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

2 files changed, 913 insertions, 0 deletions

diff --git a/tests/lean/misc/no_nested_borrows/Base/Primitives.lean b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
new file mode 100644
index 00000000..79958d94
--- /dev/null
+++ b/tests/lean/misc/no_nested_borrows/Base/Primitives.lean
@@ -0,0 +1,373 @@
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+
+-------------
+-- PRELUDE --
+-------------
+
+-- Results & monadic combinators
+
+-- TODO: use syntactic conventions and capitalize error, result, etc.
+
+inductive error where
+   | assertionFailure: error
+   | integerOverflow: error
+   | arrayOutOfBounds: error
+   | maximumSizeExceeded: error
+   | panic: error
+deriving Repr, BEq
+
+open error
+
+inductive result (α : Type u) where
+  | ret (v: α): result α
+  | fail (e: error): result α 
+deriving Repr, BEq
+
+open result
+
+/- HELPERS -/
+
+-- TODO: is there automated syntax for these discriminators?
+def is_ret {α: Type} (r: result α): Bool :=
+  match r with
+  | result.ret _ => true
+  | result.fail _ => false
+
+def massert (b:Bool) : result Unit :=
+  if b then .ret () else fail assertionFailure
+
+def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+  match x with
+  | result.fail _ => by contradiction
+  | result.ret x => x
+
+/- DO-DSL SUPPORT -/
+
+def bind (x: result α) (f: α -> result β) : result β :=
+  match x with
+  | ret v  => f v 
+  | fail v => fail v
+
+-- Allows using result in do-blocks
+instance : Bind result where
+  bind := bind
+
+-- Allows using return x in do-blocks
+instance : Pure result where
+  pure := fun x => ret x
+
+/- CUSTOM-DSL SUPPORT -/
+
+-- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- because we may need a hypothesis for equational reasoning in the scope. We
+-- rely on subtype, and a custom let-binding operator, in effect recreating our
+-- own variant of the do-dsl
+
+def result.attach : (o : result α) → result { x : α // o = ret x }
+  | .ret x => .ret ⟨x, rfl⟩
+  | .fail e   => .fail e
+
+macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+
+-- Silly example of the kind of reasoning that this notation enables
+#eval do
+  let h: y <-- .ret (0: Nat)
+  let _: y = 0 := by cases h; decide
+  let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
+  .ret r
+
+----------------------
+-- MACHINE INTEGERS --
+----------------------
+
+-- NOTE: we reuse the USize type from prelude.lean, because at least we know
+-- it's defined in an idiomatic style that is going to make proofs easy (and
+-- indeed, several proofs here are much shortened compared to Aymeric's earlier
+-- attempt.) This is not stricto sensu the *correct* thing to do, because one
+-- can query at run-time the value of USize, which we do *not* want to do (we
+-- don't know what target we'll run on!), but when the day comes, we'll just
+-- define our own USize.
+-- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
+-- not something we want to define (I think), so we use our own monadic sub (but
+-- is it in line with the Rust behavior?)
+
+-- TODO: I am somewhat under the impression that subtraction is defined as a
+-- total function over nats...? the hypothesis in the if condition is not used
+-- in the then-branch which confuses me quite a bit
+
+-- TODO: add a refinement for the result (just like vec_push_back below) that
+-- explains that the toNat of the result (in the case of success) is the sub of
+-- the toNat of the arguments (i.e. intrinsic specification)
+-- ... do we want intrinsic specifications for the builtins? that might require
+-- some careful type annotations in the monadic notation for clients, but may
+-- give us more "for free"
+
+-- Note from Chris Bailey: "If there's more than one salient property of your
+-- definition then the subtyping strategy might get messy, and the property part
+-- of a subtype is less discoverable by the simplifier or tactics like
+-- library_search." Try to settle this with a Lean expert on what is the most
+-- productive way to go about this?
+
+-- One needs to perform a little bit of reasoning in order to successfully
+-- inject constants into USize, so we provide a general-purpose macro
+
+syntax "intlit" : tactic
+
+macro_rules
+  | `(tactic| intlit) => `(tactic|
+    match USize.size, usize_size_eq with
+    | _, Or.inl rfl => decide
+    | _, Or.inr rfl => decide)
+
+-- This is how the macro is expected to be used
+#eval USize.ofNatCore 0 (by intlit)
+
+-- Also works for other integer types (at the expense of a needless disjunction)
+#eval UInt32.ofNatCore 0 (by intlit)
+
+-- Further thoughts: look at what has been done here:
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
+-- and
+-- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
+-- which both contain a fair amount of reasoning already!
+def USize.checked_sub (n: USize) (m: USize): result USize :=
+  -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
+  if n >= m then
+    let n' := USize.toNat n
+    let m' := USize.toNat n
+    let r := USize.ofNatCore (n' - m') (by
+      have h: n' - m' <= n' := by
+        apply Nat.sub_le_of_le_add
+        case h => rewrite [ Nat.add_comm ]; apply Nat.le_add_left
+      apply Nat.lt_of_le_of_lt h
+      apply n.val.isLt
+    )
+    return r
+  else
+    fail integerOverflow
+
+def USize.checked_add (n: USize) (m: USize): result USize :=
+  if h: n.val.val + m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val + m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val + m.val < USize.size then
+    .ret ⟨ n.val + m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_rem (n: USize) (m: USize): result USize :=
+  if h: m > 0 then
+    .ret ⟨ n.val % m.val, by
+      have h1: ↑m.val < USize.size := m.val.isLt
+      have h2: n.val.val % m.val.val < m.val.val := @Nat.mod_lt n.val m.val h
+      apply Nat.lt_trans h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_mul (n: USize) (m: USize): result USize :=
+    if h: n.val.val * m.val.val <= 4294967295 then
+    .ret ⟨ n.val.val * m.val.val, by
+      have h': 4294967295 < USize.size := by intlit
+      apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: n.val * m.val < USize.size then
+    .ret ⟨ n.val * m.val, h ⟩
+  else
+    .fail integerOverflow
+
+def USize.checked_div (n: USize) (m: USize): result USize :=
+  if m > 0 then
+    .ret ⟨ n.val / m.val, by
+      have h1: ↑n.val < USize.size := n.val.isLt
+      have h2: n.val.val / m.val.val <= n.val.val := @Nat.div_le_self n.val m.val
+      apply Nat.lt_of_le_of_lt h2 h1
+    ⟩
+  else
+    .fail integerOverflow
+
+class MachineInteger (t: Type) where
+  size: Nat
+  val: t -> Fin size
+  ofNatCore: (n:Nat) -> LT.lt n size -> t
+
+set_option hygiene false in
+run_cmd
+  for typeName in [`UInt8, `UInt16, `UInt32, `UInt64, `USize].map Lean.mkIdent do
+  Lean.Elab.Command.elabCommand (← `(
+    namespace $typeName
+    instance: MachineInteger $typeName where
+      size := size
+      val := val
+      ofNatCore := ofNatCore
+    end $typeName
+  ))
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+  if h: MachineInteger.val x < MachineInteger.size dst then
+    .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
+  else
+    .fail integerOverflow
+
+
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-------------
+-- VECTORS --
+-------------
+
+-- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
+-- rather than maximum values (usize_max).
+def vec (α : Type u) := { l : List α // List.length l < USize.size }
+
+def vec_new (α : Type u): vec α := ⟨ [], by {
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => simp
+  | _, Or.inr rfl => simp
+  } ⟩
+
+#check vec_new
+
+def vec_len (α : Type u) (v : vec α) : USize :=
+  let ⟨ v, l ⟩ := v
+  USize.ofNatCore (List.length v) l
+
+#eval vec_len Nat (vec_new Nat)
+ 
+def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+
+-- NOTE: old version trying to use a subtype notation, but probably better to
+-- leave result elimination to auxiliary lemmas with suitable preconditions
+-- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
+-- make the proof work in that case? Probably need to import tactics from
+-- mathlib to deal with inequalities... would love to see an example.
+def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+  match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
+  :=
+  if h : List.length v.val + 1 < USize.size then
+    ⟨ return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩, by simp ⟩
+  else
+    ⟨ fail maximumSizeExceeded, by simp ⟩
+
+#eval do
+  -- NOTE: the // notation is syntactic sugar for Subtype, a refinement with
+  -- fields val and property. However, Lean's elaborator can automatically
+  -- select the `val` field if the context provides a type annotation. We
+  -- annotate `x`, which relieves us of having to write `.val` on the right-hand
+  -- side of the monadic let.
+  let v := vec_new Nat
+  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  -- TODO: strengthen post-condition above and do a demo to show that we can
+  -- safely eliminate the `fail` case
+  return (vec_len Nat x)
+
+def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+  :=
+  if h : List.length v.val + 1 <= 4294967295 then
+    return ⟨ List.concat v.val x,
+      by
+        rw [List.length_concat]
+        have h': 4294967295 < USize.size := by intlit
+        apply Nat.lt_of_le_of_lt h h'
+    ⟩
+  else if h: List.length v.val + 1 < USize.size then
+    return ⟨List.concat v.val x,
+      by
+        rw [List.length_concat]
+        assumption
+     ⟩
+  else
+    fail maximumSizeExceeded
+
+def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+  if h: i.val < List.length v.val then
+    .ret (List.get v.val ⟨i.val, h⟩)
+  else
+    .fail arrayOutOfBounds
+
+def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+  if i.val < List.length v.val then
+    .ret ⟨ List.set v.val i.val x, by
+      have h: List.length v.val < USize.size := v.property
+      rewrite [ List.length_set v.val i.val x ]
+      assumption
+    ⟩
+  else
+    .fail arrayOutOfBounds
+
+----------
+-- MISC --
+----------
+
+def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
+  x
+
+def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
+  y
+
+--------------------
+-- ASSERT COMMAND --
+--------------------
+
+open Lean Elab Command Term Meta
+
+syntax (name := assert) "#assert" term: command
+
+@[command_elab assert]
+def assertImpl : CommandElab := fun (_stx: Syntax) => do
+  logInfo "Reducing and asserting: "
+  logInfo _stx[1]
+  runTermElabM (fun _ => do
+    let e ← Term.elabTerm _stx[1] none
+    logInfo (Expr.dbgToString e)
+    -- How to evaluate the term and compare the result to true?
+    pure ())
+  -- logInfo (Expr.dbgToString (``true))
+  -- throwError "TODO: assert"
+
+#eval 2 == 2
+#assert (2 == 2)
diff --git a/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
new file mode 100644
index 00000000..d871392b
--- /dev/null
+++ b/tests/lean/misc/no_nested_borrows/NoNestedBorrows.lean
@@ -0,0 +1,540 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [no_nested_borrows]
+import Base.Primitives
+
+structure OpaqueDefs where
+  
+  /- [no_nested_borrows::Pair] -/
+  structure pair_t (T1 T2 : Type) where  pair_x : T1 pair_y : T2 
+  
+  /- [no_nested_borrows::List] -/
+  inductive list_t (T : Type) :=
+  | ListCons : T -> list_t T -> list_t T
+  | ListNil : list_t T
+  
+  /- [no_nested_borrows::One] -/
+  inductive one_t (T1 : Type) := | OneOne : T1 -> one_t T1
+  
+  /- [no_nested_borrows::EmptyEnum] -/
+  inductive empty_enum_t := | EmptyEnumEmpty : empty_enum_t
+  
+  /- [no_nested_borrows::Enum] -/
+  inductive enum_t := | EnumVariant1 : enum_t | EnumVariant2 : enum_t
+  
+  /- [no_nested_borrows::EmptyStruct] -/
+  structure empty_struct_t where   
+  
+  /- [no_nested_borrows::Sum] -/
+  inductive sum_t (T1 T2 : Type) :=
+  | SumLeft : T1 -> sum_t T1 T2
+  | SumRight : T2 -> sum_t T1 T2
+  
+  /- [no_nested_borrows::neg_test] -/
+  def neg_test_fwd (x : Int32) : result Int32 := Int32.checked_neg x
+  
+  /- [no_nested_borrows::add_test] -/
+  def add_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_add x y
+  
+  /- [no_nested_borrows::subs_test] -/
+  def subs_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_sub x y
+  
+  /- [no_nested_borrows::div_test] -/
+  def div_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_div x y
+  
+  /- [no_nested_borrows::div_test1] -/
+  def div_test1_fwd (x : UInt32) : result UInt32 :=
+    UInt32.checked_div x (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::rem_test] -/
+  def rem_test_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    UInt32.checked_rem x y
+  
+  /- [no_nested_borrows::cast_test] -/
+  def cast_test_fwd (x : UInt32) : result Int32 := scalar_cast Int32 x
+  
+  /- [no_nested_borrows::test2] -/
+  def test2_fwd : result Unit :=
+    do
+      let _ <- UInt32.checked_add (UInt32.ofNatCore 23 (by intlit))
+        (UInt32.ofNatCore 44 (by intlit))
+      result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test2] -/
+  #assert (test2_fwd = .ret ())
+  
+  /- [no_nested_borrows::get_max] -/
+  def get_max_fwd (x : UInt32) (y : UInt32) : result UInt32 :=
+    if x >= y then result.ret x else result.ret y
+  
+  /- [no_nested_borrows::test3] -/
+  def test3_fwd : result Unit :=
+    do
+      let x <-
+        get_max_fwd (UInt32.ofNatCore 4 (by intlit))
+          (UInt32.ofNatCore 3 (by intlit))
+      let y <-
+        get_max_fwd (UInt32.ofNatCore 10 (by intlit))
+          (UInt32.ofNatCore 11 (by intlit))
+      let z <- UInt32.checked_add x y
+      if not (z = (UInt32.ofNatCore 15 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test3] -/
+  #assert (test3_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_neg1] -/
+  def test_neg1_fwd : result Unit :=
+    do
+      let y <- Int32.checked_neg (Int32.ofNatCore 3 (by intlit))
+      if not (y = (Int32.ofNatCore -3 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_neg1] -/
+  #assert (test_neg1_fwd = .ret ())
+  
+  /- [no_nested_borrows::refs_test1] -/
+  def refs_test1_fwd : result Unit :=
+    if not ((Int32.ofNatCore 1 (by intlit)) = (Int32.ofNatCore 1 (by intlit)))
+    then result.fail error.panic
+    else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::refs_test1] -/
+  #assert (refs_test1_fwd = .ret ())
+  
+  /- [no_nested_borrows::refs_test2] -/
+  def refs_test2_fwd : result Unit :=
+    if not ((Int32.ofNatCore 2 (by intlit)) = (Int32.ofNatCore 2 (by intlit)))
+    then result.fail error.panic
+    else
+      if not ((Int32.ofNatCore 0 (by intlit)) =
+        (Int32.ofNatCore 0 (by intlit)))
+      then result.fail error.panic
+      else
+        if not ((Int32.ofNatCore 2 (by intlit)) =
+          (Int32.ofNatCore 2 (by intlit)))
+        then result.fail error.panic
+        else
+          if not ((Int32.ofNatCore 2 (by intlit)) =
+            (Int32.ofNatCore 2 (by intlit)))
+          then result.fail error.panic
+          else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::refs_test2] -/
+  #assert (refs_test2_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_list1] -/
+  def test_list1_fwd : result Unit := result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_list1] -/
+  #assert (test_list1_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_box1] -/
+  def test_box1_fwd : result Unit :=
+    let b := (Int32.ofNatCore 1 (by intlit))
+    let x := b
+    if not (x = (Int32.ofNatCore 1 (by intlit)))
+    then result.fail error.panic
+    else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_box1] -/
+  #assert (test_box1_fwd = .ret ())
+  
+  /- [no_nested_borrows::copy_int] -/
+  def copy_int_fwd (x : Int32) : result Int32 := result.ret x
+  
+  /- [no_nested_borrows::test_unreachable] -/
+  def test_unreachable_fwd (b : Bool) : result Unit :=
+    if b then result.fail error.panic else result.ret ()
+  
+  /- [no_nested_borrows::test_panic] -/
+  def test_panic_fwd (b : Bool) : result Unit :=
+    if b then result.fail error.panic else result.ret ()
+  
+  /- [no_nested_borrows::test_copy_int] -/
+  def test_copy_int_fwd : result Unit :=
+    do
+      let y <- copy_int_fwd (Int32.ofNatCore 0 (by intlit))
+      if not ((Int32.ofNatCore 0 (by intlit)) = y)
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_copy_int] -/
+  #assert (test_copy_int_fwd = .ret ())
+  
+  /- [no_nested_borrows::is_cons] -/
+  def is_cons_fwd (T : Type) (l : list_t T) : result Bool :=
+    match l with
+    | list_t.ListCons t l0 => result.ret true
+    | list_t.ListNil => result.ret false
+    
+  
+  /- [no_nested_borrows::test_is_cons] -/
+  def test_is_cons_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let b <-
+        is_cons_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) l)
+      if not b then result.fail error.panic else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_is_cons] -/
+  #assert (test_is_cons_fwd = .ret ())
+  
+  /- [no_nested_borrows::split_list] -/
+  def split_list_fwd (T : Type) (l : list_t T) : result (T × (list_t T)) :=
+    match l with
+    | list_t.ListCons hd tl => result.ret (hd, tl)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::test_split_list] -/
+  def test_split_list_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let p <-
+        split_list_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
+          l)
+      let (hd, _) := p
+      if not (hd = (Int32.ofNatCore 0 (by intlit)))
+      then result.fail error.panic
+      else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_split_list] -/
+  #assert (test_split_list_fwd = .ret ())
+  
+  /- [no_nested_borrows::choose] -/
+  def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : result T :=
+    if b then result.ret x else result.ret y
+  
+  /- [no_nested_borrows::choose] -/
+  def choose_back
+    (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : result (T × T) :=
+    if b then result.ret (ret0, y) else result.ret (x, ret0)
+  
+  /- [no_nested_borrows::choose_test] -/
+  def choose_test_fwd : result Unit :=
+    do
+      let z <-
+        choose_fwd Int32 true (Int32.ofNatCore 0 (by intlit))
+          (Int32.ofNatCore 0 (by intlit))
+      let z0 <- Int32.checked_add z (Int32.ofNatCore 1 (by intlit))
+      if not (z0 = (Int32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let (x, y) <-
+            choose_back Int32 true (Int32.ofNatCore 0 (by intlit))
+              (Int32.ofNatCore 0 (by intlit)) z0
+          if not (x = (Int32.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            if not (y = (Int32.ofNatCore 0 (by intlit)))
+            then result.fail error.panic
+            else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::choose_test] -/
+  #assert (choose_test_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_char] -/
+  def test_char_fwd : result Char := result.ret 'a'
+  
+  /- [no_nested_borrows::NodeElem] -/
+  mutual inductive node_elem_t (T : Type) :=
+  | NodeElemCons : tree_t T -> node_elem_t T -> node_elem_t T
+  | NodeElemNil : node_elem_t T
+  
+  /- [no_nested_borrows::Tree] -/
+  inductive tree_t (T : Type) :=
+  | TreeLeaf : T -> tree_t T
+  | TreeNode : T -> node_elem_t T -> tree_t T -> tree_t T
+  
+  /- [no_nested_borrows::list_length] -/
+  def list_length_fwd (T : Type) (l : list_t T) : result UInt32 :=
+    match l with
+    | list_t.ListCons t l1 =>
+      do
+        let i <- list_length_fwd T l1
+        UInt32.checked_add (UInt32.ofNatCore 1 (by intlit)) i
+    | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+    
+  
+  /- [no_nested_borrows::list_nth_shared] -/
+  def list_nth_shared_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_shared_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_nth_mut] -/
+  def list_nth_mut_fwd (T : Type) (l : list_t T) (i : UInt32) : result T :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret x
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          list_nth_mut_fwd T tl i0
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_nth_mut] -/
+  def list_nth_mut_back
+    (T : Type) (l : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+    match l with
+    | list_t.ListCons x tl =>
+      if i = (UInt32.ofNatCore 0 (by intlit))
+      then result.ret (list_t.ListCons ret0 tl)
+      else
+        do
+          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl0 <- list_nth_mut_back T tl i0 ret0
+          result.ret (list_t.ListCons x tl0)
+    | list_t.ListNil => result.fail error.panic
+    
+  
+  /- [no_nested_borrows::list_rev_aux] -/
+  def list_rev_aux_fwd
+    (T : Type) (li : list_t T) (lo : list_t T) : result (list_t T) :=
+    match li with
+    | list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo)
+    | list_t.ListNil => result.ret lo
+    
+  
+  /- [no_nested_borrows::list_rev] -/
+  def list_rev_fwd_back (T : Type) (l : list_t T) : result (list_t T) :=
+    let li := mem_replace_fwd (list_t T) l list_t.ListNil
+    list_rev_aux_fwd T li list_t.ListNil
+  
+  /- [no_nested_borrows::test_list_functions] -/
+  def test_list_functions_fwd : result Unit :=
+    do
+      let l := list_t.ListNil
+      let l0 := list_t.ListCons (Int32.ofNatCore 2 (by intlit)) l
+      let l1 := list_t.ListCons (Int32.ofNatCore 1 (by intlit)) l0
+      let i <-
+        list_length_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit))
+          l1)
+      if not (i = (UInt32.ofNatCore 3 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let i0 <-
+            list_nth_shared_fwd Int32 (list_t.ListCons
+              (Int32.ofNatCore 0 (by intlit)) l1)
+              (UInt32.ofNatCore 0 (by intlit))
+          if not (i0 = (Int32.ofNatCore 0 (by intlit)))
+          then result.fail error.panic
+          else
+            do
+              let i1 <-
+                list_nth_shared_fwd Int32 (list_t.ListCons
+                  (Int32.ofNatCore 0 (by intlit)) l1)
+                  (UInt32.ofNatCore 1 (by intlit))
+              if not (i1 = (Int32.ofNatCore 1 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let i2 <-
+                    list_nth_shared_fwd Int32 (list_t.ListCons
+                      (Int32.ofNatCore 0 (by intlit)) l1)
+                      (UInt32.ofNatCore 2 (by intlit))
+                  if not (i2 = (Int32.ofNatCore 2 (by intlit)))
+                  then result.fail error.panic
+                  else
+                    do
+                      let ls <-
+                        list_nth_mut_back Int32 (list_t.ListCons
+                          (Int32.ofNatCore 0 (by intlit)) l1)
+                          (UInt32.ofNatCore 1 (by intlit))
+                          (Int32.ofNatCore 3 (by intlit))
+                      let i3 <-
+                        list_nth_shared_fwd Int32 ls
+                          (UInt32.ofNatCore 0 (by intlit))
+                      if not (i3 = (Int32.ofNatCore 0 (by intlit)))
+                      then result.fail error.panic
+                      else
+                        do
+                          let i4 <-
+                            list_nth_shared_fwd Int32 ls
+                              (UInt32.ofNatCore 1 (by intlit))
+                          if not (i4 = (Int32.ofNatCore 3 (by intlit)))
+                          then result.fail error.panic
+                          else
+                            do
+                              let i5 <-
+                                list_nth_shared_fwd Int32 ls
+                                  (UInt32.ofNatCore 2 (by intlit))
+                              if not (i5 = (Int32.ofNatCore 2 (by intlit)))
+                              then result.fail error.panic
+                              else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_list_functions] -/
+  #assert (test_list_functions_fwd = .ret ())
+  
+  /- [no_nested_borrows::id_mut_pair1] -/
+  def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : result (T1 × T2) :=
+    result.ret (x, y)
+  
+  /- [no_nested_borrows::id_mut_pair1] -/
+  def id_mut_pair1_back
+    (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := ret0 result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair2] -/
+  def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := p result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair2] -/
+  def id_mut_pair2_back
+    (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := ret0 result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair3] -/
+  def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : result (T1 × T2) :=
+    result.ret (x, y)
+  
+  /- [no_nested_borrows::id_mut_pair3] -/
+  def id_mut_pair3_back'a
+    (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : result T1 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::id_mut_pair3] -/
+  def id_mut_pair3_back'b
+    (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : result T2 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::id_mut_pair4] -/
+  def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : result (T1 × T2) :=
+    let (t, t0) := p result.ret (t, t0)
+  
+  /- [no_nested_borrows::id_mut_pair4] -/
+  def id_mut_pair4_back'a
+    (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : result T1 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::id_mut_pair4] -/
+  def id_mut_pair4_back'b
+    (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : result T2 :=
+    result.ret ret0
+  
+  /- [no_nested_borrows::StructWithTuple] -/
+  structure struct_with_tuple_t (T1 T2 : Type) where
+  
+    struct_with_tuple_p : (T1 × T2)
+  
+  
+  /- [no_nested_borrows::new_tuple1] -/
+  def new_tuple1_fwd : result (struct_with_tuple_t UInt32 UInt32) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((UInt32.ofNatCore 1 (by intlit)),
+                               (UInt32.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::new_tuple2] -/
+  def new_tuple2_fwd : result (struct_with_tuple_t Int16 Int16) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((Int16.ofNatCore 1 (by intlit)),
+                               (Int16.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::new_tuple3] -/
+  def new_tuple3_fwd : result (struct_with_tuple_t UInt64 Int64) :=
+    result.ret
+    {
+      struct_with_tuple_p := ((UInt64.ofNatCore 1 (by intlit)),
+                               (Int64.ofNatCore 2 (by intlit)))
+    }
+  
+  /- [no_nested_borrows::StructWithPair] -/
+  structure struct_with_pair_t (T1 T2 : Type) where
+  
+    struct_with_pair_p : pair_t T1 T2
+  
+  
+  /- [no_nested_borrows::new_pair1] -/
+  def new_pair1_fwd : result (struct_with_pair_t UInt32 UInt32) :=
+    result.ret
+    {
+      struct_with_pair_p := {
+                              pair_x := (UInt32.ofNatCore 1 (by intlit)),
+                              pair_y := (UInt32.ofNatCore 2 (by intlit))
+                            }
+    }
+  
+  /- [no_nested_borrows::test_constants] -/
+  def test_constants_fwd : result Unit :=
+    do
+      let swt <- new_tuple1_fwd
+      let (i, _) := swt.struct_with_tuple_p
+      if not (i = (UInt32.ofNatCore 1 (by intlit)))
+      then result.fail error.panic
+      else
+        do
+          let swt0 <- new_tuple2_fwd
+          let (i0, _) := swt0.struct_with_tuple_p
+          if not (i0 = (Int16.ofNatCore 1 (by intlit)))
+          then result.fail error.panic
+          else
+            do
+              let swt1 <- new_tuple3_fwd
+              let (i1, _) := swt1.struct_with_tuple_p
+              if not (i1 = (UInt64.ofNatCore 1 (by intlit)))
+              then result.fail error.panic
+              else
+                do
+                  let swp <- new_pair1_fwd
+                  if not (swp.struct_with_pair_p.pair_x =
+                    (UInt32.ofNatCore 1 (by intlit)))
+                  then result.fail error.panic
+                  else result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_constants] -/
+  #assert (test_constants_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_weird_borrows1] -/
+  def test_weird_borrows1_fwd : result Unit := result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_weird_borrows1] -/
+  #assert (test_weird_borrows1_fwd = .ret ())
+  
+  /- [no_nested_borrows::test_mem_replace] -/
+  def test_mem_replace_fwd_back (px : UInt32) : result UInt32 :=
+    let y := mem_replace_fwd UInt32 px (UInt32.ofNatCore 1 (by intlit))
+    if not (y = (UInt32.ofNatCore 0 (by intlit)))
+    then result.fail error.panic
+    else result.ret (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool1] -/
+  def test_shared_borrow_bool1_fwd (b : Bool) : result UInt32 :=
+    if b
+    then result.ret (UInt32.ofNatCore 0 (by intlit))
+    else result.ret (UInt32.ofNatCore 1 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool2] -/
+  def test_shared_borrow_bool2_fwd : result UInt32 :=
+    result.ret (UInt32.ofNatCore 0 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_enum1] -/
+  def test_shared_borrow_enum1_fwd (l : list_t UInt32) : result UInt32 :=
+    match l with
+    | list_t.ListCons i l0 => result.ret (UInt32.ofNatCore 1 (by intlit))
+    | list_t.ListNil => result.ret (UInt32.ofNatCore 0 (by intlit))
+    
+  
+  /- [no_nested_borrows::test_shared_borrow_enum2] -/
+  def test_shared_borrow_enum2_fwd : result UInt32 :=
+    result.ret (UInt32.ofNatCore 0 (by intlit))
+