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Diffstat (limited to '')
| -rw-r--r-- | backends/lean/Primitives.lean | 584 |
1 files changed, 390 insertions, 194 deletions
diff --git a/backends/lean/Primitives.lean b/backends/lean/Primitives.lean index 346e4b89..6401bca2 100644 --- a/backends/lean/Primitives.lean +++ b/backends/lean/Primitives.lean @@ -3,6 +3,28 @@ 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 -- ------------- @@ -12,6 +34,7 @@ import Mathlib.Tactic.RunCmd inductive Error where | assertionFailure: Error | integerOverflow: Error + | divisionByZero: Error | arrayOutOfBounds: Error | maximumSizeExceeded: Error | panic: Error @@ -125,222 +148,425 @@ 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`). +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 + +structure Scalar (ty : ScalarTy) where + val : Int + hmin : Scalar.min ty <= val + hmax : val <= Scalar.max ty + +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 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 - -@[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 := - 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 * 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 - --- 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 - 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 +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 +def Isize := Scalar .Isize +def I8 := Scalar .I8 +def I16 := Scalar .I16 +def I32 := Scalar .I32 +def I64 := Scalar .I64 +def I128 := Scalar .I128 +def Usize := Scalar .Usize +def U8 := Scalar .U8 +def U16 := Scalar .U16 +def U32 := Scalar .U32 +def U64 := Scalar .U64 +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 +def Isize.neg := @Scalar.neg .Isize +def I8.neg := @Scalar.neg .I8 +def I16.neg := @Scalar.neg .I16 +def I32.neg := @Scalar.neg .I32 +def I64.neg := @Scalar.neg .I64 +def I128.neg := @Scalar.neg .I128 + +-- Division +def Isize.div := @Scalar.div .Isize +def I8.div := @Scalar.div .I8 +def I16.div := @Scalar.div .I16 +def I32.div := @Scalar.div .I32 +def I64.div := @Scalar.div .I64 +def I128.div := @Scalar.div .I128 +def Usize.div := @Scalar.div .Usize +def U8.div := @Scalar.div .U8 +def U16.div := @Scalar.div .U16 +def U32.div := @Scalar.div .U32 +def U64.div := @Scalar.div .U64 +def U128.div := @Scalar.div .U128 + +-- Remainder +def Isize.rem := @Scalar.rem .Isize +def I8.rem := @Scalar.rem .I8 +def I16.rem := @Scalar.rem .I16 +def I32.rem := @Scalar.rem .I32 +def I64.rem := @Scalar.rem .I64 +def I128.rem := @Scalar.rem .I128 +def Usize.rem := @Scalar.rem .Usize +def U8.rem := @Scalar.rem .U8 +def U16.rem := @Scalar.rem .U16 +def U32.rem := @Scalar.rem .U32 +def U64.rem := @Scalar.rem .U64 +def U128.rem := @Scalar.rem .U128 + +-- Addition +def Isize.add := @Scalar.add .Isize +def I8.add := @Scalar.add .I8 +def I16.add := @Scalar.add .I16 +def I32.add := @Scalar.add .I32 +def I64.add := @Scalar.add .I64 +def I128.add := @Scalar.add .I128 +def Usize.add := @Scalar.add .Usize +def U8.add := @Scalar.add .U8 +def U16.add := @Scalar.add .U16 +def U32.add := @Scalar.add .U32 +def U64.add := @Scalar.add .U64 +def U128.add := @Scalar.add .U128 + +-- Substraction +def Isize.sub := @Scalar.sub .Isize +def I8.sub := @Scalar.sub .I8 +def I16.sub := @Scalar.sub .I16 +def I32.sub := @Scalar.sub .I32 +def I64.sub := @Scalar.sub .I64 +def I128.sub := @Scalar.sub .I128 +def Usize.sub := @Scalar.sub .Usize +def U8.sub := @Scalar.sub .U8 +def U16.sub := @Scalar.sub .U16 +def U32.sub := @Scalar.sub .U32 +def U64.sub := @Scalar.sub .U64 +def U128.sub := @Scalar.sub .U128 + +-- Multiplication +def Isize.mul := @Scalar.mul .Isize +def I8.mul := @Scalar.mul .I8 +def I16.mul := @Scalar.mul .I16 +def I32.mul := @Scalar.mul .I32 +def I64.mul := @Scalar.mul .I64 +def I128.mul := @Scalar.mul .I128 +def Usize.mul := @Scalar.mul .Usize +def U8.mul := @Scalar.mul .U8 +def U16.mul := @Scalar.mul .U16 +def U32.mul := @Scalar.mul .U32 +def U64.mul := @Scalar.mul .U64 +def U128.mul := @Scalar.mul .U128 + +-- ofIntCore +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 +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 + + +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) + +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 .. + +def Scalar.toInt {ty} (n : Scalar ty) : Int := n.val + +-- -- We now define a type class that subsumes the various machine integer types, so +-- -- as to write a concise definition for scalar_cast, rather than exhaustively +-- -- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- -- and fails if a cast operation would involve a truncation or modulo. + +-- class MachineInteger (t: Type) where +-- size: Nat +-- val: t -> Fin size +-- ofNatCore: (n:Nat) -> LT.lt n size -> t + +-- set_option hygiene false in +-- run_cmd +-- for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do +-- Lean.Elab.Command.elabCommand (← `( +-- namespace $typeName +-- instance: MachineInteger $typeName where +-- size := size +-- val := val +-- ofNatCore := ofNatCore +-- end $typeName +-- )) + +-- -- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- -- Lean to infer `src`. + +-- def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := +-- if h: MachineInteger.val x < MachineInteger.size dst then +-- .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) +-- else +-- .fail integerOverflow ------------- -- 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 - } ⟩ +def Vec (α : Type u) := { l : List α // List.length l <= Usize.max } -#check vec_new +def vec_new (α : Type u): Vec α := ⟨ [], by sorry ⟩ -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) + Usize.ofIntCore (List.length v) (by sorry) l -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 ⟩ +def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () -#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) +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 - ⟩ + 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 := +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 + 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 := +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 + have h: List.length v.val <= Usize.max := v.property rewrite [ List.length_set v.val i.val x ] assumption ⟩ @@ -360,33 +586,3 @@ def mem_replace_back (a : Type) (_ : a) (y : a) : a := /-- Aeneas-translated function -- useful to reduce non-recursive definitions. Use with `simp [ aeneas ]` -/ register_simp_attr aeneas - --------------------- --- 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) - -------------------- --- SANITY CHECKS -- -------------------- - --- TODO: add more once we have signed integers - -#assert (USize.checked_rem 1 2 == .ret 1) |