diff options
Diffstat (limited to 'tests/lean/misc-loops')
| -rw-r--r-- | tests/lean/misc-loops/Base/Primitives.lean | 622 | ||||
| -rw-r--r-- | tests/lean/misc-loops/Loops/Clauses/Clauses.lean | 42 | ||||
| -rw-r--r-- | tests/lean/misc-loops/Loops/Clauses/Template.lean | 45 | ||||
| -rw-r--r-- | tests/lean/misc-loops/Loops/Funs.lean | 281 |
4 files changed, 567 insertions, 423 deletions
diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean index 5b64e908..034f41b2 100644 --- a/tests/lean/misc-loops/Base/Primitives.lean +++ b/tests/lean/misc-loops/Base/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 @@ -89,17 +112,13 @@ macro "let" e:term " <-- " f:term : doElem => -- MACHINE INTEGERS -- ---------------------- --- 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. +-- We redefine our machine integers types. --- 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.) +-- 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 @@ -111,236 +130,435 @@ macro "let" e:term " <-- " f:term : doElem => -- 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 - -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) - --- 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 + +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 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 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 -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 +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 -- ------------- --- 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 ⟩ - -#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 - ⟩ + 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 + -- 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.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 := - if h: i.val < List.length v.val then +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 := +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 +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) := +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.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 +578,3 @@ 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) diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean index 5ddb65ca..89a7ce34 100644 --- a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean +++ b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean @@ -4,7 +4,7 @@ import Loops.Types /- [loops::sum]: termination measure -/ @[simp] -def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) +def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) syntax "sum_loop_decreases" term+ : tactic @@ -13,8 +13,7 @@ macro_rules /- [loops::sum_with_mut_borrows]: termination measure -/ @[simp] -def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) - (ms : UInt32) := +def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) := (max, mi, ms) syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic @@ -24,8 +23,7 @@ macro_rules /- [loops::sum_with_shared_borrows]: termination measure -/ @[simp] -def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) - (s : UInt32) := +def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic @@ -34,7 +32,7 @@ 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 U32) (i : Usize) := (v, i) syntax "clear_loop_decreases" term+ : tactic @@ -43,7 +41,7 @@ macro_rules /- [loops::list_mem]: termination measure -/ @[simp] -def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls) +def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls) syntax "list_mem_loop_decreases" term+ : tactic @@ -52,8 +50,7 @@ macro_rules /- [loops::list_nth_mut_loop]: termination measure -/ @[simp] -def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) - := +def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) := (ls, i) syntax "list_nth_mut_loop_loop_decreases" term+ : tactic @@ -63,8 +60,7 @@ macro_rules /- [loops::list_nth_shared_loop]: termination measure -/ @[simp] -def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) - (i : UInt32) := +def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) := (ls, i) syntax "list_nth_shared_loop_loop_decreases" term+ : tactic @@ -74,7 +70,7 @@ macro_rules /- [loops::get_elem_mut]: termination measure -/ @[simp] -def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) syntax "get_elem_mut_loop_decreases" term+ : tactic @@ -83,7 +79,7 @@ macro_rules /- [loops::get_elem_shared]: termination measure -/ @[simp] -def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) syntax "get_elem_shared_loop_decreases" term+ : tactic @@ -92,7 +88,7 @@ macro_rules /- [loops::list_nth_mut_loop_with_id]: termination measure -/ @[simp] -def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -103,7 +99,7 @@ macro_rules /- [loops::list_nth_shared_loop_with_id]: termination measure -/ @[simp] -def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -115,7 +111,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair]: termination measure -/ @[simp] def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic @@ -126,7 +122,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair]: termination measure -/ @[simp] def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic @@ -138,7 +134,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic @@ -150,7 +146,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic @@ -162,7 +158,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic @@ -174,7 +170,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic @@ -186,7 +182,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic @@ -198,7 +194,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean index d1e72d65..2e28a6c0 100644 --- a/tests/lean/misc-loops/Loops/Clauses/Template.lean +++ b/tests/lean/misc-loops/Loops/Clauses/Template.lean @@ -4,8 +4,7 @@ import Base.Primitives import Loops.Types /- [loops::sum]: termination measure -/ -@[simp] -def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) +@[simp] def sum_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) /- [loops::sum]: decreases_by tactic -/ syntax "sum_loop_decreases" term+ : tactic @@ -14,8 +13,7 @@ macro_rules /- [loops::sum_with_mut_borrows]: termination measure -/ @[simp] -def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) - (ms : UInt32) := +def sum_with_mut_borrows_loop_terminates (max : U32) (mi : U32) (ms : U32) := (max, mi, ms) /- [loops::sum_with_mut_borrows]: decreases_by tactic -/ @@ -25,8 +23,7 @@ macro_rules /- [loops::sum_with_shared_borrows]: termination measure -/ @[simp] -def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) - (s : UInt32) := +def sum_with_shared_borrows_loop_terminates (max : U32) (i : U32) (s : U32) := (max, i, s) /- [loops::sum_with_shared_borrows]: decreases_by tactic -/ @@ -35,7 +32,7 @@ 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 U32) (i : Usize) := (v, i) /- [loops::clear]: decreases_by tactic -/ syntax "clear_loop_decreases" term+ : tactic @@ -43,8 +40,7 @@ macro_rules | `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry) /- [loops::list_mem]: termination measure -/ -@[simp] -def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls) +@[simp] def list_mem_loop_terminates (x : U32) (ls : list_t U32) := (x, ls) /- [loops::list_mem]: decreases_by tactic -/ syntax "list_mem_loop_decreases" term+ : tactic @@ -53,8 +49,7 @@ macro_rules /- [loops::list_nth_mut_loop]: termination measure -/ @[simp] -def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) - := +def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) := (ls, i) /- [loops::list_nth_mut_loop]: decreases_by tactic -/ @@ -64,8 +59,8 @@ macro_rules /- [loops::list_nth_shared_loop]: termination measure -/ @[simp] -def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) - (i : UInt32) := +def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) (i : U32) + := (ls, i) /- [loops::list_nth_shared_loop]: decreases_by tactic -/ @@ -75,7 +70,7 @@ macro_rules /- [loops::get_elem_mut]: termination measure -/ @[simp] -def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_mut_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) /- [loops::get_elem_mut]: decreases_by tactic -/ syntax "get_elem_mut_loop_decreases" term+ : tactic @@ -84,7 +79,7 @@ macro_rules /- [loops::get_elem_shared]: termination measure -/ @[simp] -def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) +def get_elem_shared_loop_terminates (x : Usize) (ls : list_t Usize) := (x, ls) /- [loops::get_elem_shared]: decreases_by tactic -/ syntax "get_elem_shared_loop_decreases" term+ : tactic @@ -93,7 +88,7 @@ macro_rules /- [loops::list_nth_mut_loop_with_id]: termination measure -/ @[simp] -def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -104,7 +99,7 @@ macro_rules /- [loops::list_nth_shared_loop_with_id]: termination measure -/ @[simp] -def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) +def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : U32) (ls : list_t T) := (i, ls) @@ -116,7 +111,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair]: termination measure -/ @[simp] def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/ @@ -127,7 +122,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair]: termination measure -/ @[simp] def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/ @@ -139,7 +134,7 @@ macro_rules /- [loops::list_nth_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/ @@ -151,7 +146,7 @@ macro_rules /- [loops::list_nth_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/ @@ -163,7 +158,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/ @@ -175,7 +170,7 @@ macro_rules /- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/ @[simp] def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/ @@ -187,7 +182,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) - (ls1 : list_t T) (i : UInt32) := + (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/ @@ -199,7 +194,7 @@ macro_rules /- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/ @[simp] def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type) - (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0 : list_t T) (ls1 : list_t T) (i : U32) := (ls0, ls1, i) /- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/ diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean index f79a27a9..fd8d62d7 100644 --- a/tests/lean/misc-loops/Loops/Funs.lean +++ b/tests/lean/misc-loops/Loops/Funs.lean @@ -5,79 +5,78 @@ import Loops.Types import Loops.Clauses.Clauses /- [loops::sum] -/ -def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := +def sum_loop_fwd (max : U32) (i : U32) (s : U32) : (Result U32) := 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 ← s + i + let i0 ← i + (U32.ofInt 1 (by intlit)) sum_loop_fwd max i0 s0 - else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit)) + else s * (U32.ofInt 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 := - sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 0 (by intlit)) +def sum_fwd (max : U32) : Result U32 := + sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit)) /- [loops::sum_with_mut_borrows] -/ def sum_with_mut_borrows_loop_fwd - (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) := + (max : U32) (mi : U32) (ms : U32) : (Result U32) := 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 ← ms + mi + let mi0 ← mi + (U32.ofInt 1 (by intlit)) sum_with_mut_borrows_loop_fwd max mi0 ms0 - else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit)) + else ms * (U32.ofInt 2 (by intlit)) termination_by sum_with_mut_borrows_loop_fwd max mi ms => sum_with_mut_borrows_loop_terminates 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 := - sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 0 (by intlit)) +def sum_with_mut_borrows_fwd (max : U32) : Result U32 := + sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit)) + (U32.ofInt 0 (by intlit)) /- [loops::sum_with_shared_borrows] -/ def sum_with_shared_borrows_loop_fwd - (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := + (max : U32) (i : U32) (s : U32) : (Result U32) := 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 ← i + (U32.ofInt 1 (by intlit)) + let s0 ← s + i0 sum_with_shared_borrows_loop_fwd max i0 s0 - else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit)) + else s * (U32.ofInt 2 (by intlit)) termination_by sum_with_shared_borrows_loop_fwd max i s => sum_with_shared_borrows_loop_terminates 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 := - sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 0 (by intlit)) +def sum_with_shared_borrows_fwd (max : U32) : Result U32 := + sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit)) + (U32.ofInt 0 (by intlit)) /- [loops::clear] -/ -def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) := - let i0 := vec_len UInt32 v +def clear_loop_fwd_back (v : Vec U32) (i : Usize) : (Result (Vec U32)) := + let i0 := vec_len U32 v 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 ← i + (Usize.ofInt 1 (by intlit)) + let v0 ← vec_index_mut_back U32 v i (U32.ofInt 0 (by intlit)) clear_loop_fwd_back v0 i1 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) := - clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit)) +def clear_fwd_back (v : Vec U32) : Result (Vec U32) := + clear_loop_fwd_back v (Usize.ofInt 0 (by intlit)) /- [loops::list_mem] -/ -def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) := +def list_mem_loop_fwd (x : U32) (ls : list_t U32) : (Result Bool) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -88,19 +87,19 @@ 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 : U32) (ls : list_t U32) : 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) := + (T : Type) (ls : list_t T) (i : U32) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_loop_fwd T tl i0 | list_t.Nil => Result.fail Error.panic termination_by list_nth_mut_loop_loop_fwd ls i => @@ -108,19 +107,19 @@ termination_by list_nth_mut_loop_loop_fwd 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 : U32) : 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)) := + (T : Type) (ls : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0 Result.ret (list_t.Cons x tl0) | list_t.Nil => Result.fail Error.panic @@ -130,19 +129,19 @@ 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 : U32) (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) := + (T : Type) (ls : list_t T) (i : U32) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_loop_fwd T tl i0 | list_t.Nil => Result.fail Error.panic termination_by list_nth_shared_loop_loop_fwd ls i => @@ -150,12 +149,11 @@ termination_by list_nth_shared_loop_loop_fwd 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 := +def list_nth_shared_loop_fwd (T : Type) (ls : list_t T) (i : U32) : 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) := +def get_elem_mut_loop_fwd (x : Usize) (ls : list_t Usize) : (Result Usize) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -166,15 +164,15 @@ 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 ← - vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 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)) := + (x : Usize) (ls : list_t Usize) (ret0 : Usize) : (Result (list_t Usize)) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -190,18 +188,18 @@ 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 ← - vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + vec_index_mut_fwd (list_t Usize) slots (Usize.ofInt 0 (by intlit)) let l0 ← get_elem_mut_loop_back x l ret0 - vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0 + vec_index_mut_back (list_t Usize) slots (Usize.ofInt 0 (by intlit)) l0 /- [loops::get_elem_shared] -/ def get_elem_shared_loop_fwd - (x : USize) (ls : list_t USize) : (Result USize) := + (x : Usize) (ls : list_t Usize) : (Result Usize) := match h: ls with | list_t.Cons y tl => if h: y = x @@ -214,10 +212,9 @@ 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.ofInt 0 (by intlit)) get_elem_shared_loop_fwd x l /- [loops::id_mut] -/ @@ -235,14 +232,14 @@ def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) := /- [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) := + (T : Type) (i : U32) (ls : list_t T) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_with_id_loop_fwd T i0 tl | list_t.Nil => Result.fail Error.panic termination_by list_nth_mut_loop_with_id_loop_fwd i ls => @@ -251,21 +248,21 @@ 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 : U32) : Result T := do 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)) := + (T : Type) (i : U32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0 Result.ret (list_t.Cons x tl0) | list_t.Nil => Result.fail Error.panic @@ -275,7 +272,7 @@ 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 : U32) (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 @@ -283,14 +280,14 @@ def list_nth_mut_loop_with_id_back /- [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) := + (T : Type) (i : U32) (ls : list_t T) : (Result T) := match h: ls with | list_t.Cons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret x else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_with_id_loop_fwd T i0 tl | list_t.Nil => Result.fail Error.panic termination_by list_nth_shared_loop_with_id_loop_fwd i ls => @@ -299,25 +296,23 @@ 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 : U32) : Result T := do 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -327,25 +322,23 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl0) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00) | list_t.Nil => Result.fail Error.panic @@ -356,25 +349,25 @@ 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x1 tl10) | list_t.Nil => Result.fail Error.panic @@ -385,25 +378,23 @@ 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -413,25 +404,21 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -441,27 +428,25 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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)) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (T × T)) : (Result ((list_t T) × (list_t T))) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then let (t, t0) := ret0 Result.ret (list_t.Cons t tl0, list_t.Cons t0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let (tl00, tl10) ← list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00, list_t.Cons x1 tl10) @@ -473,25 +458,23 @@ 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)) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : (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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -501,25 +484,21 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -529,25 +508,23 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl0) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl00 ← list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00) @@ -559,25 +536,23 @@ 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -587,25 +562,23 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl0) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl00 ← list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x0 tl00) @@ -617,25 +590,23 @@ 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -645,25 +616,23 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl10 ← list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x1 tl10) @@ -675,25 +644,23 @@ 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : 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)) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : (Result (T × T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (x0, x1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 | list_t.Nil => Result.fail Error.panic | list_t.Nil => Result.fail Error.panic @@ -703,25 +670,23 @@ 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) - := + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) : 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : (Result (list_t T)) := match h: ls0 with | list_t.Cons x0 tl0 => match h: ls1 with | list_t.Cons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (U32.ofInt 0 (by intlit)) then Result.ret (list_t.Cons ret0 tl1) else do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let i0 ← i - (U32.ofInt 1 (by intlit)) let tl10 ← list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 Result.ret (list_t.Cons x1 tl10) @@ -733,7 +698,7 @@ 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) : + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : U32) (ret0 : T) : Result (list_t T) := list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0 |