diff options
Diffstat (limited to '')
| -rw-r--r-- | tests/lean/misc/loops/Base/Primitives.lean | 231 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Loops/Clauses/Template.lean | 2 | ||||
| -rw-r--r-- | tests/lean/misc/loops/Loops/Funs.lean | 517 |
3 files changed, 386 insertions, 364 deletions
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 |