Make minor fixes, improve formatting for Lean and generate code for all the test suite

5 files changed, 1587 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..79958d94
--- /dev/null
+++ b/tests/lean/misc/loops/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/loops/Loops/Clauses/Clauses.lean b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean
new file mode 100644
index 00000000..5ddb65ca
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Clauses/Clauses.lean
@@ -0,0 +1,209 @@
+-- [loops]: decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s)
+
+syntax "sum_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::sum_with_mut_borrows]: termination measure -/
+@[simp]
+def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (max, mi, ms)
+
+syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
+
+/- [loops::sum_with_shared_borrows]: termination measure -/
+@[simp]
+def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (max, i, s)
+
+syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::clear]: termination measure -/
+@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i)
+
+syntax "clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
+
+/- [loops::list_mem]: termination measure -/
+@[simp]
+def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls)
+
+syntax "list_mem_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop]: termination measure -/
+@[simp]
+def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32)
+  :=
+  (ls, i)
+
+syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop]: termination measure -/
+@[simp]
+def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T)
+  (i : UInt32) :=
+  (ls, i)
+
+syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::get_elem_mut]: termination measure -/
+@[simp]
+def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_mut_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::get_elem_shared]: termination measure -/
+@[simp]
+def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_shared_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/misc/loops/Loops/Clauses/Template.lean b/tests/lean/misc/loops/Loops/Clauses/Template.lean
new file mode 100644
index 00000000..3c0f2f7c
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean
@@ -0,0 +1,210 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: templates for the decreases clauses
+import Base.Primitives
+import Loops.Types
+
+/- [loops::sum]: termination measure -/
+@[simp]
+def sum_loop_terminates (max : UInt32) (i : UInt32) (s : UInt32) := (max, i, s)
+
+syntax "sum_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::sum_with_mut_borrows]: termination measure -/
+@[simp]
+def sum_with_mut_borrows_loop_terminates (max : UInt32) (mi : UInt32)
+  (ms : UInt32) :=
+  (max, mi, ms)
+
+syntax "sum_with_mut_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_mut_borrows_loop_decreases $max $mi $ms) =>`(tactic| sorry)
+
+/- [loops::sum_with_shared_borrows]: termination measure -/
+@[simp]
+def sum_with_shared_borrows_loop_terminates (max : UInt32) (i : UInt32)
+  (s : UInt32) :=
+  (max, i, s)
+
+syntax "sum_with_shared_borrows_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
+
+/- [loops::clear]: termination measure -/
+@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i)
+
+syntax "clear_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| clear_loop_decreases $v $i) =>`(tactic| sorry)
+
+/- [loops::list_mem]: termination measure -/
+@[simp]
+def list_mem_loop_terminates (x : UInt32) (ls : list_t UInt32) := (x, ls)
+
+syntax "list_mem_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_mem_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop]: termination measure -/
+@[simp]
+def list_nth_mut_loop_loop_terminates (T : Type) (ls : list_t T) (i : UInt32)
+  :=
+  (ls, i)
+
+syntax "list_nth_mut_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop]: termination measure -/
+@[simp]
+def list_nth_shared_loop_loop_terminates (T : Type) (ls : list_t T)
+  (i : UInt32) :=
+  (ls, i)
+
+syntax "list_nth_shared_loop_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_loop_decreases $ls $i) =>`(tactic| sorry)
+
+/- [loops::get_elem_mut]: termination measure -/
+@[simp]
+def get_elem_mut_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_mut_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_mut_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::get_elem_shared]: termination measure -/
+@[simp]
+def get_elem_shared_loop_terminates (x : USize) (ls : list_t USize) := (x, ls)
+
+syntax "get_elem_shared_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| get_elem_shared_loop_decreases $x $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_mut_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_mut_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_with_id]: termination measure -/
+@[simp]
+def list_nth_shared_loop_with_id_loop_terminates (T : Type) (i : UInt32)
+  (ls : list_t T) :=
+  (i, ls)
+
+syntax "list_nth_shared_loop_with_id_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_with_id_loop_decreases $i $ls) =>`(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>`(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_loop_pair_merge_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_mut_shared_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_mut_shared_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_mut_shared_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_loop_terminates (T : Type) (ls0 : list_t T)
+  (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: termination measure -/
+@[simp]
+def list_nth_shared_mut_loop_pair_merge_loop_terminates (T : Type)
+  (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :=
+  (ls0, ls1, i)
+
+syntax "list_nth_shared_mut_loop_pair_merge_loop_decreases" term+ : tactic
+
+macro_rules
+| `(tactic| list_nth_shared_mut_loop_pair_merge_loop_decreases $ls0 $ls1 $i) =>
+  `(tactic| sorry)
+
diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean
new file mode 100644
index 00000000..5fe5b4ff
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Funs.lean
@@ -0,0 +1,786 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: function definitions
+import Base.Primitives
+import Loops.Types
+import Loops.Clauses.Clauses
+
+/- [loops::sum] -/
+def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
+  if i < max
+  then
+    do
+      let s0 <- UInt32.checked_add s i
+      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      sum_loop_fwd max i0 s0
+  else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
+termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
+decreasing_by sum_loop_decreases max i s
+
+/- [loops::sum] -/
+def sum_fwd (max : UInt32) : result UInt32 :=
+  sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::sum_with_mut_borrows] -/
+def sum_with_mut_borrows_loop_fwd
+  (max : UInt32) (mi : UInt32) (ms : UInt32) : (result UInt32) :=
+  if mi < max
+  then
+    do
+      let ms0 <- UInt32.checked_add ms mi
+      let mi0 <- UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
+      sum_with_mut_borrows_loop_fwd max mi0 ms0
+  else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit))
+termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
+                                                         sum_with_mut_borrows_loop_terminates
+                                                         max mi ms
+decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
+
+/- [loops::sum_with_mut_borrows] -/
+def sum_with_mut_borrows_fwd (max : UInt32) : result UInt32 :=
+  sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::sum_with_shared_borrows] -/
+def sum_with_shared_borrows_loop_fwd
+  (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
+  if i < max
+  then
+    do
+      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      let s0 <- UInt32.checked_add s i0
+      sum_with_shared_borrows_loop_fwd max i0 s0
+  else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
+termination_by sum_with_shared_borrows_loop_fwd max i s =>
+                                                          sum_with_shared_borrows_loop_terminates
+                                                          max i s
+decreasing_by sum_with_shared_borrows_loop_decreases max i s
+
+/- [loops::sum_with_shared_borrows] -/
+def sum_with_shared_borrows_fwd (max : UInt32) : result UInt32 :=
+  sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
+    (UInt32.ofNatCore 0 (by intlit))
+
+/- [loops::clear] -/
+def clear_loop_fwd_back (v : vec UInt32) (i : USize) : (result (vec UInt32)) :=
+  let i0 := vec_len UInt32 v
+  if i < i0
+  then
+    do
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let v0 <- vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit))
+      clear_loop_fwd_back v0 i1
+  else result.ret v
+termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
+decreasing_by clear_loop_decreases v i
+
+/- [loops::clear] -/
+def clear_fwd_back (v : vec UInt32) : result (vec UInt32) :=
+  clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit))
+
+/- [loops::list_mem] -/
+def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (result Bool) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret true else list_mem_loop_fwd x tl
+  | list_t.ListNil => result.ret false
+  
+termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
+decreasing_by list_mem_loop_decreases x ls
+
+/- [loops::list_mem] -/
+def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : result Bool :=
+  list_mem_loop_fwd x ls
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_loop_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_mut_loop_loop_fwd T tl i0
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_loop_fwd ls i =>
+                                                 list_nth_mut_loop_loop_terminates
+                                                 T ls i
+decreasing_by list_nth_mut_loop_loop_decreases ls i
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  list_nth_mut_loop_loop_fwd T ls i
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_loop_back
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 <- list_nth_mut_loop_loop_back T tl i0 ret0
+        result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_loop_back ls i ret0 =>
+                                                       list_nth_mut_loop_loop_terminates
+                                                       T ls i
+decreasing_by list_nth_mut_loop_loop_decreases ls i
+
+/- [loops::list_nth_mut_loop] -/
+def list_nth_mut_loop_back
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+  list_nth_mut_loop_loop_back T ls i ret0
+
+/- [loops::list_nth_shared_loop] -/
+def list_nth_shared_loop_loop_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_shared_loop_loop_fwd T tl i0
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_loop_fwd ls i =>
+                                                    list_nth_shared_loop_loop_terminates
+                                                    T ls i
+decreasing_by list_nth_shared_loop_loop_decreases ls i
+
+/- [loops::list_nth_shared_loop] -/
+def list_nth_shared_loop_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  list_nth_shared_loop_loop_fwd T ls i
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (result USize) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret y else get_elem_mut_loop_fwd x tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
+decreasing_by get_elem_mut_loop_decreases x ls
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_fwd (slots : vec (list_t USize)) (x : USize) : result USize :=
+  do
+    let l <-
+      vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    get_elem_mut_loop_fwd x l
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_loop_back
+  (x : USize) (ls : list_t USize) (ret0 : USize) : (result (list_t USize)) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let tl0 <- get_elem_mut_loop_back x tl ret0
+        result.ret (list_t.ListCons y tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by get_elem_mut_loop_back x ls ret0 => get_elem_mut_loop_terminates
+                                                  x ls
+decreasing_by get_elem_mut_loop_decreases x ls
+
+/- [loops::get_elem_mut] -/
+def get_elem_mut_back
+  (slots : vec (list_t USize)) (x : USize) (ret0 : USize) :
+  result (vec (list_t USize))
+  :=
+  do
+    let l <-
+      vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    let l0 <- get_elem_mut_loop_back x l ret0
+    vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0
+
+/- [loops::get_elem_shared] -/
+def get_elem_shared_loop_fwd
+  (x : USize) (ls : list_t USize) : (result USize) :=
+  match ls with
+  | list_t.ListCons y tl =>
+    if y = x then result.ret y else get_elem_shared_loop_fwd x tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by get_elem_shared_loop_fwd x ls => get_elem_shared_loop_terminates
+                                               x ls
+decreasing_by get_elem_shared_loop_decreases x ls
+
+/- [loops::get_elem_shared] -/
+def get_elem_shared_fwd
+  (slots : vec (list_t USize)) (x : USize) : result USize :=
+  do
+    let l <- vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    get_elem_shared_loop_fwd x l
+
+/- [loops::id_mut] -/
+def id_mut_fwd (T : Type) (ls : list_t T) : result (list_t T) := result.ret ls
+
+/- [loops::id_mut] -/
+def id_mut_back
+  (T : Type) (ls : list_t T) (ret0 : list_t T) : result (list_t T) :=
+  result.ret ret0
+
+/- [loops::id_shared] -/
+def id_shared_fwd (T : Type) (ls : list_t T) : result (list_t T) :=
+  result.ret ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_loop_fwd
+  (T : Type) (i : UInt32) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_mut_loop_with_id_loop_fwd T i0 tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
+                                                         list_nth_mut_loop_with_id_loop_terminates
+                                                         T i ls
+decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  do
+    let ls0 <- id_mut_fwd T ls
+    list_nth_mut_loop_with_id_loop_fwd T i ls0
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_loop_back
+  (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (result (list_t T)) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret (list_t.ListCons ret0 tl)
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 <- list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
+                                                               list_nth_mut_loop_with_id_loop_terminates
+                                                               T i ls
+decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
+
+/- [loops::list_nth_mut_loop_with_id] -/
+def list_nth_mut_loop_with_id_back
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+  do
+    let ls0 <- id_mut_fwd T ls
+    let l <- list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+    id_mut_back T ls l
+
+/- [loops::list_nth_shared_loop_with_id] -/
+def list_nth_shared_loop_with_id_loop_fwd
+  (T : Type) (i : UInt32) (ls : list_t T) : (result T) :=
+  match ls with
+  | list_t.ListCons x tl =>
+    if i = (UInt32.ofNatCore 0 (by intlit))
+    then result.ret x
+    else
+      do
+        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        list_nth_shared_loop_with_id_loop_fwd T i0 tl
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
+                                                            list_nth_shared_loop_with_id_loop_terminates
+                                                            T i ls
+decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
+
+/- [loops::list_nth_shared_loop_with_id] -/
+def list_nth_shared_loop_with_id_fwd
+  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  do
+    let ls0 <- id_shared_fwd T ls
+    list_nth_shared_loop_with_id_loop_fwd T i ls0
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
+                                                           list_nth_mut_loop_pair_loop_terminates
+                                                           T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_loop_back'a
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <- list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
+                                                                   list_nth_mut_loop_pair_loop_terminates
+                                                                   T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_back'a
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_loop_back'b
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <- list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
+                                                                   list_nth_mut_loop_pair_loop_terminates
+                                                                   T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair] -/
+def list_nth_mut_loop_pair_back'b
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair] -/
+def list_nth_shared_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
+                                                              list_nth_shared_loop_pair_loop_terminates
+                                                              T ls0 ls1 i
+decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_loop_pair] -/
+def list_nth_shared_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
+                                                                 list_nth_mut_loop_pair_merge_loop_terminates
+                                                                 T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) :
+  (result ((list_t T) × (list_t T)))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then
+        let (t, t0) := ret0
+        result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let (tl00, tl10) <-
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
+   list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge] -/
+def list_nth_mut_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) :
+  result ((list_t T) × (list_t T))
+  :=
+  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair_merge] -/
+def list_nth_shared_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
+                                                                    list_nth_shared_loop_pair_merge_loop_terminates
+                                                                    T ls0 ls1 i
+decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_loop_pair_merge] -/
+def list_nth_shared_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
+                                                                  list_nth_mut_shared_loop_pair_loop_terminates
+                                                                  T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
+   list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair] -/
+def list_nth_mut_shared_loop_pair_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
+   list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl0)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 <-
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
+   list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+def list_nth_mut_shared_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
+                                                                  list_nth_shared_mut_loop_pair_loop_terminates
+                                                                  T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
+   list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair] -/
+def list_nth_shared_mut_loop_pair_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_loop_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  (result (T × T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (x0, x1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
+   list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_fwd
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
+  result (T × T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  (result (list_t T))
+  :=
+  match ls0 with
+  | list_t.ListCons x0 tl0 =>
+    match ls1 with
+    | list_t.ListCons x1 tl1 =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl1)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 <-
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => result.fail error.panic
+    
+  | list_t.ListNil => result.fail error.panic
+  
+termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
+   list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
+decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+def list_nth_shared_mut_loop_pair_merge_back
+  (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
+  result (list_t T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
diff --git a/tests/lean/misc/loops/Loops/Types.lean b/tests/lean/misc/loops/Loops/Types.lean
new file mode 100644
index 00000000..f4b6809e
--- /dev/null
+++ b/tests/lean/misc/loops/Loops/Types.lean
@@ -0,0 +1,9 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: type definitions
+import Base.Primitives
+
+/- [loops::List] -/
+inductive list_t (T : Type) :=
+| ListCons : T -> list_t T -> list_t T
+| ListNil : list_t T
+