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Diffstat (limited to 'backends/lean/Base')
| -rw-r--r-- | backends/lean/Base/Primitives.lean | 650 |
1 files changed, 650 insertions, 0 deletions
diff --git a/backends/lean/Base/Primitives.lean b/backends/lean/Base/Primitives.lean new file mode 100644 index 00000000..d3de1d10 --- /dev/null +++ b/backends/lean/Base/Primitives.lean @@ -0,0 +1,650 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd +import Mathlib.Tactic.Linarith + +-------------------- +-- ASSERT COMMAND --Std. +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + 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 + cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at * + cases System.Platform.numBits_eq <;> + unfold System.Platform.numBits at * <;> + simp [*] + +theorem Scalar.cMax_bound ty : Scalar.cMax ty ≤ Scalar.max ty := by + cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at * <;> + cases System.Platform.numBits_eq <;> + unfold System.Platform.numBits at * <;> + simp [*] + +theorem Scalar.cMin_suffices ty (h : Scalar.cMin ty ≤ x) : Scalar.min ty ≤ x := by + cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at * <;> + cases System.Platform.numBits_eq <;> + unfold System.Platform.numBits at * <;> + simp [*] at * + -- TODO: I would have expected terms like `-(1 + 1) ^ 63` to be simplified + linarith + +theorem Scalar.cMax_suffices ty (h : x ≤ Scalar.cMax ty) : x ≤ Scalar.max ty := by + cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at * <;> + cases System.Platform.numBits_eq <;> + unfold System.Platform.numBits at * <;> + simp [*] at * <;> + -- TODO: I would have expected terms like `-(1 + 1) ^ 63` to be simplified + linarith + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty ≤ val + hmax : val ≤ Scalar.max ty +deriving Repr + +theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) : + Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty -> + Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty + := + λ h => by + apply And.intro <;> have hmin := Scalar.cMin_bound ty <;> have hmax := Scalar.cMax_bound ty <;> linarith + +def Scalar.ofIntCore {ty : ScalarTy} (x : Int) + (hmin : Scalar.min ty ≤ x) (hmax : x ≤ Scalar.max ty) : Scalar ty := + { val := x, hmin := hmin, hmax := hmax } + +def Scalar.ofInt {ty : ScalarTy} (x : Int) + (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : Scalar ty := + -- Remark: we initially wrote: + -- let ⟨ hmin, hmax ⟩ := h + -- Scalar.ofIntCore x hmin hmax + -- We updated to the line below because a similar pattern in `Scalar.tryMk` + -- made reduction block. Both versions seem to work for `Scalar.ofInt`, though. + -- TODO: investigate + Scalar.ofIntCore x h.left h.right + +@[simp] def Scalar.check_bounds (ty : ScalarTy) (x : Int) : Bool := + (Scalar.cMin ty ≤ x || Scalar.min ty ≤ x) ∧ (x ≤ Scalar.cMax ty || x ≤ Scalar.max ty) + +theorem Scalar.check_bounds_prop {ty : ScalarTy} {x : Int} (h: Scalar.check_bounds ty x) : + Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty := by + simp at * + have ⟨ hmin, hmax ⟩ := h + have hbmin := Scalar.cMin_bound ty + have hbmax := Scalar.cMax_bound ty + cases hmin <;> cases hmax <;> apply And.intro <;> linarith + +-- Further thoughts: look at what has been done here: +-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean +-- and +-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean +-- which both contain a fair amount of reasoning already! +def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) := + if h:Scalar.check_bounds ty x then + -- If we do: + -- ``` + -- let ⟨ hmin, hmax ⟩ := (Scalar.check_bounds_prop h) + -- Scalar.ofIntCore x hmin hmax + -- ``` + -- then normalization blocks (for instance, some proofs which use reflexivity fail). + -- However, the version below doesn't block reduction (TODO: investigate): + return Scalar.ofInt x (Scalar.check_bounds_prop h) + else fail integerOverflow + +def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val) + +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 + +-- Our custom remainder operation, which satisfies the semantics of Rust +-- TODO: is there a better way? +def scalar_rem (x y : Int) : Int := + if 0 ≤ x then |x| % |y| + else - (|x| % |y|) + +-- Our custom division operation, which satisfies the semantics of Rust +-- TODO: is there a better way? +def scalar_div (x y : Int) : Int := + if 0 ≤ x && 0 ≤ y then |x| / |y| + else if 0 ≤ x && y < 0 then - (|x| / |y|) + else if x < 0 && 0 ≤ y then - (|x| / |y|) + else |x| / |y| + +-- Checking that the remainder operation is correct +#assert scalar_rem 1 2 = 1 +#assert scalar_rem (-1) 2 = -1 +#assert scalar_rem 1 (-2) = 1 +#assert scalar_rem (-1) (-2) = -1 +#assert scalar_rem 7 3 = (1:Int) +#assert scalar_rem (-7) 3 = -1 +#assert scalar_rem 7 (-3) = 1 +#assert scalar_rem (-7) (-3) = -1 + +-- Checking that the division operation is correct +#assert scalar_div 3 2 = 1 +#assert scalar_div (-3) 2 = -1 +#assert scalar_div 3 (-2) = -1 +#assert scalar_div (-3) (-2) = 1 +#assert scalar_div 7 3 = 2 +#assert scalar_div (-7) 3 = -2 +#assert scalar_div 7 (-3) = -2 +#assert scalar_div (-7) (-3) = 2 + +def Scalar.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 apply Scalar.cMax_suffices .Usize; simp ⟩ + +def vec_len (α : Type u) (v : Vec α) : Usize := + let ⟨ v, l ⟩ := v + Usize.ofIntCore (List.length v) (by simp [Scalar.min]) 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) + := + let nlen := List.length v.val + 1 + if h : nlen ≤ U32.max || nlen ≤ Usize.max then + have h : nlen ≤ Usize.max := by + simp at * + cases System.Platform.numBits_eq <;> + unfold System.Platform.numBits at * <;> + simp [*] at * <;> + try assumption + cases h <;> + linarith + return ⟨ List.concat v.val x, by simp at *; 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 + -- TODO: maybe we should redefine a list library which uses integers + -- (instead of natural numbers) + let i := i.val.toNat + .ret ⟨ List.set v.val i x, by + have h: List.length v.val ≤ Usize.max := v.property + simp [*] at * + assumption + ⟩ + else + .fail arrayOutOfBounds + +def vec_index_to_fin {α : Type u} {v: Vec α} {i: Usize} (h : i.val < List.length v.val) : + Fin (List.length v.val) := + let j := i.val.toNat + let h: j < List.length v.val := by + have heq := @Int.toNat_lt (List.length v.val) i.val i.hmin + apply heq.mpr + assumption + ⟨j, h⟩ + +def vec_index_fwd (α : Type u) (v: Vec α) (i: Usize): Result α := + if h: i.val < List.length v.val then + let i := vec_index_to_fin h + .ret (List.get v.val i) + 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 + let i := vec_index_to_fin h + .ret (List.get v.val i) + else + .fail arrayOutOfBounds + +def vec_index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α): Result (Vec α) := + if h: i.val < List.length v.val then + let i := vec_index_to_fin h + .ret ⟨ List.set v.val i x, by + have h: List.length v.val ≤ Usize.max := v.property + simp [*] at * + assumption + ⟩ + else + .fail arrayOutOfBounds + +---------- +-- MISC -- +---------- + +@[simp] def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := x +@[simp] def mem_replace_back (a : Type) (_ : a) (y : a) : a := y + +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas |