From 87d6f6c7c90bf7b427397d6bd2e2c70d610678e3 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Tue, 4 Jul 2023 14:57:51 +0200
Subject: Reorganize the Lean tests

---
 tests/lean/misc-loops/Base/Primitives.lean | 583 -----------------------------
 1 file changed, 583 deletions(-)
 delete mode 100644 tests/lean/misc-loops/Base/Primitives.lean

(limited to 'tests/lean/misc-loops/Base')

diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean
deleted file mode 100644
index 4a66a453..00000000
--- a/tests/lean/misc-loops/Base/Primitives.lean
+++ /dev/null
@@ -1,583 +0,0 @@
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-
---------------------
--- ASSERT COMMAND --
---------------------
-
-open Lean Elab Command Term Meta
-
-syntax (name := assert) "#assert" term: command
-
-@[command_elab assert]
-unsafe
-def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  runTermElabM (fun _ => do
-    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
-    if not r then
-      logInfo "Assertion failed for: "
-      logInfo _stx[1]
-      logError "Expression reduced to false"
-    pure ())
-
-#eval 2 == 2
-#assert (2 == 2)
-
--------------
--- PRELUDE --
--------------
-
--- Results & monadic combinators
-
-inductive Error where
-   | assertionFailure: Error
-   | integerOverflow: Error
-   | divisionByZero: Error
-   | arrayOutOfBounds: Error
-   | maximumSizeExceeded: Error
-   | panic: Error
-deriving Repr, BEq
-
-open Error
-
-inductive Result (α : Type u) where
-  | ret (v: α): Result α
-  | fail (e: Error): Result α
-deriving Repr, BEq
-
-open Result
-
-instance Result_Inhabited (α : Type u) : Inhabited (Result α) :=
-  Inhabited.mk (fail panic)
-
-/- HELPERS -/
-
-def ret? {α: Type} (r: Result α): Bool :=
-  match r with
-  | Result.ret _ => true
-  | Result.fail _ => false
-
-def massert (b:Bool) : Result Unit :=
-  if b then .ret () else fail assertionFailure
-
-def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
-  match x with
-  | Result.fail _ => by contradiction
-  | Result.ret x => x
-
-/- DO-DSL SUPPORT -/
-
-def bind (x: Result α) (f: α -> Result β) : Result β :=
-  match x with
-  | ret v  => f v 
-  | fail v => fail v
-
--- Allows using Result in do-blocks
-instance : Bind Result where
-  bind := bind
-
--- Allows using return x in do-blocks
-instance : Pure Result where
-  pure := fun x => ret x
-
-/- CUSTOM-DSL SUPPORT -/
-
--- Let-binding the Result of a monadic operation is oftentimes not sufficient,
--- because we may need a hypothesis for equational reasoning in the scope. We
--- rely on subtype, and a custom let-binding operator, in effect recreating our
--- own variant of the do-dsl
-
-def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
-  match o with
-  | .ret x => .ret ⟨x, rfl⟩
-  | .fail e => .fail e
-
-macro "let" e:term " ⟵ " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- TODO: any way to factorize both definitions?
-macro "let" e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
-
--- We call the hypothesis `h`, in effect making it unavailable to the user
--- (because too much shadowing). But in practice, once can use the French single
--- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
--- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
-#eval do
-  let y <-- .ret (0: Nat)
-  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
-  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
-  .ret r
-
-----------------------
--- MACHINE INTEGERS --
-----------------------
-
--- We redefine our machine integers types.
-
--- For Isize/Usize, we reuse `getNumBits` from `USize`. You cannot reduce `getNumBits`
--- using the simplifier, meaning that proofs do not depend on the compile-time value of
--- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really support, at
--- least officially, 16-bit microcontrollers, so this seems like a fine design decision
--- for now.)
-
--- Note from Chris Bailey: "If there's more than one salient property of your
--- definition then the subtyping strategy might get messy, and the property part
--- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." So, we will not add refinements on the return values of the
--- operations defined on Primitives, but will rather rely on custom lemmas to
--- invert on possible return values of the primitive operations.
-
--- Machine integer constants, done via `ofNatCore`, which requires a proof that
--- the `Nat` fits within the desired integer type. We provide a custom tactic.
-
-open System.Platform.getNumBits
-
--- TODO: is there a way of only importing System.Platform.getNumBits?
---
-@[simp] def size_num_bits : Nat := (System.Platform.getNumBits ()).val
-
--- Remark: Lean seems to use < for the comparisons with the upper bounds by convention.
--- We keep the F* convention for now.
-@[simp] def Isize.min : Int := - (HPow.hPow 2 (size_num_bits - 1))
-@[simp] def Isize.max : Int := (HPow.hPow 2 (size_num_bits - 1)) - 1
-@[simp] def I8.min    : Int := - (HPow.hPow 2 7)
-@[simp] def I8.max    : Int := HPow.hPow 2 7 - 1
-@[simp] def I16.min   : Int := - (HPow.hPow 2 15)
-@[simp] def I16.max   : Int := HPow.hPow 2 15 - 1
-@[simp] def I32.min   : Int := -(HPow.hPow 2 31)
-@[simp] def I32.max   : Int := HPow.hPow 2 31 - 1
-@[simp] def I64.min   : Int := -(HPow.hPow 2 63)
-@[simp] def I64.max   : Int := HPow.hPow 2 63 - 1
-@[simp] def I128.min  : Int := -(HPow.hPow 2 127)
-@[simp] def I128.max  : Int := HPow.hPow 2 127 - 1
-@[simp] def Usize.min : Int := 0
-@[simp] def Usize.max : Int := HPow.hPow 2 size_num_bits - 1
-@[simp] def U8.min    : Int := 0
-@[simp] def U8.max    : Int := HPow.hPow 2 8 - 1
-@[simp] def U16.min   : Int := 0
-@[simp] def U16.max   : Int := HPow.hPow 2 16 - 1
-@[simp] def U32.min   : Int := 0
-@[simp] def U32.max   : Int := HPow.hPow 2 32 - 1
-@[simp] def U64.min   : Int := 0
-@[simp] def U64.max   : Int := HPow.hPow 2 64 - 1
-@[simp] def U128.min  : Int := 0
-@[simp] def U128.max  : Int := HPow.hPow 2 128 - 1
-
-#assert (I8.min   == -128)
-#assert (I8.max   == 127)
-#assert (I16.min  == -32768)
-#assert (I16.max  == 32767)
-#assert (I32.min  == -2147483648)
-#assert (I32.max  == 2147483647)
-#assert (I64.min  == -9223372036854775808)
-#assert (I64.max  == 9223372036854775807)
-#assert (I128.min == -170141183460469231731687303715884105728)
-#assert (I128.max == 170141183460469231731687303715884105727)
-#assert (U8.min   == 0)
-#assert (U8.max   == 255)
-#assert (U16.min  == 0)
-#assert (U16.max  == 65535)
-#assert (U32.min  == 0)
-#assert (U32.max  == 4294967295)
-#assert (U64.min  == 0)
-#assert (U64.max  == 18446744073709551615)
-#assert (U128.min == 0)
-#assert (U128.max == 340282366920938463463374607431768211455)
-
-inductive ScalarTy :=
-| Isize
-| I8
-| I16
-| I32
-| I64
-| I128
-| Usize
-| U8
-| U16
-| U32
-| U64
-| U128
-
-def Scalar.min (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.min
-  | .I8    => I8.min
-  | .I16   => I16.min
-  | .I32   => I32.min
-  | .I64   => I64.min
-  | .I128  => I128.min
-  | .Usize => Usize.min
-  | .U8    => U8.min
-  | .U16   => U16.min
-  | .U32   => U32.min
-  | .U64   => U64.min
-  | .U128  => U128.min
-
-def Scalar.max (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => Isize.max
-  | .I8    => I8.max
-  | .I16   => I16.max
-  | .I32   => I32.max
-  | .I64   => I64.max
-  | .I128  => I128.max
-  | .Usize => Usize.max
-  | .U8    => U8.max
-  | .U16   => U16.max
-  | .U32   => U32.max
-  | .U64   => U64.max
-  | .U128  => U128.max
-
--- "Conservative" bounds
--- We use those because we can't compare to the isize bounds (which can't
--- reduce at compile-time). Whenever we perform an arithmetic operation like
--- addition we need to check that the result is in bounds: we first compare
--- to the conservative bounds, which reduce, then compare to the real bounds.
--- This is useful for the various #asserts that we want to reduce at
--- type-checking time.
-def Scalar.cMin (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.min
-  | _ => Scalar.min ty
-
-def Scalar.cMax (ty : ScalarTy) : Int :=
-  match ty with
-  | .Isize => I32.max
-  | .Usize => U32.max
-  | _ => Scalar.max ty
-
-theorem Scalar.cMin_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-theorem Scalar.cMax_bound ty : Scalar.min ty <= Scalar.cMin ty := by sorry
-
-structure Scalar (ty : ScalarTy) where
-  val : Int
-  hmin : Scalar.min ty <= val
-  hmax : val <= Scalar.max ty
-
-theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
-  Scalar.cMin ty <= x && x <= Scalar.cMax ty ->
-  (decide (Scalar.min ty ≤ x) && decide (x ≤ Scalar.max ty)) = true
-  := by sorry
-
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty <= x) (hmax : x <= Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty <= x && x <= Scalar.max ty) : Scalar ty :=
-  let hmin: Scalar.min ty <= x := by sorry
-  let hmax: x <= Scalar.max ty := by sorry
-  Scalar.ofIntCore x hmin hmax
-
--- Further thoughts: look at what has been done here:
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
--- and
--- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
--- which both contain a fair amount of reasoning already!
-def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
-  -- TODO: write this with only one if then else
-  if hmin_cons: Scalar.cMin ty <= x || Scalar.min ty <= x then
-    if hmax_cons: x <= Scalar.cMax ty || x <= Scalar.max ty then
-      let hmin: Scalar.min ty <= x := by sorry
-      let hmax: x <= Scalar.max ty := by sorry
-      return Scalar.ofIntCore x hmin hmax
-    else fail integerOverflow
-  else fail integerOverflow
-
-def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
-
-def Scalar.div {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val / y.val) else fail divisionByZero
-
--- Checking that the % operation in Lean computes the same as the remainder operation in Rust
-#assert 1 % 2 = (1:Int)
-#assert (-1) % 2 = -1
-#assert 1 % (-2) = 1
-#assert (-1) % (-2) = -1
-
-def Scalar.rem {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  if y.val != 0 then Scalar.tryMk ty (x.val % y.val) else fail divisionByZero
-
-def Scalar.add {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val + y.val)
-
-def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val - y.val)
-
-def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) :=
-  Scalar.tryMk ty (x.val * y.val)
-
--- TODO: instances of +, -, * etc. for scalars
-
--- Cast an integer from a [src_ty] to a [tgt_ty]
--- TODO: check the semantics of casts in Rust
-def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) :=
-  Scalar.tryMk tgt_ty x.val
-
--- The scalar types
--- We declare the definitions as reducible so that Lean can unfold them (useful
--- for type class resolution for instance).
-@[reducible] def Isize := Scalar .Isize
-@[reducible] def I8    := Scalar .I8
-@[reducible] def I16   := Scalar .I16
-@[reducible] def I32   := Scalar .I32
-@[reducible] def I64   := Scalar .I64
-@[reducible] def I128  := Scalar .I128
-@[reducible] def Usize := Scalar .Usize
-@[reducible] def U8    := Scalar .U8
-@[reducible] def U16   := Scalar .U16
-@[reducible] def U32   := Scalar .U32
-@[reducible] def U64   := Scalar .U64
-@[reducible] def U128  := Scalar .U128
-
--- TODO: below: not sure this is the best way.
--- Should we rather overload operations like +, -, etc.?
--- Also, it is possible to automate the generation of those definitions
--- with macros (but would it be a good idea? It would be less easy to
--- read the file, which is not supposed to change a lot)
-
--- Negation
-
-/--
-Remark: there is no heterogeneous negation in the Lean prelude: we thus introduce
-one here.
-
-The notation typeclass for heterogeneous addition.
-This enables the notation `- a : β` where `a : α`.
--/
-class HNeg (α : Type u) (β : outParam (Type v)) where
-  /-- `- a` computes the negation of `a`.
-  The meaning of this notation is type-dependent. -/
-  hNeg : α → β
-
-prefix:75  "-"   => HNeg.hNeg
-
-instance : HNeg Isize (Result Isize) where hNeg x := Scalar.neg x
-instance : HNeg I8 (Result I8) where hNeg x := Scalar.neg x
-instance : HNeg I16 (Result I16) where hNeg x := Scalar.neg x
-instance : HNeg I32 (Result I32) where hNeg x := Scalar.neg x
-instance : HNeg I64 (Result I64) where hNeg x := Scalar.neg x
-instance : HNeg I128 (Result I128) where hNeg x := Scalar.neg x
-
--- Addition
-instance {ty} : HAdd (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hAdd x y := Scalar.add x y
-
--- Substraction
-instance {ty} : HSub (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hSub x y := Scalar.sub x y
-
--- Multiplication
-instance {ty} : HMul (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMul x y := Scalar.mul x y
-
--- Division
-instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hDiv x y := Scalar.div x y
-
--- Remainder
-instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where
-  hMod x y := Scalar.rem x y
-
--- ofIntCore
--- TODO: typeclass?
-def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-def I8.ofIntCore    := @Scalar.ofIntCore .I8
-def I16.ofIntCore   := @Scalar.ofIntCore .I16
-def I32.ofIntCore   := @Scalar.ofIntCore .I32
-def I64.ofIntCore   := @Scalar.ofIntCore .I64
-def I128.ofIntCore  := @Scalar.ofIntCore .I128
-def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-def U8.ofIntCore    := @Scalar.ofIntCore .U8
-def U16.ofIntCore   := @Scalar.ofIntCore .U16
-def U32.ofIntCore   := @Scalar.ofIntCore .U32
-def U64.ofIntCore   := @Scalar.ofIntCore .U64
-def U128.ofIntCore  := @Scalar.ofIntCore .U128
-
---  ofInt
--- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- Comparisons
-instance {ty} : LT (Scalar ty) where
-  lt a b := LT.lt a.val b.val
-
-instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
-
-instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
-instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
-
-theorem Scalar.eq_of_val_eq {ty} : ∀ {i j : Scalar ty}, Eq i.val j.val → Eq i j
-  | ⟨_, _, _⟩, ⟨_, _, _⟩, rfl => rfl
-
-theorem Scalar.val_eq_of_eq {ty} {i j : Scalar ty} (h : Eq i j) : Eq i.val j.val :=
-  h ▸ rfl
-
-theorem Scalar.ne_of_val_ne {ty} {i j : Scalar ty} (h : Not (Eq i.val j.val)) : Not (Eq i j) :=
-  fun h' => absurd (val_eq_of_eq h') h
-
-instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
-  fun i j =>
-    match decEq i.val j.val with
-    | isTrue h  => isTrue (Scalar.eq_of_val_eq h)
-    | isFalse h => isFalse (Scalar.ne_of_val_ne h)
-
-def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val
-
--- Tactic to prove that integers are in bounds
-syntax "intlit" : tactic
-
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices ; decide)
-
--- -- We now define a type class that subsumes the various machine integer types, so
--- -- as to write a concise definition for scalar_cast, rather than exhaustively
--- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
--- -- and fails if a cast operation would involve a truncation or modulo.
-
--- class MachineInteger (t: Type) where
---   size: Nat
---   val: t -> Fin size
---   ofNatCore: (n:Nat) -> LT.lt n size -> t
-
--- set_option hygiene false in
--- run_cmd
---   for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
---   Lean.Elab.Command.elabCommand (← `(
---     namespace $typeName
---     instance: MachineInteger $typeName where
---       size := size
---       val := val
---       ofNatCore := ofNatCore
---     end $typeName
---   ))
-
--- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on
--- -- Lean to infer `src`.
-
--- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
---   if h: MachineInteger.val x < MachineInteger.size dst then
---     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
---   else
---     .fail integerOverflow
-
--------------
--- VECTORS --
--------------
-
-def Vec (α : Type u) := { l : List α // List.length l <= Usize.max }
-
-def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩
-
-def vec_len (α : Type u) (v : Vec α) : Usize :=
-  let ⟨ v, l ⟩ := v
-  Usize.ofIntCore (List.length v) (by sorry) l
- 
-def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
-
-def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
-  :=
-  if h : List.length v.val <= U32.max || List.length v.val <= Usize.max then
-    return ⟨ List.concat v.val x, by sorry ⟩
-  else
-    fail maximumSizeExceeded
-
-def vec_insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_insert_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    -- TODO: maybe we should redefine a list library which uses integers
-    -- (instead of natural numbers)
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_back (α : Type u) (v: Vec α) (i: Usize) (_: α): Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: Usize): Result α :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    let h: i < List.length v.val := by sorry
-    .ret (List.get v.val ⟨i.val, h⟩)
-  else
-    .fail arrayOutOfBounds
-
-def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) :=
-  if i.val < List.length v.val then
-    let i : Nat :=
-      match i.val with
-      | .ofNat n => n
-      | .negSucc n => by sorry -- TODO: we can't get here
-    let isLt: i < USize.size := by sorry
-    let i : Fin USize.size := { val := i, isLt := isLt }
-    .ret ⟨ List.set v.val i.val x, by
-      have h: List.length v.val <= Usize.max := v.property
-      rewrite [ List.length_set v.val i.val x ]
-      assumption
-    ⟩
-  else
-    .fail arrayOutOfBounds
-
-----------
--- MISC --
-----------
-
-def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
-  x
-
-def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
-  y
-
-/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
- Use with `simp [ aeneas ]` -/
-register_simp_attr aeneas
-- 
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