y_fwd
+ def yval_body : Result Int32 := unwrap_y_fwd
def yval_c : Int32 := eval_global yval_body (by simp)
/- [constants::get_z1::Z1] -/
- def get_z1_z1_body : result Int32 :=
- result.ret (Int32.ofNatCore 3 (by intlit))
+ def get_z1_z1_body : Result Int32 :=
+ Result.ret (Int32.ofNatCore 3 (by intlit))
def get_z1_z1_c : Int32 := eval_global get_z1_z1_body (by simp)
/- [constants::get_z1] -/
- def get_z1_fwd : result Int32 :=
- result.ret get_z1_z1_c
+ def get_z1_fwd : Result Int32 :=
+ Result.ret get_z1_z1_c
/- [constants::add] -/
- def add_fwd (a : Int32) (b : Int32) : result Int32 :=
+ def add_fwd (a : Int32) (b : Int32) : Result Int32 :=
Int32.checked_add a b
/- [constants::Q1] -/
- def q1_body : result Int32 := result.ret (Int32.ofNatCore 5 (by intlit))
+ def q1_body : Result Int32 := Result.ret (Int32.ofNatCore 5 (by intlit))
def q1_c : Int32 := eval_global q1_body (by simp)
/- [constants::Q2] -/
- def q2_body : result Int32 := result.ret q1_c
+ def q2_body : Result Int32 := Result.ret q1_c
def q2_c : Int32 := eval_global q2_body (by simp)
/- [constants::Q3] -/
- def q3_body : result Int32 := add_fwd q2_c (Int32.ofNatCore 3 (by intlit))
+ def q3_body : Result Int32 := add_fwd q2_c (Int32.ofNatCore 3 (by intlit))
def q3_c : Int32 := eval_global q3_body (by simp)
/- [constants::get_z2] -/
- def get_z2_fwd : result Int32 :=
+ def get_z2_fwd : Result Int32 :=
do
- let i <- get_z1_fwd
- let i0 <- add_fwd i q3_c
+ let i ← get_z1_fwd
+ let i0 ← add_fwd i q3_c
add_fwd q1_c i0
/- [constants::S1] -/
- def s1_body : result UInt32 := result.ret (UInt32.ofNatCore 6 (by intlit))
+ def s1_body : Result UInt32 := Result.ret (UInt32.ofNatCore 6 (by intlit))
def s1_c : UInt32 := eval_global s1_body (by simp)
/- [constants::S2] -/
- def s2_body : result UInt32 := incr_fwd s1_c
+ def s2_body : Result UInt32 := incr_fwd s1_c
def s2_c : UInt32 := eval_global s2_body (by simp)
/- [constants::S3] -/
- def s3_body : result (pair_t UInt32 UInt32) := result.ret p3_c
+ def s3_body : Result (pair_t UInt32 UInt32) := Result.ret p3_c
def s3_c : pair_t UInt32 UInt32 := eval_global s3_body (by simp)
/- [constants::S4] -/
- def s4_body : result (pair_t UInt32 UInt32) :=
+ def s4_body : Result (pair_t UInt32 UInt32) :=
mk_pair1_fwd (UInt32.ofNatCore 7 (by intlit))
(UInt32.ofNatCore 8 (by intlit))
def s4_c : pair_t UInt32 UInt32 := eval_global s4_body (by simp)
diff --git a/tests/lean/misc/external/Base/Primitives.lean b/tests/lean/misc/external/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/misc/external/Base/Primitives.lean
+++ b/tests/lean/misc/external/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
-- Results & monadic combinators
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
- | assertionFailure: error
- | integerOverflow: error
- | arrayOutOfBounds: error
- | maximumSizeExceeded: error
- | panic: error
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
deriving Repr, BEq
-open error
+open Error
-inductive result (α : Type u) where
- | ret (v: α): result α
- | fail (e: error): result α
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
-open result
+open Result
/- HELPERS -/
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
match r with
- | result.ret _ => true
- | result.fail _ => false
+ | Result.ret _ => true
+ | Result.fail _ => false
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
if b then .ret () else fail assertionFailure
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
match x with
- | result.fail _ => by contradiction
- | result.ret x => x
+ | Result.fail _ => by contradiction
+ | Result.ret x => x
/- DO-DSL SUPPORT -/
-def bind (x: result α) (f: α -> result β) : result β :=
+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
+-- Allows using Result in do-blocks
+instance : Bind Result where
bind := bind
-- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
pure := fun x => ret x
/- CUSTOM-DSL SUPPORT -/
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- 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 : (o : result α) → result { x : α // o = ret x }
+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
+ | .fail e => .fail e
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+ `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$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 h: y <-- .ret (0: Nat)
- let _: y = 0 := by cases h; decide
+ 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
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-- MACHINE INTEGERS --
----------------------
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: 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." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- 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.
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
syntax "intlit" : tactic
@@ -129,12 +125,21 @@ macro_rules
-- Also works for other integer types (at the expense of a needless disjunction)
#eval UInt32.ofNatCore 0 (by intlit)
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
-- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
if n >= m then
let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
else
fail integerOverflow
-def USize.checked_add (n: USize) (m: USize): result USize :=
- if h: n.val.val + m.val.val <= 4294967295 then
- .ret ⟨ n.val.val + m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+ | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+ if h: n.val + m.val < USize.size then
.ret ⟨ n.val + m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
if h: m > 0 then
.ret ⟨ n.val % m.val, by
have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
-def USize.checked_mul (n: USize) (m: USize): result USize :=
- if h: n.val.val * m.val.val <= 4294967295 then
- .ret ⟨ n.val.val * m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+ if h: n.val * m.val < USize.size then
.ret ⟨ n.val * m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
if m > 0 then
.ret ⟨ n.val / m.val, by
have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- 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
@@ -209,30 +223,24 @@ run_cmd
end $typeName
))
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- 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
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
-------------
-- VECTORS --
-------------
-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
-- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
match USize.size, usize_size_eq with
| _, Or.inl rfl => simp
| _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
#check vec_new
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
let ⟨ v, l ⟩ := v
USize.ofNatCore (List.length v) l
#eval vec_len Nat (vec_new Nat)
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
-- make the proof work in that case? Probably need to import tactics from
-- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
:=
if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec
-- annotate `x`, which relieves us of having to write `.val` on the right-hand
-- side of the monadic let.
let v := vec_new Nat
- let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+ let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-- TODO: strengthen post-condition above and do a demo to show that we can
-- safely eliminate the `fail` case
return (vec_len Nat x)
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
if h : List.length v.val + 1 <= 4294967295 then
return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
else
fail maximumSizeExceeded
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
else
.fail arrayOutOfBounds
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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 :=
+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 :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
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
+
--------------------
-- ASSERT COMMAND --
--------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
syntax (name := assert) "#assert" term: command
@[command_elab assert]
+unsafe
def assertImpl : CommandElab := fun (_stx: Syntax) => do
- logInfo "Reducing and asserting: "
- logInfo _stx[1]
runTermElabM (fun _ => do
- let e ← Term.elabTerm _stx[1] none
- logInfo (Expr.dbgToString e)
- -- How to evaluate the term and compare the result to true?
+ 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 ())
- -- logInfo (Expr.dbgToString (``true))
- -- throwError "TODO: assert"
#eval 2 == 2
#assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/misc/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean
index bb1e296d..4e1f36a1 100644
--- a/tests/lean/misc/external/External/Funs.lean
+++ b/tests/lean/misc/external/External/Funs.lean
@@ -8,86 +8,86 @@ section variable (opaque_defs: OpaqueDefs)
/- [external::swap] -/
def swap_fwd
- (T : Type) (x : T) (y : T) (st : state) : result (state × Unit) :=
+ (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, ())
+ 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))
+ (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))
+ 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 : UInt32) (st : state) :
- result (state × core_num_nonzero_non_zero_u32_t)
+ (x : UInt32) (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
+ 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 :=
+def test_vec_fwd : Result Unit :=
do
let v := vec_new UInt32
- let _ <- vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit))
- result.ret ()
+ let _ ← vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit))
+ Result.ret ()
/- Unit test for [external::test_vec] -/
-#assert (test_vec_fwd = .ret ())
+#assert (test_vec_fwd == .ret ())
/- [external::custom_swap] -/
def custom_swap_fwd
- (T : Type) (x : T) (y : T) (st : state) : result (state × T) :=
+ (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)
+ 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))
+ (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))
+ 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 : UInt32) (y : UInt32) (st : state) : result (state × Unit) :=
+ (x : UInt32) (y : UInt32) (st : State) : Result (State × Unit) :=
do
- let (st0, _) <- custom_swap_fwd UInt32 x y st
- result.ret (st0, ())
+ let (st0, _) ← custom_swap_fwd UInt32 x y st
+ Result.ret (st0, ())
/- [external::test_custom_swap] -/
def test_custom_swap_back
- (x : UInt32) (y : UInt32) (st : state) (st0 : state) :
- result (state × (UInt32 × UInt32))
+ (x : UInt32) (y : UInt32) (st : State) (st0 : State) :
+ Result (State × (UInt32 × UInt32))
:=
custom_swap_back UInt32 x y st (UInt32.ofNatCore 1 (by intlit)) st0
/- [external::test_swap_non_zero] -/
def test_swap_non_zero_fwd
- (x : UInt32) (st : state) : result (state × UInt32) :=
+ (x : UInt32) (st : State) : Result (State × UInt32) :=
do
- let (st0, _) <- swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st
- let (st1, (x0, _)) <-
+ let (st0, _) ← swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st
+ let (st1, (x0, _)) ←
swap_back UInt32 x (UInt32.ofNatCore 0 (by intlit)) st st0
- if x0 = (UInt32.ofNatCore 0 (by intlit))
- then result.fail error.panic
- else result.ret (st1, x0)
+ if h: x0 = (UInt32.ofNatCore 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
index 40ccc313..d3582de3 100644
--- a/tests/lean/misc/external/External/Opaque.lean
+++ b/tests/lean/misc/external/External/Opaque.lean
@@ -6,23 +6,23 @@ import External.Types
structure OpaqueDefs where
/- [core::mem::swap] -/
- core_mem_swap_fwd (T : Type) : T -> T -> state -> result (state × Unit)
+ 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)
+ (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)
+ (T : Type) : T -> T -> State -> State -> Result (State × T)
/- [core::num::nonzero::NonZeroU32::{14}::new] -/
core_num_nonzero_non_zero_u32_new_fwd
:
- UInt32 -> state -> result (state × (Option
+ UInt32 -> 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)
+ (T : Type) : Option T -> State -> Result (State × T)
diff --git a/tests/lean/misc/external/External/Types.lean b/tests/lean/misc/external/External/Types.lean
index b6fa292b..386832f4 100644
--- a/tests/lean/misc/external/External/Types.lean
+++ b/tests/lean/misc/external/External/Types.lean
@@ -4,5 +4,5 @@ import Base.Primitives
/- [core::num::nonzero::NonZeroU32] -/
axiom core_num_nonzero_non_zero_u32_t : Type
-/- The state type used in the state-error monad -/ axiom state : Type
+/- The state type used in the state-error monad -/ axiom State : Type
diff --git a/tests/lean/misc/loops/Base/Primitives.lean b/tests/lean/misc/loops/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/misc/loops/Base/Primitives.lean
+++ b/tests/lean/misc/loops/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
-- Results & monadic combinators
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
- | assertionFailure: error
- | integerOverflow: error
- | arrayOutOfBounds: error
- | maximumSizeExceeded: error
- | panic: error
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
deriving Repr, BEq
-open error
+open Error
-inductive result (α : Type u) where
- | ret (v: α): result α
- | fail (e: error): result α
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
-open result
+open Result
/- HELPERS -/
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
match r with
- | result.ret _ => true
- | result.fail _ => false
+ | Result.ret _ => true
+ | Result.fail _ => false
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
if b then .ret () else fail assertionFailure
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
match x with
- | result.fail _ => by contradiction
- | result.ret x => x
+ | Result.fail _ => by contradiction
+ | Result.ret x => x
/- DO-DSL SUPPORT -/
-def bind (x: result α) (f: α -> result β) : result β :=
+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
+-- Allows using Result in do-blocks
+instance : Bind Result where
bind := bind
-- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
pure := fun x => ret x
/- CUSTOM-DSL SUPPORT -/
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- 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 : (o : result α) → result { x : α // o = ret x }
+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
+ | .fail e => .fail e
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+ `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$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 h: y <-- .ret (0: Nat)
- let _: y = 0 := by cases h; decide
+ 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
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-- MACHINE INTEGERS --
----------------------
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: 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." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- 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.
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
syntax "intlit" : tactic
@@ -129,12 +125,21 @@ macro_rules
-- Also works for other integer types (at the expense of a needless disjunction)
#eval UInt32.ofNatCore 0 (by intlit)
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
-- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
if n >= m then
let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
else
fail integerOverflow
-def USize.checked_add (n: USize) (m: USize): result USize :=
- if h: n.val.val + m.val.val <= 4294967295 then
- .ret ⟨ n.val.val + m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+ | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+ if h: n.val + m.val < USize.size then
.ret ⟨ n.val + m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
if h: m > 0 then
.ret ⟨ n.val % m.val, by
have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
-def USize.checked_mul (n: USize) (m: USize): result USize :=
- if h: n.val.val * m.val.val <= 4294967295 then
- .ret ⟨ n.val.val * m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+ if h: n.val * m.val < USize.size then
.ret ⟨ n.val * m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
if m > 0 then
.ret ⟨ n.val / m.val, by
have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- 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
@@ -209,30 +223,24 @@ run_cmd
end $typeName
))
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- 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
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
-------------
-- VECTORS --
-------------
-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
-- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
match USize.size, usize_size_eq with
| _, Or.inl rfl => simp
| _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
#check vec_new
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
let ⟨ v, l ⟩ := v
USize.ofNatCore (List.length v) l
#eval vec_len Nat (vec_new Nat)
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
-- make the proof work in that case? Probably need to import tactics from
-- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
:=
if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec
-- annotate `x`, which relieves us of having to write `.val` on the right-hand
-- side of the monadic let.
let v := vec_new Nat
- let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+ let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-- TODO: strengthen post-condition above and do a demo to show that we can
-- safely eliminate the `fail` case
return (vec_len Nat x)
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
if h : List.length v.val + 1 <= 4294967295 then
return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
else
fail maximumSizeExceeded
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
else
.fail arrayOutOfBounds
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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 :=
+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 :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
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
+
--------------------
-- ASSERT COMMAND --
--------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
syntax (name := assert) "#assert" term: command
@[command_elab assert]
+unsafe
def assertImpl : CommandElab := fun (_stx: Syntax) => do
- logInfo "Reducing and asserting: "
- logInfo _stx[1]
runTermElabM (fun _ => do
- let e ← Term.elabTerm _stx[1] none
- logInfo (Expr.dbgToString e)
- -- How to evaluate the term and compare the result to true?
+ 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 ())
- -- logInfo (Expr.dbgToString (``true))
- -- throwError "TODO: assert"
#eval 2 == 2
#assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/misc/loops/Loops/Clauses/Template.lean b/tests/lean/misc/loops/Loops/Clauses/Template.lean
index 3c0f2f7c..d74f71e1 100644
--- a/tests/lean/misc/loops/Loops/Clauses/Template.lean
+++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean
@@ -35,7 +35,7 @@ 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 UInt32) (i : USize) := (v, i)
+@[simp] def clear_loop_terminates (v : Vec UInt32) (i : USize) := (v, i)
syntax "clear_loop_decreases" term+ : tactic
diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean
index 55f0c87d..5a81ebff 100644
--- a/tests/lean/misc/loops/Loops/Funs.lean
+++ b/tests/lean/misc/loops/Loops/Funs.lean
@@ -5,30 +5,30 @@ import Loops.Types
import Loops.Clauses.Clauses
/- [loops::sum] -/
-def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
- if i < max
+def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) :=
+ if h: i < max
then
do
- let s0 <- UInt32.checked_add s i
- let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+ let s0 ← UInt32.checked_add s i
+ let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
sum_loop_fwd max i0 s0
else UInt32.checked_mul s (UInt32.ofNatCore 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 : UInt32) : result UInt32 :=
+def sum_fwd (max : UInt32) : Result UInt32 :=
sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
(UInt32.ofNatCore 0 (by intlit))
/- [loops::sum_with_mut_borrows] -/
def sum_with_mut_borrows_loop_fwd
- (max : UInt32) (mi : UInt32) (ms : UInt32) : (result UInt32) :=
- if mi < max
+ (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) :=
+ if h: mi < max
then
do
- let ms0 <- UInt32.checked_add ms mi
- let mi0 <- UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
+ let ms0 ← UInt32.checked_add ms mi
+ let mi0 ← UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
sum_with_mut_borrows_loop_fwd max mi0 ms0
else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit))
termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
@@ -36,18 +36,18 @@ termination_by sum_with_mut_borrows_loop_fwd 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 : UInt32) : result UInt32 :=
+def sum_with_mut_borrows_fwd (max : UInt32) : Result UInt32 :=
sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
(UInt32.ofNatCore 0 (by intlit))
/- [loops::sum_with_shared_borrows] -/
def sum_with_shared_borrows_loop_fwd
- (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
- if i < max
+ (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) :=
+ if h: i < max
then
do
- let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
- let s0 <- UInt32.checked_add s i0
+ let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+ let s0 ← UInt32.checked_add s i0
sum_with_shared_borrows_loop_fwd max i0 s0
else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
termination_by sum_with_shared_borrows_loop_fwd max i s =>
@@ -55,271 +55,272 @@ termination_by sum_with_shared_borrows_loop_fwd 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 : UInt32) : result UInt32 :=
+def sum_with_shared_borrows_fwd (max : UInt32) : Result UInt32 :=
sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
(UInt32.ofNatCore 0 (by intlit))
/- [loops::clear] -/
-def clear_loop_fwd_back (v : vec UInt32) (i : USize) : (result (vec UInt32)) :=
+def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) :=
let i0 := vec_len UInt32 v
- if i < i0
+ if h: i < i0
then
do
- let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
- let v0 <- vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit))
+ let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit))
+ let v0 ← vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit))
clear_loop_fwd_back v0 i1
- else result.ret v
+ 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 UInt32) : result (vec UInt32) :=
+def clear_fwd_back (v : Vec UInt32) : Result (Vec UInt32) :=
clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit))
/- [loops::list_mem] -/
-def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (result Bool) :=
- match ls with
+def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) :=
+ match h: ls with
| list_t.ListCons y tl =>
- if y = x
- then result.ret true
+ if h: y = x
+ then Result.ret true
else list_mem_loop_fwd x tl
- | list_t.ListNil => result.ret false
+ | list_t.ListNil => 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 : UInt32) (ls : list_t UInt32) : result Bool :=
+def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : 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 : UInt32) : (result T) :=
- match ls with
+ (T : Type) (ls : list_t T) (i : UInt32) : (Result T) :=
+ match h: ls with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_loop_loop_fwd T tl i0
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 : UInt32) : result T :=
+def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : 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 : UInt32) (ret0 : T) : (result (list_t T)) :=
- match ls with
+ (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (Result (list_t T)) :=
+ match h: ls with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl0 <- list_nth_mut_loop_loop_back T tl i0 ret0
- result.ret (list_t.ListCons x tl0)
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+ Result.ret (list_t.ListCons x tl0)
+ | list_t.ListNil => 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 : UInt32) (ret0 : T) : result (list_t T) :=
+ (T : Type) (ls : list_t T) (i : UInt32) (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 : UInt32) : (result T) :=
- match ls with
+ (T : Type) (ls : list_t T) (i : UInt32) : (Result T) :=
+ match h: ls with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_loop_loop_fwd T tl i0
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 : UInt32) : result T :=
+ (T : Type) (ls : list_t T) (i : UInt32) : 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 ls with
+def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (Result USize) :=
+ match h: ls with
| list_t.ListCons y tl =>
- if y = x
- then result.ret y
+ if h: y = x
+ then Result.ret y
else get_elem_mut_loop_fwd x tl
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 :=
+def get_elem_mut_fwd (slots : Vec (list_t USize)) (x : USize) : Result USize :=
do
- let l <-
+ let l ←
vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 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 ls with
+ (x : USize) (ls : list_t USize) (ret0 : USize) : (Result (list_t USize)) :=
+ match h: ls with
| list_t.ListCons y tl =>
- if y = x
- then result.ret (list_t.ListCons ret0 tl)
+ if h: y = x
+ then Result.ret (list_t.ListCons ret0 tl)
else
do
- let tl0 <- get_elem_mut_loop_back x tl ret0
- result.ret (list_t.ListCons y tl0)
- | list_t.ListNil => result.fail error.panic
+ let tl0 ← get_elem_mut_loop_back x tl ret0
+ Result.ret (list_t.ListCons y tl0)
+ | list_t.ListNil => 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))
+ (slots : Vec (list_t USize)) (x : USize) (ret0 : USize) :
+ Result (Vec (list_t USize))
:=
do
- let l <-
+ let l ←
vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
- let l0 <- get_elem_mut_loop_back x l ret0
+ let l0 ← get_elem_mut_loop_back x l ret0
vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0
/- [loops::get_elem_shared] -/
def get_elem_shared_loop_fwd
- (x : USize) (ls : list_t USize) : (result USize) :=
- match ls with
+ (x : USize) (ls : list_t USize) : (Result USize) :=
+ match h: ls with
| list_t.ListCons y tl =>
- if y = x
- then result.ret y
+ if h: y = x
+ then Result.ret y
else get_elem_shared_loop_fwd x tl
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 :=
+ (slots : Vec (list_t USize)) (x : USize) : Result USize :=
do
- let l <- vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+ let l ←
+ vec_index_fwd (list_t USize) slots (USize.ofNatCore 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
+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
+ (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
+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 : UInt32) (ls : list_t T) : (result T) :=
- match ls with
+ (T : Type) (i : UInt32) (ls : list_t T) : (Result T) :=
+ match h: ls with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_loop_with_id_loop_fwd T i0 tl
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 : UInt32) : result T :=
+ (T : Type) (ls : list_t T) (i : UInt32) : Result T :=
do
- let ls0 <- id_mut_fwd T ls
+ 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 : UInt32) (ls : list_t T) (ret0 : T) : (result (list_t T)) :=
- match ls with
+ (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) :=
+ match h: ls with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl0 <- list_nth_mut_loop_with_id_loop_back T i0 tl ret0
- result.ret (list_t.ListCons x tl0)
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+ Result.ret (list_t.ListCons x tl0)
+ | list_t.ListNil => 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 : UInt32) (ret0 : T) : result (list_t T) :=
+ (T : Type) (ls : list_t T) (i : UInt32) (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
+ 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 : UInt32) (ls : list_t T) : (result T) :=
- match ls with
+ (T : Type) (i : UInt32) (ls : list_t T) : (Result T) :=
+ match h: ls with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_loop_with_id_loop_fwd T i0 tl
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => 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 : UInt32) : result T :=
+ (T : Type) (ls : list_t T) (i : UInt32) : Result T :=
do
- let ls0 <- id_shared_fwd T ls
+ 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -327,28 +328,28 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) (ret0 : T) :
- (result (list_t T))
+ (Result (list_t T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl0)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl0)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl00 <- list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x0 tl00)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+ Result.ret (list_t.ListCons x0 tl00)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -356,28 +357,28 @@ 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 : UInt32) (ret0 : T) :
- result (list_t 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 : UInt32) (ret0 : T) :
- (result (list_t T))
+ (Result (list_t T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl10 <- list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x1 tl10)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+ Result.ret (list_t.ListCons x1 tl10)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -385,27 +386,27 @@ 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 : UInt32) (ret0 : T) :
- result (list_t 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -413,27 +414,27 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -441,31 +442,31 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) (ret0 : (T × T)) :
- (result ((list_t T) × (list_t T)))
+ (Result ((list_t T) × (list_t T)))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
then
let (t, t0) := ret0
- result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
+ Result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let (tl00, tl10) <-
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let (tl00, tl10) ←
list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ Result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -473,27 +474,27 @@ 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 : UInt32) (ret0 : (T × T)) :
- result ((list_t T) × (list_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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -501,27 +502,27 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -529,28 +530,29 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) (ret0 : T) :
- (result (list_t T))
+ (Result (list_t T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl0)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl0)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl00 <- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x0 tl00)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl00 ←
+ list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+ Result.ret (list_t.ListCons x0 tl00)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -558,27 +560,27 @@ 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 : UInt32) (ret0 : T) :
- result (list_t 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -586,29 +588,29 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) (ret0 : T) :
- (result (list_t T))
+ (Result (list_t T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl0)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl0)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl00 <-
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl00 ←
list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x0 tl00)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ Result.ret (list_t.ListCons x0 tl00)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -616,27 +618,27 @@ 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 : UInt32) (ret0 : T) :
- result (list_t 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -644,28 +646,29 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) (ret0 : T) :
- (result (list_t T))
+ (Result (list_t T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl10 <- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x1 tl10)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl10 ←
+ list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+ Result.ret (list_t.ListCons x1 tl10)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -673,27 +676,27 @@ 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 : UInt32) (ret0 : T) :
- result (list_t 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 : UInt32) :
- (result (T × T))
+ (Result (T × T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (x0, x1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (x0, x1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -701,29 +704,29 @@ 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 : UInt32) :
- result (T × T)
+ 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 : UInt32) (ret0 : T) :
- (result (list_t T))
+ (Result (list_t T))
:=
- match ls0 with
+ match h: ls0 with
| list_t.ListCons x0 tl0 =>
- match ls1 with
+ match h: ls1 with
| list_t.ListCons x1 tl1 =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl1)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl1)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl10 <-
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl10 ←
list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
- result.ret (list_t.ListCons x1 tl10)
- | list_t.ListNil => result.fail error.panic
- | list_t.ListNil => result.fail error.panic
+ Result.ret (list_t.ListCons x1 tl10)
+ | list_t.ListNil => Result.fail Error.panic
+ | list_t.ListNil => 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
@@ -731,7 +734,7 @@ 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 : UInt32) (ret0 : T) :
- result (list_t 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/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
+++ b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
-- Results & monadic combinators
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
- | assertionFailure: error
- | integerOverflow: error
- | arrayOutOfBounds: error
- | maximumSizeExceeded: error
- | panic: error
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
deriving Repr, BEq
-open error
+open Error
-inductive result (α : Type u) where
- | ret (v: α): result α
- | fail (e: error): result α
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
-open result
+open Result
/- HELPERS -/
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
match r with
- | result.ret _ => true
- | result.fail _ => false
+ | Result.ret _ => true
+ | Result.fail _ => false
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
if b then .ret () else fail assertionFailure
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
match x with
- | result.fail _ => by contradiction
- | result.ret x => x
+ | Result.fail _ => by contradiction
+ | Result.ret x => x
/- DO-DSL SUPPORT -/
-def bind (x: result α) (f: α -> result β) : result β :=
+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
+-- Allows using Result in do-blocks
+instance : Bind Result where
bind := bind
-- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
pure := fun x => ret x
/- CUSTOM-DSL SUPPORT -/
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- 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 : (o : result α) → result { x : α // o = ret x }
+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
+ | .fail e => .fail e
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+ `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$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 h: y <-- .ret (0: Nat)
- let _: y = 0 := by cases h; decide
+ 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
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-- MACHINE INTEGERS --
----------------------
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: 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." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- 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.
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
syntax "intlit" : tactic
@@ -129,12 +125,21 @@ macro_rules
-- Also works for other integer types (at the expense of a needless disjunction)
#eval UInt32.ofNatCore 0 (by intlit)
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
-- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
if n >= m then
let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
else
fail integerOverflow
-def USize.checked_add (n: USize) (m: USize): result USize :=
- if h: n.val.val + m.val.val <= 4294967295 then
- .ret ⟨ n.val.val + m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+ | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+ if h: n.val + m.val < USize.size then
.ret ⟨ n.val + m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
if h: m > 0 then
.ret ⟨ n.val % m.val, by
have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
-def USize.checked_mul (n: USize) (m: USize): result USize :=
- if h: n.val.val * m.val.val <= 4294967295 then
- .ret ⟨ n.val.val * m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+ if h: n.val * m.val < USize.size then
.ret ⟨ n.val * m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
if m > 0 then
.ret ⟨ n.val / m.val, by
have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- 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
@@ -209,30 +223,24 @@ run_cmd
end $typeName
))
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- 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
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
-------------
-- VECTORS --
-------------
-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
-- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
match USize.size, usize_size_eq with
| _, Or.inl rfl => simp
| _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
#check vec_new
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
let ⟨ v, l ⟩ := v
USize.ofNatCore (List.length v) l
#eval vec_len Nat (vec_new Nat)
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
-- make the proof work in that case? Probably need to import tactics from
-- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
:=
if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec
-- annotate `x`, which relieves us of having to write `.val` on the right-hand
-- side of the monadic let.
let v := vec_new Nat
- let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+ let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-- TODO: strengthen post-condition above and do a demo to show that we can
-- safely eliminate the `fail` case
return (vec_len Nat x)
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
if h : List.length v.val + 1 <= 4294967295 then
return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
else
fail maximumSizeExceeded
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
else
.fail arrayOutOfBounds
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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 :=
+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 :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
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
+
--------------------
-- ASSERT COMMAND --
--------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
syntax (name := assert) "#assert" term: command
@[command_elab assert]
+unsafe
def assertImpl : CommandElab := fun (_stx: Syntax) => do
- logInfo "Reducing and asserting: "
- logInfo _stx[1]
runTermElabM (fun _ => do
- let e ← Term.elabTerm _stx[1] none
- logInfo (Expr.dbgToString e)
- -- How to evaluate the term and compare the result to true?
+ 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 ())
- -- logInfo (Expr.dbgToString (``true))
- -- throwError "TODO: assert"
#eval 2 == 2
#assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
index 608aabc1..a20ee9fd 100644
--- a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
+++ b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
@@ -30,232 +30,234 @@ structure OpaqueDefs where
| SumRight : T2 -> sum_t T1 T2
/- [no_nested_borrows::neg_test] -/
- def neg_test_fwd (x : Int32) : result Int32 :=
+ def neg_test_fwd (x : Int32) : Result Int32 :=
Int32.checked_neg x
/- [no_nested_borrows::add_test] -/
- def add_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+ def add_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 :=
UInt32.checked_add x y
/- [no_nested_borrows::subs_test] -/
- def subs_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+ def subs_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 :=
UInt32.checked_sub x y
/- [no_nested_borrows::div_test] -/
- def div_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+ def div_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 :=
UInt32.checked_div x y
/- [no_nested_borrows::div_test1] -/
- def div_test1_fwd (x : UInt32) : result UInt32 :=
+ def div_test1_fwd (x : UInt32) : Result UInt32 :=
UInt32.checked_div x (UInt32.ofNatCore 2 (by intlit))
/- [no_nested_borrows::rem_test] -/
- def rem_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+ def rem_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 :=
UInt32.checked_rem x y
/- [no_nested_borrows::cast_test] -/
- def cast_test_fwd (x : UInt32) : result Int32 :=
+ def cast_test_fwd (x : UInt32) : Result Int32 :=
scalar_cast Int32 x
/- [no_nested_borrows::test2] -/
- def test2_fwd : result Unit :=
+ def test2_fwd : Result Unit :=
do
- let _ <- UInt32.checked_add (UInt32.ofNatCore 23 (by intlit))
+ let _ ← UInt32.checked_add (UInt32.ofNatCore 23 (by intlit))
(UInt32.ofNatCore 44 (by intlit))
- result.ret ()
+ Result.ret ()
/- Unit test for [no_nested_borrows::test2] -/
- #assert (test2_fwd = .ret ())
+ #assert (test2_fwd == .ret ())
/- [no_nested_borrows::get_max] -/
- def get_max_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
- if x >= y
- then result.ret x
- else result.ret y
+ def get_max_fwd (x : UInt32) (y : UInt32) : Result UInt32 :=
+ if h: x >= y
+ then Result.ret x
+ else Result.ret y
/- [no_nested_borrows::test3] -/
- def test3_fwd : result Unit :=
+ def test3_fwd : Result Unit :=
do
- let x <-
+ let x ←
get_max_fwd (UInt32.ofNatCore 4 (by intlit))
(UInt32.ofNatCore 3 (by intlit))
- let y <-
+ let y ←
get_max_fwd (UInt32.ofNatCore 10 (by intlit))
(UInt32.ofNatCore 11 (by intlit))
- let z <- UInt32.checked_add x y
- if not (z = (UInt32.ofNatCore 15 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ let z ← UInt32.checked_add x y
+ if h: not (z = (UInt32.ofNatCore 15 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::test3] -/
- #assert (test3_fwd = .ret ())
+ #assert (test3_fwd == .ret ())
/- [no_nested_borrows::test_neg1] -/
- def test_neg1_fwd : result Unit :=
+ def test_neg1_fwd : Result Unit :=
do
- let y <- Int32.checked_neg (Int32.ofNatCore 3 (by intlit))
- if not (y = (Int32.ofNatCore -3 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ let y ← Int32.checked_neg (Int32.ofNatCore 3 (by intlit))
+ if h: not (y = (Int32.ofNatCore -3 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::test_neg1] -/
- #assert (test_neg1_fwd = .ret ())
+ #assert (test_neg1_fwd == .ret ())
/- [no_nested_borrows::refs_test1] -/
- def refs_test1_fwd : result Unit :=
- if not ((Int32.ofNatCore 1 (by intlit)) = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ def refs_test1_fwd : Result Unit :=
+ if h: not ((Int32.ofNatCore 1 (by intlit)) =
+ (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::refs_test1] -/
- #assert (refs_test1_fwd = .ret ())
+ #assert (refs_test1_fwd == .ret ())
/- [no_nested_borrows::refs_test2] -/
- def refs_test2_fwd : result Unit :=
- if not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit)))
- then result.fail error.panic
+ def refs_test2_fwd : Result Unit :=
+ if h: not ((Int32.ofNatCore 2 (by intlit)) =
+ (Int32.ofNatCore 2 (by intlit)))
+ then Result.fail Error.panic
else
- if not ((Int32.ofNatCore 0 (by intlit)) =
+ if h: not ((Int32.ofNatCore 0 (by intlit)) =
(Int32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
+ then Result.fail Error.panic
else
- if not ((Int32.ofNatCore 2 (by intlit)) =
+ if h: not ((Int32.ofNatCore 2 (by intlit)) =
(Int32.ofNatCore 2 (by intlit)))
- then result.fail error.panic
+ then Result.fail Error.panic
else
- if not ((Int32.ofNatCore 2 (by intlit)) =
+ if h: not ((Int32.ofNatCore 2 (by intlit)) =
(Int32.ofNatCore 2 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::refs_test2] -/
- #assert (refs_test2_fwd = .ret ())
+ #assert (refs_test2_fwd == .ret ())
/- [no_nested_borrows::test_list1] -/
- def test_list1_fwd : result Unit :=
- result.ret ()
+ def test_list1_fwd : Result Unit :=
+ Result.ret ()
/- Unit test for [no_nested_borrows::test_list1] -/
- #assert (test_list1_fwd = .ret ())
+ #assert (test_list1_fwd == .ret ())
/- [no_nested_borrows::test_box1] -/
- def test_box1_fwd : result Unit :=
+ def test_box1_fwd : Result Unit :=
let b := (Int32.ofNatCore 1 (by intlit))
let x := b
- if not (x = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ if h: not (x = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::test_box1] -/
- #assert (test_box1_fwd = .ret ())
+ #assert (test_box1_fwd == .ret ())
/- [no_nested_borrows::copy_int] -/
- def copy_int_fwd (x : Int32) : result Int32 :=
- result.ret x
+ def copy_int_fwd (x : Int32) : Result Int32 :=
+ Result.ret x
/- [no_nested_borrows::test_unreachable] -/
- def test_unreachable_fwd (b : Bool) : result Unit :=
- if b
- then result.fail error.panic
- else result.ret ()
+ 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 b
- then result.fail error.panic
- else result.ret ()
+ 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 :=
+ def test_copy_int_fwd : Result Unit :=
do
- let y <- copy_int_fwd (Int32.ofNatCore 0 (by intlit))
- if not ((Int32.ofNatCore 0 (by intlit)) = y)
- then result.fail error.panic
- else result.ret ()
+ let y ← copy_int_fwd (Int32.ofNatCore 0 (by intlit))
+ if h: not ((Int32.ofNatCore 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 ())
+ #assert (test_copy_int_fwd == .ret ())
/- [no_nested_borrows::is_cons] -/
- def is_cons_fwd (T : Type) (l : list_t T) : result Bool :=
- match l with
- | list_t.ListCons t l0 => result.ret true
- | list_t.ListNil => result.ret false
+ def is_cons_fwd (T : Type) (l : list_t T) : Result Bool :=
+ match h: l with
+ | list_t.ListCons t l0 => Result.ret true
+ | list_t.ListNil => Result.ret false
/- [no_nested_borrows::test_is_cons] -/
- def test_is_cons_fwd : result Unit :=
+ def test_is_cons_fwd : Result Unit :=
do
let l := list_t.ListNil
- let b <-
+ let b ←
is_cons_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) l)
- if not b
- then result.fail error.panic
- else result.ret ()
+ 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 ())
+ #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 l with
- | list_t.ListCons hd tl => result.ret (hd, tl)
- | list_t.ListNil => result.fail error.panic
+ def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) :=
+ match h: l with
+ | list_t.ListCons hd tl => Result.ret (hd, tl)
+ | list_t.ListNil => Result.fail Error.panic
/- [no_nested_borrows::test_split_list] -/
- def test_split_list_fwd : result Unit :=
+ def test_split_list_fwd : Result Unit :=
do
let l := list_t.ListNil
- let p <-
+ let p ←
split_list_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
l)
let (hd, _) := p
- if not (hd = (Int32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ if h: not (hd = (Int32.ofNatCore 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 ())
+ #assert (test_split_list_fwd == .ret ())
/- [no_nested_borrows::choose] -/
- def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : result T :=
- if b
- then result.ret x
- else result.ret y
+ 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 b
- then result.ret (ret0, y)
- else result.ret (x, ret0)
+ (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 :=
+ def choose_test_fwd : Result Unit :=
do
- let z <-
+ let z ←
choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit))
(Int32.ofNatCore 0 (by intlit))
- let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
- if not (z0 = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+ if h: not (z0 = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
do
- let (x, y) <-
+ let (x, y) ←
choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
(Int32.ofNatCore 0 (by intlit)) z0
- if not (x = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ if h: not (x = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
- if not (y = (Int32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ if h: not (y = (Int32.ofNatCore 0 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::choose_test] -/
- #assert (choose_test_fwd = .ret ())
+ #assert (choose_test_fwd == .ret ())
/- [no_nested_borrows::test_char] -/
- def test_char_fwd : result Char :=
- result.ret 'a'
+ def test_char_fwd : Result Char :=
+ Result.ret 'a'
/- [no_nested_borrows::NodeElem] -/
mutual inductive node_elem_t (T : Type) :=
@@ -268,179 +270,179 @@ structure OpaqueDefs where
| TreeNode : T -> node_elem_t T -> tree_t T -> tree_t T
/- [no_nested_borrows::list_length] -/
- def list_length_fwd (T : Type) (l : list_t T) : result UInt32 :=
- match l with
+ def list_length_fwd (T : Type) (l : list_t T) : Result UInt32 :=
+ match h: l with
| list_t.ListCons t l1 =>
do
- let i <- list_length_fwd T l1
+ let i ← list_length_fwd T l1
UInt32.checked_add (UInt32.ofNatCore 1 (by intlit)) i
- | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+ | list_t.ListNil => Result.ret (UInt32.ofNatCore 0 (by intlit))
/- [no_nested_borrows::list_nth_shared] -/
- def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
- match l with
+ def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T :=
+ match h: l with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_shared_fwd T tl i0
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
/- [no_nested_borrows::list_nth_mut] -/
- def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
- match l with
+ def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T :=
+ match h: l with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_fwd T tl i0
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
/- [no_nested_borrows::list_nth_mut] -/
def list_nth_mut_back
- (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
- match l with
+ (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) :=
+ match h: l with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl0 <- list_nth_mut_back T tl i0 ret0
- result.ret (list_t.ListCons x tl0)
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl0 ← list_nth_mut_back T tl i0 ret0
+ Result.ret (list_t.ListCons x tl0)
+ | list_t.ListNil => 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 li with
+ (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) :=
+ match h: li with
| list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo)
- | list_t.ListNil => result.ret lo
+ | list_t.ListNil => Result.ret lo
/- [no_nested_borrows::list_rev] -/
- def list_rev_fwd_back (T : Type) (l : list_t T) : result (list_t T) :=
+ 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.ListNil
list_rev_aux_fwd T li list_t.ListNil
/- [no_nested_borrows::test_list_functions] -/
- def test_list_functions_fwd : result Unit :=
+ def test_list_functions_fwd : Result Unit :=
do
let l := list_t.ListNil
let l0 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l
let l1 := list_t.ListCons (Int32.ofNatCore 1 (by intlit)) l0
- let i <-
+ let i ←
list_length_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
l1)
- if not (i = (UInt32.ofNatCore 3 (by intlit)))
- then result.fail error.panic
+ if h: not (i = (UInt32.ofNatCore 3 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i0 <-
+ let i0 ←
list_nth_shared_fwd Int32 (list_t.ListCons
(Int32.ofNatCore 0 (by intlit)) l1)
(UInt32.ofNatCore 0 (by intlit))
- if not (i0 = (Int32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
+ if h: not (i0 = (Int32.ofNatCore 0 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i1 <-
+ let i1 ←
list_nth_shared_fwd Int32 (list_t.ListCons
(Int32.ofNatCore 0 (by intlit)) l1)
(UInt32.ofNatCore 1 (by intlit))
- if not (i1 = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ if h: not (i1 = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i2 <-
+ let i2 ←
list_nth_shared_fwd Int32 (list_t.ListCons
(Int32.ofNatCore 0 (by intlit)) l1)
(UInt32.ofNatCore 2 (by intlit))
- if not (i2 = (Int32.ofNatCore 2 (by intlit)))
- then result.fail error.panic
+ if h: not (i2 = (Int32.ofNatCore 2 (by intlit)))
+ then Result.fail Error.panic
else
do
- let ls <-
+ let ls ←
list_nth_mut_back Int32 (list_t.ListCons
(Int32.ofNatCore 0 (by intlit)) l1)
(UInt32.ofNatCore 1 (by intlit))
(Int32.ofNatCore 3 (by intlit))
- let i3 <-
+ let i3 ←
list_nth_shared_fwd Int32 ls
(UInt32.ofNatCore 0 (by intlit))
- if not (i3 = (Int32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
+ if h: not (i3 = (Int32.ofNatCore 0 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i4 <-
+ let i4 ←
list_nth_shared_fwd Int32 ls
(UInt32.ofNatCore 1 (by intlit))
- if not (i4 = (Int32.ofNatCore 3 (by intlit)))
- then result.fail error.panic
+ if h: not (i4 = (Int32.ofNatCore 3 (by intlit)))
+ then Result.fail Error.panic
else
do
- let i5 <-
+ let i5 ←
list_nth_shared_fwd Int32 ls
(UInt32.ofNatCore 2 (by intlit))
- if not (i5 = (Int32.ofNatCore 2 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ if h: not (i5 = (Int32.ofNatCore 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 ())
+ #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)
+ 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) :=
+ (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
let (t, t0) := ret0
- result.ret (t, t0)
+ Result.ret (t, t0)
/- [no_nested_borrows::id_mut_pair2] -/
- def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : result (T1 × T2) :=
+ def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
let (t, t0) := p
- result.ret (t, t0)
+ 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) :=
+ (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
let (t, t0) := ret0
- result.ret (t, t0)
+ 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)
+ 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
+ (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
+ (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) :=
+ def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
let (t, t0) := p
- result.ret (t, t0)
+ 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
+ (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
+ (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
@@ -449,24 +451,24 @@ structure OpaqueDefs where
/- [no_nested_borrows::new_tuple1] -/
- def new_tuple1_fwd : result (struct_with_tuple_t UInt32 UInt32) :=
- result.ret
+ def new_tuple1_fwd : Result (struct_with_tuple_t UInt32 UInt32) :=
+ Result.ret
{
struct_with_tuple_p := ((UInt32.ofNatCore 1 (by intlit)),
(UInt32.ofNatCore 2 (by intlit)))
}
/- [no_nested_borrows::new_tuple2] -/
- def new_tuple2_fwd : result (struct_with_tuple_t Int16 Int16) :=
- result.ret
+ def new_tuple2_fwd : Result (struct_with_tuple_t Int16 Int16) :=
+ Result.ret
{
struct_with_tuple_p := ((Int16.ofNatCore 1 (by intlit)),
(Int16.ofNatCore 2 (by intlit)))
}
/- [no_nested_borrows::new_tuple3] -/
- def new_tuple3_fwd : result (struct_with_tuple_t UInt64 Int64) :=
- result.ret
+ def new_tuple3_fwd : Result (struct_with_tuple_t UInt64 Int64) :=
+ Result.ret
{
struct_with_tuple_p := ((UInt64.ofNatCore 1 (by intlit)),
(Int64.ofNatCore 2 (by intlit)))
@@ -479,8 +481,8 @@ structure OpaqueDefs where
/- [no_nested_borrows::new_pair1] -/
- def new_pair1_fwd : result (struct_with_pair_t UInt32 UInt32) :=
- result.ret
+ def new_pair1_fwd : Result (struct_with_pair_t UInt32 UInt32) :=
+ Result.ret
{
struct_with_pair_p := {
pair_x := (UInt32.ofNatCore 1 (by intlit)),
@@ -489,66 +491,66 @@ structure OpaqueDefs where
}
/- [no_nested_borrows::test_constants] -/
- def test_constants_fwd : result Unit :=
+ def test_constants_fwd : Result Unit :=
do
- let swt <- new_tuple1_fwd
+ let swt ← new_tuple1_fwd
let (i, _) := swt.struct_with_tuple_p
- if not (i = (UInt32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ if h: not (i = (UInt32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
do
- let swt0 <- new_tuple2_fwd
+ let swt0 ← new_tuple2_fwd
let (i0, _) := swt0.struct_with_tuple_p
- if not (i0 = (Int16.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ if h: not (i0 = (Int16.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
do
- let swt1 <- new_tuple3_fwd
+ let swt1 ← new_tuple3_fwd
let (i1, _) := swt1.struct_with_tuple_p
- if not (i1 = (UInt64.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ if h: not (i1 = (UInt64.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
do
- let swp <- new_pair1_fwd
- if not (swp.struct_with_pair_p.pair_x =
+ let swp ← new_pair1_fwd
+ if h: not (swp.struct_with_pair_p.pair_x =
(UInt32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [no_nested_borrows::test_constants] -/
- #assert (test_constants_fwd = .ret ())
+ #assert (test_constants_fwd == .ret ())
/- [no_nested_borrows::test_weird_borrows1] -/
- def test_weird_borrows1_fwd : result Unit :=
- result.ret ()
+ def test_weird_borrows1_fwd : Result Unit :=
+ Result.ret ()
/- Unit test for [no_nested_borrows::test_weird_borrows1] -/
- #assert (test_weird_borrows1_fwd = .ret ())
+ #assert (test_weird_borrows1_fwd == .ret ())
/- [no_nested_borrows::test_mem_replace] -/
- def test_mem_replace_fwd_back (px : UInt32) : result UInt32 :=
+ def test_mem_replace_fwd_back (px : UInt32) : Result UInt32 :=
let y := mem_replace_fwd UInt32 px (UInt32.ofNatCore 1 (by intlit))
- if not (y = (UInt32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
- else result.ret (UInt32.ofNatCore 2 (by intlit))
+ if h: not (y = (UInt32.ofNatCore 0 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret (UInt32.ofNatCore 2 (by intlit))
/- [no_nested_borrows::test_shared_borrow_bool1] -/
- def test_shared_borrow_bool1_fwd (b : Bool) : result UInt32 :=
- if b
- then result.ret (UInt32.ofNatCore 0 (by intlit))
- else result.ret (UInt32.ofNatCore 1 (by intlit))
+ def test_shared_borrow_bool1_fwd (b : Bool) : Result UInt32 :=
+ if h: b
+ then Result.ret (UInt32.ofNatCore 0 (by intlit))
+ else Result.ret (UInt32.ofNatCore 1 (by intlit))
/- [no_nested_borrows::test_shared_borrow_bool2] -/
- def test_shared_borrow_bool2_fwd : result UInt32 :=
- result.ret (UInt32.ofNatCore 0 (by intlit))
+ def test_shared_borrow_bool2_fwd : Result UInt32 :=
+ Result.ret (UInt32.ofNatCore 0 (by intlit))
/- [no_nested_borrows::test_shared_borrow_enum1] -/
- def test_shared_borrow_enum1_fwd (l : list_t UInt32) : result UInt32 :=
- match l with
- | list_t.ListCons i l0 => result.ret (UInt32.ofNatCore 1 (by intlit))
- | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+ def test_shared_borrow_enum1_fwd (l : list_t UInt32) : Result UInt32 :=
+ match h: l with
+ | list_t.ListCons i l0 => Result.ret (UInt32.ofNatCore 1 (by intlit))
+ | list_t.ListNil => Result.ret (UInt32.ofNatCore 0 (by intlit))
/- [no_nested_borrows::test_shared_borrow_enum2] -/
- def test_shared_borrow_enum2_fwd : result UInt32 :=
- result.ret (UInt32.ofNatCore 0 (by intlit))
+ def test_shared_borrow_enum2_fwd : Result UInt32 :=
+ Result.ret (UInt32.ofNatCore 0 (by intlit))
diff --git a/tests/lean/misc/paper/Base/Primitives.lean b/tests/lean/misc/paper/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/misc/paper/Base/Primitives.lean
+++ b/tests/lean/misc/paper/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
-- Results & monadic combinators
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
- | assertionFailure: error
- | integerOverflow: error
- | arrayOutOfBounds: error
- | maximumSizeExceeded: error
- | panic: error
+inductive Error where
+ | assertionFailure: Error
+ | integerOverflow: Error
+ | arrayOutOfBounds: Error
+ | maximumSizeExceeded: Error
+ | panic: Error
deriving Repr, BEq
-open error
+open Error
-inductive result (α : Type u) where
- | ret (v: α): result α
- | fail (e: error): result α
+inductive Result (α : Type u) where
+ | ret (v: α): Result α
+ | fail (e: Error): Result α
deriving Repr, BEq
-open result
+open Result
/- HELPERS -/
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
match r with
- | result.ret _ => true
- | result.fail _ => false
+ | Result.ret _ => true
+ | Result.fail _ => false
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
if b then .ret () else fail assertionFailure
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
match x with
- | result.fail _ => by contradiction
- | result.ret x => x
+ | Result.fail _ => by contradiction
+ | Result.ret x => x
/- DO-DSL SUPPORT -/
-def bind (x: result α) (f: α -> result β) : result β :=
+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
+-- Allows using Result in do-blocks
+instance : Bind Result where
bind := bind
-- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
pure := fun x => ret x
/- CUSTOM-DSL SUPPORT -/
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- 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 : (o : result α) → result { x : α // o = ret x }
+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
+ | .fail e => .fail e
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
- `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+ `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$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 h: y <-- .ret (0: Nat)
- let _: y = 0 := by cases h; decide
+ 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
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-- MACHINE INTEGERS --
----------------------
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: 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." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- 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.
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
syntax "intlit" : tactic
@@ -129,12 +125,21 @@ macro_rules
-- Also works for other integer types (at the expense of a needless disjunction)
#eval UInt32.ofNatCore 0 (by intlit)
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
-- 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 USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
-- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
if n >= m then
let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
else
fail integerOverflow
-def USize.checked_add (n: USize) (m: USize): result USize :=
- if h: n.val.val + m.val.val <= 4294967295 then
- .ret ⟨ n.val.val + m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+ | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+ if h: n.val + m.val < USize.size then
.ret ⟨ n.val + m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
if h: m > 0 then
.ret ⟨ n.val % m.val, by
have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
-def USize.checked_mul (n: USize) (m: USize): result USize :=
- if h: n.val.val * m.val.val <= 4294967295 then
- .ret ⟨ n.val.val * m.val.val, by
- have h': 4294967295 < USize.size := by intlit
- apply Nat.lt_of_le_of_lt h h'
- ⟩
- else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+ if h: n.val * m.val < USize.size then
.ret ⟨ n.val * m.val, h ⟩
else
.fail integerOverflow
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
if m > 0 then
.ret ⟨ n.val / m.val, by
have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
else
.fail integerOverflow
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- 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
@@ -209,30 +223,24 @@ run_cmd
end $typeName
))
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- 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
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
-------------
-- VECTORS --
-------------
-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
-- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
match USize.size, usize_size_eq with
| _, Or.inl rfl => simp
| _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
#check vec_new
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
let ⟨ v, l ⟩ := v
USize.ofNatCore (List.length v) l
#eval vec_len Nat (vec_new Nat)
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
-- make the proof work in that case? Probably need to import tactics from
-- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
:=
if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec
-- annotate `x`, which relieves us of having to write `.val` on the right-hand
-- side of the monadic let.
let v := vec_new Nat
- let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+ let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
-- TODO: strengthen post-condition above and do a demo to show that we can
-- safely eliminate the `fail` case
return (vec_len Nat x)
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
:=
if h : List.length v.val + 1 <= 4294967295 then
return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
else
fail maximumSizeExceeded
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
else
.fail arrayOutOfBounds
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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 :=
+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 :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
if h: i.val < List.length v.val then
.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) :=
+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
.ret ⟨ List.set v.val i.val x, by
have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
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
+
--------------------
-- ASSERT COMMAND --
--------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
syntax (name := assert) "#assert" term: command
@[command_elab assert]
+unsafe
def assertImpl : CommandElab := fun (_stx: Syntax) => do
- logInfo "Reducing and asserting: "
- logInfo _stx[1]
runTermElabM (fun _ => do
- let e ← Term.elabTerm _stx[1] none
- logInfo (Expr.dbgToString e)
- -- How to evaluate the term and compare the result to true?
+ 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 ())
- -- logInfo (Expr.dbgToString (``true))
- -- throwError "TODO: assert"
#eval 2 == 2
#assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/misc/paper/Paper.lean b/tests/lean/misc/paper/Paper.lean
index adcd1eae..4faf36ee 100644
--- a/tests/lean/misc/paper/Paper.lean
+++ b/tests/lean/misc/paper/Paper.lean
@@ -5,56 +5,56 @@ import Base.Primitives
structure OpaqueDefs where
/- [paper::ref_incr] -/
- def ref_incr_fwd_back (x : Int32) : result Int32 :=
+ def ref_incr_fwd_back (x : Int32) : Result Int32 :=
Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
/- [paper::test_incr] -/
- def test_incr_fwd : result Unit :=
+ def test_incr_fwd : Result Unit :=
do
- let x <- ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit))
- if not (x = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ let x ← ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit))
+ if h: not (x = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [paper::test_incr] -/
- #assert (test_incr_fwd = .ret ())
+ #assert (test_incr_fwd == .ret ())
/- [paper::choose] -/
- def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : result T :=
- if b
- then result.ret x
- else result.ret y
+ 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 b
- then result.ret (ret0, y)
- else result.ret (x, ret0)
+ (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 :=
+ def test_choose_fwd : Result Unit :=
do
- let z <-
+ let z ←
choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit))
(Int32.ofNatCore 0 (by intlit))
- let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
- if not (z0 = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+ if h: not (z0 = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
do
- let (x, y) <-
+ let (x, y) ←
choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
(Int32.ofNatCore 0 (by intlit)) z0
- if not (x = (Int32.ofNatCore 1 (by intlit)))
- then result.fail error.panic
+ if h: not (x = (Int32.ofNatCore 1 (by intlit)))
+ then Result.fail Error.panic
else
- if not (y = (Int32.ofNatCore 0 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ if h: not (y = (Int32.ofNatCore 0 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [paper::test_choose] -/
- #assert (test_choose_fwd = .ret ())
+ #assert (test_choose_fwd == .ret ())
/- [paper::List] -/
inductive list_t (T : Type) :=
@@ -62,67 +62,67 @@ structure OpaqueDefs where
| ListNil : list_t T
/- [paper::list_nth_mut] -/
- def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
- match l with
+ def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T :=
+ match h: l with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret x
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret x
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
list_nth_mut_fwd T tl i0
- | list_t.ListNil => result.fail error.panic
+ | list_t.ListNil => Result.fail Error.panic
/- [paper::list_nth_mut] -/
def list_nth_mut_back
- (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
- match l with
+ (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) :=
+ match h: l with
| list_t.ListCons x tl =>
- if i = (UInt32.ofNatCore 0 (by intlit))
- then result.ret (list_t.ListCons ret0 tl)
+ if h: i = (UInt32.ofNatCore 0 (by intlit))
+ then Result.ret (list_t.ListCons ret0 tl)
else
do
- let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
- let tl0 <- list_nth_mut_back T tl i0 ret0
- result.ret (list_t.ListCons x tl0)
- | list_t.ListNil => result.fail error.panic
+ let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+ let tl0 ← list_nth_mut_back T tl i0 ret0
+ Result.ret (list_t.ListCons x tl0)
+ | list_t.ListNil => Result.fail Error.panic
/- [paper::sum] -/
- def sum_fwd (l : list_t Int32) : result Int32 :=
- match l with
+ def sum_fwd (l : list_t Int32) : Result Int32 :=
+ match h: l with
| list_t.ListCons x tl => do
- let i <- sum_fwd tl
+ let i ← sum_fwd tl
Int32.checked_add x i
- | list_t.ListNil => result.ret (Int32.ofNatCore 0 (by intlit))
+ | list_t.ListNil => Result.ret (Int32.ofNatCore 0 (by intlit))
/- [paper::test_nth] -/
- def test_nth_fwd : result Unit :=
+ def test_nth_fwd : Result Unit :=
do
let l := list_t.ListNil
let l0 := list_t.ListCons (Int32.ofNatCore 3 (by intlit)) l
let l1 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l0
- let x <-
+ let x ←
list_nth_mut_fwd Int32 (list_t.ListCons (Int32.ofNatCore 1 (by intlit))
l1) (UInt32.ofNatCore 2 (by intlit))
- let x0 <- Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
- let l2 <-
+ let x0 ← Int32.checked_add x (Int32.ofNatCore 1 (by intlit))
+ let l2 ←
list_nth_mut_back Int32 (list_t.ListCons
(Int32.ofNatCore 1 (by intlit)) l1) (UInt32.ofNatCore 2 (by intlit))
x0
- let i <- sum_fwd l2
- if not (i = (Int32.ofNatCore 7 (by intlit)))
- then result.fail error.panic
- else result.ret ()
+ let i ← sum_fwd l2
+ if h: not (i = (Int32.ofNatCore 7 (by intlit)))
+ then Result.fail Error.panic
+ else Result.ret ()
/- Unit test for [paper::test_nth] -/
- #assert (test_nth_fwd = .ret ())
+ #assert (test_nth_fwd == .ret ())
/- [paper::call_choose] -/
- def call_choose_fwd (p : (UInt32 × UInt32)) : result UInt32 :=
+ def call_choose_fwd (p : (UInt32 × UInt32)) : Result UInt32 :=
do
let (px, py) := p
- let pz <- choose_fwd UInt32 true px py
- let pz0 <- UInt32.checked_add pz (UInt32.ofNatCore 1 (by intlit))
- let (px0, _) <- choose_back UInt32 true px py pz0
- result.ret px0
+ let pz ← choose_fwd UInt32 true px py
+ let pz0 ← UInt32.checked_add pz (UInt32.ofNatCore 1 (by intlit))
+ let (px0, _) ← choose_back UInt32 true px py pz0
+ Result.ret px0