diff options
author | Son Ho | 2023-03-07 13:46:55 +0100 |
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committer | Son HO | 2023-06-04 21:44:33 +0200 |
commit | 051e2a19f3268d272a0acd0425d2107ebea020c5 (patch) | |
tree | 2ad36d00054ac891e48cb35c4dc1940433c5e707 /tests/lean/misc-loops | |
parent | 463cbb90c93ac2e825048d685c254431b99c4d96 (diff) |
Reorganize the Lean tests and extract the Polonius tests to Lean
Diffstat (limited to 'tests/lean/misc-loops')
-rw-r--r-- | tests/lean/misc-loops/Base/Primitives.lean | 392 | ||||
-rw-r--r-- | tests/lean/misc-loops/Loops/Clauses/Clauses.lean | 209 | ||||
-rw-r--r-- | tests/lean/misc-loops/Loops/Clauses/Template.lean | 210 | ||||
-rw-r--r-- | tests/lean/misc-loops/Loops/Funs.lean | 740 | ||||
-rw-r--r-- | tests/lean/misc-loops/Loops/Types.lean | 9 | ||||
-rw-r--r-- | tests/lean/misc-loops/lakefile.lean | 18 |
6 files changed, 1578 insertions, 0 deletions
diff --git a/tests/lean/misc-loops/Base/Primitives.lean b/tests/lean/misc-loops/Base/Primitives.lean new file mode 100644 index 00000000..5b64e908 --- /dev/null +++ b/tests/lean/misc-loops/Base/Primitives.lean @@ -0,0 +1,392 @@ +import Lean +import Lean.Meta.Tactic.Simp +import Init.Data.List.Basic +import Mathlib.Tactic.RunCmd + +------------- +-- PRELUDE -- +------------- + +-- Results & monadic combinators + +inductive Error where + | assertionFailure: Error + | integerOverflow: Error + | arrayOutOfBounds: Error + | maximumSizeExceeded: Error + | panic: Error +deriving Repr, BEq + +open Error + +inductive Result (α : Type u) where + | ret (v: α): Result α + | fail (e: Error): Result α +deriving Repr, BEq + +open Result + +/- HELPERS -/ + +def ret? {α: Type} (r: Result α): Bool := + match r with + | Result.ret _ => true + | Result.fail _ => false + +def massert (b:Bool) : Result Unit := + if b then .ret () else fail assertionFailure + +def eval_global {α: Type} (x: Result α) (_: ret? x): α := + match x with + | Result.fail _ => by contradiction + | Result.ret x => x + +/- DO-DSL SUPPORT -/ + +def bind (x: Result α) (f: α -> Result β) : Result β := + match x with + | ret v => f v + | fail v => fail v + +-- Allows using Result in do-blocks +instance : Bind Result where + bind := bind + +-- Allows using return x in do-blocks +instance : Pure Result where + pure := fun x => ret x + +/- CUSTOM-DSL SUPPORT -/ + +-- Let-binding the Result of a monadic operation is oftentimes not sufficient, +-- because we may need a hypothesis for equational reasoning in the scope. We +-- rely on subtype, and a custom let-binding operator, in effect recreating our +-- own variant of the do-dsl + +def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } := + match o with + | .ret x => .ret ⟨x, rfl⟩ + | .fail e => .fail e + +macro "let" e:term " ⟵ " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- TODO: any way to factorize both definitions? +macro "let" e:term " <-- " f:term : doElem => + `(doElem| let ⟨$e, h⟩ ← Result.attach $f) + +-- We call the hypothesis `h`, in effect making it unavailable to the user +-- (because too much shadowing). But in practice, once can use the French single +-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable +-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x` +#eval do + let y <-- .ret (0: Nat) + let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide + let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩ + .ret r + +---------------------- +-- MACHINE INTEGERS -- +---------------------- + +-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ..., +-- USize. They are generally defined in an idiomatic style, except that there is +-- not a single type class to rule them all (more on that below). The absence of +-- type class is intentional, and allows the Lean compiler to efficiently map +-- them to machine integers during compilation. + +-- USize is designed properly: you cannot reduce `getNumBits` using the +-- simplifier, meaning that proofs do not depend on the compile-time value of +-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really +-- support, at least officially, 16-bit microcontrollers, so this seems like a +-- fine design decision for now.) + +-- Note from Chris Bailey: "If there's more than one salient property of your +-- definition then the subtyping strategy might get messy, and the property part +-- of a subtype is less discoverable by the simplifier or tactics like +-- library_search." So, we will not add refinements on the return values of the +-- operations defined on Primitives, but will rather rely on custom lemmas to +-- invert on possible return values of the primitive operations. + +-- Machine integer constants, done via `ofNatCore`, which requires a proof that +-- the `Nat` fits within the desired integer type. We provide a custom tactic. + +syntax "intlit" : tactic + +macro_rules + | `(tactic| intlit) => `(tactic| + match USize.size, usize_size_eq with + | _, Or.inl rfl => decide + | _, Or.inr rfl => decide) + +-- This is how the macro is expected to be used +#eval USize.ofNatCore 0 (by intlit) + +-- Also works for other integer types (at the expense of a needless disjunction) +#eval UInt32.ofNatCore 0 (by intlit) + +-- The machine integer operations (e.g. sub) are always total, which is not what +-- we want. We therefore define "checked" variants, below. Note that we add a +-- tiny bit of complexity for the USize variant: we first check whether the +-- result is < 2^32; if it is, we can compute the definition, rather than +-- returning a term that is computationally stuck (the comparison to USize.size +-- cannot reduce at compile-time, per the remark about regarding `getNumBits`). +-- This is useful for the various #asserts that we want to reduce at +-- type-checking time. + +-- Further thoughts: look at what has been done here: +-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean +-- and +-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean +-- which both contain a fair amount of reasoning already! +def USize.checked_sub (n: USize) (m: USize): Result USize := + -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed? + if n >= m then + let n' := USize.toNat n + let m' := USize.toNat n + let r := USize.ofNatCore (n' - m') (by + have h: n' - m' <= n' := by + apply Nat.sub_le_of_le_add + case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left + apply Nat.lt_of_le_of_lt h + apply n.val.isLt + ) + return r + else + fail integerOverflow + +@[simp] +theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size := + match USize.size, usize_size_eq with + | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide) + | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide) + +def USize.checked_add (n: USize) (m: USize): Result USize := + if h: n.val + m.val < USize.size then + .ret ⟨ n.val + m.val, h ⟩ + else + .fail integerOverflow + +def USize.checked_rem (n: USize) (m: USize): Result USize := + if h: m > 0 then + .ret ⟨ n.val % m.val, by + have h1: ↑m.val < USize.size := m.val.isLt + have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h + apply Nat.lt_trans h2 h1 + ⟩ + else + .fail integerOverflow + +def USize.checked_mul (n: USize) (m: USize): Result USize := + if h: n.val * m.val < USize.size then + .ret ⟨ n.val * m.val, h ⟩ + else + .fail integerOverflow + +def USize.checked_div (n: USize) (m: USize): Result USize := + if m > 0 then + .ret ⟨ n.val / m.val, by + have h1: ↑n.val < USize.size := n.val.isLt + have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val + apply Nat.lt_of_le_of_lt h2 h1 + ⟩ + else + .fail integerOverflow + +-- Test behavior... +#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0 + +#eval USize.checked_sub 20 10 +-- NOTE: compare with concrete behavior here, which I do not think we want +#eval USize.sub 0 1 +#eval UInt8.add 255 255 + +-- We now define a type class that subsumes the various machine integer types, so +-- as to write a concise definition for scalar_cast, rather than exhaustively +-- enumerating all of the possible pairs. We remark that Rust has sane semantics +-- and fails if a cast operation would involve a truncation or modulo. + +class MachineInteger (t: Type) where + size: Nat + val: t -> Fin size + ofNatCore: (n:Nat) -> LT.lt n size -> t + +set_option hygiene false in +run_cmd + for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do + Lean.Elab.Command.elabCommand (← `( + namespace $typeName + instance: MachineInteger $typeName where + size := size + val := val + ofNatCore := ofNatCore + end $typeName + )) + +-- Aeneas only instantiates the destination type (`src` is implicit). We rely on +-- Lean to infer `src`. + +def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst := + if h: MachineInteger.val x < MachineInteger.size dst then + .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h) + else + .fail integerOverflow + +------------- +-- VECTORS -- +------------- + +-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size) +-- rather than maximum values (usize_max). +def Vec (α : Type u) := { l : List α // List.length l < USize.size } + +def vec_new (α : Type u): Vec α := ⟨ [], by { + match USize.size, usize_size_eq with + | _, Or.inl rfl => simp + | _, Or.inr rfl => simp + } ⟩ + +#check vec_new + +def vec_len (α : Type u) (v : Vec α) : USize := + let ⟨ v, l ⟩ := v + USize.ofNatCore (List.length v) l + +#eval vec_len Nat (vec_new Nat) + +def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := () + +-- NOTE: old version trying to use a subtype notation, but probably better to +-- leave Result elimination to auxiliary lemmas with suitable preconditions +-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one +-- make the proof work in that case? Probably need to import tactics from +-- mathlib to deal with inequalities... would love to see an example. +def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) // + match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1} + := + if h : List.length v.val + 1 < USize.size then + ⟨ return ⟨List.concat v.val x, + by + rw [List.length_concat] + assumption + ⟩, by simp ⟩ + else + ⟨ fail maximumSizeExceeded, by simp ⟩ + +#eval do + -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with + -- fields val and property. However, Lean's elaborator can automatically + -- select the `val` field if the context provides a type annotation. We + -- annotate `x`, which relieves us of having to write `.val` on the right-hand + -- side of the monadic let. + let v := vec_new Nat + let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here? + -- TODO: strengthen post-condition above and do a demo to show that we can + -- safely eliminate the `fail` case + return (vec_len Nat x) + +def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α) + := + if h : List.length v.val + 1 <= 4294967295 then + return ⟨ List.concat v.val x, + by + rw [List.length_concat] + have h': 4294967295 < USize.size := by intlit + apply Nat.lt_of_le_of_lt h h' + ⟩ + else if h: List.length v.val + 1 < USize.size then + return ⟨List.concat v.val x, + by + rw [List.length_concat] + assumption + ⟩ + else + fail maximumSizeExceeded + +def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := + if i.val < List.length v.val then + .ret () + else + .fail arrayOutOfBounds + +def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := + if i.val < List.length v.val then + .ret ⟨ List.set v.val i.val x, by + have h: List.length v.val < USize.size := v.property + rewrite [ List.length_set v.val i.val x ] + assumption + ⟩ + else + .fail arrayOutOfBounds + +def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α := + if h: i.val < List.length v.val then + .ret (List.get v.val ⟨i.val, h⟩) + else + .fail arrayOutOfBounds + +def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit := + if i.val < List.length v.val then + .ret () + else + .fail arrayOutOfBounds + +def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α := + if h: i.val < List.length v.val then + .ret (List.get v.val ⟨i.val, h⟩) + else + .fail arrayOutOfBounds + +def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) := + if i.val < List.length v.val then + .ret ⟨ List.set v.val i.val x, by + have h: List.length v.val < USize.size := v.property + rewrite [ List.length_set v.val i.val x ] + assumption + ⟩ + else + .fail arrayOutOfBounds + +---------- +-- MISC -- +---------- + +def mem_replace_fwd (a : Type) (x : a) (_ : a) : a := + x + +def mem_replace_back (a : Type) (_ : a) (y : a) : a := + y + +/-- Aeneas-translated function -- useful to reduce non-recursive definitions. + Use with `simp [ aeneas ]` -/ +register_simp_attr aeneas + +-------------------- +-- ASSERT COMMAND -- +-------------------- + +open Lean Elab Command Term Meta + +syntax (name := assert) "#assert" term: command + +@[command_elab assert] +unsafe +def assertImpl : CommandElab := fun (_stx: Syntax) => do + runTermElabM (fun _ => do + let r ← evalTerm Bool (mkConst ``Bool) _stx[1] + if not r then + logInfo "Assertion failed for: " + logInfo _stx[1] + logError "Expression reduced to false" + pure ()) + +#eval 2 == 2 +#assert (2 == 2) + +------------------- +-- SANITY CHECKS -- +------------------- + +-- TODO: add more once we have signed integers + +#assert (USize.checked_rem 1 2 == .ret 1) diff --git a/tests/lean/misc-loops/Loops/Clauses/Clauses.lean b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean new file mode 100644 index 00000000..5ddb65ca --- /dev/null +++ b/tests/lean/misc-loops/Loops/Clauses/Clauses.lean @@ -0,0 +1,209 @@ +-- [loops]: decreases clauses +import Base.Primitives +import Loops.Types + +/- [loops::sum]: termination measure -/ +@[simp] +def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) + +syntax "sum_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry) + +/- [loops::sum_with_mut_borrows]: termination measure -/ +@[simp] +def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) + (ms : UInt32) := + (max, mi, ms) + +syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry) + +/- [loops::sum_with_shared_borrows]: termination measure -/ +@[simp] +def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) + (s : UInt32) := + (max, i, s) + +syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry) + +/- [loops::clear]: termination measure -/ +@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i) + +syntax "clear_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry) + +/- [loops::list_mem]: termination measure -/ +@[simp] +def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls) + +syntax "list_mem_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry) + +/- [loops::list_nth_mut_loop]: termination measure -/ +@[simp] +def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) + := + (ls, i) + +syntax "list_nth_mut_loop_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry) + +/- [loops::list_nth_shared_loop]: termination measure -/ +@[simp] +def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) + (i : UInt32) := + (ls, i) + +syntax "list_nth_shared_loop_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry) + +/- [loops::get_elem_mut]: termination measure -/ +@[simp] +def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) + +syntax "get_elem_mut_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry) + +/- [loops::get_elem_shared]: termination measure -/ +@[simp] +def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) + +syntax "get_elem_shared_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry) + +/- [loops::list_nth_mut_loop_with_id]: termination measure -/ +@[simp] +def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) + (ls : list_t T) := + (i, ls) + +syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) + +/- [loops::list_nth_shared_loop_with_id]: termination measure -/ +@[simp] +def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) + (ls : list_t T) := + (i, ls) + +syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) + +/- [loops::list_nth_mut_loop_pair]: termination measure -/ +@[simp] +def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry) + +/- [loops::list_nth_shared_loop_pair]: termination measure -/ +@[simp] +def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/ +@[simp] +def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type) + (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/ +@[simp] +def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type) + (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic + +macro_rules +| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + diff --git a/tests/lean/misc-loops/Loops/Clauses/Template.lean b/tests/lean/misc-loops/Loops/Clauses/Template.lean new file mode 100644 index 00000000..d1e72d65 --- /dev/null +++ b/tests/lean/misc-loops/Loops/Clauses/Template.lean @@ -0,0 +1,210 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [loops]: templates for the decreases clauses +import Base.Primitives +import Loops.Types + +/- [loops::sum]: termination measure -/ +@[simp] +def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s) + +/- [loops::sum]: decreases_by tactic -/ +syntax "sum_loop_decreases" term+ : tactic +macro_rules +| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry) + +/- [loops::sum_with_mut_borrows]: termination measure -/ +@[simp] +def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32) + (ms : UInt32) := + (max, mi, ms) + +/- [loops::sum_with_mut_borrows]: decreases_by tactic -/ +syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic +macro_rules +| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry) + +/- [loops::sum_with_shared_borrows]: termination measure -/ +@[simp] +def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32) + (s : UInt32) := + (max, i, s) + +/- [loops::sum_with_shared_borrows]: decreases_by tactic -/ +syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic +macro_rules +| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry) + +/- [loops::clear]: termination measure -/ +@[simp] def clear_loop_terminates (v : Vec UInt32) (i : USize) := (v, i) + +/- [loops::clear]: decreases_by tactic -/ +syntax "clear_loop_decreases" term+ : tactic +macro_rules +| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry) + +/- [loops::list_mem]: termination measure -/ +@[simp] +def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls) + +/- [loops::list_mem]: decreases_by tactic -/ +syntax "list_mem_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry) + +/- [loops::list_nth_mut_loop]: termination measure -/ +@[simp] +def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32) + := + (ls, i) + +/- [loops::list_nth_mut_loop]: decreases_by tactic -/ +syntax "list_nth_mut_loop_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry) + +/- [loops::list_nth_shared_loop]: termination measure -/ +@[simp] +def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T) + (i : UInt32) := + (ls, i) + +/- [loops::list_nth_shared_loop]: decreases_by tactic -/ +syntax "list_nth_shared_loop_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry) + +/- [loops::get_elem_mut]: termination measure -/ +@[simp] +def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) + +/- [loops::get_elem_mut]: decreases_by tactic -/ +syntax "get_elem_mut_loop_decreases" term+ : tactic +macro_rules +| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry) + +/- [loops::get_elem_shared]: termination measure -/ +@[simp] +def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls) + +/- [loops::get_elem_shared]: decreases_by tactic -/ +syntax "get_elem_shared_loop_decreases" term+ : tactic +macro_rules +| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry) + +/- [loops::list_nth_mut_loop_with_id]: termination measure -/ +@[simp] +def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32) + (ls : list_t T) := + (i, ls) + +/- [loops::list_nth_mut_loop_with_id]: decreases_by tactic -/ +syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) + +/- [loops::list_nth_shared_loop_with_id]: termination measure -/ +@[simp] +def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32) + (ls : list_t T) := + (i, ls) + +/- [loops::list_nth_shared_loop_with_id]: decreases_by tactic -/ +syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry) + +/- [loops::list_nth_mut_loop_pair]: termination measure -/ +@[simp] +def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_mut_loop_pair]: decreases_by tactic -/ +syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry) + +/- [loops::list_nth_shared_loop_pair]: termination measure -/ +@[simp] +def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_shared_loop_pair]: decreases_by tactic -/ +syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_mut_loop_pair_merge]: decreases_by tactic -/ +syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_shared_loop_pair_merge]: decreases_by tactic -/ +syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/ +@[simp] +def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_mut_shared_loop_pair]: decreases_by tactic -/ +syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type) + (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_mut_shared_loop_pair_merge]: decreases_by tactic -/ +syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/ +@[simp] +def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T) + (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_shared_mut_loop_pair]: decreases_by tactic -/ +syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + +/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/ +@[simp] +def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type) + (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) := + (ls0, ls1, i) + +/- [loops::list_nth_shared_mut_loop_pair_merge]: decreases_by tactic -/ +syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic +macro_rules +| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) => + `(tactic| sorry) + diff --git a/tests/lean/misc-loops/Loops/Funs.lean b/tests/lean/misc-loops/Loops/Funs.lean new file mode 100644 index 00000000..5a81ebff --- /dev/null +++ b/tests/lean/misc-loops/Loops/Funs.lean @@ -0,0 +1,740 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [loops]: function definitions +import Base.Primitives +import Loops.Types +import Loops.Clauses.Clauses + +/- [loops::sum] -/ +def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := + if h: i < max + then + do + let s0 ← UInt32.checked_add s i + let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) + sum_loop_fwd max i0 s0 + else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit)) +termination_by sum_loop_fwd max i s => sum_loop_terminates max i s +decreasing_by sum_loop_decreases max i s + +/- [loops::sum] -/ +def sum_fwd (max : UInt32) : Result UInt32 := + sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) + (UInt32.ofNatCore 0 (by intlit)) + +/- [loops::sum_with_mut_borrows] -/ +def sum_with_mut_borrows_loop_fwd + (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) := + if h: mi < max + then + do + let ms0 ← UInt32.checked_add ms mi + let mi0 ← UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit)) + sum_with_mut_borrows_loop_fwd max mi0 ms0 + else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit)) +termination_by sum_with_mut_borrows_loop_fwd max mi ms => + sum_with_mut_borrows_loop_terminates max mi ms +decreasing_by sum_with_mut_borrows_loop_decreases max mi ms + +/- [loops::sum_with_mut_borrows] -/ +def sum_with_mut_borrows_fwd (max : UInt32) : Result UInt32 := + sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) + (UInt32.ofNatCore 0 (by intlit)) + +/- [loops::sum_with_shared_borrows] -/ +def sum_with_shared_borrows_loop_fwd + (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) := + if h: i < max + then + do + let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit)) + let s0 ← UInt32.checked_add s i0 + sum_with_shared_borrows_loop_fwd max i0 s0 + else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit)) +termination_by sum_with_shared_borrows_loop_fwd max i s => + sum_with_shared_borrows_loop_terminates max i s +decreasing_by sum_with_shared_borrows_loop_decreases max i s + +/- [loops::sum_with_shared_borrows] -/ +def sum_with_shared_borrows_fwd (max : UInt32) : Result UInt32 := + sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit)) + (UInt32.ofNatCore 0 (by intlit)) + +/- [loops::clear] -/ +def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) := + let i0 := vec_len UInt32 v + if h: i < i0 + then + do + let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit)) + let v0 ← vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit)) + clear_loop_fwd_back v0 i1 + else Result.ret v +termination_by clear_loop_fwd_back v i => clear_loop_terminates v i +decreasing_by clear_loop_decreases v i + +/- [loops::clear] -/ +def clear_fwd_back (v : Vec UInt32) : Result (Vec UInt32) := + clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit)) + +/- [loops::list_mem] -/ +def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) := + match h: ls with + | list_t.ListCons y tl => + if h: y = x + then Result.ret true + else list_mem_loop_fwd x tl + | list_t.ListNil => Result.ret false +termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls +decreasing_by list_mem_loop_decreases x ls + +/- [loops::list_mem] -/ +def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : Result Bool := + list_mem_loop_fwd x ls + +/- [loops::list_nth_mut_loop] -/ +def list_nth_mut_loop_loop_fwd + (T : Type) (ls : list_t T) (i : UInt32) : (Result T) := + match h: ls with + | list_t.ListCons x tl => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_mut_loop_loop_fwd T tl i0 + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_loop_fwd ls i => + list_nth_mut_loop_loop_terminates T ls i +decreasing_by list_nth_mut_loop_loop_decreases ls i + +/- [loops::list_nth_mut_loop] -/ +def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : Result T := + list_nth_mut_loop_loop_fwd T ls i + +/- [loops::list_nth_mut_loop] -/ +def list_nth_mut_loop_loop_back + (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (Result (list_t T)) := + match h: ls with + | list_t.ListCons x tl => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0 + Result.ret (list_t.ListCons x tl0) + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_loop_back ls i ret0 => + list_nth_mut_loop_loop_terminates T ls i +decreasing_by list_nth_mut_loop_loop_decreases ls i + +/- [loops::list_nth_mut_loop] -/ +def list_nth_mut_loop_back + (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := + list_nth_mut_loop_loop_back T ls i ret0 + +/- [loops::list_nth_shared_loop] -/ +def list_nth_shared_loop_loop_fwd + (T : Type) (ls : list_t T) (i : UInt32) : (Result T) := + match h: ls with + | list_t.ListCons x tl => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_shared_loop_loop_fwd T tl i0 + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_loop_loop_fwd ls i => + list_nth_shared_loop_loop_terminates T ls i +decreasing_by list_nth_shared_loop_loop_decreases ls i + +/- [loops::list_nth_shared_loop] -/ +def list_nth_shared_loop_fwd + (T : Type) (ls : list_t T) (i : UInt32) : Result T := + list_nth_shared_loop_loop_fwd T ls i + +/- [loops::get_elem_mut] -/ +def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (Result USize) := + match h: ls with + | list_t.ListCons y tl => + if h: y = x + then Result.ret y + else get_elem_mut_loop_fwd x tl + | list_t.ListNil => Result.fail Error.panic +termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls +decreasing_by get_elem_mut_loop_decreases x ls + +/- [loops::get_elem_mut] -/ +def get_elem_mut_fwd (slots : Vec (list_t USize)) (x : USize) : Result USize := + do + let l ← + vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + get_elem_mut_loop_fwd x l + +/- [loops::get_elem_mut] -/ +def get_elem_mut_loop_back + (x : USize) (ls : list_t USize) (ret0 : USize) : (Result (list_t USize)) := + match h: ls with + | list_t.ListCons y tl => + if h: y = x + then Result.ret (list_t.ListCons ret0 tl) + else + do + let tl0 ← get_elem_mut_loop_back x tl ret0 + Result.ret (list_t.ListCons y tl0) + | list_t.ListNil => Result.fail Error.panic +termination_by get_elem_mut_loop_back x ls ret0 => + get_elem_mut_loop_terminates x ls +decreasing_by get_elem_mut_loop_decreases x ls + +/- [loops::get_elem_mut] -/ +def get_elem_mut_back + (slots : Vec (list_t USize)) (x : USize) (ret0 : USize) : + Result (Vec (list_t USize)) + := + do + let l ← + vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + let l0 ← get_elem_mut_loop_back x l ret0 + vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0 + +/- [loops::get_elem_shared] -/ +def get_elem_shared_loop_fwd + (x : USize) (ls : list_t USize) : (Result USize) := + match h: ls with + | list_t.ListCons y tl => + if h: y = x + then Result.ret y + else get_elem_shared_loop_fwd x tl + | list_t.ListNil => Result.fail Error.panic +termination_by get_elem_shared_loop_fwd x ls => + get_elem_shared_loop_terminates x ls +decreasing_by get_elem_shared_loop_decreases x ls + +/- [loops::get_elem_shared] -/ +def get_elem_shared_fwd + (slots : Vec (list_t USize)) (x : USize) : Result USize := + do + let l ← + vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit)) + get_elem_shared_loop_fwd x l + +/- [loops::id_mut] -/ +def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) := + Result.ret ls + +/- [loops::id_mut] -/ +def id_mut_back + (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) := + Result.ret ret0 + +/- [loops::id_shared] -/ +def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) := + Result.ret ls + +/- [loops::list_nth_mut_loop_with_id] -/ +def list_nth_mut_loop_with_id_loop_fwd + (T : Type) (i : UInt32) (ls : list_t T) : (Result T) := + match h: ls with + | list_t.ListCons x tl => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_mut_loop_with_id_loop_fwd T i0 tl + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_with_id_loop_fwd i ls => + list_nth_mut_loop_with_id_loop_terminates T i ls +decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls + +/- [loops::list_nth_mut_loop_with_id] -/ +def list_nth_mut_loop_with_id_fwd + (T : Type) (ls : list_t T) (i : UInt32) : Result T := + do + let ls0 ← id_mut_fwd T ls + list_nth_mut_loop_with_id_loop_fwd T i ls0 + +/- [loops::list_nth_mut_loop_with_id] -/ +def list_nth_mut_loop_with_id_loop_back + (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) := + match h: ls with + | list_t.ListCons x tl => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0 + Result.ret (list_t.ListCons x tl0) + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 => + list_nth_mut_loop_with_id_loop_terminates T i ls +decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls + +/- [loops::list_nth_mut_loop_with_id] -/ +def list_nth_mut_loop_with_id_back + (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) := + do + let ls0 ← id_mut_fwd T ls + let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0 + id_mut_back T ls l + +/- [loops::list_nth_shared_loop_with_id] -/ +def list_nth_shared_loop_with_id_loop_fwd + (T : Type) (i : UInt32) (ls : list_t T) : (Result T) := + match h: ls with + | list_t.ListCons x tl => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret x + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_shared_loop_with_id_loop_fwd T i0 tl + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_loop_with_id_loop_fwd i ls => + list_nth_shared_loop_with_id_loop_terminates T i ls +decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls + +/- [loops::list_nth_shared_loop_with_id] -/ +def list_nth_shared_loop_with_id_fwd + (T : Type) (ls : list_t T) (i : UInt32) : Result T := + do + let ls0 ← id_shared_fwd T ls + list_nth_shared_loop_with_id_loop_fwd T i ls0 + +/- [loops::list_nth_mut_loop_pair] -/ +def list_nth_mut_loop_pair_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i => + list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair] -/ +def list_nth_mut_loop_pair_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair] -/ +def list_nth_mut_loop_pair_loop_back'a + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (Result (list_t T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl0) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x0 tl00) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 => + list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair] -/ +def list_nth_mut_loop_pair_back'a + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + Result (list_t T) + := + list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0 + +/- [loops::list_nth_mut_loop_pair] -/ +def list_nth_mut_loop_pair_loop_back'b + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (Result (list_t T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x1 tl10) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 => + list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair] -/ +def list_nth_mut_loop_pair_back'b + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + Result (list_t T) + := + list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0 + +/- [loops::list_nth_shared_loop_pair] -/ +def list_nth_shared_loop_pair_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i => + list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_shared_loop_pair] -/ +def list_nth_shared_loop_pair_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair_merge] -/ +def list_nth_mut_loop_pair_merge_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i => + list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair_merge] -/ +def list_nth_mut_loop_pair_merge_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair_merge] -/ +def list_nth_mut_loop_pair_merge_loop_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) : + (Result ((list_t T) × (list_t T))) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then + let (t, t0) := ret0 + Result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let (tl00, tl10) ← + list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 => + list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_loop_pair_merge] -/ +def list_nth_mut_loop_pair_merge_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) : + Result ((list_t T) × (list_t T)) + := + list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0 + +/- [loops::list_nth_shared_loop_pair_merge] -/ +def list_nth_shared_loop_pair_merge_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i => + list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_shared_loop_pair_merge] -/ +def list_nth_shared_loop_pair_merge_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair] -/ +def list_nth_mut_shared_loop_pair_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i => + list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair] -/ +def list_nth_mut_shared_loop_pair_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair] -/ +def list_nth_mut_shared_loop_pair_loop_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (Result (list_t T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl0) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl00 ← + list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x0 tl00) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 => + list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair] -/ +def list_nth_mut_shared_loop_pair_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + Result (list_t T) + := + list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0 + +/- [loops::list_nth_mut_shared_loop_pair_merge] -/ +def list_nth_mut_shared_loop_pair_merge_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i => + list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair_merge] -/ +def list_nth_mut_shared_loop_pair_merge_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair_merge] -/ +def list_nth_mut_shared_loop_pair_merge_loop_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (Result (list_t T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl0) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl00 ← + list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x0 tl00) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 => + list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_mut_shared_loop_pair_merge] -/ +def list_nth_mut_shared_loop_pair_merge_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + Result (list_t T) + := + list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0 + +/- [loops::list_nth_shared_mut_loop_pair] -/ +def list_nth_shared_mut_loop_pair_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i => + list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_shared_mut_loop_pair] -/ +def list_nth_shared_mut_loop_pair_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_shared_mut_loop_pair] -/ +def list_nth_shared_mut_loop_pair_loop_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (Result (list_t T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl10 ← + list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x1 tl10) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 => + list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i +decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i + +/- [loops::list_nth_shared_mut_loop_pair] -/ +def list_nth_shared_mut_loop_pair_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + Result (list_t T) + := + list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0 + +/- [loops::list_nth_shared_mut_loop_pair_merge] -/ +def list_nth_shared_mut_loop_pair_merge_loop_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + (Result (T × T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (x0, x1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0 + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i => + list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_shared_mut_loop_pair_merge] -/ +def list_nth_shared_mut_loop_pair_merge_fwd + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) : + Result (T × T) + := + list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i + +/- [loops::list_nth_shared_mut_loop_pair_merge] -/ +def list_nth_shared_mut_loop_pair_merge_loop_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + (Result (list_t T)) + := + match h: ls0 with + | list_t.ListCons x0 tl0 => + match h: ls1 with + | list_t.ListCons x1 tl1 => + if h: i = (UInt32.ofNatCore 0 (by intlit)) + then Result.ret (list_t.ListCons ret0 tl1) + else + do + let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit)) + let tl10 ← + list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0 + Result.ret (list_t.ListCons x1 tl10) + | list_t.ListNil => Result.fail Error.panic + | list_t.ListNil => Result.fail Error.panic +termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 => + list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i +decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i + +/- [loops::list_nth_shared_mut_loop_pair_merge] -/ +def list_nth_shared_mut_loop_pair_merge_back + (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) : + Result (list_t T) + := + list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0 + diff --git a/tests/lean/misc-loops/Loops/Types.lean b/tests/lean/misc-loops/Loops/Types.lean new file mode 100644 index 00000000..f4b6809e --- /dev/null +++ b/tests/lean/misc-loops/Loops/Types.lean @@ -0,0 +1,9 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [loops]: type definitions +import Base.Primitives + +/- [loops::List] -/ +inductive list_t (T : Type) := +| ListCons : T -> list_t T -> list_t T +| ListNil : list_t T + diff --git a/tests/lean/misc-loops/lakefile.lean b/tests/lean/misc-loops/lakefile.lean new file mode 100644 index 00000000..0d20ba1f --- /dev/null +++ b/tests/lean/misc-loops/lakefile.lean @@ -0,0 +1,18 @@ +import Lake +open Lake DSL + +require mathlib from git + "https://github.com/leanprover-community/mathlib4.git" + +package «loops» { + -- add package configuration options here +} + +lean_lib «Base» { + -- add library configuration options here +} + +lean_lib «Loops» { + -- add library configuration options here +} + |