Reorganize the Lean tests and extract the Polonius tests to Lean

3 files changed, 966 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..5b64e908
--- /dev/null
+++ b/tests/lean/misc-no_nested_borrows/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-no_nested_borrows/NoNestedBorrows.lean b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
new file mode 100644
index 00000000..a20ee9fd
--- /dev/null
+++ b/tests/lean/misc-no_nested_borrows/NoNestedBorrows.lean
@@ -0,0 +1,556 @@
+-- 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 h: 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 h: not (z = (UInt32.ofNatCore 15 (by intlit)))
+      then Result.fail Error.panic
+      else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test3] -/
+  #assert (test3_fwd == .ret ())
+  
+  /- [no_nested_borrows::test_neg1] -/
+  def test_neg1_fwd : Result Unit :=
+    do
+      let y ← Int32.checked_neg (Int32.ofNatCore 3 (by intlit))
+      if h: not (y = (Int32.ofNatCore -3 (by intlit)))
+      then Result.fail Error.panic
+      else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_neg1] -/
+  #assert (test_neg1_fwd == .ret ())
+  
+  /- [no_nested_borrows::refs_test1] -/
+  def refs_test1_fwd : Result Unit :=
+    if h: not ((Int32.ofNatCore 1 (by intlit)) =
+      (Int32.ofNatCore 1 (by intlit)))
+    then Result.fail Error.panic
+    else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::refs_test1] -/
+  #assert (refs_test1_fwd == .ret ())
+  
+  /- [no_nested_borrows::refs_test2] -/
+  def refs_test2_fwd : Result Unit :=
+    if h: not ((Int32.ofNatCore 2 (by intlit)) =
+      (Int32.ofNatCore 2 (by intlit)))
+    then Result.fail Error.panic
+    else
+      if h: not ((Int32.ofNatCore 0 (by intlit)) =
+        (Int32.ofNatCore 0 (by intlit)))
+      then Result.fail Error.panic
+      else
+        if h: not ((Int32.ofNatCore 2 (by intlit)) =
+          (Int32.ofNatCore 2 (by intlit)))
+        then Result.fail Error.panic
+        else
+          if h: 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 h: not (x = (Int32.ofNatCore 1 (by intlit)))
+    then Result.fail Error.panic
+    else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_box1] -/
+  #assert (test_box1_fwd == .ret ())
+  
+  /- [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 h: b
+    then Result.fail Error.panic
+    else Result.ret ()
+  
+  /- [no_nested_borrows::test_panic] -/
+  def test_panic_fwd (b : Bool) : Result Unit :=
+    if h: b
+    then Result.fail Error.panic
+    else Result.ret ()
+  
+  /- [no_nested_borrows::test_copy_int] -/
+  def test_copy_int_fwd : Result Unit :=
+    do
+      let y ← copy_int_fwd (Int32.ofNatCore 0 (by intlit))
+      if h: not ((Int32.ofNatCore 0 (by intlit)) = y)
+      then Result.fail Error.panic
+      else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_copy_int] -/
+  #assert (test_copy_int_fwd == .ret ())
+  
+  /- [no_nested_borrows::is_cons] -/
+  def is_cons_fwd (T : Type) (l : list_t T) : Result Bool :=
+    match h: l with
+    | list_t.ListCons t l0 => Result.ret true
+    | list_t.ListNil => Result.ret false
+  
+  /- [no_nested_borrows::test_is_cons] -/
+  def test_is_cons_fwd : Result Unit :=
+    do
+      let l := list_t.ListNil
+      let b ←
+        is_cons_fwd Int32 (list_t.ListCons (Int32.ofNatCore 0 (by intlit)) l)
+      if h: not b
+      then Result.fail Error.panic
+      else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_is_cons] -/
+  #assert (test_is_cons_fwd == .ret ())
+  
+  /- [no_nested_borrows::split_list] -/
+  def split_list_fwd (T : Type) (l : list_t T) : Result (T × (list_t T)) :=
+    match h: l with
+    | list_t.ListCons hd tl => Result.ret (hd, tl)
+    | list_t.ListNil => Result.fail Error.panic
+  
+  /- [no_nested_borrows::test_split_list] -/
+  def test_split_list_fwd : Result Unit :=
+    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 h: not (hd = (Int32.ofNatCore 0 (by intlit)))
+      then Result.fail Error.panic
+      else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_split_list] -/
+  #assert (test_split_list_fwd == .ret ())
+  
+  /- [no_nested_borrows::choose] -/
+  def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+    if h: b
+    then Result.ret x
+    else Result.ret y
+  
+  /- [no_nested_borrows::choose] -/
+  def choose_back
+    (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
+    if h: 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 h: 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 h: not (x = (Int32.ofNatCore 1 (by intlit)))
+          then Result.fail Error.panic
+          else
+            if h: not (y = (Int32.ofNatCore 0 (by intlit)))
+            then Result.fail Error.panic
+            else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::choose_test] -/
+  #assert (choose_test_fwd == .ret ())
+  
+  /- [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 h: 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 h: l 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_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 h: l 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_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 h: l 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_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 h: li with
+    | list_t.ListCons hd tl => list_rev_aux_fwd T tl (list_t.ListCons hd lo)
+    | list_t.ListNil => Result.ret lo
+  
+  /- [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 h: 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 h: 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 h: 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 h: 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 h: 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 h: 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 h: not (i5 = (Int32.ofNatCore 2 (by intlit)))
+                              then Result.fail Error.panic
+                              else Result.ret ()
+  
+  /- Unit test for [no_nested_borrows::test_list_functions] -/
+  #assert (test_list_functions_fwd == .ret ())
+  
+  /- [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 h: 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 h: 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 h: not (i1 = (UInt64.ofNatCore 1 (by intlit)))
+              then Result.fail Error.panic
+              else
+                do
+                  let swp ← new_pair1_fwd
+                  if h: not (swp.struct_with_pair_p.pair_x =
+                    (UInt32.ofNatCore 1 (by intlit)))
+                  then Result.fail Error.panic
+                  else Result.ret ()
+  
+  /- 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 h: not (y = (UInt32.ofNatCore 0 (by intlit)))
+    then Result.fail Error.panic
+    else Result.ret (UInt32.ofNatCore 2 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool1] -/
+  def test_shared_borrow_bool1_fwd (b : Bool) : Result UInt32 :=
+    if h: b
+    then Result.ret (UInt32.ofNatCore 0 (by intlit))
+    else Result.ret (UInt32.ofNatCore 1 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_bool2] -/
+  def test_shared_borrow_bool2_fwd : Result UInt32 :=
+    Result.ret (UInt32.ofNatCore 0 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_enum1] -/
+  def test_shared_borrow_enum1_fwd (l : list_t UInt32) : Result UInt32 :=
+    match h: l with
+    | list_t.ListCons i l0 => Result.ret (UInt32.ofNatCore 1 (by intlit))
+    | list_t.ListNil => Result.ret (UInt32.ofNatCore 0 (by intlit))
+  
+  /- [no_nested_borrows::test_shared_borrow_enum2] -/
+  def test_shared_borrow_enum2_fwd : Result UInt32 :=
+    Result.ret (UInt32.ofNatCore 0 (by intlit))
+  
diff --git a/tests/lean/misc-no_nested_borrows/lakefile.lean b/tests/lean/misc-no_nested_borrows/lakefile.lean
new file mode 100644
index 00000000..e4460813
--- /dev/null
+++ b/tests/lean/misc-no_nested_borrows/lakefile.lean
@@ -0,0 +1,18 @@
+import Lake
+open Lake DSL
+
+require mathlib from git
+  "https://github.com/leanprover-community/mathlib4.git"
+
+package «no_nested_borrows» {
+  -- add package configuration options here
+}
+
+lean_lib «Base» {
+  -- add library configuration options here
+}
+
+lean_lib «NoNestedBorrows» {
+  -- add library configuration options here
+}
+