diff options
Diffstat (limited to '')
21 files changed, 1600 insertions, 1489 deletions
diff --git a/backends/lean/Primitives.lean b/backends/lean/Primitives.lean index e558e476..346e4b89 100644 --- a/backends/lean/Primitives.lean +++ b/backends/lean/Primitives.lean @@ -21,7 +21,7 @@ open Error inductive Result (α : Type u) where | ret (v: α): Result α - | fail (e: Error): Result α + | fail (e: Error): Result α deriving Repr, BEq open Result diff --git a/tests/lean/hashmap/Base/Primitives.lean b/tests/lean/hashmap/Base/Primitives.lean index 79958d94..5b64e908 100644 --- a/tests/lean/hashmap/Base/Primitives.lean +++ b/tests/lean/hashmap/Base/Primitives.lean @@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd -- 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 +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error deriving Repr, BEq -open error +open Error -inductive result (α : Type u) where - | ret (v: α): result α - | fail (e: error): result α +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α deriving Repr, BEq -open result +open Result /- HELPERS -/ --- TODO: is there automated syntax for these discriminators? -def is_ret {α: Type} (r: result α): Bool := +def ret? {α: Type} (r: Result α): Bool := match r with - | result.ret _ => true - | result.fail _ => false + | Result.ret _ => true + | Result.fail _ => false -def massert (b:Bool) : result Unit := +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 := +def eval_global {α: Type} (x: Result α) (_: ret? x): α := match x with - | result.fail _ => by contradiction - | result.ret x => x + | Result.fail _ => by contradiction + | Result.ret x => x /- DO-DSL SUPPORT -/ -def bind (x: result α) (f: α -> result β) : result β := +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 +-- Allows using Result in do-blocks +instance : Bind Result where bind := bind -- Allows using return x in do-blocks -instance : Pure result where +instance : Pure Result where pure := fun x => ret x /- CUSTOM-DSL SUPPORT -/ --- Let-binding the result of a monadic operation is oftentimes not sufficient, +-- 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 } +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e + | .fail e => .fail e -macro "let" h:ident " : " e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, $h⟩ ← result.attach $f) +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) --- Silly example of the kind of reasoning that this notation enables +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` #eval do - let h: y <-- .ret (0: Nat) - let _: y = 0 := by cases h; decide + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ .ret r @@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem => -- 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: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part -- of a subtype is less discoverable by the simplifier or tactics like --- library_search." Try to settle this with a Lean expert on what is the most --- productive way to go about this? +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. --- One needs to perform a little bit of reasoning in order to successfully --- inject constants into USize, so we provide a general-purpose macro +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. syntax "intlit" : tactic @@ -129,12 +125,21 @@ macro_rules -- Also works for other integer types (at the expense of a needless disjunction) #eval UInt32.ofNatCore 0 (by intlit) +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): result USize := +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 @@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize := 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 +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then .ret ⟨ n.val + m.val, h ⟩ else .fail integerOverflow -def USize.checked_rem (n: USize) (m: USize): result USize := +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 @@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize := 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 +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then .ret ⟨ n.val * m.val, h ⟩ else .fail integerOverflow -def USize.checked_div (n: USize) (m: USize): result USize := +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 @@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize := else .fail integerOverflow +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + class MachineInteger (t: Type) where size: Nat val: t -> Fin size @@ -209,30 +223,24 @@ run_cmd end $typeName )) -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst := +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := if h: MachineInteger.val x < MachineInteger.size dst then .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) else .fail integerOverflow - --- 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 (α : Type u) := { l : List α // List.length l < USize.size } -def vec_new (α : Type u): vec α := ⟨ [], by { +def vec_new (α : Type u): Vec α := ⟨ [], by { match USize.size, usize_size_eq with | _, Or.inl rfl => simp | _, Or.inr rfl => simp @@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by { #check vec_new -def vec_len (α : Type u) (v : vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : USize := let ⟨ v, l ⟩ := v USize.ofNatCore (List.length v) l #eval vec_len Nat (vec_new Nat) -def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := () +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 +-- 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) // +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 @@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec -- 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? + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? -- TODO: strengthen post-condition above and do a demo to show that we can -- safely eliminate the `fail` case return (vec_len Nat x) -def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := if h : List.length v.val + 1 <= 4294967295 then return ⟨ List.concat v.val x, @@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := def mem_replace_back (a : Type) (_ : a) (y : a) : a := y +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + -------------------- -- ASSERT COMMAND -- -------------------- @@ -358,16 +370,23 @@ open Lean Elab Command Term Meta syntax (name := assert) "#assert" term: command @[command_elab assert] +unsafe 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? + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" pure ()) - -- logInfo (Expr.dbgToString (``true)) - -- throwError "TODO: assert" #eval 2 == 2 #assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/hashmap/Hashmap/Clauses/Template.lean b/tests/lean/hashmap/Hashmap/Clauses/Template.lean index 2bc92153..b767a0eb 100644 --- a/tests/lean/hashmap/Hashmap/Clauses/Template.lean +++ b/tests/lean/hashmap/Hashmap/Clauses/Template.lean @@ -5,7 +5,7 @@ import Hashmap.Types /- [hashmap::HashMap::{0}::allocate_slots]: termination measure -/ @[simp] -def hash_map_allocate_slots_loop_terminates (T : Type) (slots : vec (list_t T)) +def hash_map_allocate_slots_loop_terminates (T : Type) (slots : Vec (list_t T)) (n : USize) := (slots, n) @@ -16,7 +16,7 @@ macro_rules /- [hashmap::HashMap::{0}::clear]: termination measure -/ @[simp] -def hash_map_clear_loop_terminates (T : Type) (slots : vec (list_t T)) +def hash_map_clear_loop_terminates (T : Type) (slots : Vec (list_t T)) (i : USize) := (slots, i) @@ -52,7 +52,7 @@ macro_rules /- [hashmap::HashMap::{0}::move_elements]: termination measure -/ @[simp] def hash_map_move_elements_loop_terminates (T : Type) (ntable : hash_map_t T) - (slots : vec (list_t T)) (i : USize) := + (slots : Vec (list_t T)) (i : USize) := (ntable, slots, i) syntax "hash_map_move_elements_loop_decreases" term+ : tactic diff --git a/tests/lean/hashmap/Hashmap/Funs.lean b/tests/lean/hashmap/Hashmap/Funs.lean index 3bdd9dd2..0b3708fa 100644 --- a/tests/lean/hashmap/Hashmap/Funs.lean +++ b/tests/lean/hashmap/Hashmap/Funs.lean @@ -5,42 +5,42 @@ import Hashmap.Types import Hashmap.Clauses.Clauses /- [hashmap::hash_key] -/ -def hash_key_fwd (k : USize) : result USize := - result.ret k +def hash_key_fwd (k : USize) : Result USize := + Result.ret k /- [hashmap::HashMap::{0}::allocate_slots] -/ def hash_map_allocate_slots_loop_fwd - (T : Type) (slots : vec (list_t T)) (n : USize) : - (result (vec (list_t T))) + (T : Type) (slots : Vec (list_t T)) (n : USize) : + (Result (Vec (list_t T))) := - if n > (USize.ofNatCore 0 (by intlit)) + if h: n > (USize.ofNatCore 0 (by intlit)) then do - let slots0 <- vec_push_back (list_t T) slots list_t.ListNil - let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit)) + let slots0 ← vec_push_back (list_t T) slots list_t.ListNil + let n0 ← USize.checked_sub n (USize.ofNatCore 1 (by intlit)) hash_map_allocate_slots_loop_fwd T slots0 n0 - else result.ret slots + else Result.ret slots termination_by hash_map_allocate_slots_loop_fwd slots n => hash_map_allocate_slots_loop_terminates T slots n decreasing_by hash_map_allocate_slots_loop_decreases slots n /- [hashmap::HashMap::{0}::allocate_slots] -/ def hash_map_allocate_slots_fwd - (T : Type) (slots : vec (list_t T)) (n : USize) : result (vec (list_t T)) := + (T : Type) (slots : Vec (list_t T)) (n : USize) : Result (Vec (list_t T)) := hash_map_allocate_slots_loop_fwd T slots n /- [hashmap::HashMap::{0}::new_with_capacity] -/ def hash_map_new_with_capacity_fwd (T : Type) (capacity : USize) (max_load_dividend : USize) (max_load_divisor : USize) : - result (hash_map_t T) + Result (hash_map_t T) := do let v := vec_new (list_t T) - let slots <- hash_map_allocate_slots_fwd T v capacity - let i <- USize.checked_mul capacity max_load_dividend - let i0 <- USize.checked_div i max_load_divisor - result.ret + let slots ← hash_map_allocate_slots_fwd T v capacity + let i ← USize.checked_mul capacity max_load_dividend + let i0 ← USize.checked_div i max_load_divisor + Result.ret { hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), hash_map_max_load_factor := (max_load_dividend, max_load_divisor), @@ -49,35 +49,35 @@ def hash_map_new_with_capacity_fwd } /- [hashmap::HashMap::{0}::new] -/ -def hash_map_new_fwd (T : Type) : result (hash_map_t T) := +def hash_map_new_fwd (T : Type) : Result (hash_map_t T) := hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit)) (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit)) /- [hashmap::HashMap::{0}::clear] -/ def hash_map_clear_loop_fwd_back - (T : Type) (slots : vec (list_t T)) (i : USize) : - (result (vec (list_t T))) + (T : Type) (slots : Vec (list_t T)) (i : USize) : + (Result (Vec (list_t T))) := let i0 := vec_len (list_t T) slots - if i < i0 + if h: i < i0 then do - let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) - let slots0 <- vec_index_mut_back (list_t T) slots i list_t.ListNil + let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let slots0 ← vec_index_mut_back (list_t T) slots i list_t.ListNil hash_map_clear_loop_fwd_back T slots0 i1 - else result.ret slots + else Result.ret slots termination_by hash_map_clear_loop_fwd_back slots i => hash_map_clear_loop_terminates T slots i decreasing_by hash_map_clear_loop_decreases slots i /- [hashmap::HashMap::{0}::clear] -/ def hash_map_clear_fwd_back - (T : Type) (self : hash_map_t T) : result (hash_map_t T) := + (T : Type) (self : hash_map_t T) : Result (hash_map_t T) := do - let v <- + let v ← hash_map_clear_loop_fwd_back T self.hash_map_slots (USize.ofNatCore 0 (by intlit)) - result.ret + Result.ret { hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), hash_map_max_load_factor := self.hash_map_max_load_factor, @@ -86,69 +86,69 @@ def hash_map_clear_fwd_back } /- [hashmap::HashMap::{0}::len] -/ -def hash_map_len_fwd (T : Type) (self : hash_map_t T) : result USize := - result.ret self.hash_map_num_entries +def hash_map_len_fwd (T : Type) (self : hash_map_t T) : Result USize := + Result.ret self.hash_map_num_entries /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_loop_fwd - (T : Type) (key : USize) (value : T) (ls : list_t T) : (result Bool) := - match ls with + (T : Type) (key : USize) (value : T) (ls : list_t T) : (Result Bool) := + match h: ls with | list_t.ListCons ckey cvalue tl => - if ckey = key - then result.ret false + if h: ckey = key + then Result.ret false else hash_map_insert_in_list_loop_fwd T key value tl - | list_t.ListNil => result.ret true + | list_t.ListNil => Result.ret true termination_by hash_map_insert_in_list_loop_fwd key value ls => hash_map_insert_in_list_loop_terminates T key value ls decreasing_by hash_map_insert_in_list_loop_decreases key value ls /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_fwd - (T : Type) (key : USize) (value : T) (ls : list_t T) : result Bool := + (T : Type) (key : USize) (value : T) (ls : list_t T) : Result Bool := hash_map_insert_in_list_loop_fwd T key value ls /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_loop_back - (T : Type) (key : USize) (value : T) (ls : list_t T) : (result (list_t T)) := - match ls with + (T : Type) (key : USize) (value : T) (ls : list_t T) : (Result (list_t T)) := + match h: ls with | list_t.ListCons ckey cvalue tl => - if ckey = key - then result.ret (list_t.ListCons ckey value tl) + if h: ckey = key + then Result.ret (list_t.ListCons ckey value tl) else do - let tl0 <- hash_map_insert_in_list_loop_back T key value tl - result.ret (list_t.ListCons ckey cvalue tl0) + let tl0 ← hash_map_insert_in_list_loop_back T key value tl + Result.ret (list_t.ListCons ckey cvalue tl0) | list_t.ListNil => let l := list_t.ListNil - result.ret (list_t.ListCons key value l) + Result.ret (list_t.ListCons key value l) termination_by hash_map_insert_in_list_loop_back key value ls => hash_map_insert_in_list_loop_terminates T key value ls decreasing_by hash_map_insert_in_list_loop_decreases key value ls /- [hashmap::HashMap::{0}::insert_in_list] -/ def hash_map_insert_in_list_back - (T : Type) (key : USize) (value : T) (ls : list_t T) : result (list_t T) := + (T : Type) (key : USize) (value : T) (ls : list_t T) : Result (list_t T) := hash_map_insert_in_list_loop_back T key value ls /- [hashmap::HashMap::{0}::insert_no_resize] -/ def hash_map_insert_no_resize_fwd_back (T : Type) (self : hash_map_t T) (key : USize) (value : T) : - result (hash_map_t T) + Result (hash_map_t T) := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod - let inserted <- hash_map_insert_in_list_fwd T key value l - if inserted + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod + let inserted ← hash_map_insert_in_list_fwd T key value l + if h: inserted then do - let i0 <- USize.checked_add self.hash_map_num_entries + let i0 ← USize.checked_add self.hash_map_num_entries (USize.ofNatCore 1 (by intlit)) - let l0 <- hash_map_insert_in_list_back T key value l - let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 - result.ret + let l0 ← hash_map_insert_in_list_back T key value l + let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 + Result.ret { hash_map_num_entries := i0, hash_map_max_load_factor := self.hash_map_max_load_factor, @@ -157,9 +157,9 @@ def hash_map_insert_no_resize_fwd_back } else do - let l0 <- hash_map_insert_in_list_back T key value l - let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 - result.ret + let l0 ← hash_map_insert_in_list_back T key value l + let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 + Result.ret { hash_map_num_entries := self.hash_map_num_entries, hash_map_max_load_factor := self.hash_map_max_load_factor, @@ -168,76 +168,76 @@ def hash_map_insert_no_resize_fwd_back } /- [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_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) /- [hashmap::HashMap::{0}::move_elements_from_list] -/ def hash_map_move_elements_from_list_loop_fwd_back (T : Type) (ntable : hash_map_t T) (ls : list_t T) : - (result (hash_map_t T)) + (Result (hash_map_t T)) := - match ls with + match h: ls with | list_t.ListCons k v tl => do - let ntable0 <- hash_map_insert_no_resize_fwd_back T ntable k v + let ntable0 ← hash_map_insert_no_resize_fwd_back T ntable k v hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl - | list_t.ListNil => result.ret ntable + | list_t.ListNil => Result.ret ntable termination_by hash_map_move_elements_from_list_loop_fwd_back ntable ls => hash_map_move_elements_from_list_loop_terminates T ntable ls decreasing_by hash_map_move_elements_from_list_loop_decreases ntable ls /- [hashmap::HashMap::{0}::move_elements_from_list] -/ def hash_map_move_elements_from_list_fwd_back - (T : Type) (ntable : hash_map_t T) (ls : list_t T) : result (hash_map_t T) := + (T : Type) (ntable : hash_map_t T) (ls : list_t T) : Result (hash_map_t T) := hash_map_move_elements_from_list_loop_fwd_back T ntable ls /- [hashmap::HashMap::{0}::move_elements] -/ def hash_map_move_elements_loop_fwd_back - (T : Type) (ntable : hash_map_t T) (slots : vec (list_t T)) (i : USize) : - (result ((hash_map_t T) × (vec (list_t T)))) + (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : USize) : + (Result ((hash_map_t T) × (Vec (list_t T)))) := let i0 := vec_len (list_t T) slots - if i < i0 + if h: i < i0 then do - let l <- vec_index_mut_fwd (list_t T) slots i + let l ← vec_index_mut_fwd (list_t T) slots i let ls := mem_replace_fwd (list_t T) l list_t.ListNil - let ntable0 <- hash_map_move_elements_from_list_fwd_back T ntable ls - let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let ntable0 ← hash_map_move_elements_from_list_fwd_back T ntable ls + let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) let l0 := mem_replace_back (list_t T) l list_t.ListNil - let slots0 <- vec_index_mut_back (list_t T) slots i l0 + let slots0 ← vec_index_mut_back (list_t T) slots i l0 hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1 - else result.ret (ntable, slots) + else Result.ret (ntable, slots) termination_by hash_map_move_elements_loop_fwd_back ntable slots i => hash_map_move_elements_loop_terminates T ntable slots i decreasing_by hash_map_move_elements_loop_decreases ntable slots i /- [hashmap::HashMap::{0}::move_elements] -/ def hash_map_move_elements_fwd_back - (T : Type) (ntable : hash_map_t T) (slots : vec (list_t T)) (i : USize) : - result ((hash_map_t T) × (vec (list_t T))) + (T : Type) (ntable : hash_map_t T) (slots : Vec (list_t T)) (i : USize) : + Result ((hash_map_t T) × (Vec (list_t T))) := hash_map_move_elements_loop_fwd_back T ntable slots i /- [hashmap::HashMap::{0}::try_resize] -/ def hash_map_try_resize_fwd_back - (T : Type) (self : hash_map_t T) : result (hash_map_t T) := + (T : Type) (self : hash_map_t T) : Result (hash_map_t T) := do - let max_usize <- scalar_cast USize core_num_u32_max_c + let max_usize ← scalar_cast USize core_num_u32_max_c let capacity := vec_len (list_t T) self.hash_map_slots - let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) + let n1 ← USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) let (i, i0) := self.hash_map_max_load_factor - let i1 <- USize.checked_div n1 i - if capacity <= i1 + let i1 ← USize.checked_div n1 i + if h: capacity <= i1 then do - let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) - let ntable <- hash_map_new_with_capacity_fwd T i2 i i0 - let (ntable0, _) <- + let i2 ← USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) + let ntable ← hash_map_new_with_capacity_fwd T i2 i i0 + let (ntable0, _) ← hash_map_move_elements_fwd_back T ntable self.hash_map_slots (USize.ofNatCore 0 (by intlit)) - result.ret + Result.ret { hash_map_num_entries := self.hash_map_num_entries, hash_map_max_load_factor := (i, i0), @@ -245,7 +245,7 @@ def hash_map_try_resize_fwd_back hash_map_slots := ntable0.hash_map_slots } else - result.ret + Result.ret { hash_map_num_entries := self.hash_map_num_entries, hash_map_max_load_factor := (i, i0), @@ -256,133 +256,133 @@ def hash_map_try_resize_fwd_back /- [hashmap::HashMap::{0}::insert] -/ def hash_map_insert_fwd_back (T : Type) (self : hash_map_t T) (key : USize) (value : T) : - result (hash_map_t T) + Result (hash_map_t T) := do - let self0 <- hash_map_insert_no_resize_fwd_back T self key value - let i <- hash_map_len_fwd T self0 - if i > self0.hash_map_max_load + let self0 ← hash_map_insert_no_resize_fwd_back T self key value + let i ← hash_map_len_fwd T self0 + if h: i > self0.hash_map_max_load then hash_map_try_resize_fwd_back T self0 - else result.ret self0 + else Result.ret self0 /- [hashmap::HashMap::{0}::contains_key_in_list] -/ def hash_map_contains_key_in_list_loop_fwd - (T : Type) (key : USize) (ls : list_t T) : (result Bool) := - match ls with + (T : Type) (key : USize) (ls : list_t T) : (Result Bool) := + match h: ls with | list_t.ListCons ckey t tl => - if ckey = key - then result.ret true + if h: ckey = key + then Result.ret true else hash_map_contains_key_in_list_loop_fwd T key tl - | list_t.ListNil => result.ret false + | list_t.ListNil => Result.ret false termination_by hash_map_contains_key_in_list_loop_fwd key ls => hash_map_contains_key_in_list_loop_terminates T key ls decreasing_by hash_map_contains_key_in_list_loop_decreases key ls /- [hashmap::HashMap::{0}::contains_key_in_list] -/ def hash_map_contains_key_in_list_fwd - (T : Type) (key : USize) (ls : list_t T) : result Bool := + (T : Type) (key : USize) (ls : list_t T) : Result Bool := hash_map_contains_key_in_list_loop_fwd T key ls /- [hashmap::HashMap::{0}::contains_key] -/ def hash_map_contains_key_fwd - (T : Type) (self : hash_map_t T) (key : USize) : result Bool := + (T : Type) (self : hash_map_t T) (key : USize) : Result Bool := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_fwd (list_t T) self.hash_map_slots hash_mod + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod hash_map_contains_key_in_list_fwd T key l /- [hashmap::HashMap::{0}::get_in_list] -/ def hash_map_get_in_list_loop_fwd - (T : Type) (key : USize) (ls : list_t T) : (result T) := - match ls with + (T : Type) (key : USize) (ls : list_t T) : (Result T) := + match h: ls with | list_t.ListCons ckey cvalue tl => - if ckey = key - then result.ret cvalue + if h: ckey = key + then Result.ret cvalue else hash_map_get_in_list_loop_fwd T key tl - | list_t.ListNil => result.fail error.panic + | list_t.ListNil => Result.fail Error.panic termination_by hash_map_get_in_list_loop_fwd key ls => hash_map_get_in_list_loop_terminates T key ls decreasing_by hash_map_get_in_list_loop_decreases key ls /- [hashmap::HashMap::{0}::get_in_list] -/ def hash_map_get_in_list_fwd - (T : Type) (key : USize) (ls : list_t T) : result T := + (T : Type) (key : USize) (ls : list_t T) : Result T := hash_map_get_in_list_loop_fwd T key ls /- [hashmap::HashMap::{0}::get] -/ def hash_map_get_fwd - (T : Type) (self : hash_map_t T) (key : USize) : result T := + (T : Type) (self : hash_map_t T) (key : USize) : Result T := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_fwd (list_t T) self.hash_map_slots hash_mod + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_fwd (list_t T) self.hash_map_slots hash_mod hash_map_get_in_list_fwd T key l /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_loop_fwd - (T : Type) (ls : list_t T) (key : USize) : (result T) := - match ls with + (T : Type) (ls : list_t T) (key : USize) : (Result T) := + match h: ls with | list_t.ListCons ckey cvalue tl => - if ckey = key - then result.ret cvalue + if h: ckey = key + then Result.ret cvalue else hash_map_get_mut_in_list_loop_fwd T tl key - | list_t.ListNil => result.fail error.panic + | list_t.ListNil => Result.fail Error.panic termination_by hash_map_get_mut_in_list_loop_fwd ls key => hash_map_get_mut_in_list_loop_terminates T ls key decreasing_by hash_map_get_mut_in_list_loop_decreases ls key /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_fwd - (T : Type) (ls : list_t T) (key : USize) : result T := + (T : Type) (ls : list_t T) (key : USize) : Result T := hash_map_get_mut_in_list_loop_fwd T ls key /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_loop_back - (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : (result (list_t T)) := - match ls with + (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : (Result (list_t T)) := + match h: ls with | list_t.ListCons ckey cvalue tl => - if ckey = key - then result.ret (list_t.ListCons ckey ret0 tl) + if h: ckey = key + then Result.ret (list_t.ListCons ckey ret0 tl) else do - let tl0 <- hash_map_get_mut_in_list_loop_back T tl key ret0 - result.ret (list_t.ListCons ckey cvalue tl0) - | list_t.ListNil => result.fail error.panic + let tl0 ← hash_map_get_mut_in_list_loop_back T tl key ret0 + Result.ret (list_t.ListCons ckey cvalue tl0) + | list_t.ListNil => Result.fail Error.panic termination_by hash_map_get_mut_in_list_loop_back ls key ret0 => hash_map_get_mut_in_list_loop_terminates T ls key decreasing_by hash_map_get_mut_in_list_loop_decreases ls key /- [hashmap::HashMap::{0}::get_mut_in_list] -/ def hash_map_get_mut_in_list_back - (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : result (list_t T) := + (T : Type) (ls : list_t T) (key : USize) (ret0 : T) : Result (list_t T) := hash_map_get_mut_in_list_loop_back T ls key ret0 /- [hashmap::HashMap::{0}::get_mut] -/ def hash_map_get_mut_fwd - (T : Type) (self : hash_map_t T) (key : USize) : result T := + (T : Type) (self : hash_map_t T) (key : USize) : Result T := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod hash_map_get_mut_in_list_fwd T l key /- [hashmap::HashMap::{0}::get_mut] -/ def hash_map_get_mut_back (T : Type) (self : hash_map_t T) (key : USize) (ret0 : T) : - result (hash_map_t T) + Result (hash_map_t T) := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod - let l0 <- hash_map_get_mut_in_list_back T l key ret0 - let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 - result.ret + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod + let l0 ← hash_map_get_mut_in_list_back T l key ret0 + let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 + Result.ret { hash_map_num_entries := self.hash_map_num_entries, hash_map_max_load_factor := self.hash_map_max_load_factor, @@ -392,85 +392,85 @@ def hash_map_get_mut_back /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_loop_fwd - (T : Type) (key : USize) (ls : list_t T) : (result (Option T)) := - match ls with + (T : Type) (key : USize) (ls : list_t T) : (Result (Option T)) := + match h: ls with | list_t.ListCons ckey t tl => - if ckey = key + if h: ckey = key then let mv_ls := mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil - match mv_ls with - | list_t.ListCons i cvalue tl0 => result.ret (Option.some cvalue) - | list_t.ListNil => result.fail error.panic + match h: mv_ls with + | list_t.ListCons i cvalue tl0 => Result.ret (Option.some cvalue) + | list_t.ListNil => Result.fail Error.panic else hash_map_remove_from_list_loop_fwd T key tl - | list_t.ListNil => result.ret Option.none + | list_t.ListNil => Result.ret Option.none termination_by hash_map_remove_from_list_loop_fwd key ls => hash_map_remove_from_list_loop_terminates T key ls decreasing_by hash_map_remove_from_list_loop_decreases key ls /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_fwd - (T : Type) (key : USize) (ls : list_t T) : result (Option T) := + (T : Type) (key : USize) (ls : list_t T) : Result (Option T) := hash_map_remove_from_list_loop_fwd T key ls /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_loop_back - (T : Type) (key : USize) (ls : list_t T) : (result (list_t T)) := - match ls with + (T : Type) (key : USize) (ls : list_t T) : (Result (list_t T)) := + match h: ls with | list_t.ListCons ckey t tl => - if ckey = key + if h: ckey = key then let mv_ls := mem_replace_fwd (list_t T) (list_t.ListCons ckey t tl) list_t.ListNil - match mv_ls with - | list_t.ListCons i cvalue tl0 => result.ret tl0 - | list_t.ListNil => result.fail error.panic + match h: mv_ls with + | list_t.ListCons i cvalue tl0 => Result.ret tl0 + | list_t.ListNil => Result.fail Error.panic else do - let tl0 <- hash_map_remove_from_list_loop_back T key tl - result.ret (list_t.ListCons ckey t tl0) - | list_t.ListNil => result.ret list_t.ListNil + let tl0 ← hash_map_remove_from_list_loop_back T key tl + Result.ret (list_t.ListCons ckey t tl0) + | list_t.ListNil => Result.ret list_t.ListNil termination_by hash_map_remove_from_list_loop_back key ls => hash_map_remove_from_list_loop_terminates T key ls decreasing_by hash_map_remove_from_list_loop_decreases key ls /- [hashmap::HashMap::{0}::remove_from_list] -/ def hash_map_remove_from_list_back - (T : Type) (key : USize) (ls : list_t T) : result (list_t T) := + (T : Type) (key : USize) (ls : list_t T) : Result (list_t T) := hash_map_remove_from_list_loop_back T key ls /- [hashmap::HashMap::{0}::remove] -/ def hash_map_remove_fwd - (T : Type) (self : hash_map_t T) (key : USize) : result (Option T) := + (T : Type) (self : hash_map_t T) (key : USize) : Result (Option T) := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod - let x <- hash_map_remove_from_list_fwd T key l - match x with - | Option.none => result.ret Option.none + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod + let x ← hash_map_remove_from_list_fwd T key l + match h: x with + | Option.none => Result.ret Option.none | Option.some x0 => do - let _ <- USize.checked_sub self.hash_map_num_entries + let _ ← USize.checked_sub self.hash_map_num_entries (USize.ofNatCore 1 (by intlit)) - result.ret (Option.some x0) + Result.ret (Option.some x0) /- [hashmap::HashMap::{0}::remove] -/ def hash_map_remove_back - (T : Type) (self : hash_map_t T) (key : USize) : result (hash_map_t T) := + (T : Type) (self : hash_map_t T) (key : USize) : Result (hash_map_t T) := do - let hash <- hash_key_fwd key + let hash ← hash_key_fwd key let i := vec_len (list_t T) self.hash_map_slots - let hash_mod <- USize.checked_rem hash i - let l <- vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod - let x <- hash_map_remove_from_list_fwd T key l - match x with + let hash_mod ← USize.checked_rem hash i + let l ← vec_index_mut_fwd (list_t T) self.hash_map_slots hash_mod + let x ← hash_map_remove_from_list_fwd T key l + match h: x with | Option.none => do - let l0 <- hash_map_remove_from_list_back T key l - let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 - result.ret + let l0 ← hash_map_remove_from_list_back T key l + let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 + Result.ret { hash_map_num_entries := self.hash_map_num_entries, hash_map_max_load_factor := self.hash_map_max_load_factor, @@ -479,11 +479,11 @@ def hash_map_remove_back } | Option.some x0 => do - let i0 <- USize.checked_sub self.hash_map_num_entries + let i0 ← USize.checked_sub self.hash_map_num_entries (USize.ofNatCore 1 (by intlit)) - let l0 <- hash_map_remove_from_list_back T key l - let v <- vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 - result.ret + let l0 ← hash_map_remove_from_list_back T key l + let v ← vec_index_mut_back (list_t T) self.hash_map_slots hash_mod l0 + Result.ret { hash_map_num_entries := i0, hash_map_max_load_factor := self.hash_map_max_load_factor, @@ -492,67 +492,67 @@ def hash_map_remove_back } /- [hashmap::test1] -/ -def test1_fwd : result Unit := +def test1_fwd : Result Unit := do - let hm <- hash_map_new_fwd UInt64 - let hm0 <- + let hm ← hash_map_new_fwd UInt64 + let hm0 ← hash_map_insert_fwd_back UInt64 hm (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit)) - let hm1 <- + let hm1 ← hash_map_insert_fwd_back UInt64 hm0 (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit)) - let hm2 <- + let hm2 ← hash_map_insert_fwd_back UInt64 hm1 (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit)) - let hm3 <- + let hm3 ← hash_map_insert_fwd_back UInt64 hm2 (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit)) - let i <- hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) - if not (i = (UInt64.ofNatCore 18 (by intlit))) - then result.fail error.panic + let i ← hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) + if h: not (i = (UInt64.ofNatCore 18 (by intlit))) + then Result.fail Error.panic else do - let hm4 <- + let hm4 ← hash_map_get_mut_back UInt64 hm3 (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 56 (by intlit)) - let i0 <- + let i0 ← hash_map_get_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit)) - if not (i0 = (UInt64.ofNatCore 56 (by intlit))) - then result.fail error.panic + if h: not (i0 = (UInt64.ofNatCore 56 (by intlit))) + then Result.fail Error.panic else do - let x <- + let x ← hash_map_remove_fwd UInt64 hm4 (USize.ofNatCore 1024 (by intlit)) - match x with - | Option.none => result.fail error.panic + match h: x with + | Option.none => Result.fail Error.panic | Option.some x0 => - if not (x0 = (UInt64.ofNatCore 56 (by intlit))) - then result.fail error.panic + if h: not (x0 = (UInt64.ofNatCore 56 (by intlit))) + then Result.fail Error.panic else do - let hm5 <- + let hm5 ← hash_map_remove_back UInt64 hm4 (USize.ofNatCore 1024 (by intlit)) - let i1 <- + let i1 ← hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 0 (by intlit)) - if not (i1 = (UInt64.ofNatCore 42 (by intlit))) - then result.fail error.panic + if h: not (i1 = (UInt64.ofNatCore 42 (by intlit))) + then Result.fail Error.panic else do - let i2 <- + let i2 ← hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 128 (by intlit)) - if not (i2 = (UInt64.ofNatCore 18 (by intlit))) - then result.fail error.panic + if h: not (i2 = (UInt64.ofNatCore 18 (by intlit))) + then Result.fail Error.panic else do - let i3 <- + let i3 ← hash_map_get_fwd UInt64 hm5 (USize.ofNatCore 1056 (by intlit)) - if not (i3 = (UInt64.ofNatCore 256 (by intlit))) - then result.fail error.panic - else result.ret () + if h: not (i3 = (UInt64.ofNatCore 256 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [hashmap::test1] -/ -#assert (test1_fwd = .ret ()) +#assert (test1_fwd == .ret ()) diff --git a/tests/lean/hashmap/Hashmap/Types.lean b/tests/lean/hashmap/Hashmap/Types.lean index 9f08bd60..750bf6de 100644 --- a/tests/lean/hashmap/Hashmap/Types.lean +++ b/tests/lean/hashmap/Hashmap/Types.lean @@ -13,6 +13,6 @@ structure hash_map_t (T : Type) where hash_map_num_entries : USize hash_map_max_load_factor : (USize × USize) hash_map_max_load : USize - hash_map_slots : vec (list_t T) + hash_map_slots : Vec (list_t T) diff --git a/tests/lean/hashmap_on_disk/Base/Primitives.lean b/tests/lean/hashmap_on_disk/Base/Primitives.lean index e230dcab..5b64e908 100644 --- a/tests/lean/hashmap_on_disk/Base/Primitives.lean +++ b/tests/lean/hashmap_on_disk/Base/Primitives.lean @@ -21,7 +21,7 @@ open Error inductive Result (α : Type u) where | ret (v: α): Result α - | fail (e: Error): Result α + | fail (e: Error): Result α deriving Repr, BEq open Result diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean index a514c58a..e64419a6 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean @@ -15,17 +15,16 @@ macro_rules | `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) => `(tactic| sorry) -/- [hashmap_main::hashmap::HashMap::{0}::clear_slots]: termination measure -/ +/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/ @[simp] -def hashmap_hash_map_clear_slots_loop_terminates (T : Type) +def hashmap_hash_map_clear_loop_terminates (T : Type) (slots : Vec (hashmap_list_t T)) (i : USize) := (slots, i) -syntax "hashmap_hash_map_clear_slots_loop_decreases" term+ : tactic +syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic macro_rules -| `(tactic| hashmap_hash_map_clear_slots_loop_decreases $slots $i) => - `(tactic| sorry) +| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry) /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/ @[simp] diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean index 392c8816..c85d14f4 100644 --- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean +++ b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean @@ -60,8 +60,8 @@ def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) := hashmap_hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit)) (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit)) -/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/ -def hashmap_hash_map_clear_slots_loop_fwd_back +/- [hashmap_main::hashmap::HashMap::{0}::clear] -/ +def hashmap_hash_map_clear_loop_fwd_back (T : Type) (slots : Vec (hashmap_list_t T)) (i : USize) : (Result (Vec (hashmap_list_t T))) := @@ -73,26 +73,19 @@ def hashmap_hash_map_clear_slots_loop_fwd_back let slots0 ← vec_index_mut_back (hashmap_list_t T) slots i hashmap_list_t.HashmapListNil - hashmap_hash_map_clear_slots_loop_fwd_back T slots0 i1 + hashmap_hash_map_clear_loop_fwd_back T slots0 i1 else Result.ret slots -termination_by hashmap_hash_map_clear_slots_loop_fwd_back slots i => - hashmap_hash_map_clear_slots_loop_terminates T slots i -decreasing_by hashmap_hash_map_clear_slots_loop_decreases slots i - -/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/ -def hashmap_hash_map_clear_slots_fwd_back - (T : Type) (slots : Vec (hashmap_list_t T)) : - Result (Vec (hashmap_list_t T)) - := - hashmap_hash_map_clear_slots_loop_fwd_back T slots - (USize.ofNatCore 0 (by intlit)) +termination_by hashmap_hash_map_clear_loop_fwd_back slots i => + hashmap_hash_map_clear_loop_terminates T slots i +decreasing_by hashmap_hash_map_clear_loop_decreases slots i /- [hashmap_main::hashmap::HashMap::{0}::clear] -/ def hashmap_hash_map_clear_fwd_back (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) := do let v ← - hashmap_hash_map_clear_slots_fwd_back T self.hashmap_hash_map_slots + hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots + (USize.ofNatCore 0 (by intlit)) Result.ret { hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)), diff --git a/tests/lean/misc/constants/Base/Primitives.lean b/tests/lean/misc/constants/Base/Primitives.lean index 79958d94..5b64e908 100644 --- a/tests/lean/misc/constants/Base/Primitives.lean +++ b/tests/lean/misc/constants/Base/Primitives.lean @@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd -- 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 +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error deriving Repr, BEq -open error +open Error -inductive result (α : Type u) where - | ret (v: α): result α - | fail (e: error): result α +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α deriving Repr, BEq -open result +open Result /- HELPERS -/ --- TODO: is there automated syntax for these discriminators? -def is_ret {α: Type} (r: result α): Bool := +def ret? {α: Type} (r: Result α): Bool := match r with - | result.ret _ => true - | result.fail _ => false + | Result.ret _ => true + | Result.fail _ => false -def massert (b:Bool) : result Unit := +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 := +def eval_global {α: Type} (x: Result α) (_: ret? x): α := match x with - | result.fail _ => by contradiction - | result.ret x => x + | Result.fail _ => by contradiction + | Result.ret x => x /- DO-DSL SUPPORT -/ -def bind (x: result α) (f: α -> result β) : result β := +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 +-- Allows using Result in do-blocks +instance : Bind Result where bind := bind -- Allows using return x in do-blocks -instance : Pure result where +instance : Pure Result where pure := fun x => ret x /- CUSTOM-DSL SUPPORT -/ --- Let-binding the result of a monadic operation is oftentimes not sufficient, +-- 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 } +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e + | .fail e => .fail e -macro "let" h:ident " : " e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, $h⟩ ← result.attach $f) +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) --- Silly example of the kind of reasoning that this notation enables +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` #eval do - let h: y <-- .ret (0: Nat) - let _: y = 0 := by cases h; decide + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ .ret r @@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem => -- 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: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part -- of a subtype is less discoverable by the simplifier or tactics like --- library_search." Try to settle this with a Lean expert on what is the most --- productive way to go about this? +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. --- One needs to perform a little bit of reasoning in order to successfully --- inject constants into USize, so we provide a general-purpose macro +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. syntax "intlit" : tactic @@ -129,12 +125,21 @@ macro_rules -- Also works for other integer types (at the expense of a needless disjunction) #eval UInt32.ofNatCore 0 (by intlit) +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): result USize := +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 @@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize := 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 +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then .ret ⟨ n.val + m.val, h ⟩ else .fail integerOverflow -def USize.checked_rem (n: USize) (m: USize): result USize := +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 @@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize := 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 +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then .ret ⟨ n.val * m.val, h ⟩ else .fail integerOverflow -def USize.checked_div (n: USize) (m: USize): result USize := +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 @@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize := else .fail integerOverflow +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + class MachineInteger (t: Type) where size: Nat val: t -> Fin size @@ -209,30 +223,24 @@ run_cmd end $typeName )) -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst := +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := if h: MachineInteger.val x < MachineInteger.size dst then .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) else .fail integerOverflow - --- 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 (α : Type u) := { l : List α // List.length l < USize.size } -def vec_new (α : Type u): vec α := ⟨ [], by { +def vec_new (α : Type u): Vec α := ⟨ [], by { match USize.size, usize_size_eq with | _, Or.inl rfl => simp | _, Or.inr rfl => simp @@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by { #check vec_new -def vec_len (α : Type u) (v : vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : USize := let ⟨ v, l ⟩ := v USize.ofNatCore (List.length v) l #eval vec_len Nat (vec_new Nat) -def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := () +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 +-- 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) // +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 @@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec -- 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? + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? -- TODO: strengthen post-condition above and do a demo to show that we can -- safely eliminate the `fail` case return (vec_len Nat x) -def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := if h : List.length v.val + 1 <= 4294967295 then return ⟨ List.concat v.val x, @@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := def mem_replace_back (a : Type) (_ : a) (y : a) : a := y +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + -------------------- -- ASSERT COMMAND -- -------------------- @@ -358,16 +370,23 @@ open Lean Elab Command Term Meta syntax (name := assert) "#assert" term: command @[command_elab assert] +unsafe 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? + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" pure ()) - -- logInfo (Expr.dbgToString (``true)) - -- throwError "TODO: assert" #eval 2 == 2 #assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc/constants/Constants.lean b/tests/lean/misc/constants/Constants.lean index 9ef9ca44..57f6e403 100644 --- a/tests/lean/misc/constants/Constants.lean +++ b/tests/lean/misc/constants/Constants.lean @@ -5,64 +5,64 @@ import Base.Primitives structure OpaqueDefs where /- [constants::X0] -/ - def x0_body : result UInt32 := result.ret (UInt32.ofNatCore 0 (by intlit)) + 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_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_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_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 := + 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_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) + 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 } + 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) := + 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) := + 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 + 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 + def p3_body : Result (pair_t UInt32 UInt32) := + Result.ret { pair_x := (UInt32.ofNatCore 0 (by intlit)), pair_y := (UInt32.ofNatCore 1 (by intlit)) @@ -73,68 +73,68 @@ structure OpaqueDefs where 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 } + 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) := + 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 + def unwrap_y_fwd : Result Int32 := + Result.ret y_c.wrap_val /- [constants::YVAL] -/ - def yval_body : result Int32 := unwrap_y_fwd + 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_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 + def get_z1_fwd : Result Int32 := + Result.ret get_z1_z1_c /- [constants::add] -/ - def add_fwd (a : Int32) (b : Int32) : result Int32 := + 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_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_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_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 := + def get_z2_fwd : Result Int32 := do - let i <- get_z1_fwd - let i0 <- add_fwd i q3_c + 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_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_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_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) := + 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 index 79958d94..5b64e908 100644 --- a/tests/lean/misc/external/Base/Primitives.lean +++ b/tests/lean/misc/external/Base/Primitives.lean @@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd -- 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 +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error deriving Repr, BEq -open error +open Error -inductive result (α : Type u) where - | ret (v: α): result α - | fail (e: error): result α +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α deriving Repr, BEq -open result +open Result /- HELPERS -/ --- TODO: is there automated syntax for these discriminators? -def is_ret {α: Type} (r: result α): Bool := +def ret? {α: Type} (r: Result α): Bool := match r with - | result.ret _ => true - | result.fail _ => false + | Result.ret _ => true + | Result.fail _ => false -def massert (b:Bool) : result Unit := +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 := +def eval_global {α: Type} (x: Result α) (_: ret? x): α := match x with - | result.fail _ => by contradiction - | result.ret x => x + | Result.fail _ => by contradiction + | Result.ret x => x /- DO-DSL SUPPORT -/ -def bind (x: result α) (f: α -> result β) : result β := +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 +-- Allows using Result in do-blocks +instance : Bind Result where bind := bind -- Allows using return x in do-blocks -instance : Pure result where +instance : Pure Result where pure := fun x => ret x /- CUSTOM-DSL SUPPORT -/ --- Let-binding the result of a monadic operation is oftentimes not sufficient, +-- 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 } +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e + | .fail e => .fail e -macro "let" h:ident " : " e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, $h⟩ ← result.attach $f) +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) --- Silly example of the kind of reasoning that this notation enables +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` #eval do - let h: y <-- .ret (0: Nat) - let _: y = 0 := by cases h; decide + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ .ret r @@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem => -- 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: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part -- of a subtype is less discoverable by the simplifier or tactics like --- library_search." Try to settle this with a Lean expert on what is the most --- productive way to go about this? +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. --- One needs to perform a little bit of reasoning in order to successfully --- inject constants into USize, so we provide a general-purpose macro +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. syntax "intlit" : tactic @@ -129,12 +125,21 @@ macro_rules -- Also works for other integer types (at the expense of a needless disjunction) #eval UInt32.ofNatCore 0 (by intlit) +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): result USize := +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 @@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize := 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 +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then .ret ⟨ n.val + m.val, h ⟩ else .fail integerOverflow -def USize.checked_rem (n: USize) (m: USize): result USize := +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 @@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize := 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 +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then .ret ⟨ n.val * m.val, h ⟩ else .fail integerOverflow -def USize.checked_div (n: USize) (m: USize): result USize := +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 @@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize := else .fail integerOverflow +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + class MachineInteger (t: Type) where size: Nat val: t -> Fin size @@ -209,30 +223,24 @@ run_cmd end $typeName )) -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst := +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := if h: MachineInteger.val x < MachineInteger.size dst then .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) else .fail integerOverflow - --- 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 (α : Type u) := { l : List α // List.length l < USize.size } -def vec_new (α : Type u): vec α := ⟨ [], by { +def vec_new (α : Type u): Vec α := ⟨ [], by { match USize.size, usize_size_eq with | _, Or.inl rfl => simp | _, Or.inr rfl => simp @@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by { #check vec_new -def vec_len (α : Type u) (v : vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : USize := let ⟨ v, l ⟩ := v USize.ofNatCore (List.length v) l #eval vec_len Nat (vec_new Nat) -def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := () +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 +-- 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) // +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 @@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec -- 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? + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? -- TODO: strengthen post-condition above and do a demo to show that we can -- safely eliminate the `fail` case return (vec_len Nat x) -def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := if h : List.length v.val + 1 <= 4294967295 then return ⟨ List.concat v.val x, @@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := def mem_replace_back (a : Type) (_ : a) (y : a) : a := y +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + -------------------- -- ASSERT COMMAND -- -------------------- @@ -358,16 +370,23 @@ open Lean Elab Command Term Meta syntax (name := assert) "#assert" term: command @[command_elab assert] +unsafe 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? + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" pure ()) - -- logInfo (Expr.dbgToString (``true)) - -- throwError "TODO: assert" #eval 2 == 2 #assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc/external/External/Funs.lean b/tests/lean/misc/external/External/Funs.lean index bb1e296d..4e1f36a1 100644 --- a/tests/lean/misc/external/External/Funs.lean +++ b/tests/lean/misc/external/External/Funs.lean @@ -8,86 +8,86 @@ section variable (opaque_defs: OpaqueDefs) /- [external::swap] -/ def swap_fwd - (T : Type) (x : T) (y : T) (st : state) : result (state × Unit) := + (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, ()) + 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)) + (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)) + 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) + (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 + 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 := +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 () + let _ ← vec_push_back UInt32 v (UInt32.ofNatCore 0 (by intlit)) + Result.ret () /- Unit test for [external::test_vec] -/ -#assert (test_vec_fwd = .ret ()) +#assert (test_vec_fwd == .ret ()) /- [external::custom_swap] -/ def custom_swap_fwd - (T : Type) (x : T) (y : T) (st : state) : result (state × T) := + (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) + 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)) + (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)) + 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) := + (x : UInt32) (y : UInt32) (st : State) : Result (State × Unit) := do - let (st0, _) <- custom_swap_fwd UInt32 x y st - result.ret (st0, ()) + 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)) + (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) := + (x : UInt32) (st : State) : Result (State × UInt32) := do - let (st0, _) <- swap_fwd UInt32 x (UInt32.ofNatCore 0 (by intlit)) st - let (st1, (x0, _)) <- + 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) + if h: x0 = (UInt32.ofNatCore 0 (by intlit)) + then Result.fail Error.panic + else Result.ret (st1, x0) diff --git a/tests/lean/misc/external/External/Opaque.lean b/tests/lean/misc/external/External/Opaque.lean index 40ccc313..d3582de3 100644 --- a/tests/lean/misc/external/External/Opaque.lean +++ b/tests/lean/misc/external/External/Opaque.lean @@ -6,23 +6,23 @@ import External.Types structure OpaqueDefs where /- [core::mem::swap] -/ - core_mem_swap_fwd (T : Type) : T -> T -> state -> result (state × Unit) + 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) + (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) + (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 + 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) + (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 index b6fa292b..386832f4 100644 --- a/tests/lean/misc/external/External/Types.lean +++ b/tests/lean/misc/external/External/Types.lean @@ -4,5 +4,5 @@ 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 +/- 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 index 79958d94..5b64e908 100644 --- a/tests/lean/misc/loops/Base/Primitives.lean +++ b/tests/lean/misc/loops/Base/Primitives.lean @@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd -- 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 +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error deriving Repr, BEq -open error +open Error -inductive result (α : Type u) where - | ret (v: α): result α - | fail (e: error): result α +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α deriving Repr, BEq -open result +open Result /- HELPERS -/ --- TODO: is there automated syntax for these discriminators? -def is_ret {α: Type} (r: result α): Bool := +def ret? {α: Type} (r: Result α): Bool := match r with - | result.ret _ => true - | result.fail _ => false + | Result.ret _ => true + | Result.fail _ => false -def massert (b:Bool) : result Unit := +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 := +def eval_global {α: Type} (x: Result α) (_: ret? x): α := match x with - | result.fail _ => by contradiction - | result.ret x => x + | Result.fail _ => by contradiction + | Result.ret x => x /- DO-DSL SUPPORT -/ -def bind (x: result α) (f: α -> result β) : result β := +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 +-- Allows using Result in do-blocks +instance : Bind Result where bind := bind -- Allows using return x in do-blocks -instance : Pure result where +instance : Pure Result where pure := fun x => ret x /- CUSTOM-DSL SUPPORT -/ --- Let-binding the result of a monadic operation is oftentimes not sufficient, +-- 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 } +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e + | .fail e => .fail e -macro "let" h:ident " : " e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, $h⟩ ← result.attach $f) +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) --- Silly example of the kind of reasoning that this notation enables +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` #eval do - let h: y <-- .ret (0: Nat) - let _: y = 0 := by cases h; decide + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ .ret r @@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem => -- 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: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part -- of a subtype is less discoverable by the simplifier or tactics like --- library_search." Try to settle this with a Lean expert on what is the most --- productive way to go about this? +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. --- One needs to perform a little bit of reasoning in order to successfully --- inject constants into USize, so we provide a general-purpose macro +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. syntax "intlit" : tactic @@ -129,12 +125,21 @@ macro_rules -- Also works for other integer types (at the expense of a needless disjunction) #eval UInt32.ofNatCore 0 (by intlit) +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): result USize := +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 @@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize := 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 +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then .ret ⟨ n.val + m.val, h ⟩ else .fail integerOverflow -def USize.checked_rem (n: USize) (m: USize): result USize := +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 @@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize := 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 +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then .ret ⟨ n.val * m.val, h ⟩ else .fail integerOverflow -def USize.checked_div (n: USize) (m: USize): result USize := +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 @@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize := else .fail integerOverflow +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + class MachineInteger (t: Type) where size: Nat val: t -> Fin size @@ -209,30 +223,24 @@ run_cmd end $typeName )) -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst := +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := if h: MachineInteger.val x < MachineInteger.size dst then .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) else .fail integerOverflow - --- 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 (α : Type u) := { l : List α // List.length l < USize.size } -def vec_new (α : Type u): vec α := ⟨ [], by { +def vec_new (α : Type u): Vec α := ⟨ [], by { match USize.size, usize_size_eq with | _, Or.inl rfl => simp | _, Or.inr rfl => simp @@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by { #check vec_new -def vec_len (α : Type u) (v : vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : USize := let ⟨ v, l ⟩ := v USize.ofNatCore (List.length v) l #eval vec_len Nat (vec_new Nat) -def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := () +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 +-- 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) // +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 @@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec -- 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? + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? -- TODO: strengthen post-condition above and do a demo to show that we can -- safely eliminate the `fail` case return (vec_len Nat x) -def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := if h : List.length v.val + 1 <= 4294967295 then return ⟨ List.concat v.val x, @@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := def mem_replace_back (a : Type) (_ : a) (y : a) : a := y +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + -------------------- -- ASSERT COMMAND -- -------------------- @@ -358,16 +370,23 @@ open Lean Elab Command Term Meta syntax (name := assert) "#assert" term: command @[command_elab assert] +unsafe 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? + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" pure ()) - -- logInfo (Expr.dbgToString (``true)) - -- throwError "TODO: assert" #eval 2 == 2 #assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc/loops/Loops/Clauses/Template.lean b/tests/lean/misc/loops/Loops/Clauses/Template.lean index 3c0f2f7c..d74f71e1 100644 --- a/tests/lean/misc/loops/Loops/Clauses/Template.lean +++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean @@ -35,7 +35,7 @@ macro_rules | `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry) /- [loops::clear]: termination measure -/ -@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i) +@[simp] def clear_loop_terminates (v : Vec UInt32) (i : USize) := (v, i) syntax "clear_loop_decreases" term+ : tactic diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean index 55f0c87d..5a81ebff 100644 --- a/tests/lean/misc/loops/Loops/Funs.lean +++ b/tests/lean/misc/loops/Loops/Funs.lean @@ -5,30 +5,30 @@ import Loops.Types import Loops.Clauses.Clauses /- [loops::sum] -/ -def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) := - if i < max +def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := + if h: i < max then do - let s0 <- UInt32.checked_add s i - let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) + 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 := +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 + (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) := + if h: mi < max then do - let ms0 <- UInt32.checked_add ms mi - let mi0 <- UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit)) + 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 => @@ -36,18 +36,18 @@ termination_by sum_with_mut_borrows_loop_fwd 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 := +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 + (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := + if h: i < max then do - let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) - let s0 <- UInt32.checked_add s i0 + 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 => @@ -55,271 +55,272 @@ termination_by sum_with_shared_borrows_loop_fwd 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 := +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)) := +def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) := let i0 := vec_len UInt32 v - if i < i0 + if h: i < i0 then do - let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) - let v0 <- vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit)) + let i1 ← 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 + 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) := +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 +def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) := + match h: ls with | list_t.ListCons y tl => - if y = x - then result.ret true + if h: y = x + then Result.ret true else list_mem_loop_fwd x tl - | list_t.ListNil => result.ret false + | 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 := +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 + (T : Type) (ls : list_t T) (i : UInt32) : (Result T) := + match h: ls with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 := +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 + (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (Result (list_t T)) := + match h: ls with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 <- list_nth_mut_loop_loop_back T tl i0 ret0 - result.ret (list_t.ListCons x tl0) - | list_t.ListNil => result.fail error.panic + 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) := + (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 + (T : Type) (ls : list_t T) (i : UInt32) : (Result T) := + match h: ls with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 := + (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 +def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (Result USize) := + match h: ls with | list_t.ListCons y tl => - if y = x - then result.ret y + if h: y = x + then Result.ret y else get_elem_mut_loop_fwd x tl - | list_t.ListNil => result.fail error.panic + | 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 := +def get_elem_mut_fwd (slots : Vec (list_t USize)) (x : USize) : Result USize := do - let l <- + 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 + (x : USize) (ls : list_t USize) (ret0 : USize) : (Result (list_t USize)) := + match h: ls with | list_t.ListCons y tl => - if y = x - then result.ret (list_t.ListCons ret0 tl) + if h: y = x + then Result.ret (list_t.ListCons ret0 tl) else do - let tl0 <- get_elem_mut_loop_back x tl ret0 - result.ret (list_t.ListCons y tl0) - | list_t.ListNil => result.fail error.panic + 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)) + (slots : Vec (list_t USize)) (x : USize) (ret0 : USize) : + Result (Vec (list_t USize)) := do - let l <- + 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 + 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 + (x : USize) (ls : list_t USize) : (Result USize) := + match h: ls with | list_t.ListCons y tl => - if y = x - then result.ret y + if h: y = x + then Result.ret y else get_elem_shared_loop_fwd x tl - | list_t.ListNil => result.fail error.panic + | 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 := + (slots : Vec (list_t USize)) (x : USize) : Result USize := do - let l <- vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + let l ← + vec_index_fwd (list_t USize) slots (USize.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 +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 + (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 +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 + (T : Type) (i : UInt32) (ls : list_t T) : (Result T) := + match h: ls with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 := + (T : Type) (ls : list_t T) (i : UInt32) : Result T := do - let ls0 <- id_mut_fwd T ls + 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 + (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) := + match h: ls with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 <- list_nth_mut_loop_with_id_loop_back T i0 tl ret0 - result.ret (list_t.ListCons x tl0) - | list_t.ListNil => result.fail error.panic + 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) := + (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 + 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 + (T : Type) (i : UInt32) (ls : list_t T) : (Result T) := + match h: ls with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 := + (T : Type) (ls : list_t T) (i : UInt32) : Result T := do - let ls0 <- id_shared_fwd T ls + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -327,28 +328,28 @@ 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) + 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)) + (Result (list_t T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl0) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl0) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl00 <- list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0 - result.ret (list_t.ListCons x0 tl00) - | list_t.ListNil => result.fail error.panic - | list_t.ListNil => result.fail error.panic + 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 @@ -356,28 +357,28 @@ 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) + 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)) + (Result (list_t T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl10 <- list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0 - result.ret (list_t.ListCons x1 tl10) - | list_t.ListNil => result.fail error.panic - | list_t.ListNil => result.fail error.panic + 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 @@ -385,27 +386,27 @@ 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) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -413,27 +414,27 @@ 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) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -441,31 +442,31 @@ 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) + 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))) + (Result ((list_t T) × (list_t T))) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) + if h: i = (UInt32.ofNatCore 0 (by intlit)) then let (t, t0) := ret0 - result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1) + 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) <- + 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 + 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 @@ -473,27 +474,27 @@ 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)) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -501,27 +502,27 @@ 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) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -529,28 +530,29 @@ 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) + 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)) + (Result (list_t T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl0) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl0) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl00 <- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0 - result.ret (list_t.ListCons x0 tl00) - | list_t.ListNil => result.fail error.panic - | list_t.ListNil => result.fail error.panic + 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 @@ -558,27 +560,27 @@ 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) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -586,29 +588,29 @@ 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) + 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)) + (Result (list_t T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl0) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl0) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl00 <- + 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 + 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 @@ -616,27 +618,27 @@ 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) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -644,28 +646,29 @@ 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) + 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)) + (Result (list_t T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl10 <- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0 - result.ret (list_t.ListCons x1 tl10) - | list_t.ListNil => result.fail error.panic - | list_t.ListNil => result.fail error.panic + 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 @@ -673,27 +676,27 @@ 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) + 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)) + (Result (T × T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (x0, x1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 @@ -701,29 +704,29 @@ 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) + 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)) + (Result (list_t T)) := - match ls0 with + match h: ls0 with | list_t.ListCons x0 tl0 => - match ls1 with + match h: ls1 with | list_t.ListCons x1 tl1 => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl1) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl1) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl10 <- + 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 + 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 @@ -731,7 +734,7 @@ decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i /- [loops::list_nth_shared_mut_loop_pair_merge] -/ def list_nth_shared_mut_loop_pair_merge_back (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : - result (list_t 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/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean index 79958d94..5b64e908 100644 --- a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean +++ b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean @@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd -- 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 +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error deriving Repr, BEq -open error +open Error -inductive result (α : Type u) where - | ret (v: α): result α - | fail (e: error): result α +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α deriving Repr, BEq -open result +open Result /- HELPERS -/ --- TODO: is there automated syntax for these discriminators? -def is_ret {α: Type} (r: result α): Bool := +def ret? {α: Type} (r: Result α): Bool := match r with - | result.ret _ => true - | result.fail _ => false + | Result.ret _ => true + | Result.fail _ => false -def massert (b:Bool) : result Unit := +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 := +def eval_global {α: Type} (x: Result α) (_: ret? x): α := match x with - | result.fail _ => by contradiction - | result.ret x => x + | Result.fail _ => by contradiction + | Result.ret x => x /- DO-DSL SUPPORT -/ -def bind (x: result α) (f: α -> result β) : result β := +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 +-- Allows using Result in do-blocks +instance : Bind Result where bind := bind -- Allows using return x in do-blocks -instance : Pure result where +instance : Pure Result where pure := fun x => ret x /- CUSTOM-DSL SUPPORT -/ --- Let-binding the result of a monadic operation is oftentimes not sufficient, +-- 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 } +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e + | .fail e => .fail e -macro "let" h:ident " : " e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, $h⟩ ← result.attach $f) +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) --- Silly example of the kind of reasoning that this notation enables +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` #eval do - let h: y <-- .ret (0: Nat) - let _: y = 0 := by cases h; decide + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ .ret r @@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem => -- 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: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part -- of a subtype is less discoverable by the simplifier or tactics like --- library_search." Try to settle this with a Lean expert on what is the most --- productive way to go about this? +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. --- One needs to perform a little bit of reasoning in order to successfully --- inject constants into USize, so we provide a general-purpose macro +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. syntax "intlit" : tactic @@ -129,12 +125,21 @@ macro_rules -- Also works for other integer types (at the expense of a needless disjunction) #eval UInt32.ofNatCore 0 (by intlit) +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): result USize := +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 @@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize := 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 +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then .ret ⟨ n.val + m.val, h ⟩ else .fail integerOverflow -def USize.checked_rem (n: USize) (m: USize): result USize := +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 @@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize := 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 +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then .ret ⟨ n.val * m.val, h ⟩ else .fail integerOverflow -def USize.checked_div (n: USize) (m: USize): result USize := +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 @@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize := else .fail integerOverflow +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + class MachineInteger (t: Type) where size: Nat val: t -> Fin size @@ -209,30 +223,24 @@ run_cmd end $typeName )) -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst := +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := if h: MachineInteger.val x < MachineInteger.size dst then .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) else .fail integerOverflow - --- 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 (α : Type u) := { l : List α // List.length l < USize.size } -def vec_new (α : Type u): vec α := ⟨ [], by { +def vec_new (α : Type u): Vec α := ⟨ [], by { match USize.size, usize_size_eq with | _, Or.inl rfl => simp | _, Or.inr rfl => simp @@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by { #check vec_new -def vec_len (α : Type u) (v : vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : USize := let ⟨ v, l ⟩ := v USize.ofNatCore (List.length v) l #eval vec_len Nat (vec_new Nat) -def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := () +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 +-- 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) // +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 @@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec -- 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? + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? -- TODO: strengthen post-condition above and do a demo to show that we can -- safely eliminate the `fail` case return (vec_len Nat x) -def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := if h : List.length v.val + 1 <= 4294967295 then return ⟨ List.concat v.val x, @@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := def mem_replace_back (a : Type) (_ : a) (y : a) : a := y +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + -------------------- -- ASSERT COMMAND -- -------------------- @@ -358,16 +370,23 @@ open Lean Elab Command Term Meta syntax (name := assert) "#assert" term: command @[command_elab assert] +unsafe 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? + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" pure ()) - -- logInfo (Expr.dbgToString (``true)) - -- throwError "TODO: assert" #eval 2 == 2 #assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean index 608aabc1..a20ee9fd 100644 --- a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean +++ b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean @@ -30,232 +30,234 @@ structure OpaqueDefs where | SumRight : T2 -> sum_t T1 T2 /- [no_nested_borrows::neg_test] -/ - def neg_test_fwd (x : Int32) : result Int32 := + 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 := + 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 := + 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 := + 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 := + 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 := + 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 := + def cast_test_fwd (x : UInt32) : Result Int32 := scalar_cast Int32 x /- [no_nested_borrows::test2] -/ - def test2_fwd : result Unit := + def test2_fwd : Result Unit := do - let _ <- UInt32.checked_add (UInt32.ofNatCore 23 (by intlit)) + let _ ← UInt32.checked_add (UInt32.ofNatCore 23 (by intlit)) (UInt32.ofNatCore 44 (by intlit)) - result.ret () + Result.ret () /- Unit test for [no_nested_borrows::test2] -/ - #assert (test2_fwd = .ret ()) + #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 + def get_max_fwd (x : UInt32) (y : UInt32) : Result UInt32 := + if h: x >= y + then Result.ret x + else Result.ret y /- [no_nested_borrows::test3] -/ - def test3_fwd : result Unit := + def test3_fwd : Result Unit := do - let x <- + let x ← get_max_fwd (UInt32.ofNatCore 4 (by intlit)) (UInt32.ofNatCore 3 (by intlit)) - let y <- + 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 () + let z ← UInt32.checked_add x y + if h: not (z = (UInt32.ofNatCore 15 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test3] -/ - #assert (test3_fwd = .ret ()) + #assert (test3_fwd == .ret ()) /- [no_nested_borrows::test_neg1] -/ - def test_neg1_fwd : result Unit := + 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 () + let y ← Int32.checked_neg (Int32.ofNatCore 3 (by intlit)) + if h: not (y = (Int32.ofNatCore -3 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_neg1] -/ - #assert (test_neg1_fwd = .ret ()) + #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 () + def refs_test1_fwd : Result Unit := + if h: not ((Int32.ofNatCore 1 (by intlit)) = + (Int32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::refs_test1] -/ - #assert (refs_test1_fwd = .ret ()) + #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 + def refs_test2_fwd : Result Unit := + if h: not ((Int32.ofNatCore 2 (by intlit)) = + (Int32.ofNatCore 2 (by intlit))) + then Result.fail Error.panic else - if not ((Int32.ofNatCore 0 (by intlit)) = + if h: not ((Int32.ofNatCore 0 (by intlit)) = (Int32.ofNatCore 0 (by intlit))) - then result.fail error.panic + then Result.fail Error.panic else - if not ((Int32.ofNatCore 2 (by intlit)) = + if h: not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit))) - then result.fail error.panic + then Result.fail Error.panic else - if not ((Int32.ofNatCore 2 (by intlit)) = + if h: not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit))) - then result.fail error.panic - else result.ret () + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::refs_test2] -/ - #assert (refs_test2_fwd = .ret ()) + #assert (refs_test2_fwd == .ret ()) /- [no_nested_borrows::test_list1] -/ - def test_list1_fwd : result Unit := - result.ret () + def test_list1_fwd : Result Unit := + Result.ret () /- Unit test for [no_nested_borrows::test_list1] -/ - #assert (test_list1_fwd = .ret ()) + #assert (test_list1_fwd == .ret ()) /- [no_nested_borrows::test_box1] -/ - def test_box1_fwd : result Unit := + 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 () + if h: not (x = (Int32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_box1] -/ - #assert (test_box1_fwd = .ret ()) + #assert (test_box1_fwd == .ret ()) /- [no_nested_borrows::copy_int] -/ - def copy_int_fwd (x : Int32) : result Int32 := - result.ret x + 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 () + def test_unreachable_fwd (b : Bool) : Result Unit := + if h: b + then Result.fail Error.panic + else Result.ret () /- [no_nested_borrows::test_panic] -/ - def test_panic_fwd (b : Bool) : result Unit := - if b - then result.fail error.panic - else result.ret () + def test_panic_fwd (b : Bool) : Result Unit := + if h: b + then Result.fail Error.panic + else Result.ret () /- [no_nested_borrows::test_copy_int] -/ - def test_copy_int_fwd : result Unit := + 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 () + let y ← copy_int_fwd (Int32.ofNatCore 0 (by intlit)) + if h: not ((Int32.ofNatCore 0 (by intlit)) = y) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_copy_int] -/ - #assert (test_copy_int_fwd = .ret ()) + #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 + def is_cons_fwd (T : Type) (l : list_t T) : Result Bool := + match h: l with + | list_t.ListCons t l0 => Result.ret true + | list_t.ListNil => Result.ret false /- [no_nested_borrows::test_is_cons] -/ - def test_is_cons_fwd : result Unit := + def test_is_cons_fwd : Result Unit := do let l := list_t.ListNil - let b <- + 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 () + if h: not b + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_is_cons] -/ - #assert (test_is_cons_fwd = .ret ()) + #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 + def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) := + match h: l with + | list_t.ListCons hd tl => Result.ret (hd, tl) + | list_t.ListNil => Result.fail Error.panic /- [no_nested_borrows::test_split_list] -/ - def test_split_list_fwd : result Unit := + def test_split_list_fwd : Result Unit := do let l := list_t.ListNil - let p <- + 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 () + if h: not (hd = (Int32.ofNatCore 0 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_split_list] -/ - #assert (test_split_list_fwd = .ret ()) + #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 + def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := + if h: b + then Result.ret x + else Result.ret y /- [no_nested_borrows::choose] -/ def choose_back - (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : result (T × T) := - if b - then result.ret (ret0, y) - else result.ret (x, ret0) + (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := + if h: b + then Result.ret (ret0, y) + else Result.ret (x, ret0) /- [no_nested_borrows::choose_test] -/ - def choose_test_fwd : result Unit := + def choose_test_fwd : Result Unit := do - let z <- + 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 + let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit)) + if h: not (z0 = (Int32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic else do - let (x, y) <- + 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 + if h: 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 () + if h: not (y = (Int32.ofNatCore 0 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::choose_test] -/ - #assert (choose_test_fwd = .ret ()) + #assert (choose_test_fwd == .ret ()) /- [no_nested_borrows::test_char] -/ - def test_char_fwd : result Char := - result.ret 'a' + def test_char_fwd : Result Char := + Result.ret 'a' /- [no_nested_borrows::NodeElem] -/ mutual inductive node_elem_t (T : Type) := @@ -268,179 +270,179 @@ structure OpaqueDefs where | 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 + def list_length_fwd (T : Type) (l : list_t T) : Result UInt32 := + match h: l with | list_t.ListCons t l1 => do - let i <- list_length_fwd T l1 + 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)) + | 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 + def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := + match h: l with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 + def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := + match h: l with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 + (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := + match h: l with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 <- list_nth_mut_back T tl i0 ret0 - result.ret (list_t.ListCons x tl0) - | list_t.ListNil => result.fail error.panic + 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 + (T : Type) (li : list_t T) (lo : list_t T) : Result (list_t T) := + match h: li with | list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo) - | list_t.ListNil => result.ret lo + | 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) := + 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 := + 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 <- + 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 + if h: not (i = (UInt32.ofNatCore 3 (by intlit))) + then Result.fail Error.panic else do - let i0 <- + 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 + if h: not (i0 = (Int32.ofNatCore 0 (by intlit))) + then Result.fail Error.panic else do - let i1 <- + 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 + if h: not (i1 = (Int32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic else do - let i2 <- + 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 + if h: not (i2 = (Int32.ofNatCore 2 (by intlit))) + then Result.fail Error.panic else do - let ls <- + 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 <- + 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 + if h: not (i3 = (Int32.ofNatCore 0 (by intlit))) + then Result.fail Error.panic else do - let i4 <- + 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 + if h: not (i4 = (Int32.ofNatCore 3 (by intlit))) + then Result.fail Error.panic else do - let i5 <- + 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 () + if h: not (i5 = (Int32.ofNatCore 2 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_list_functions] -/ - #assert (test_list_functions_fwd = .ret ()) + #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) + 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) := + (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) := let (t, t0) := ret0 - result.ret (t, t0) + Result.ret (t, t0) /- [no_nested_borrows::id_mut_pair2] -/ - def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : result (T1 × T2) := + def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := let (t, t0) := p - result.ret (t, t0) + 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) := + (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) := let (t, t0) := ret0 - result.ret (t, t0) + 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) + 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 + (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 + (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) := + def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) := let (t, t0) := p - result.ret (t, t0) + 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 + (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 + (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 @@ -449,24 +451,24 @@ structure OpaqueDefs where /- [no_nested_borrows::new_tuple1] -/ - def new_tuple1_fwd : result (struct_with_tuple_t UInt32 UInt32) := - result.ret + 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 + 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 + 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))) @@ -479,8 +481,8 @@ structure OpaqueDefs where /- [no_nested_borrows::new_pair1] -/ - def new_pair1_fwd : result (struct_with_pair_t UInt32 UInt32) := - result.ret + def new_pair1_fwd : Result (struct_with_pair_t UInt32 UInt32) := + Result.ret { struct_with_pair_p := { pair_x := (UInt32.ofNatCore 1 (by intlit)), @@ -489,66 +491,66 @@ structure OpaqueDefs where } /- [no_nested_borrows::test_constants] -/ - def test_constants_fwd : result Unit := + def test_constants_fwd : Result Unit := do - let swt <- new_tuple1_fwd + 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 + if h: not (i = (UInt32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic else do - let swt0 <- new_tuple2_fwd + 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 + if h: not (i0 = (Int16.ofNatCore 1 (by intlit))) + then Result.fail Error.panic else do - let swt1 <- new_tuple3_fwd + 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 + if h: 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 = + let swp ← new_pair1_fwd + if h: not (swp.struct_with_pair_p.pair_x = (UInt32.ofNatCore 1 (by intlit))) - then result.fail error.panic - else result.ret () + then Result.fail Error.panic + else Result.ret () /- Unit test for [no_nested_borrows::test_constants] -/ - #assert (test_constants_fwd = .ret ()) + #assert (test_constants_fwd == .ret ()) /- [no_nested_borrows::test_weird_borrows1] -/ - def test_weird_borrows1_fwd : result Unit := - result.ret () + def test_weird_borrows1_fwd : Result Unit := + Result.ret () /- Unit test for [no_nested_borrows::test_weird_borrows1] -/ - #assert (test_weird_borrows1_fwd = .ret ()) + #assert (test_weird_borrows1_fwd == .ret ()) /- [no_nested_borrows::test_mem_replace] -/ - def test_mem_replace_fwd_back (px : UInt32) : result UInt32 := + 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)) + if h: not (y = (UInt32.ofNatCore 0 (by intlit))) + then Result.fail Error.panic + else Result.ret (UInt32.ofNatCore 2 (by intlit)) /- [no_nested_borrows::test_shared_borrow_bool1] -/ - def test_shared_borrow_bool1_fwd (b : Bool) : result UInt32 := - if b - then result.ret (UInt32.ofNatCore 0 (by intlit)) - else result.ret (UInt32.ofNatCore 1 (by intlit)) + def test_shared_borrow_bool1_fwd (b : Bool) : Result UInt32 := + if h: b + then Result.ret (UInt32.ofNatCore 0 (by intlit)) + else Result.ret (UInt32.ofNatCore 1 (by intlit)) /- [no_nested_borrows::test_shared_borrow_bool2] -/ - def test_shared_borrow_bool2_fwd : result UInt32 := - result.ret (UInt32.ofNatCore 0 (by intlit)) + 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)) + def test_shared_borrow_enum1_fwd (l : list_t UInt32) : Result UInt32 := + match h: l with + | list_t.ListCons i l0 => Result.ret (UInt32.ofNatCore 1 (by intlit)) + | list_t.ListNil => Result.ret (UInt32.ofNatCore 0 (by intlit)) /- [no_nested_borrows::test_shared_borrow_enum2] -/ - def test_shared_borrow_enum2_fwd : result UInt32 := - result.ret (UInt32.ofNatCore 0 (by intlit)) + 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 index 79958d94..5b64e908 100644 --- a/tests/lean/misc/paper/Base/Primitives.lean +++ b/tests/lean/misc/paper/Base/Primitives.lean @@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd -- 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 +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error deriving Repr, BEq -open error +open Error -inductive result (α : Type u) where - | ret (v: α): result α - | fail (e: error): result α +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α deriving Repr, BEq -open result +open Result /- HELPERS -/ --- TODO: is there automated syntax for these discriminators? -def is_ret {α: Type} (r: result α): Bool := +def ret? {α: Type} (r: Result α): Bool := match r with - | result.ret _ => true - | result.fail _ => false + | Result.ret _ => true + | Result.fail _ => false -def massert (b:Bool) : result Unit := +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 := +def eval_global {α: Type} (x: Result α) (_: ret? x): α := match x with - | result.fail _ => by contradiction - | result.ret x => x + | Result.fail _ => by contradiction + | Result.ret x => x /- DO-DSL SUPPORT -/ -def bind (x: result α) (f: α -> result β) : result β := +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 +-- Allows using Result in do-blocks +instance : Bind Result where bind := bind -- Allows using return x in do-blocks -instance : Pure result where +instance : Pure Result where pure := fun x => ret x /- CUSTOM-DSL SUPPORT -/ --- Let-binding the result of a monadic operation is oftentimes not sufficient, +-- 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 } +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with | .ret x => .ret ⟨x, rfl⟩ - | .fail e => .fail e + | .fail e => .fail e -macro "let" h:ident " : " e:term " <-- " f:term : doElem => - `(doElem| let ⟨$e, $h⟩ ← result.attach $f) +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) --- Silly example of the kind of reasoning that this notation enables +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` #eval do - let h: y <-- .ret (0: Nat) - let _: y = 0 := by cases h; decide + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ .ret r @@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem => -- 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: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) -- Note from Chris Bailey: "If there's more than one salient property of your -- definition then the subtyping strategy might get messy, and the property part -- of a subtype is less discoverable by the simplifier or tactics like --- library_search." Try to settle this with a Lean expert on what is the most --- productive way to go about this? +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. --- One needs to perform a little bit of reasoning in order to successfully --- inject constants into USize, so we provide a general-purpose macro +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. syntax "intlit" : tactic @@ -129,12 +125,21 @@ macro_rules -- Also works for other integer types (at the expense of a needless disjunction) #eval UInt32.ofNatCore 0 (by intlit) +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + -- Further thoughts: look at what has been done here: -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean -- and -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean -- which both contain a fair amount of reasoning already! -def USize.checked_sub (n: USize) (m: USize): result USize := +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 @@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize := 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 +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then .ret ⟨ n.val + m.val, h ⟩ else .fail integerOverflow -def USize.checked_rem (n: USize) (m: USize): result USize := +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 @@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize := 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 +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then .ret ⟨ n.val * m.val, h ⟩ else .fail integerOverflow -def USize.checked_div (n: USize) (m: USize): result USize := +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 @@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize := else .fail integerOverflow +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + class MachineInteger (t: Type) where size: Nat val: t -> Fin size @@ -209,30 +223,24 @@ run_cmd end $typeName )) -def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst := +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := if h: MachineInteger.val x < MachineInteger.size dst then .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) else .fail integerOverflow - --- 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 (α : Type u) := { l : List α // List.length l < USize.size } -def vec_new (α : Type u): vec α := ⟨ [], by { +def vec_new (α : Type u): Vec α := ⟨ [], by { match USize.size, usize_size_eq with | _, Or.inl rfl => simp | _, Or.inr rfl => simp @@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by { #check vec_new -def vec_len (α : Type u) (v : vec α) : USize := +def vec_len (α : Type u) (v : Vec α) : USize := let ⟨ v, l ⟩ := v USize.ofNatCore (List.length v) l #eval vec_len Nat (vec_new Nat) -def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := () +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 +-- 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) // +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 @@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec -- 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? + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? -- TODO: strengthen post-condition above and do a demo to show that we can -- safely eliminate the `fail` case return (vec_len Nat x) -def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) := if h : List.length v.val + 1 <= 4294967295 then return ⟨ List.concat v.val x, @@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α) else fail maximumSizeExceeded -def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α else .fail arrayOutOfBounds -def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit := +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := if i.val < List.length v.val then .ret () else .fail arrayOutOfBounds -def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α := +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := if h: i.val < List.length v.val then .ret (List.get v.val ⟨i.val, h⟩) else .fail arrayOutOfBounds -def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) := +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := if i.val < List.length v.val then .ret ⟨ List.set v.val i.val x, by have h: List.length v.val < USize.size := v.property @@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := def mem_replace_back (a : Type) (_ : a) (y : a) : a := y +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + -------------------- -- ASSERT COMMAND -- -------------------- @@ -358,16 +370,23 @@ open Lean Elab Command Term Meta syntax (name := assert) "#assert" term: command @[command_elab assert] +unsafe 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? + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" pure ()) - -- logInfo (Expr.dbgToString (``true)) - -- throwError "TODO: assert" #eval 2 == 2 #assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc/paper/Paper.lean b/tests/lean/misc/paper/Paper.lean index adcd1eae..4faf36ee 100644 --- a/tests/lean/misc/paper/Paper.lean +++ b/tests/lean/misc/paper/Paper.lean @@ -5,56 +5,56 @@ import Base.Primitives structure OpaqueDefs where /- [paper::ref_incr] -/ - def ref_incr_fwd_back (x : Int32) : result Int32 := + 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 := + 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 () + let x ← ref_incr_fwd_back (Int32.ofNatCore 0 (by intlit)) + if h: not (x = (Int32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [paper::test_incr] -/ - #assert (test_incr_fwd = .ret ()) + #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 + def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T := + if h: b + then Result.ret x + else Result.ret y /- [paper::choose] -/ def choose_back - (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : result (T × T) := - if b - then result.ret (ret0, y) - else result.ret (x, ret0) + (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) := + if h: b + then Result.ret (ret0, y) + else Result.ret (x, ret0) /- [paper::test_choose] -/ - def test_choose_fwd : result Unit := + def test_choose_fwd : Result Unit := do - let z <- + 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 + let z0 ← Int32.checked_add z (Int32.ofNatCore 1 (by intlit)) + if h: not (z0 = (Int32.ofNatCore 1 (by intlit))) + then Result.fail Error.panic else do - let (x, y) <- + 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 + if h: 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 () + if h: not (y = (Int32.ofNatCore 0 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [paper::test_choose] -/ - #assert (test_choose_fwd = .ret ()) + #assert (test_choose_fwd == .ret ()) /- [paper::List] -/ inductive list_t (T : Type) := @@ -62,67 +62,67 @@ structure OpaqueDefs where | 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 + def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : Result T := + match h: l with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret x + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + 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 + | 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 + (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := + match h: l with | list_t.ListCons x tl => - if i = (UInt32.ofNatCore 0 (by intlit)) - then result.ret (list_t.ListCons ret0 tl) + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl) else do - let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) - let tl0 <- list_nth_mut_back T tl i0 ret0 - result.ret (list_t.ListCons x tl0) - | list_t.ListNil => result.fail error.panic + 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 + def sum_fwd (l : list_t Int32) : Result Int32 := + match h: l with | list_t.ListCons x tl => do - let i <- sum_fwd tl + let i ← sum_fwd tl Int32.checked_add x i - | list_t.ListNil => result.ret (Int32.ofNatCore 0 (by intlit)) + | list_t.ListNil => Result.ret (Int32.ofNatCore 0 (by intlit)) /- [paper::test_nth] -/ - def test_nth_fwd : result Unit := + 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 <- + 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 <- + 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 () + let i ← sum_fwd l2 + if h: not (i = (Int32.ofNatCore 7 (by intlit))) + then Result.fail Error.panic + else Result.ret () /- Unit test for [paper::test_nth] -/ - #assert (test_nth_fwd = .ret ()) + #assert (test_nth_fwd == .ret ()) /- [paper::call_choose] -/ - def call_choose_fwd (p : (UInt32 × UInt32)) : result UInt32 := + 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 + 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 |