diff options
Diffstat (limited to 'tests/lean/misc')
| -rw-r--r-- | tests/lean/misc/constants/Base/Primitives.lean | 373 | ||||
| -rw-r--r-- | tests/lean/misc/constants/Constants.lean | 138 | ||||
| -rw-r--r-- | tests/lean/misc/external/Base/Primitives.lean | 373 | ||||
| -rw-r--r-- | tests/lean/misc/external/External/Funs.lean | 93 | ||||
| -rw-r--r-- | tests/lean/misc/external/External/Opaque.lean | 28 | ||||
| -rw-r--r-- | tests/lean/misc/external/External/Types.lean | 8 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Base/Primitives.lean | 373 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Loops/Clauses/Clauses.lean | 209 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Loops/Clauses/Template.lean | 210 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Loops/Funs.lean | 786 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Loops/Types.lean | 9 | ||||
| -rw-r--r-- | tests/lean/misc/no_nested_borrows/Base/Primitives.lean | 373 | ||||
| -rw-r--r-- | tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean | 540 | ||||
| -rw-r--r-- | tests/lean/misc/paper/Base/Primitives.lean | 373 | ||||
| -rw-r--r-- | tests/lean/misc/paper/Paper.lean | 127 |
15 files changed, 4013 insertions, 0 deletions
diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean new file mode 100644 index 00000000..79958d94 --- /dev/null +++ b/tests/lean/misc/constants/Base/Primitives.lean @@ -0,0 +1,373 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd + +------------- +-- PRELUDE -- +------------- + +-- Results & monadic combinators + +-- TODO: use syntactic conventions and capitalize error, result, etc. + +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 -/ + +-- TODO: is there automated syntax for these discriminators? +def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x } + | .ret x => .ret ⟨x, rfl⟩ + | .fail e => .fail e + +macro "let" h:ident " : " e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, $h⟩ ← result.attach $f) + +-- Silly example of the kind of reasoning that this notation enables +#eval do + let h: y <-- .ret (0: Nat) + let _: y = 0 := by cases h; decide + let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ + .ret r + +---------------------- +-- MACHINE INTEGERS -- +---------------------- + +-- NOTE: we reuse the USize type from prelude.lean, because at least we know +-- it's defined in an idiomatic style that is going to make proofs easy (and +-- indeed, several proofs here are much shortened compared to Aymeric's earlier +-- attempt.) This is not stricto sensu the *correct* thing to do, because one +-- can query at run-time the value of USize, which we do *not* want to do (we +-- don't know what target we'll run on!), but when the day comes, we'll just +-- define our own USize. +-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is +-- not something we want to define (I think), so we use our own monadic sub (but +-- is it in line with the Rust behavior?) + +-- TODO: I am somewhat under the impression that subtraction is defined as a +-- total function over nats...? the hypothesis in the if condition is not used +-- in the then-branch which confuses me quite a bit + +-- TODO: add a refinement for the result (just like vec_push_back below) that +-- explains that the toNat of the result (in the case of success) is the sub of +-- the toNat of the arguments (i.e. intrinsic specification) +-- ... do we want intrinsic specifications for the builtins? that might require +-- some careful type annotations in the monadic notation for clients, but may +-- give us more "for free" + +-- 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." Try to settle this with a Lean expert on what is the most +-- productive way to go about this? + +-- One needs to perform a little bit of reasoning in order to successfully +-- inject constants into USize, so we provide a general-purpose macro + +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) + +-- 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 + +def USize.checked_add (n: USize) (m: USize): result USize := + if h: n.val.val + m.val.val <= 4294967295 then + .ret ⟨ n.val.val + m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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.val * m.val.val <= 4294967295 then + .ret ⟨ n.val.val * m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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 + +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 + )) + +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 + + +-- 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 + +------------- +-- 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 + +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +def assertImpl : CommandElab := fun (_stx: Syntax) => do + logInfo "Reducing and asserting: " + logInfo _stx[1] + runTermElabM (fun _ => do + let e ← Term.elabTerm _stx[1] none + logInfo (Expr.dbgToString e) + -- How to evaluate the term and compare the result to true? + pure ()) + -- logInfo (Expr.dbgToString (``true)) + -- throwError "TODO: assert" + +#eval 2 == 2 +#assert (2 == 2) diff --git a/tests/lean/misc/constants/Constants.lean b/tests/lean/misc/constants/Constants.lean new file mode 100644 index 00000000..a5cbe363 --- /dev/null +++ b/tests/lean/misc/constants/Constants.lean @@ -0,0 +1,138 @@ +-- 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/external/Base/Primitives.lean b/tests/lean/misc/external/Base/Primitives.lean new file mode 100644 index 00000000..79958d94 --- /dev/null +++ b/tests/lean/misc/external/Base/Primitives.lean @@ -0,0 +1,373 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd + +------------- +-- PRELUDE -- +------------- + +-- Results & monadic combinators + +-- TODO: use syntactic conventions and capitalize error, result, etc. + +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 -/ + +-- TODO: is there automated syntax for these discriminators? +def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x } + | .ret x => .ret ⟨x, rfl⟩ + | .fail e => .fail e + +macro "let" h:ident " : " e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, $h⟩ ← result.attach $f) + +-- Silly example of the kind of reasoning that this notation enables +#eval do + let h: y <-- .ret (0: Nat) + let _: y = 0 := by cases h; decide + let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ + .ret r + +---------------------- +-- MACHINE INTEGERS -- +---------------------- + +-- NOTE: we reuse the USize type from prelude.lean, because at least we know +-- it's defined in an idiomatic style that is going to make proofs easy (and +-- indeed, several proofs here are much shortened compared to Aymeric's earlier +-- attempt.) This is not stricto sensu the *correct* thing to do, because one +-- can query at run-time the value of USize, which we do *not* want to do (we +-- don't know what target we'll run on!), but when the day comes, we'll just +-- define our own USize. +-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is +-- not something we want to define (I think), so we use our own monadic sub (but +-- is it in line with the Rust behavior?) + +-- TODO: I am somewhat under the impression that subtraction is defined as a +-- total function over nats...? the hypothesis in the if condition is not used +-- in the then-branch which confuses me quite a bit + +-- TODO: add a refinement for the result (just like vec_push_back below) that +-- explains that the toNat of the result (in the case of success) is the sub of +-- the toNat of the arguments (i.e. intrinsic specification) +-- ... do we want intrinsic specifications for the builtins? that might require +-- some careful type annotations in the monadic notation for clients, but may +-- give us more "for free" + +-- 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." Try to settle this with a Lean expert on what is the most +-- productive way to go about this? + +-- One needs to perform a little bit of reasoning in order to successfully +-- inject constants into USize, so we provide a general-purpose macro + +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) + +-- 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 + +def USize.checked_add (n: USize) (m: USize): result USize := + if h: n.val.val + m.val.val <= 4294967295 then + .ret ⟨ n.val.val + m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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.val * m.val.val <= 4294967295 then + .ret ⟨ n.val.val * m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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 + +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 + )) + +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 + + +-- 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 + +------------- +-- 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 + +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +def assertImpl : CommandElab := fun (_stx: Syntax) => do + logInfo "Reducing and asserting: " + logInfo _stx[1] + runTermElabM (fun _ => do + let e ← Term.elabTerm _stx[1] none + logInfo (Expr.dbgToString e) + -- How to evaluate the term and compare the result to true? + pure ()) + -- logInfo (Expr.dbgToString (``true)) + -- throwError "TODO: assert" + +#eval 2 == 2 +#assert (2 == 2) diff --git a/tests/lean/misc/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean new file mode 100644 index 00000000..bb1e296d --- /dev/null +++ b/tests/lean/misc/external/External/Funs.lean @@ -0,0 +1,93 @@ +-- 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 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 new file mode 100644 index 00000000..40ccc313 --- /dev/null +++ b/tests/lean/misc/external/External/Opaque.lean @@ -0,0 +1,28 @@ +-- 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 new file mode 100644 index 00000000..b6fa292b --- /dev/null +++ b/tests/lean/misc/external/External/Types.lean @@ -0,0 +1,8 @@ +-- 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/loops/Base/Primitives.lean b/tests/lean/misc/loops/Base/Primitives.lean new file mode 100644 index 00000000..79958d94 --- /dev/null +++ b/tests/lean/misc/loops/Base/Primitives.lean @@ -0,0 +1,373 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd + +------------- +-- PRELUDE -- +------------- + +-- Results & monadic combinators + +-- TODO: use syntactic conventions and capitalize error, result, etc. + +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 -/ + +-- TODO: is there automated syntax for these discriminators? +def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x } + | .ret x => .ret ⟨x, rfl⟩ + | .fail e => .fail e + +macro "let" h:ident " : " e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, $h⟩ ← result.attach $f) + +-- Silly example of the kind of reasoning that this notation enables +#eval do + let h: y <-- .ret (0: Nat) + let _: y = 0 := by cases h; decide + let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ + .ret r + +---------------------- +-- MACHINE INTEGERS -- +---------------------- + +-- NOTE: we reuse the USize type from prelude.lean, because at least we know +-- it's defined in an idiomatic style that is going to make proofs easy (and +-- indeed, several proofs here are much shortened compared to Aymeric's earlier +-- attempt.) This is not stricto sensu the *correct* thing to do, because one +-- can query at run-time the value of USize, which we do *not* want to do (we +-- don't know what target we'll run on!), but when the day comes, we'll just +-- define our own USize. +-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is +-- not something we want to define (I think), so we use our own monadic sub (but +-- is it in line with the Rust behavior?) + +-- TODO: I am somewhat under the impression that subtraction is defined as a +-- total function over nats...? the hypothesis in the if condition is not used +-- in the then-branch which confuses me quite a bit + +-- TODO: add a refinement for the result (just like vec_push_back below) that +-- explains that the toNat of the result (in the case of success) is the sub of +-- the toNat of the arguments (i.e. intrinsic specification) +-- ... do we want intrinsic specifications for the builtins? that might require +-- some careful type annotations in the monadic notation for clients, but may +-- give us more "for free" + +-- 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." Try to settle this with a Lean expert on what is the most +-- productive way to go about this? + +-- One needs to perform a little bit of reasoning in order to successfully +-- inject constants into USize, so we provide a general-purpose macro + +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) + +-- 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 + +def USize.checked_add (n: USize) (m: USize): result USize := + if h: n.val.val + m.val.val <= 4294967295 then + .ret ⟨ n.val.val + m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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.val * m.val.val <= 4294967295 then + .ret ⟨ n.val.val * m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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 + +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 + )) + +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 + + +-- 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 + +------------- +-- 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 + +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +def assertImpl : CommandElab := fun (_stx: Syntax) => do + logInfo "Reducing and asserting: " + logInfo _stx[1] + runTermElabM (fun _ => do + let e ← Term.elabTerm _stx[1] none + logInfo (Expr.dbgToString e) + -- How to evaluate the term and compare the result to true? + pure ()) + -- logInfo (Expr.dbgToString (``true)) + -- throwError "TODO: assert" + +#eval 2 == 2 +#assert (2 == 2) diff --git a/tests/lean/misc/loops/Loops/Clauses/Clauses.lean b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean new file mode 100644 index 00000000..5ddb65ca --- /dev/null +++ b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean @@ -0,0 +1,209 @@ +-- [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 new file mode 100644 index 00000000..3c0f2f7c --- /dev/null +++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean @@ -0,0 +1,210 @@ +-- 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) + +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/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean new file mode 100644 index 00000000..5fe5b4ff --- /dev/null +++ b/tests/lean/misc/loops/Loops/Funs.lean @@ -0,0 +1,786 @@ +-- 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 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 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 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 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 ls with + | list_t.ListCons y tl => + if 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 ls with + | list_t.ListCons x tl => + if 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 ls with + | list_t.ListCons x tl => + if 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 ls with + | list_t.ListCons x tl => + if 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 ls with + | list_t.ListCons y tl => + if 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 ls with + | list_t.ListCons y tl => + if 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 ls with + | list_t.ListCons y tl => + if 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 ls with + | list_t.ListCons x tl => + if 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 ls with + | list_t.ListCons x tl => + if 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 ls with + | list_t.ListCons x tl => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 ls0 with + | list_t.ListCons x0 tl0 => + match ls1 with + | list_t.ListCons x1 tl1 => + if 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 new file mode 100644 index 00000000..f4b6809e --- /dev/null +++ b/tests/lean/misc/loops/Loops/Types.lean @@ -0,0 +1,9 @@ +-- 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/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean new file mode 100644 index 00000000..79958d94 --- /dev/null +++ b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean @@ -0,0 +1,373 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd + +------------- +-- PRELUDE -- +------------- + +-- Results & monadic combinators + +-- TODO: use syntactic conventions and capitalize error, result, etc. + +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 -/ + +-- TODO: is there automated syntax for these discriminators? +def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x } + | .ret x => .ret ⟨x, rfl⟩ + | .fail e => .fail e + +macro "let" h:ident " : " e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, $h⟩ ← result.attach $f) + +-- Silly example of the kind of reasoning that this notation enables +#eval do + let h: y <-- .ret (0: Nat) + let _: y = 0 := by cases h; decide + let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ + .ret r + +---------------------- +-- MACHINE INTEGERS -- +---------------------- + +-- NOTE: we reuse the USize type from prelude.lean, because at least we know +-- it's defined in an idiomatic style that is going to make proofs easy (and +-- indeed, several proofs here are much shortened compared to Aymeric's earlier +-- attempt.) This is not stricto sensu the *correct* thing to do, because one +-- can query at run-time the value of USize, which we do *not* want to do (we +-- don't know what target we'll run on!), but when the day comes, we'll just +-- define our own USize. +-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is +-- not something we want to define (I think), so we use our own monadic sub (but +-- is it in line with the Rust behavior?) + +-- TODO: I am somewhat under the impression that subtraction is defined as a +-- total function over nats...? the hypothesis in the if condition is not used +-- in the then-branch which confuses me quite a bit + +-- TODO: add a refinement for the result (just like vec_push_back below) that +-- explains that the toNat of the result (in the case of success) is the sub of +-- the toNat of the arguments (i.e. intrinsic specification) +-- ... do we want intrinsic specifications for the builtins? that might require +-- some careful type annotations in the monadic notation for clients, but may +-- give us more "for free" + +-- 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." Try to settle this with a Lean expert on what is the most +-- productive way to go about this? + +-- One needs to perform a little bit of reasoning in order to successfully +-- inject constants into USize, so we provide a general-purpose macro + +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) + +-- 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 + +def USize.checked_add (n: USize) (m: USize): result USize := + if h: n.val.val + m.val.val <= 4294967295 then + .ret ⟨ n.val.val + m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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.val * m.val.val <= 4294967295 then + .ret ⟨ n.val.val * m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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 + +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 + )) + +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 + + +-- 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 + +------------- +-- 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 + +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +def assertImpl : CommandElab := fun (_stx: Syntax) => do + logInfo "Reducing and asserting: " + logInfo _stx[1] + runTermElabM (fun _ => do + let e ← Term.elabTerm _stx[1] none + logInfo (Expr.dbgToString e) + -- How to evaluate the term and compare the result to true? + pure ()) + -- logInfo (Expr.dbgToString (``true)) + -- throwError "TODO: assert" + +#eval 2 == 2 +#assert (2 == 2) diff --git a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean new file mode 100644 index 00000000..d871392b --- /dev/null +++ b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean @@ -0,0 +1,540 @@ +-- 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 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 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 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 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 not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit))) + then result.fail error.panic + else + if not ((Int32.ofNatCore 0 (by intlit)) = + (Int32.ofNatCore 0 (by intlit))) + then result.fail error.panic + else + if not ((Int32.ofNatCore 2 (by intlit)) = + (Int32.ofNatCore 2 (by intlit))) + then result.fail error.panic + else + if 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 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 b then result.fail error.panic else result.ret () + + /- [no_nested_borrows::test_panic] -/ + def test_panic_fwd (b : Bool) : result Unit := + if 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 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 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 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 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 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 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 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 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 not (x = (Int32.ofNatCore 1 (by intlit))) + then result.fail error.panic + else + if 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 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 l with + | list_t.ListCons x tl => + if 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 l with + | list_t.ListCons x tl => + if 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 l with + | list_t.ListCons x tl => + if 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 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 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 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 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 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 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 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 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 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 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 not (i1 = (UInt64.ofNatCore 1 (by intlit))) + then result.fail error.panic + else + do + let swp <- new_pair1_fwd + if 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 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 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 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/paper/Base/Primitives.lean b/tests/lean/misc/paper/Base/Primitives.lean new file mode 100644 index 00000000..79958d94 --- /dev/null +++ b/tests/lean/misc/paper/Base/Primitives.lean @@ -0,0 +1,373 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd + +------------- +-- PRELUDE -- +------------- + +-- Results & monadic combinators + +-- TODO: use syntactic conventions and capitalize error, result, etc. + +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 -/ + +-- TODO: is there automated syntax for these discriminators? +def is_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) (_: is_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 : (o : result α) → result { x : α // o = ret x } + | .ret x => .ret ⟨x, rfl⟩ + | .fail e => .fail e + +macro "let" h:ident " : " e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, $h⟩ ← result.attach $f) + +-- Silly example of the kind of reasoning that this notation enables +#eval do + let h: y <-- .ret (0: Nat) + let _: y = 0 := by cases h; decide + let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ + .ret r + +---------------------- +-- MACHINE INTEGERS -- +---------------------- + +-- NOTE: we reuse the USize type from prelude.lean, because at least we know +-- it's defined in an idiomatic style that is going to make proofs easy (and +-- indeed, several proofs here are much shortened compared to Aymeric's earlier +-- attempt.) This is not stricto sensu the *correct* thing to do, because one +-- can query at run-time the value of USize, which we do *not* want to do (we +-- don't know what target we'll run on!), but when the day comes, we'll just +-- define our own USize. +-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is +-- not something we want to define (I think), so we use our own monadic sub (but +-- is it in line with the Rust behavior?) + +-- TODO: I am somewhat under the impression that subtraction is defined as a +-- total function over nats...? the hypothesis in the if condition is not used +-- in the then-branch which confuses me quite a bit + +-- TODO: add a refinement for the result (just like vec_push_back below) that +-- explains that the toNat of the result (in the case of success) is the sub of +-- the toNat of the arguments (i.e. intrinsic specification) +-- ... do we want intrinsic specifications for the builtins? that might require +-- some careful type annotations in the monadic notation for clients, but may +-- give us more "for free" + +-- 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." Try to settle this with a Lean expert on what is the most +-- productive way to go about this? + +-- One needs to perform a little bit of reasoning in order to successfully +-- inject constants into USize, so we provide a general-purpose macro + +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) + +-- 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 + +def USize.checked_add (n: USize) (m: USize): result USize := + if h: n.val.val + m.val.val <= 4294967295 then + .ret ⟨ n.val.val + m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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.val * m.val.val <= 4294967295 then + .ret ⟨ n.val.val * m.val.val, by + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else 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 + +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 + )) + +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 + + +-- 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 + +------------- +-- 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 + +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +def assertImpl : CommandElab := fun (_stx: Syntax) => do + logInfo "Reducing and asserting: " + logInfo _stx[1] + runTermElabM (fun _ => do + let e ← Term.elabTerm _stx[1] none + logInfo (Expr.dbgToString e) + -- How to evaluate the term and compare the result to true? + pure ()) + -- logInfo (Expr.dbgToString (``true)) + -- throwError "TODO: assert" + +#eval 2 == 2 +#assert (2 == 2) diff --git a/tests/lean/misc/paper/Paper.lean b/tests/lean/misc/paper/Paper.lean new file mode 100644 index 00000000..2d23f394 --- /dev/null +++ b/tests/lean/misc/paper/Paper.lean @@ -0,0 +1,127 @@ +-- 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 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 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 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 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 not (x = (Int32.ofNatCore 1 (by intlit))) + then result.fail error.panic + else + if 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 l with + | list_t.ListCons x tl => + if 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 l with + | list_t.ListCons x tl => + if 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 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 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 + |