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authorSon Ho2023-02-05 18:40:30 +0100
committerSon HO2023-06-04 21:44:33 +0200
commit985abfa5406e55a8a4e091486119e18b60896911 (patch)
tree3b8d6c8ff7f6f3a76c1d9b44aa71b7577b8789a3 /tests/lean/misc/external
parent569513587ac168683c40cef03c1e3a74579e6e44 (diff)
Make minor fixes, improve formatting for Lean and generate code for all the test suite
Diffstat (limited to 'tests/lean/misc/external')
-rw-r--r--tests/lean/misc/external/Base/Primitives.lean373
-rw-r--r--tests/lean/misc/external/External/Funs.lean93
-rw-r--r--tests/lean/misc/external/External/Opaque.lean28
-rw-r--r--tests/lean/misc/external/External/Types.lean8
4 files changed, 502 insertions, 0 deletions
diff --git a/tests/lean/misc/external/Base/Primitives.lean b/tests/lean/misc/external/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/external/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- 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
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+ | ret (v: α): result α
+ | fail (e: error): result α
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+ match r with
+ | result.ret _ => true
+ | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+ if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+ match x with
+ | result.fail _ => by contradiction
+ | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+ match x with
+ | ret v => f v
+ | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+ bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+ pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+ | .ret x => .ret ⟨x, rfl⟩
+ | .fail e => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+ `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+ let h: y <-- .ret (0: Nat)
+ let _: y = 0 := by cases h; decide
+ let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+ .ret r
+
+----------------------
+-- 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 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?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+ | `(tactic| intlit) => `(tactic|
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => decide
+ | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- 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 :=
+ -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+ if n >= m then
+ let n' := USize.toNat n
+ let m' := USize.toNat n
+ let r := USize.ofNatCore (n' - m') (by
+ have h: n' - m' <= n' := by
+ apply Nat.sub_le_of_le_add
+ case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+ apply Nat.lt_of_le_of_lt h
+ apply n.val.isLt
+ )
+ return r
+ 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
+ .ret ⟨ n.val + m.val, h ⟩
+ else
+ .fail integerOverflow
+
+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
+ have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+ apply Nat.lt_trans h2 h1
+ ⟩
+ 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
+ .ret ⟨ n.val * m.val, h ⟩
+ else
+ .fail integerOverflow
+
+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
+ have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+ apply Nat.lt_of_le_of_lt h2 h1
+ ⟩
+ else
+ .fail integerOverflow
+
+class MachineInteger (t: Type) where
+ size: Nat
+ val: t -> Fin size
+ ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+ for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+ Lean.Elab.Command.elabCommand (← `(
+ namespace $typeName
+ instance: MachineInteger $typeName where
+ size := size
+ val := val
+ ofNatCore := ofNatCore
+ end $typeName
+ ))
+
+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_new (α : Type u): vec α := ⟨ [], by {
+ match USize.size, usize_size_eq with
+ | _, Or.inl rfl => simp
+ | _, Or.inr rfl => simp
+ } ⟩
+
+#check vec_new
+
+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 := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- 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) //
+ 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
+ ⟨ return ⟨List.concat v.val x,
+ by
+ rw [List.length_concat]
+ assumption
+ ⟩, by simp ⟩
+ else
+ ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+ -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+ -- fields val and property. However, Lean's elaborator can automatically
+ -- select the `val` field if the context provides a type annotation. We
+ -- 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?
+ -- 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)
+ :=
+ if h : List.length v.val + 1 <= 4294967295 then
+ return ⟨ List.concat v.val x,
+ by
+ rw [List.length_concat]
+ have h': 4294967295 < USize.size := by intlit
+ apply Nat.lt_of_le_of_lt h h'
+ ⟩
+ else if h: List.length v.val + 1 < USize.size then
+ return ⟨List.concat v.val x,
+ by
+ rw [List.length_concat]
+ assumption
+ ⟩
+ else
+ fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+ if i.val < List.length v.val then
+ .ret ()
+ else
+ .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+ if i.val < List.length v.val then
+ .ret ⟨ List.set v.val i.val x, by
+ have h: List.length v.val < USize.size := v.property
+ rewrite [ List.length_set v.val i.val x ]
+ assumption
+ ⟩
+ else
+ .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+ if 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 :=
+ if i.val < List.length v.val then
+ .ret ()
+ else
+ .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+ if 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) :=
+ 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
+ rewrite [ List.length_set v.val i.val x ]
+ assumption
+ ⟩
+ else
+ .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+ x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+ y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+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?
+ pure ())
+ -- logInfo (Expr.dbgToString (``true))
+ -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean
new file mode 100644
index 00000000..bb1e296d
--- /dev/null
+++ b/tests/lean/misc/external/External/Funs.lean
@@ -0,0 +1,93 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: function definitions
+import Base.Primitives
+import External.Types
+import External.Opaque
+
+section variable (opaque_defs: OpaqueDefs)
+
+/- [external::swap] -/
+def swap_fwd
+ (T : Type) (x : T) (y : T) (st : state) : result (state × Unit) :=
+ do
+ let (st0, _) <- opaque_defs.core_mem_swap_fwd T x y st
+ let (st1, _) <- opaque_defs.core_mem_swap_back0 T x y st st0
+ let (st2, _) <- opaque_defs.core_mem_swap_back1 T x y st st1
+ result.ret (st2, ())
+
+/- [external::swap] -/
+def swap_back
+ (T : Type) (x : T) (y : T) (st : state) (st0 : state) :
+ result (state × (T × T))
+ :=
+ do
+ let (st1, _) <- opaque_defs.core_mem_swap_fwd T x y st
+ let (st2, x0) <- opaque_defs.core_mem_swap_back0 T x y st st1
+ let (_, y0) <- opaque_defs.core_mem_swap_back1 T x y st st2
+ result.ret (st0, (x0, y0))
+
+/- [external::test_new_non_zero_u32] -/
+def test_new_non_zero_u32_fwd
+ (x : 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
+ opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t
+ opt st0
+
+/- [external::test_vec] -/
+def test_vec_fwd : result Unit :=
+ do
+ let v := vec_new UInt32
+ let _ <- vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit))
+ result.ret ()
+
+/- Unit test for [external::test_vec] -/
+#assert (test_vec_fwd = .ret ())
+
+/- [external::custom_swap] -/
+def custom_swap_fwd
+ (T : Type) (x : T) (y : T) (st : state) : result (state × T) :=
+ do
+ let (st0, _) <- opaque_defs.core_mem_swap_fwd T x y st
+ let (st1, x0) <- opaque_defs.core_mem_swap_back0 T x y st st0
+ let (st2, _) <- opaque_defs.core_mem_swap_back1 T x y st st1
+ result.ret (st2, x0)
+
+/- [external::custom_swap] -/
+def custom_swap_back
+ (T : Type) (x : T) (y : T) (st : state) (ret0 : T) (st0 : state) :
+ result (state × (T × T))
+ :=
+ do
+ let (st1, _) <- opaque_defs.core_mem_swap_fwd T x y st
+ let (st2, _) <- opaque_defs.core_mem_swap_back0 T x y st st1
+ let (_, y0) <- opaque_defs.core_mem_swap_back1 T x y st st2
+ result.ret (st0, (ret0, y0))
+
+/- [external::test_custom_swap] -/
+def test_custom_swap_fwd
+ (x : UInt32) (y : UInt32) (st : state) : result (state × Unit) :=
+ do
+ 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))
+ :=
+ 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) :=
+ do
+ 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)
+
diff --git a/tests/lean/misc/external/External/Opaque.lean b/tests/lean/misc/external/External/Opaque.lean
new file mode 100644
index 00000000..40ccc313
--- /dev/null
+++ b/tests/lean/misc/external/External/Opaque.lean
@@ -0,0 +1,28 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: opaque function definitions
+import Base.Primitives
+import External.Types
+
+structure OpaqueDefs where
+
+ /- [core::mem::swap] -/
+ core_mem_swap_fwd (T : Type) : T -> T -> state -> result (state × Unit)
+
+ /- [core::mem::swap] -/
+ core_mem_swap_back0
+ (T : Type) : T -> T -> state -> state -> result (state × T)
+
+ /- [core::mem::swap] -/
+ core_mem_swap_back1
+ (T : Type) : T -> T -> state -> state -> result (state × T)
+
+ /- [core::num::nonzero::NonZeroU32::{14}::new] -/
+ core_num_nonzero_non_zero_u32_new_fwd
+ :
+ 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)
+
diff --git a/tests/lean/misc/external/External/Types.lean b/tests/lean/misc/external/External/Types.lean
new file mode 100644
index 00000000..b6fa292b
--- /dev/null
+++ b/tests/lean/misc/external/External/Types.lean
@@ -0,0 +1,8 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [external]: type definitions
+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
+