diff options
Diffstat (limited to 'tests/lean/misc')
20 files changed, 0 insertions, 4172 deletions
diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean deleted file mode 100644 index 5b64e908..00000000 --- a/tests/lean/misc/constants/Base/Primitives.lean +++ /dev/null @@ -1,392 +0,0 @@ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd - -------------- --- PRELUDE -- -------------- - --- Results & monadic combinators - -inductive Error where - | assertionFailure: Error - | integerOverflow: Error - | arrayOutOfBounds: Error - | maximumSizeExceeded: Error - | panic: Error -deriving Repr, BEq - -open Error - -inductive Result (α : Type u) where - | ret (v: α): Result α - | fail (e: Error): Result α -deriving Repr, BEq - -open Result - -/- HELPERS -/ - -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 -- ----------------------- - --- 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. - --- 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.) - --- 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. - -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`). --- This is useful for the various #asserts that we want to reduce at --- type-checking time. - --- 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 - -------------- --- VECTORS -- -------------- - --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ - -#check vec_new - -def vec_len (α : Type u) (v : Vec α) : USize := - let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) - -def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () - --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - -def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) - := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ - else - fail maximumSizeExceeded - -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - ----------- --- MISC -- ----------- - -def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := - x - -def mem_replace_back (a : Type) (_ : a) (y : a) : a := - y - -/-- 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/constants/Constants.lean b/tests/lean/misc/constants/Constants.lean deleted file mode 100644 index 57f6e403..00000000 --- a/tests/lean/misc/constants/Constants.lean +++ /dev/null @@ -1,141 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [constants] -import Base.Primitives - -structure OpaqueDefs where - - /- [constants::X0] -/ - def x0_body : Result UInt32 := Result.ret (UInt32.ofNatCore 0 (by intlit)) - def x0_c : UInt32 := eval_global x0_body (by simp) - - /- [core::num::u32::{9}::MAX] -/ - def core_num_u32_max_body : Result UInt32 := - Result.ret (UInt32.ofNatCore 4294967295 (by intlit)) - def core_num_u32_max_c : UInt32 := - eval_global core_num_u32_max_body (by simp) - - /- [constants::X1] -/ - def x1_body : Result UInt32 := Result.ret core_num_u32_max_c - def x1_c : UInt32 := eval_global x1_body (by simp) - - /- [constants::X2] -/ - def x2_body : Result UInt32 := Result.ret (UInt32.ofNatCore 3 (by intlit)) - def x2_c : UInt32 := eval_global x2_body (by simp) - - /- [constants::incr] -/ - def incr_fwd (n : UInt32) : Result UInt32 := - UInt32.checked_add n (UInt32.ofNatCore 1 (by intlit)) - - /- [constants::X3] -/ - def x3_body : Result UInt32 := incr_fwd (UInt32.ofNatCore 32 (by intlit)) - def x3_c : UInt32 := eval_global x3_body (by simp) - - /- [constants::mk_pair0] -/ - def mk_pair0_fwd (x : UInt32) (y : UInt32) : Result (UInt32 × UInt32) := - Result.ret (x, y) - - /- [constants::Pair] -/ - structure pair_t (T1 T2 : Type) where pair_x : T1 pair_y : T2 - - /- [constants::mk_pair1] -/ - def mk_pair1_fwd (x : UInt32) (y : UInt32) : Result (pair_t UInt32 UInt32) := - Result.ret { pair_x := x, pair_y := y } - - /- [constants::P0] -/ - def p0_body : Result (UInt32 × UInt32) := - mk_pair0_fwd (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 1 (by intlit)) - def p0_c : (UInt32 × UInt32) := eval_global p0_body (by simp) - - /- [constants::P1] -/ - def p1_body : Result (pair_t UInt32 UInt32) := - mk_pair1_fwd (UInt32.ofNatCore 0 (by intlit)) - (UInt32.ofNatCore 1 (by intlit)) - def p1_c : pair_t UInt32 UInt32 := eval_global p1_body (by simp) - - /- [constants::P2] -/ - def p2_body : Result (UInt32 × UInt32) := - Result.ret - ((UInt32.ofNatCore 0 (by intlit)), - (UInt32.ofNatCore 1 (by intlit))) - def p2_c : (UInt32 × UInt32) := eval_global p2_body (by simp) - - /- [constants::P3] -/ - def p3_body : Result (pair_t UInt32 UInt32) := - Result.ret - { - pair_x := (UInt32.ofNatCore 0 (by intlit)), - pair_y := (UInt32.ofNatCore 1 (by intlit)) - } - def p3_c : pair_t UInt32 UInt32 := eval_global p3_body (by simp) - - /- [constants::Wrap] -/ - structure wrap_t (T : Type) where wrap_val : T - - /- [constants::Wrap::{0}::new] -/ - def wrap_new_fwd (T : Type) (val : T) : Result (wrap_t T) := - Result.ret { wrap_val := val } - - /- [constants::Y] -/ - def y_body : Result (wrap_t Int32) := - wrap_new_fwd Int32 (Int32.ofNatCore 2 (by intlit)) - def y_c : wrap_t Int32 := eval_global y_body (by simp) - - /- [constants::unwrap_y] -/ - def unwrap_y_fwd : Result Int32 := - Result.ret y_c.wrap_val - - /- [constants::YVAL] -/ - def yval_body : Result Int32 := unwrap_y_fwd - def yval_c : Int32 := eval_global yval_body (by simp) - - /- [constants::get_z1::Z1] -/ - def get_z1_z1_body : Result Int32 := - Result.ret (Int32.ofNatCore 3 (by intlit)) - def get_z1_z1_c : Int32 := eval_global get_z1_z1_body (by simp) - - /- [constants::get_z1] -/ - def get_z1_fwd : Result Int32 := - Result.ret get_z1_z1_c - - /- [constants::add] -/ - def add_fwd (a : Int32) (b : Int32) : Result Int32 := - Int32.checked_add a b - - /- [constants::Q1] -/ - def q1_body : Result Int32 := Result.ret (Int32.ofNatCore 5 (by intlit)) - def q1_c : Int32 := eval_global q1_body (by simp) - - /- [constants::Q2] -/ - def q2_body : Result Int32 := Result.ret q1_c - def q2_c : Int32 := eval_global q2_body (by simp) - - /- [constants::Q3] -/ - def q3_body : Result Int32 := add_fwd q2_c (Int32.ofNatCore 3 (by intlit)) - def q3_c : Int32 := eval_global q3_body (by simp) - - /- [constants::get_z2] -/ - def get_z2_fwd : Result Int32 := - do - let i ← get_z1_fwd - let i0 ← add_fwd i q3_c - add_fwd q1_c i0 - - /- [constants::S1] -/ - def s1_body : Result UInt32 := Result.ret (UInt32.ofNatCore 6 (by intlit)) - def s1_c : UInt32 := eval_global s1_body (by simp) - - /- [constants::S2] -/ - def s2_body : Result UInt32 := incr_fwd s1_c - def s2_c : UInt32 := eval_global s2_body (by simp) - - /- [constants::S3] -/ - def s3_body : Result (pair_t UInt32 UInt32) := Result.ret p3_c - def s3_c : pair_t UInt32 UInt32 := eval_global s3_body (by simp) - - /- [constants::S4] -/ - def s4_body : Result (pair_t UInt32 UInt32) := - mk_pair1_fwd (UInt32.ofNatCore 7 (by intlit)) - (UInt32.ofNatCore 8 (by intlit)) - def s4_c : pair_t UInt32 UInt32 := eval_global s4_body (by simp) - diff --git a/tests/lean/misc/constants/lakefile.lean b/tests/lean/misc/constants/lakefile.lean deleted file mode 100644 index ed8eebc2..00000000 --- a/tests/lean/misc/constants/lakefile.lean +++ /dev/null @@ -1,18 +0,0 @@ -import Lake -open Lake DSL - -require mathlib from git - "https://github.com/leanprover-community/mathlib4.git" - -package «constants» { - -- add package configuration options here -} - -lean_lib «Base» { - -- add library configuration options here -} - -lean_lib «Constants» { - -- add library configuration options here -} - diff --git a/tests/lean/misc/external/Base/Primitives.lean b/tests/lean/misc/external/Base/Primitives.lean deleted file mode 100644 index 5b64e908..00000000 --- a/tests/lean/misc/external/Base/Primitives.lean +++ /dev/null @@ -1,392 +0,0 @@ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd - -------------- --- PRELUDE -- -------------- - --- Results & monadic combinators - -inductive Error where - | assertionFailure: Error - | integerOverflow: Error - | arrayOutOfBounds: Error - | maximumSizeExceeded: Error - | panic: Error -deriving Repr, BEq - -open Error - -inductive Result (α : Type u) where - | ret (v: α): Result α - | fail (e: Error): Result α -deriving Repr, BEq - -open Result - -/- HELPERS -/ - -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 -- ----------------------- - --- 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. - --- 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.) - --- 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. - -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`). --- This is useful for the various #asserts that we want to reduce at --- type-checking time. - --- 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 - -------------- --- VECTORS -- -------------- - --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ - -#check vec_new - -def vec_len (α : Type u) (v : Vec α) : USize := - let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) - -def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () - --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - -def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) - := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ - else - fail maximumSizeExceeded - -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - ----------- --- MISC -- ----------- - -def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := - x - -def mem_replace_back (a : Type) (_ : a) (y : a) : a := - y - -/-- 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/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean deleted file mode 100644 index 4e1f36a1..00000000 --- a/tests/lean/misc/external/External/Funs.lean +++ /dev/null @@ -1,93 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [external]: function definitions -import Base.Primitives -import External.Types -import External.Opaque - -section variable (opaque_defs: OpaqueDefs) - -/- [external::swap] -/ -def swap_fwd - (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) := - do - let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st - let (st1, _) ← opaque_defs.core_mem_swap_back0 T x y st st0 - let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1 - Result.ret (st2, ()) - -/- [external::swap] -/ -def swap_back - (T : Type) (x : T) (y : T) (st : State) (st0 : State) : - Result (State × (T × T)) - := - do - let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st - let (st2, x0) ← opaque_defs.core_mem_swap_back0 T x y st st1 - let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2 - Result.ret (st0, (x0, y0)) - -/- [external::test_new_non_zero_u32] -/ -def test_new_non_zero_u32_fwd - (x : UInt32) (st : State) : - Result (State × core_num_nonzero_non_zero_u32_t) - := - do - let (st0, opt) ← opaque_defs.core_num_nonzero_non_zero_u32_new_fwd x st - opaque_defs.core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t - opt st0 - -/- [external::test_vec] -/ -def test_vec_fwd : Result Unit := - do - let v := vec_new UInt32 - let _ ← vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit)) - Result.ret () - -/- Unit test for [external::test_vec] -/ -#assert (test_vec_fwd == .ret ()) - -/- [external::custom_swap] -/ -def custom_swap_fwd - (T : Type) (x : T) (y : T) (st : State) : Result (State × T) := - do - let (st0, _) ← opaque_defs.core_mem_swap_fwd T x y st - let (st1, x0) ← opaque_defs.core_mem_swap_back0 T x y st st0 - let (st2, _) ← opaque_defs.core_mem_swap_back1 T x y st st1 - Result.ret (st2, x0) - -/- [external::custom_swap] -/ -def custom_swap_back - (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) : - Result (State × (T × T)) - := - do - let (st1, _) ← opaque_defs.core_mem_swap_fwd T x y st - let (st2, _) ← opaque_defs.core_mem_swap_back0 T x y st st1 - let (_, y0) ← opaque_defs.core_mem_swap_back1 T x y st st2 - Result.ret (st0, (ret0, y0)) - -/- [external::test_custom_swap] -/ -def test_custom_swap_fwd - (x : UInt32) (y : UInt32) (st : State) : Result (State × Unit) := - do - let (st0, _) ← custom_swap_fwd UInt32 x y st - Result.ret (st0, ()) - -/- [external::test_custom_swap] -/ -def test_custom_swap_back - (x : UInt32) (y : UInt32) (st : State) (st0 : State) : - Result (State × (UInt32 × UInt32)) - := - custom_swap_back UInt32 x y st (UInt32.ofNatCore 1 (by intlit)) st0 - -/- [external::test_swap_non_zero] -/ -def test_swap_non_zero_fwd - (x : UInt32) (st : State) : Result (State × UInt32) := - do - let (st0, _) ← swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st - let (st1, (x0, _)) ← - swap_back UInt32 x (UInt32.ofNatCore 0 (by intlit)) st st0 - if h: x0 = (UInt32.ofNatCore 0 (by intlit)) - then Result.fail Error.panic - else Result.ret (st1, x0) - diff --git a/tests/lean/misc/external/External/Opaque.lean b/tests/lean/misc/external/External/Opaque.lean deleted file mode 100644 index d3582de3..00000000 --- a/tests/lean/misc/external/External/Opaque.lean +++ /dev/null @@ -1,28 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [external]: opaque function definitions -import Base.Primitives -import External.Types - -structure OpaqueDefs where - - /- [core::mem::swap] -/ - core_mem_swap_fwd (T : Type) : T -> T -> State -> Result (State × Unit) - - /- [core::mem::swap] -/ - core_mem_swap_back0 - (T : Type) : T -> T -> State -> State -> Result (State × T) - - /- [core::mem::swap] -/ - core_mem_swap_back1 - (T : Type) : T -> T -> State -> State -> Result (State × T) - - /- [core::num::nonzero::NonZeroU32::{14}::new] -/ - core_num_nonzero_non_zero_u32_new_fwd - : - UInt32 -> State -> Result (State × (Option - core_num_nonzero_non_zero_u32_t)) - - /- [core::option::Option::{0}::unwrap] -/ - core_option_option_unwrap_fwd - (T : Type) : Option T -> State -> Result (State × T) - diff --git a/tests/lean/misc/external/External/Types.lean b/tests/lean/misc/external/External/Types.lean deleted file mode 100644 index 386832f4..00000000 --- a/tests/lean/misc/external/External/Types.lean +++ /dev/null @@ -1,8 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [external]: type definitions -import Base.Primitives - -/- [core::num::nonzero::NonZeroU32] -/ -axiom core_num_nonzero_non_zero_u32_t : Type -/- The state type used in the state-error monad -/ axiom State : Type - diff --git a/tests/lean/misc/external/lakefile.lean b/tests/lean/misc/external/lakefile.lean deleted file mode 100644 index b883f4b9..00000000 --- a/tests/lean/misc/external/lakefile.lean +++ /dev/null @@ -1,18 +0,0 @@ -import Lake -open Lake DSL - -require mathlib from git - "https://github.com/leanprover-community/mathlib4.git" - -package «external» { - -- add package configuration options here -} - -lean_lib «Base» { - -- add library configuration options here -} - -lean_lib «External» { - -- add library configuration options here -} - diff --git a/tests/lean/misc/loops/Base/Primitives.lean b/tests/lean/misc/loops/Base/Primitives.lean deleted file mode 100644 index 5b64e908..00000000 --- a/tests/lean/misc/loops/Base/Primitives.lean +++ /dev/null @@ -1,392 +0,0 @@ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd - -------------- --- PRELUDE -- -------------- - --- Results & monadic combinators - -inductive Error where - | assertionFailure: Error - | integerOverflow: Error - | arrayOutOfBounds: Error - | maximumSizeExceeded: Error - | panic: Error -deriving Repr, BEq - -open Error - -inductive Result (α : Type u) where - | ret (v: α): Result α - | fail (e: Error): Result α -deriving Repr, BEq - -open Result - -/- HELPERS -/ - -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 -- ----------------------- - --- 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. - --- 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.) - --- 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. - -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`). --- This is useful for the various #asserts that we want to reduce at --- type-checking time. - --- 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 - -------------- --- VECTORS -- -------------- - --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ - -#check vec_new - -def vec_len (α : Type u) (v : Vec α) : USize := - let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) - -def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () - --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - -def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) - := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ - else - fail maximumSizeExceeded - -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - ----------- --- MISC -- ----------- - -def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := - x - -def mem_replace_back (a : Type) (_ : a) (y : a) : a := - y - -/-- 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 deleted file mode 100644 index 5ddb65ca..00000000 --- a/tests/lean/misc/loops/Loops/Clauses/Clauses.lean +++ /dev/null @@ -1,209 +0,0 @@ --- [loops]: decreases clauses -import Base.Primitives -import Loops.Types - -/- [loops::sum]: termination measure -/ -@[simp] -def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) - -syntax "sum_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry) - -/- [loops::sum_with_mut_borrows]: termination measure -/ -@[simp] -def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) - (ms : UInt32) := - (max, mi, ms) - -syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry) - -/- [loops::sum_with_shared_borrows]: termination measure -/ -@[simp] -def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) - (s : UInt32) := - (max, i, s) - -syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic - -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) - -syntax "clear_loop_decreases" term+ : tactic - -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) - -syntax "list_mem_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry) - -/- [loops::list_nth_mut_loop]: termination measure -/ -@[simp] -def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) - := - (ls, i) - -syntax "list_nth_mut_loop_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry) - -/- [loops::list_nth_shared_loop]: termination measure -/ -@[simp] -def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) - (i : UInt32) := - (ls, i) - -syntax "list_nth_shared_loop_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry) - -/- [loops::get_elem_mut]: termination measure -/ -@[simp] -def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) - -syntax "get_elem_mut_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry) - -/- [loops::get_elem_shared]: termination measure -/ -@[simp] -def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) - -syntax "get_elem_shared_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry) - -/- [loops::list_nth_mut_loop_with_id]: termination measure -/ -@[simp] -def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) - (ls : list_t T) := - (i, ls) - -syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) - -/- [loops::list_nth_shared_loop_with_id]: termination measure -/ -@[simp] -def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) - (ls : list_t T) := - (i, ls) - -syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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, ls1, i) - -syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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, ls1, i) - -syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic - -macro_rules -| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - diff --git a/tests/lean/misc/loops/Loops/Clauses/Template.lean b/tests/lean/misc/loops/Loops/Clauses/Template.lean deleted file mode 100644 index d1e72d65..00000000 --- a/tests/lean/misc/loops/Loops/Clauses/Template.lean +++ /dev/null @@ -1,210 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [loops]: templates for the decreases clauses -import Base.Primitives -import Loops.Types - -/- [loops::sum]: termination measure -/ -@[simp] -def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) - -/- [loops::sum]: decreases_by tactic -/ -syntax "sum_loop_decreases" term+ : tactic -macro_rules -| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry) - -/- [loops::sum_with_mut_borrows]: termination measure -/ -@[simp] -def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) - (ms : UInt32) := - (max, mi, ms) - -/- [loops::sum_with_mut_borrows]: decreases_by tactic -/ -syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic -macro_rules -| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry) - -/- [loops::sum_with_shared_borrows]: termination measure -/ -@[simp] -def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) - (s : UInt32) := - (max, i, s) - -/- [loops::sum_with_shared_borrows]: decreases_by tactic -/ -syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic -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) - -/- [loops::clear]: decreases_by tactic -/ -syntax "clear_loop_decreases" term+ : tactic -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) - -/- [loops::list_mem]: decreases_by tactic -/ -syntax "list_mem_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry) - -/- [loops::list_nth_mut_loop]: termination measure -/ -@[simp] -def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) - := - (ls, i) - -/- [loops::list_nth_mut_loop]: decreases_by tactic -/ -syntax "list_nth_mut_loop_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry) - -/- [loops::list_nth_shared_loop]: termination measure -/ -@[simp] -def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) - (i : UInt32) := - (ls, i) - -/- [loops::list_nth_shared_loop]: decreases_by tactic -/ -syntax "list_nth_shared_loop_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry) - -/- [loops::get_elem_mut]: termination measure -/ -@[simp] -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 -macro_rules -| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry) - -/- [loops::get_elem_shared]: termination measure -/ -@[simp] -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 -macro_rules -| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry) - -/- [loops::list_nth_mut_loop_with_id]: termination measure -/ -@[simp] -def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) - (ls : list_t T) := - (i, ls) - -/- [loops::list_nth_mut_loop_with_id]: decreases_by tactic -/ -syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) - -/- [loops::list_nth_shared_loop_with_id]: termination measure -/ -@[simp] -def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) - (ls : list_t T) := - (i, ls) - -/- [loops::list_nth_shared_loop_with_id]: decreases_by tactic -/ -syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -/- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/ -syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -/- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/ -syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -/- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/ -syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -/- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/ -syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -/- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/ -syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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, ls1, i) - -/- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/ -syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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) := - (ls0, ls1, i) - -/- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/ -syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - -/- [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, ls1, i) - -/- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/ -syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic -macro_rules -| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => - `(tactic| sorry) - diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean deleted file mode 100644 index 5a81ebff..00000000 --- a/tests/lean/misc/loops/Loops/Funs.lean +++ /dev/null @@ -1,740 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [loops]: function definitions -import Base.Primitives -import Loops.Types -import Loops.Clauses.Clauses - -/- [loops::sum] -/ -def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := - if h: i < max - then - do - let s0 ← UInt32.checked_add s i - let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) - sum_loop_fwd max i0 s0 - else UInt32.checked_mul s (UInt32.ofNatCore 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)) - -/- [loops::sum_with_mut_borrows] -/ -def sum_with_mut_borrows_loop_fwd - (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) := - if h: mi < max - then - do - let ms0 ← UInt32.checked_add ms mi - let mi0 ← UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit)) - sum_with_mut_borrows_loop_fwd max mi0 ms0 - else UInt32.checked_mul ms (UInt32.ofNatCore 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)) - -/- [loops::sum_with_shared_borrows] -/ -def sum_with_shared_borrows_loop_fwd - (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := - if h: i < max - then - do - let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) - let s0 ← UInt32.checked_add s i0 - sum_with_shared_borrows_loop_fwd max i0 s0 - else UInt32.checked_mul s (UInt32.ofNatCore 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)) - -/- [loops::clear] -/ -def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) := - let i0 := vec_len UInt32 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)) - 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)) - -/- [loops::list_mem] -/ -def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) := - match h: ls with - | list_t.ListCons y tl => - if h: y = x - then Result.ret true - else list_mem_loop_fwd x tl - | list_t.ListNil => Result.ret false -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 := - 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) := - match h: ls with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_loop_loop_fwd T tl i0 - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_loop_fwd ls i => - list_nth_mut_loop_loop_terminates T 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 := - 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)) := - match h: ls with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0 - Result.ret (list_t.ListCons x tl0) - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_loop_back ls i ret0 => - list_nth_mut_loop_loop_terminates T ls i -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) := - 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) := - match h: ls with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_loop_loop_fwd T tl i0 - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_loop_loop_fwd ls i => - list_nth_shared_loop_loop_terminates T 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 := - 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) := - match h: ls with - | list_t.ListCons y tl => - if h: y = x - then Result.ret y - else get_elem_mut_loop_fwd x tl - | list_t.ListNil => Result.fail Error.panic -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 := - do - let l ← - vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 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)) := - match h: ls with - | list_t.ListCons y tl => - if h: y = x - then Result.ret (list_t.ListCons ret0 tl) - else - do - let tl0 ← get_elem_mut_loop_back x tl ret0 - Result.ret (list_t.ListCons y tl0) - | list_t.ListNil => Result.fail Error.panic -termination_by get_elem_mut_loop_back x ls ret0 => - get_elem_mut_loop_terminates x ls -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)) - := - do - let l ← - vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 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 - -/- [loops::get_elem_shared] -/ -def get_elem_shared_loop_fwd - (x : USize) (ls : list_t USize) : (Result USize) := - match h: ls with - | list_t.ListCons y tl => - if h: y = x - then Result.ret y - else get_elem_shared_loop_fwd x tl - | list_t.ListNil => Result.fail Error.panic -termination_by get_elem_shared_loop_fwd x ls => - get_elem_shared_loop_terminates x ls -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 := - do - let l ← - vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) - get_elem_shared_loop_fwd x l - -/- [loops::id_mut] -/ -def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) := - Result.ret ls - -/- [loops::id_mut] -/ -def id_mut_back - (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) := - Result.ret ret0 - -/- [loops::id_shared] -/ -def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) := - Result.ret ls - -/- [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) := - match h: ls with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_loop_with_id_loop_fwd T i0 tl - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_with_id_loop_fwd i ls => - list_nth_mut_loop_with_id_loop_terminates T i ls -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 := - 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)) := - match h: ls with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0 - Result.ret (list_t.ListCons x tl0) - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 => - list_nth_mut_loop_with_id_loop_terminates T i ls -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) := - do - let ls0 ← id_mut_fwd T ls - let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0 - id_mut_back T ls l - -/- [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) := - match h: ls with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_loop_with_id_loop_fwd T i0 tl - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_loop_with_id_loop_fwd i ls => - list_nth_shared_loop_with_id_loop_terminates T i ls -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 := - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i => - list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i -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) - := - 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) : - (Result (list_t T)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl0) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x0 tl00) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 => - list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i -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) : - 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) : - (Result (list_t T)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x1 tl10) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 => - list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i -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) : - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i => - list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i -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) - := - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i => - list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i -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) - := - 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)) : - (Result ((list_t T) × (list_t T))) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then - let (t, t0) := ret0 - Result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let (tl00, tl10) ← - list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 => - list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i -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)) : - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i => - list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i -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) - := - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i => - list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i -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) - := - 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) : - (Result (list_t T)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl0) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl00 ← - list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x0 tl00) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 => - list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i -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) : - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i => - list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i -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) - := - 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) : - (Result (list_t T)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl0) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl00 ← - list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x0 tl00) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 => - list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i -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) : - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i => - list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i -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) - := - 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) : - (Result (list_t T)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl10 ← - list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x1 tl10) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 => - list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i -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) : - 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)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (x0, x1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i => - list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i -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) - := - 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) : - (Result (list_t T)) - := - match h: ls0 with - | list_t.ListCons x0 tl0 => - match h: ls1 with - | list_t.ListCons x1 tl1 => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl1) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl10 ← - list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 - Result.ret (list_t.ListCons x1 tl10) - | list_t.ListNil => Result.fail Error.panic - | list_t.ListNil => Result.fail Error.panic -termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 => - list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i -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) : - Result (list_t T) - := - list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0 - diff --git a/tests/lean/misc/loops/Loops/Types.lean b/tests/lean/misc/loops/Loops/Types.lean deleted file mode 100644 index f4b6809e..00000000 --- a/tests/lean/misc/loops/Loops/Types.lean +++ /dev/null @@ -1,9 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [loops]: type definitions -import Base.Primitives - -/- [loops::List] -/ -inductive list_t (T : Type) := -| ListCons : T -> list_t T -> list_t T -| ListNil : list_t T - diff --git a/tests/lean/misc/loops/lakefile.lean b/tests/lean/misc/loops/lakefile.lean deleted file mode 100644 index 0d20ba1f..00000000 --- a/tests/lean/misc/loops/lakefile.lean +++ /dev/null @@ -1,18 +0,0 @@ -import Lake -open Lake DSL - -require mathlib from git - "https://github.com/leanprover-community/mathlib4.git" - -package «loops» { - -- add package configuration options here -} - -lean_lib «Base» { - -- add library configuration options here -} - -lean_lib «Loops» { - -- add library configuration options here -} - diff --git a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean deleted file mode 100644 index 5b64e908..00000000 --- a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean +++ /dev/null @@ -1,392 +0,0 @@ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd - -------------- --- PRELUDE -- -------------- - --- Results & monadic combinators - -inductive Error where - | assertionFailure: Error - | integerOverflow: Error - | arrayOutOfBounds: Error - | maximumSizeExceeded: Error - | panic: Error -deriving Repr, BEq - -open Error - -inductive Result (α : Type u) where - | ret (v: α): Result α - | fail (e: Error): Result α -deriving Repr, BEq - -open Result - -/- HELPERS -/ - -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 -- ----------------------- - --- 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. - --- 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.) - --- 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. - -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`). --- This is useful for the various #asserts that we want to reduce at --- type-checking time. - --- 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 - -------------- --- VECTORS -- -------------- - --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ - -#check vec_new - -def vec_len (α : Type u) (v : Vec α) : USize := - let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) - -def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () - --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - -def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) - := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ - else - fail maximumSizeExceeded - -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - ----------- --- MISC -- ----------- - -def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := - x - -def mem_replace_back (a : Type) (_ : a) (y : a) : a := - y - -/-- 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/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean deleted file mode 100644 index a20ee9fd..00000000 --- a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean +++ /dev/null @@ -1,556 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [no_nested_borrows] -import Base.Primitives - -structure OpaqueDefs where - - /- [no_nested_borrows::Pair] -/ - structure pair_t (T1 T2 : Type) where pair_x : T1 pair_y : T2 - - /- [no_nested_borrows::List] -/ - inductive list_t (T : Type) := - | ListCons : T -> list_t T -> list_t T - | ListNil : list_t T - - /- [no_nested_borrows::One] -/ - inductive one_t (T1 : Type) := | OneOne : T1 -> one_t T1 - - /- [no_nested_borrows::EmptyEnum] -/ - inductive empty_enum_t := | EmptyEnumEmpty : empty_enum_t - - /- [no_nested_borrows::Enum] -/ - inductive enum_t := | EnumVariant1 : enum_t | EnumVariant2 : enum_t - - /- [no_nested_borrows::EmptyStruct] -/ - structure empty_struct_t where - - /- [no_nested_borrows::Sum] -/ - inductive sum_t (T1 T2 : Type) := - | SumLeft : T1 -> sum_t T1 T2 - | SumRight : T2 -> sum_t T1 T2 - - /- [no_nested_borrows::neg_test] -/ - def neg_test_fwd (x : Int32) : Result Int32 := - Int32.checked_neg x - - /- [no_nested_borrows::add_test] -/ - def add_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_add x y - - /- [no_nested_borrows::subs_test] -/ - def subs_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_sub x y - - /- [no_nested_borrows::div_test] -/ - def div_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_div x y - - /- [no_nested_borrows::div_test1] -/ - def div_test1_fwd (x : UInt32) : Result UInt32 := - UInt32.checked_div x (UInt32.ofNatCore 2 (by intlit)) - - /- [no_nested_borrows::rem_test] -/ - def rem_test_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - UInt32.checked_rem x y - - /- [no_nested_borrows::cast_test] -/ - def cast_test_fwd (x : UInt32) : Result Int32 := - scalar_cast Int32 x - - /- [no_nested_borrows::test2] -/ - def test2_fwd : Result Unit := - do - let _ ← UInt32.checked_add (UInt32.ofNatCore 23 (by intlit)) - (UInt32.ofNatCore 44 (by intlit)) - Result.ret () - - /- Unit test for [no_nested_borrows::test2] -/ - #assert (test2_fwd == .ret ()) - - /- [no_nested_borrows::get_max] -/ - def get_max_fwd (x : UInt32) (y : UInt32) : Result UInt32 := - if h: x >= y - then Result.ret x - else Result.ret y - - /- [no_nested_borrows::test3] -/ - def test3_fwd : Result Unit := - do - let x ← - get_max_fwd (UInt32.ofNatCore 4 (by intlit)) - (UInt32.ofNatCore 3 (by intlit)) - let y ← - get_max_fwd (UInt32.ofNatCore 10 (by intlit)) - (UInt32.ofNatCore 11 (by intlit)) - let z ← UInt32.checked_add x y - if h: not (z = (UInt32.ofNatCore 15 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test3] -/ - #assert (test3_fwd == .ret ()) - - /- [no_nested_borrows::test_neg1] -/ - def test_neg1_fwd : Result Unit := - do - let y ← Int32.checked_neg (Int32.ofNatCore 3 (by intlit)) - if h: not (y = (Int32.ofNatCore -3 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_neg1] -/ - #assert (test_neg1_fwd == .ret ()) - - /- [no_nested_borrows::refs_test1] -/ - def refs_test1_fwd : Result Unit := - if h: not ((Int32.ofNatCore 1 (by intlit)) = - (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::refs_test1] -/ - #assert (refs_test1_fwd == .ret ()) - - /- [no_nested_borrows::refs_test2] -/ - def refs_test2_fwd : Result Unit := - if h: not ((Int32.ofNatCore 2 (by intlit)) = - (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else - if h: not ((Int32.ofNatCore 0 (by intlit)) = - (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else - if h: not ((Int32.ofNatCore 2 (by intlit)) = - (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else - if h: not ((Int32.ofNatCore 2 (by intlit)) = - (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::refs_test2] -/ - #assert (refs_test2_fwd == .ret ()) - - /- [no_nested_borrows::test_list1] -/ - def test_list1_fwd : Result Unit := - Result.ret () - - /- Unit test for [no_nested_borrows::test_list1] -/ - #assert (test_list1_fwd == .ret ()) - - /- [no_nested_borrows::test_box1] -/ - def test_box1_fwd : Result Unit := - let b := (Int32.ofNatCore 1 (by intlit)) - let x := b - if h: not (x = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_box1] -/ - #assert (test_box1_fwd == .ret ()) - - /- [no_nested_borrows::copy_int] -/ - def copy_int_fwd (x : Int32) : Result Int32 := - Result.ret x - - /- [no_nested_borrows::test_unreachable] -/ - def test_unreachable_fwd (b : Bool) : Result Unit := - if h: b - then Result.fail Error.panic - else Result.ret () - - /- [no_nested_borrows::test_panic] -/ - def test_panic_fwd (b : Bool) : Result Unit := - if h: b - then Result.fail Error.panic - else Result.ret () - - /- [no_nested_borrows::test_copy_int] -/ - def test_copy_int_fwd : Result Unit := - do - let y ← copy_int_fwd (Int32.ofNatCore 0 (by intlit)) - if h: not ((Int32.ofNatCore 0 (by intlit)) = y) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_copy_int] -/ - #assert (test_copy_int_fwd == .ret ()) - - /- [no_nested_borrows::is_cons] -/ - def is_cons_fwd (T : Type) (l : list_t T) : Result Bool := - match h: l with - | list_t.ListCons t l0 => Result.ret true - | list_t.ListNil => Result.ret false - - /- [no_nested_borrows::test_is_cons] -/ - def test_is_cons_fwd : Result Unit := - do - let l := list_t.ListNil - let b ← - is_cons_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) l) - if h: not b - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_is_cons] -/ - #assert (test_is_cons_fwd == .ret ()) - - /- [no_nested_borrows::split_list] -/ - def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) := - match h: l with - | list_t.ListCons hd tl => Result.ret (hd, tl) - | list_t.ListNil => Result.fail Error.panic - - /- [no_nested_borrows::test_split_list] -/ - def test_split_list_fwd : Result Unit := - do - let l := list_t.ListNil - let p ← - split_list_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) - l) - let (hd, _) := p - if h: not (hd = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_split_list] -/ - #assert (test_split_list_fwd == .ret ()) - - /- [no_nested_borrows::choose] -/ - def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := - if h: b - then Result.ret x - else Result.ret y - - /- [no_nested_borrows::choose] -/ - def choose_back - (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := - if h: b - then Result.ret (ret0, y) - else Result.ret (x, ret0) - - /- [no_nested_borrows::choose_test] -/ - def choose_test_fwd : Result Unit := - do - let z ← - choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) - let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit)) - if h: not (z0 = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let (x, y) ← - choose_back Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) z0 - if h: not (x = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - if h: not (y = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::choose_test] -/ - #assert (choose_test_fwd == .ret ()) - - /- [no_nested_borrows::test_char] -/ - def test_char_fwd : Result Char := - Result.ret 'a' - - /- [no_nested_borrows::NodeElem] -/ - mutual inductive node_elem_t (T : Type) := - | NodeElemCons : tree_t T -> node_elem_t T -> node_elem_t T - | NodeElemNil : node_elem_t T - - /- [no_nested_borrows::Tree] -/ - inductive tree_t (T : Type) := - | TreeLeaf : T -> tree_t T - | TreeNode : T -> node_elem_t T -> tree_t T -> tree_t T - - /- [no_nested_borrows::list_length] -/ - def list_length_fwd (T : Type) (l : list_t T) : Result UInt32 := - match h: l with - | list_t.ListCons t l1 => - do - let i ← list_length_fwd T l1 - UInt32.checked_add (UInt32.ofNatCore 1 (by intlit)) i - | list_t.ListNil => Result.ret (UInt32.ofNatCore 0 (by intlit)) - - /- [no_nested_borrows::list_nth_shared] -/ - def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := - match h: l with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_shared_fwd T tl i0 - | list_t.ListNil => Result.fail Error.panic - - /- [no_nested_borrows::list_nth_mut] -/ - def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := - match h: l with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_fwd T tl i0 - | list_t.ListNil => Result.fail Error.panic - - /- [no_nested_borrows::list_nth_mut] -/ - def list_nth_mut_back - (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := - match h: l with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 ← list_nth_mut_back T tl i0 ret0 - Result.ret (list_t.ListCons x tl0) - | list_t.ListNil => Result.fail Error.panic - - /- [no_nested_borrows::list_rev_aux] -/ - def list_rev_aux_fwd - (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) := - match h: li with - | list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo) - | list_t.ListNil => Result.ret lo - - /- [no_nested_borrows::list_rev] -/ - def list_rev_fwd_back (T : Type) (l : list_t T) : Result (list_t T) := - let li := mem_replace_fwd (list_t T) l list_t.ListNil - list_rev_aux_fwd T li list_t.ListNil - - /- [no_nested_borrows::test_list_functions] -/ - def test_list_functions_fwd : Result Unit := - do - let l := list_t.ListNil - let l0 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l - let l1 := list_t.ListCons (Int32.ofNatCore 1 (by intlit)) l0 - let i ← - list_length_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) - l1) - if h: not (i = (UInt32.ofNatCore 3 (by intlit))) - then Result.fail Error.panic - else - do - let i0 ← - list_nth_shared_fwd Int32 (list_t.ListCons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 0 (by intlit)) - if h: not (i0 = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else - do - let i1 ← - list_nth_shared_fwd Int32 (list_t.ListCons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 1 (by intlit)) - if h: not (i1 = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let i2 ← - list_nth_shared_fwd Int32 (list_t.ListCons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 2 (by intlit)) - if h: not (i2 = (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else - do - let ls ← - list_nth_mut_back Int32 (list_t.ListCons - (Int32.ofNatCore 0 (by intlit)) l1) - (UInt32.ofNatCore 1 (by intlit)) - (Int32.ofNatCore 3 (by intlit)) - let i3 ← - list_nth_shared_fwd Int32 ls - (UInt32.ofNatCore 0 (by intlit)) - if h: not (i3 = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else - do - let i4 ← - list_nth_shared_fwd Int32 ls - (UInt32.ofNatCore 1 (by intlit)) - if h: not (i4 = (Int32.ofNatCore 3 (by intlit))) - then Result.fail Error.panic - else - do - let i5 ← - list_nth_shared_fwd Int32 ls - (UInt32.ofNatCore 2 (by intlit)) - if h: not (i5 = (Int32.ofNatCore 2 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_list_functions] -/ - #assert (test_list_functions_fwd == .ret ()) - - /- [no_nested_borrows::id_mut_pair1] -/ - def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) := - Result.ret (x, y) - - /- [no_nested_borrows::id_mut_pair1] -/ - def id_mut_pair1_back - (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := ret0 - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair2] -/ - def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := p - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair2] -/ - def id_mut_pair2_back - (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := ret0 - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair3] -/ - def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) := - Result.ret (x, y) - - /- [no_nested_borrows::id_mut_pair3] -/ - def id_mut_pair3_back'a - (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 := - Result.ret ret0 - - /- [no_nested_borrows::id_mut_pair3] -/ - def id_mut_pair3_back'b - (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 := - Result.ret ret0 - - /- [no_nested_borrows::id_mut_pair4] -/ - def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := - let (t, t0) := p - Result.ret (t, t0) - - /- [no_nested_borrows::id_mut_pair4] -/ - def id_mut_pair4_back'a - (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 := - Result.ret ret0 - - /- [no_nested_borrows::id_mut_pair4] -/ - def id_mut_pair4_back'b - (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 := - Result.ret ret0 - - /- [no_nested_borrows::StructWithTuple] -/ - structure struct_with_tuple_t (T1 T2 : Type) where - - struct_with_tuple_p : (T1 × T2) - - - /- [no_nested_borrows::new_tuple1] -/ - def new_tuple1_fwd : Result (struct_with_tuple_t UInt32 UInt32) := - Result.ret - { - struct_with_tuple_p := ((UInt32.ofNatCore 1 (by intlit)), - (UInt32.ofNatCore 2 (by intlit))) - } - - /- [no_nested_borrows::new_tuple2] -/ - def new_tuple2_fwd : Result (struct_with_tuple_t Int16 Int16) := - Result.ret - { - struct_with_tuple_p := ((Int16.ofNatCore 1 (by intlit)), - (Int16.ofNatCore 2 (by intlit))) - } - - /- [no_nested_borrows::new_tuple3] -/ - def new_tuple3_fwd : Result (struct_with_tuple_t UInt64 Int64) := - Result.ret - { - struct_with_tuple_p := ((UInt64.ofNatCore 1 (by intlit)), - (Int64.ofNatCore 2 (by intlit))) - } - - /- [no_nested_borrows::StructWithPair] -/ - structure struct_with_pair_t (T1 T2 : Type) where - - struct_with_pair_p : pair_t T1 T2 - - - /- [no_nested_borrows::new_pair1] -/ - def new_pair1_fwd : Result (struct_with_pair_t UInt32 UInt32) := - Result.ret - { - struct_with_pair_p := { - pair_x := (UInt32.ofNatCore 1 (by intlit)), - pair_y := (UInt32.ofNatCore 2 (by intlit)) - } - } - - /- [no_nested_borrows::test_constants] -/ - def test_constants_fwd : Result Unit := - do - let swt ← new_tuple1_fwd - let (i, _) := swt.struct_with_tuple_p - if h: not (i = (UInt32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let swt0 ← new_tuple2_fwd - let (i0, _) := swt0.struct_with_tuple_p - if h: not (i0 = (Int16.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let swt1 ← new_tuple3_fwd - let (i1, _) := swt1.struct_with_tuple_p - if h: not (i1 = (UInt64.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let swp ← new_pair1_fwd - if h: not (swp.struct_with_pair_p.pair_x = - (UInt32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [no_nested_borrows::test_constants] -/ - #assert (test_constants_fwd == .ret ()) - - /- [no_nested_borrows::test_weird_borrows1] -/ - def test_weird_borrows1_fwd : Result Unit := - Result.ret () - - /- Unit test for [no_nested_borrows::test_weird_borrows1] -/ - #assert (test_weird_borrows1_fwd == .ret ()) - - /- [no_nested_borrows::test_mem_replace] -/ - def test_mem_replace_fwd_back (px : UInt32) : Result UInt32 := - let y := mem_replace_fwd UInt32 px (UInt32.ofNatCore 1 (by intlit)) - if h: not (y = (UInt32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret (UInt32.ofNatCore 2 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_bool1] -/ - def test_shared_borrow_bool1_fwd (b : Bool) : Result UInt32 := - if h: b - then Result.ret (UInt32.ofNatCore 0 (by intlit)) - else Result.ret (UInt32.ofNatCore 1 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_bool2] -/ - def test_shared_borrow_bool2_fwd : Result UInt32 := - Result.ret (UInt32.ofNatCore 0 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_enum1] -/ - def test_shared_borrow_enum1_fwd (l : list_t UInt32) : Result UInt32 := - match h: l with - | list_t.ListCons i l0 => Result.ret (UInt32.ofNatCore 1 (by intlit)) - | list_t.ListNil => Result.ret (UInt32.ofNatCore 0 (by intlit)) - - /- [no_nested_borrows::test_shared_borrow_enum2] -/ - def test_shared_borrow_enum2_fwd : Result UInt32 := - Result.ret (UInt32.ofNatCore 0 (by intlit)) - diff --git a/tests/lean/misc/no_nested_borrows/lakefile.lean b/tests/lean/misc/no_nested_borrows/lakefile.lean deleted file mode 100644 index e4460813..00000000 --- a/tests/lean/misc/no_nested_borrows/lakefile.lean +++ /dev/null @@ -1,18 +0,0 @@ -import Lake -open Lake DSL - -require mathlib from git - "https://github.com/leanprover-community/mathlib4.git" - -package «no_nested_borrows» { - -- add package configuration options here -} - -lean_lib «Base» { - -- add library configuration options here -} - -lean_lib «NoNestedBorrows» { - -- add library configuration options here -} - diff --git a/tests/lean/misc/paper/Base/Primitives.lean b/tests/lean/misc/paper/Base/Primitives.lean deleted file mode 100644 index 5b64e908..00000000 --- a/tests/lean/misc/paper/Base/Primitives.lean +++ /dev/null @@ -1,392 +0,0 @@ -import Lean -import Lean.Meta.Tactic.Simp -import Init.Data.List.Basic -import Mathlib.Tactic.RunCmd - -------------- --- PRELUDE -- -------------- - --- Results & monadic combinators - -inductive Error where - | assertionFailure: Error - | integerOverflow: Error - | arrayOutOfBounds: Error - | maximumSizeExceeded: Error - | panic: Error -deriving Repr, BEq - -open Error - -inductive Result (α : Type u) where - | ret (v: α): Result α - | fail (e: Error): Result α -deriving Repr, BEq - -open Result - -/- HELPERS -/ - -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 -- ----------------------- - --- 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. - --- 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.) - --- 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. - -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`). --- This is useful for the various #asserts that we want to reduce at --- type-checking time. - --- 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 - -------------- --- VECTORS -- -------------- - --- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) --- rather than maximum values (usize_max). -def Vec (α : Type u) := { l : List α // List.length l < USize.size } - -def vec_new (α : Type u): Vec α := ⟨ [], by { - match USize.size, usize_size_eq with - | _, Or.inl rfl => simp - | _, Or.inr rfl => simp - } ⟩ - -#check vec_new - -def vec_len (α : Type u) (v : Vec α) : USize := - let ⟨ v, l ⟩ := v - USize.ofNatCore (List.length v) l - -#eval vec_len Nat (vec_new Nat) - -def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () - --- NOTE: old version trying to use a subtype notation, but probably better to --- leave Result elimination to auxiliary lemmas with suitable preconditions --- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one --- make the proof work in that case? Probably need to import tactics from --- mathlib to deal with inequalities... would love to see an example. -def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // - match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} - := - if h : List.length v.val + 1 < USize.size then - ⟨ return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩, by simp ⟩ - else - ⟨ fail maximumSizeExceeded, by simp ⟩ - -#eval do - -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with - -- fields val and property. However, Lean's elaborator can automatically - -- select the `val` field if the context provides a type annotation. We - -- annotate `x`, which relieves us of having to write `.val` on the right-hand - -- side of the monadic let. - let v := vec_new Nat - let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? - -- TODO: strengthen post-condition above and do a demo to show that we can - -- safely eliminate the `fail` case - return (vec_len Nat x) - -def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) - := - if h : List.length v.val + 1 <= 4294967295 then - return ⟨ List.concat v.val x, - by - rw [List.length_concat] - have h': 4294967295 < USize.size := by intlit - apply Nat.lt_of_le_of_lt h h' - ⟩ - else if h: List.length v.val + 1 < USize.size then - return ⟨List.concat v.val x, - by - rw [List.length_concat] - assumption - ⟩ - else - fail maximumSizeExceeded - -def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - -def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := - if i.val < List.length v.val then - .ret () - else - .fail arrayOutOfBounds - -def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := - if h: i.val < List.length v.val then - .ret (List.get v.val ⟨i.val, h⟩) - else - .fail arrayOutOfBounds - -def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := - if i.val < List.length v.val then - .ret ⟨ List.set v.val i.val x, by - have h: List.length v.val < USize.size := v.property - rewrite [ List.length_set v.val i.val x ] - assumption - ⟩ - else - .fail arrayOutOfBounds - ----------- --- MISC -- ----------- - -def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := - x - -def mem_replace_back (a : Type) (_ : a) (y : a) : a := - y - -/-- 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/paper/Paper.lean b/tests/lean/misc/paper/Paper.lean deleted file mode 100644 index 4faf36ee..00000000 --- a/tests/lean/misc/paper/Paper.lean +++ /dev/null @@ -1,128 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [paper] -import Base.Primitives - -structure OpaqueDefs where - - /- [paper::ref_incr] -/ - def ref_incr_fwd_back (x : Int32) : Result Int32 := - Int32.checked_add x (Int32.ofNatCore 1 (by intlit)) - - /- [paper::test_incr] -/ - def test_incr_fwd : Result Unit := - do - let x ← ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit)) - if h: not (x = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [paper::test_incr] -/ - #assert (test_incr_fwd == .ret ()) - - /- [paper::choose] -/ - def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := - if h: b - then Result.ret x - else Result.ret y - - /- [paper::choose] -/ - def choose_back - (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := - if h: b - then Result.ret (ret0, y) - else Result.ret (x, ret0) - - /- [paper::test_choose] -/ - def test_choose_fwd : Result Unit := - do - let z ← - choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) - let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit)) - if h: not (z0 = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - do - let (x, y) ← - choose_back Int32 true (Int32.ofNatCore 0 (by intlit)) - (Int32.ofNatCore 0 (by intlit)) z0 - if h: not (x = (Int32.ofNatCore 1 (by intlit))) - then Result.fail Error.panic - else - if h: not (y = (Int32.ofNatCore 0 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [paper::test_choose] -/ - #assert (test_choose_fwd == .ret ()) - - /- [paper::List] -/ - inductive list_t (T : Type) := - | ListCons : T -> list_t T -> list_t T - | ListNil : list_t T - - /- [paper::list_nth_mut] -/ - def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := - match h: l with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret x - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - list_nth_mut_fwd T tl i0 - | list_t.ListNil => Result.fail Error.panic - - /- [paper::list_nth_mut] -/ - def list_nth_mut_back - (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := - match h: l with - | list_t.ListCons x tl => - if h: i = (UInt32.ofNatCore 0 (by intlit)) - then Result.ret (list_t.ListCons ret0 tl) - else - do - let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 ← list_nth_mut_back T tl i0 ret0 - Result.ret (list_t.ListCons x tl0) - | list_t.ListNil => Result.fail Error.panic - - /- [paper::sum] -/ - def sum_fwd (l : list_t Int32) : Result Int32 := - match h: l with - | list_t.ListCons x tl => do - let i ← sum_fwd tl - Int32.checked_add x i - | list_t.ListNil => Result.ret (Int32.ofNatCore 0 (by intlit)) - - /- [paper::test_nth] -/ - def test_nth_fwd : Result Unit := - do - let l := list_t.ListNil - let l0 := list_t.ListCons (Int32.ofNatCore 3 (by intlit)) l - let l1 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l0 - let x ← - list_nth_mut_fwd Int32 (list_t.ListCons (Int32.ofNatCore 1 (by intlit)) - l1) (UInt32.ofNatCore 2 (by intlit)) - let x0 ← Int32.checked_add x (Int32.ofNatCore 1 (by intlit)) - let l2 ← - list_nth_mut_back Int32 (list_t.ListCons - (Int32.ofNatCore 1 (by intlit)) l1) (UInt32.ofNatCore 2 (by intlit)) - x0 - let i ← sum_fwd l2 - if h: not (i = (Int32.ofNatCore 7 (by intlit))) - then Result.fail Error.panic - else Result.ret () - - /- Unit test for [paper::test_nth] -/ - #assert (test_nth_fwd == .ret ()) - - /- [paper::call_choose] -/ - def call_choose_fwd (p : (UInt32 × UInt32)) : Result UInt32 := - do - let (px, py) := p - let pz ← choose_fwd UInt32 true px py - let pz0 ← UInt32.checked_add pz (UInt32.ofNatCore 1 (by intlit)) - let (px0, _) ← choose_back UInt32 true px py pz0 - Result.ret px0 - diff --git a/tests/lean/misc/paper/lakefile.lean b/tests/lean/misc/paper/lakefile.lean deleted file mode 100644 index d8affff8..00000000 --- a/tests/lean/misc/paper/lakefile.lean +++ /dev/null @@ -1,18 +0,0 @@ -import Lake -open Lake DSL - -require mathlib from git - "https://github.com/leanprover-community/mathlib4.git" - -package «paper» { - -- add package configuration options here -} - -lean_lib «Base» { - -- add library configuration options here -} - -lean_lib «Paper» { - -- add library configuration options here -} - |