Make minor modifications and regenerate the Lean files

3 files changed, 386 insertions, 364 deletions

diff --git a/tests/lean/misc/loops/Base/Primitives.lean b/tests/lean/misc/loops/Base/Primitives.lean
index 79958d94..5b64e908 100644
--- a/tests/lean/misc/loops/Base/Primitives.lean
+++ b/tests/lean/misc/loops/Base/Primitives.lean
@@ -9,74 +9,79 @@ import Mathlib.Tactic.RunCmd
 
 -- Results & monadic combinators
 
--- TODO: use syntactic conventions and capitalize error, result, etc.
-
-inductive error where
-   | assertionFailure: error
-   | integerOverflow: error
-   | arrayOutOfBounds: error
-   | maximumSizeExceeded: error
-   | panic: error
+inductive Error where
+   | assertionFailure: Error
+   | integerOverflow: Error
+   | arrayOutOfBounds: Error
+   | maximumSizeExceeded: Error
+   | panic: Error
 deriving Repr, BEq
 
-open error
+open Error
 
-inductive result (α : Type u) where
-  | ret (v: α): result α
-  | fail (e: error): result α 
+inductive Result (α : Type u) where
+  | ret (v: α): Result α
+  | fail (e: Error): Result α
 deriving Repr, BEq
 
-open result
+open Result
 
 /- HELPERS -/
 
--- TODO: is there automated syntax for these discriminators?
-def is_ret {α: Type} (r: result α): Bool :=
+def ret? {α: Type} (r: Result α): Bool :=
   match r with
-  | result.ret _ => true
-  | result.fail _ => false
+  | Result.ret _ => true
+  | Result.fail _ => false
 
-def massert (b:Bool) : result Unit :=
+def massert (b:Bool) : Result Unit :=
   if b then .ret () else fail assertionFailure
 
-def eval_global {α: Type} (x: result α) (_: is_ret x): α :=
+def eval_global {α: Type} (x: Result α) (_: ret? x): α :=
   match x with
-  | result.fail _ => by contradiction
-  | result.ret x => x
+  | Result.fail _ => by contradiction
+  | Result.ret x => x
 
 /- DO-DSL SUPPORT -/
 
-def bind (x: result α) (f: α -> result β) : result β :=
+def bind (x: Result α) (f: α -> Result β) : Result β :=
   match x with
   | ret v  => f v 
   | fail v => fail v
 
--- Allows using result in do-blocks
-instance : Bind result where
+-- Allows using Result in do-blocks
+instance : Bind Result where
   bind := bind
 
 -- Allows using return x in do-blocks
-instance : Pure result where
+instance : Pure Result where
   pure := fun x => ret x
 
 /- CUSTOM-DSL SUPPORT -/
 
--- Let-binding the result of a monadic operation is oftentimes not sufficient,
+-- Let-binding the Result of a monadic operation is oftentimes not sufficient,
 -- because we may need a hypothesis for equational reasoning in the scope. We
 -- rely on subtype, and a custom let-binding operator, in effect recreating our
 -- own variant of the do-dsl
 
-def result.attach : (o : result α) → result { x : α // o = ret x }
+def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
+  match o with
   | .ret x => .ret ⟨x, rfl⟩
-  | .fail e   => .fail e
+  | .fail e => .fail e
 
-macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+macro "let" e:term " ⟵ " f:term : doElem =>
+  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
 
--- Silly example of the kind of reasoning that this notation enables
+-- TODO: any way to factorize both definitions?
+macro "let" e:term " <-- " f:term : doElem =>
+  `(doElem| let ⟨$e, h⟩ ← Result.attach $f)
+
+-- We call the hypothesis `h`, in effect making it unavailable to the user
+-- (because too much shadowing). But in practice, once can use the French single
+-- quote notation (input with f< and f>), where `‹ h ›` finds a suitable
+-- hypothesis in the context, this is equivalent to `have x: h := by assumption in x`
 #eval do
-  let h: y <-- .ret (0: Nat)
-  let _: y = 0 := by cases h; decide
+  let y <-- .ret (0: Nat)
+  let _: y = 0 := by cases ‹ ret 0 = ret y › ; decide
   let r: { x: Nat // x = 0 } := ⟨ y, by assumption ⟩
   .ret r
 
@@ -84,36 +89,27 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
 -- MACHINE INTEGERS --
 ----------------------
 
--- NOTE: we reuse the USize type from prelude.lean, because at least we know
--- it's defined in an idiomatic style that is going to make proofs easy (and
--- indeed, several proofs here are much shortened compared to Aymeric's earlier
--- attempt.) This is not stricto sensu the *correct* thing to do, because one
--- can query at run-time the value of USize, which we do *not* want to do (we
--- don't know what target we'll run on!), but when the day comes, we'll just
--- define our own USize.
--- ANOTHER NOTE: there is USize.sub but it has wraparound semantics, which is
--- not something we want to define (I think), so we use our own monadic sub (but
--- is it in line with the Rust behavior?)
-
--- TODO: I am somewhat under the impression that subtraction is defined as a
--- total function over nats...? the hypothesis in the if condition is not used
--- in the then-branch which confuses me quite a bit
-
--- TODO: add a refinement for the result (just like vec_push_back below) that
--- explains that the toNat of the result (in the case of success) is the sub of
--- the toNat of the arguments (i.e. intrinsic specification)
--- ... do we want intrinsic specifications for the builtins? that might require
--- some careful type annotations in the monadic notation for clients, but may
--- give us more "for free"
+-- NOTE: we reuse the fixed-width integer types from prelude.lean: UInt8, ...,
+-- USize. They are generally defined in an idiomatic style, except that there is
+-- not a single type class to rule them all (more on that below). The absence of
+-- type class is intentional, and allows the Lean compiler to efficiently map
+-- them to machine integers during compilation.
+
+-- USize is designed properly: you cannot reduce `getNumBits` using the
+-- simplifier, meaning that proofs do not depend on the compile-time value of
+-- USize.size. (Lean assumes 32 or 64-bit platforms, and Rust doesn't really
+-- support, at least officially, 16-bit microcontrollers, so this seems like a
+-- fine design decision for now.)
 
 -- Note from Chris Bailey: "If there's more than one salient property of your
 -- definition then the subtyping strategy might get messy, and the property part
 -- of a subtype is less discoverable by the simplifier or tactics like
--- library_search." Try to settle this with a Lean expert on what is the most
--- productive way to go about this?
+-- library_search." So, we will not add refinements on the return values of the
+-- operations defined on Primitives, but will rather rely on custom lemmas to
+-- invert on possible return values of the primitive operations.
 
--- One needs to perform a little bit of reasoning in order to successfully
--- inject constants into USize, so we provide a general-purpose macro
+-- Machine integer constants, done via `ofNatCore`, which requires a proof that
+-- the `Nat` fits within the desired integer type. We provide a custom tactic.
 
 syntax "intlit" : tactic
 
@@ -129,12 +125,21 @@ macro_rules
 -- Also works for other integer types (at the expense of a needless disjunction)
 #eval UInt32.ofNatCore 0 (by intlit)
 
+-- The machine integer operations (e.g. sub) are always total, which is not what
+-- we want. We therefore define "checked" variants, below. Note that we add a
+-- tiny bit of complexity for the USize variant: we first check whether the
+-- result is < 2^32; if it is, we can compute the definition, rather than
+-- returning a term that is computationally stuck (the comparison to USize.size
+-- cannot reduce at compile-time, per the remark about regarding `getNumBits`).
+-- This is useful for the various #asserts that we want to reduce at
+-- type-checking time.
+
 -- Further thoughts: look at what has been done here:
 -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/Fin/Basic.lean
 -- and
 -- https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Data/UInt.lean
 -- which both contain a fair amount of reasoning already!
-def USize.checked_sub (n: USize) (m: USize): result USize :=
+def USize.checked_sub (n: USize) (m: USize): Result USize :=
   -- NOTE: the test USize.toNat n - m >= 0 seems to always succeed?
   if n >= m then
     let n' := USize.toNat n
@@ -150,18 +155,19 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
   else
     fail integerOverflow
 
-def USize.checked_add (n: USize) (m: USize): result USize :=
-  if h: n.val.val + m.val.val <= 4294967295 then
-    .ret ⟨ n.val.val + m.val.val, by
-      have h': 4294967295 < USize.size := by intlit
-      apply Nat.lt_of_le_of_lt h h'
-    ⟩
-  else if h: n.val + m.val < USize.size then
+@[simp]
+theorem usize_fits (n: Nat) (h: n <= 4294967295): n < USize.size :=
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => Nat.lt_of_le_of_lt h (by decide)
+  | _, Or.inr rfl => Nat.lt_of_le_of_lt h (by decide)
+
+def USize.checked_add (n: USize) (m: USize): Result USize :=
+  if h: n.val + m.val < USize.size then
     .ret ⟨ n.val + m.val, h ⟩
   else
     .fail integerOverflow
 
-def USize.checked_rem (n: USize) (m: USize): result USize :=
+def USize.checked_rem (n: USize) (m: USize): Result USize :=
   if h: m > 0 then
     .ret ⟨ n.val % m.val, by
       have h1: ↑m.val < USize.size := m.val.isLt
@@ -171,18 +177,13 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
   else
     .fail integerOverflow
 
-def USize.checked_mul (n: USize) (m: USize): result USize :=
-    if h: n.val.val * m.val.val <= 4294967295 then
-    .ret ⟨ n.val.val * m.val.val, by
-      have h': 4294967295 < USize.size := by intlit
-      apply Nat.lt_of_le_of_lt h h'
-    ⟩
-  else if h: n.val * m.val < USize.size then
+def USize.checked_mul (n: USize) (m: USize): Result USize :=
+  if h: n.val * m.val < USize.size then
     .ret ⟨ n.val * m.val, h ⟩
   else
     .fail integerOverflow
 
-def USize.checked_div (n: USize) (m: USize): result USize :=
+def USize.checked_div (n: USize) (m: USize): Result USize :=
   if m > 0 then
     .ret ⟨ n.val / m.val, by
       have h1: ↑n.val < USize.size := n.val.isLt
@@ -192,6 +193,19 @@ def USize.checked_div (n: USize) (m: USize): result USize :=
   else
     .fail integerOverflow
 
+-- Test behavior...
+#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
+
+#eval USize.checked_sub 20 10
+-- NOTE: compare with concrete behavior here, which I do not think we want
+#eval USize.sub 0 1
+#eval UInt8.add 255 255
+
+-- We now define a type class that subsumes the various machine integer types, so
+-- as to write a concise definition for scalar_cast, rather than exhaustively
+-- enumerating all of the possible pairs. We remark that Rust has sane semantics
+-- and fails if a cast operation would involve a truncation or modulo.
+
 class MachineInteger (t: Type) where
   size: Nat
   val: t -> Fin size
@@ -209,30 +223,24 @@ run_cmd
     end $typeName
   ))
 
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+-- Aeneas only instantiates the destination type (`src` is implicit). We rely on
+-- Lean to infer `src`.
+
+def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): Result dst :=
   if h: MachineInteger.val x < MachineInteger.size dst then
     .ret (MachineInteger.ofNatCore (MachineInteger.val x).val h)
   else
     .fail integerOverflow
 
-
--- Test behavior...
-#eval assert! USize.checked_sub 10 20 == fail integerOverflow; 0
-
-#eval USize.checked_sub 20 10
--- NOTE: compare with concrete behavior here, which I do not think we want
-#eval USize.sub 0 1
-#eval UInt8.add 255 255
-
 -------------
 -- VECTORS --
 -------------
 
 -- Note: unlike F*, Lean seems to use strict upper bounds (e.g. USize.size)
 -- rather than maximum values (usize_max).
-def vec (α : Type u) := { l : List α // List.length l < USize.size }
+def Vec (α : Type u) := { l : List α // List.length l < USize.size }
 
-def vec_new (α : Type u): vec α := ⟨ [], by {
+def vec_new (α : Type u): Vec α := ⟨ [], by {
   match USize.size, usize_size_eq with
   | _, Or.inl rfl => simp
   | _, Or.inr rfl => simp
@@ -240,20 +248,20 @@ def vec_new (α : Type u): vec α := ⟨ [], by {
 
 #check vec_new
 
-def vec_len (α : Type u) (v : vec α) : USize :=
+def vec_len (α : Type u) (v : Vec α) : USize :=
   let ⟨ v, l ⟩ := v
   USize.ofNatCore (List.length v) l
 
 #eval vec_len Nat (vec_new Nat)
  
-def vec_push_fwd (α : Type u) (_ : vec α) (_ : α) : Unit := ()
+def vec_push_fwd (α : Type u) (_ : Vec α) (_ : α) : Unit := ()
 
 -- NOTE: old version trying to use a subtype notation, but probably better to
--- leave result elimination to auxiliary lemmas with suitable preconditions
+-- leave Result elimination to auxiliary lemmas with suitable preconditions
 -- TODO: I originally wrote `List.length v.val < USize.size - 1`; how can one
 -- make the proof work in that case? Probably need to import tactics from
 -- mathlib to deal with inequalities... would love to see an example.
-def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec α) //
+def vec_push_back_old (α : Type u) (v : Vec α) (x : α) : { res: Result (Vec α) //
   match res with | fail _ => True | ret v' => List.length v'.val = List.length v.val + 1}
   :=
   if h : List.length v.val + 1 < USize.size then
@@ -272,12 +280,12 @@ def vec_push_back_old (α : Type u) (v : vec α) (x : α) : { res: result (vec �
   -- annotate `x`, which relieves us of having to write `.val` on the right-hand
   -- side of the monadic let.
   let v := vec_new Nat
-  let x: vec Nat ← (vec_push_back_old Nat v 1: result (vec Nat)) -- WHY do we need the type annotation here?
+  let x: Vec Nat ← (vec_push_back_old Nat v 1: Result (Vec Nat)) -- WHY do we need the type annotation here?
   -- TODO: strengthen post-condition above and do a demo to show that we can
   -- safely eliminate the `fail` case
   return (vec_len Nat x)
 
-def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
+def vec_push_back (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
   :=
   if h : List.length v.val + 1 <= 4294967295 then
     return ⟨ List.concat v.val x,
@@ -295,13 +303,13 @@ def vec_push_back (α : Type u) (v : vec α) (x : α) : result (vec α)
   else
     fail maximumSizeExceeded
 
-def vec_insert_fwd (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+def vec_insert_fwd (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit :=
   if i.val < List.length v.val then
     .ret ()
   else
     .fail arrayOutOfBounds
 
-def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+def vec_insert_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) :=
   if i.val < List.length v.val then
     .ret ⟨ List.set v.val i.val x, by
       have h: List.length v.val < USize.size := v.property
@@ -311,25 +319,25 @@ def vec_insert_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α
   else
     .fail arrayOutOfBounds
 
-def vec_index_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
   if h: i.val < List.length v.val then
     .ret (List.get v.val ⟨i.val, h⟩)
   else
     .fail arrayOutOfBounds
 
-def vec_index_back (α : Type u) (v: vec α) (i: USize) (_: α): result Unit :=
+def vec_index_back (α : Type u) (v: Vec α) (i: USize) (_: α): Result Unit :=
   if i.val < List.length v.val then
     .ret ()
   else
     .fail arrayOutOfBounds
 
-def vec_index_mut_fwd (α : Type u) (v: vec α) (i: USize): result α :=
+def vec_index_mut_fwd (α : Type u) (v: Vec α) (i: USize): Result α :=
   if h: i.val < List.length v.val then
     .ret (List.get v.val ⟨i.val, h⟩)
   else
     .fail arrayOutOfBounds
 
-def vec_index_mut_back (α : Type u) (v: vec α) (i: USize) (x: α): result (vec α) :=
+def vec_index_mut_back (α : Type u) (v: Vec α) (i: USize) (x: α): Result (Vec α) :=
   if i.val < List.length v.val then
     .ret ⟨ List.set v.val i.val x, by
       have h: List.length v.val < USize.size := v.property
@@ -349,6 +357,10 @@ def mem_replace_fwd (a : Type) (x : a) (_ : a) : a :=
 def mem_replace_back (a : Type) (_ : a) (y : a) : a :=
   y
 
+/-- Aeneas-translated function -- useful to reduce non-recursive definitions.
+ Use with `simp [ aeneas ]` -/
+register_simp_attr aeneas
+
 --------------------
 -- ASSERT COMMAND --
 --------------------
@@ -358,16 +370,23 @@ open Lean Elab Command Term Meta
 syntax (name := assert) "#assert" term: command
 
 @[command_elab assert]
+unsafe
 def assertImpl : CommandElab := fun (_stx: Syntax) => do
-  logInfo "Reducing and asserting: "
-  logInfo _stx[1]
   runTermElabM (fun _ => do
-    let e ← Term.elabTerm _stx[1] none
-    logInfo (Expr.dbgToString e)
-    -- How to evaluate the term and compare the result to true?
+    let r ← evalTerm Bool (mkConst ``Bool) _stx[1]
+    if not r then
+      logInfo "Assertion failed for: "
+      logInfo _stx[1]
+      logError "Expression reduced to false"
     pure ())
-  -- logInfo (Expr.dbgToString (``true))
-  -- throwError "TODO: assert"
 
 #eval 2 == 2
 #assert (2 == 2)
+
+-------------------
+-- SANITY CHECKS --
+-------------------
+
+-- TODO: add more once we have signed integers
+
+#assert (USize.checked_rem 1 2 == .ret 1)
diff --git a/tests/lean/misc/loops/Loops/Clauses/Template.lean b/tests/lean/misc/loops/Loops/Clauses/Template.lean
index 3c0f2f7c..d74f71e1 100644
--- a/tests/lean/misc/loops/Loops/Clauses/Template.lean
+++ b/tests/lean/misc/loops/Loops/Clauses/Template.lean
@@ -35,7 +35,7 @@ macro_rules
 | `(tactic| sum_with_shared_borrows_loop_decreases $max $i $s) =>`(tactic| sorry)
 
 /- [loops::clear]: termination measure -/
-@[simp] def clear_loop_terminates (v : vec UInt32) (i : USize) := (v, i)
+@[simp] def clear_loop_terminates (v : Vec UInt32) (i : USize) := (v, i)
 
 syntax "clear_loop_decreases" term+ : tactic
 
diff --git a/tests/lean/misc/loops/Loops/Funs.lean b/tests/lean/misc/loops/Loops/Funs.lean
index 55f0c87d..5a81ebff 100644
--- a/tests/lean/misc/loops/Loops/Funs.lean
+++ b/tests/lean/misc/loops/Loops/Funs.lean
@@ -5,30 +5,30 @@ import Loops.Types
 import Loops.Clauses.Clauses
 
 /- [loops::sum] -/
-def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
-  if i < max
+def sum_loop_fwd (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) :=
+  if h: i < max
   then
     do
-      let s0 <- UInt32.checked_add s i
-      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      let s0 ← UInt32.checked_add s i
+      let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
       sum_loop_fwd max i0 s0
   else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
 termination_by sum_loop_fwd max i s => sum_loop_terminates max i s
 decreasing_by sum_loop_decreases max i s
 
 /- [loops::sum] -/
-def sum_fwd (max : UInt32) : result UInt32 :=
+def sum_fwd (max : UInt32) : Result UInt32 :=
   sum_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
     (UInt32.ofNatCore 0 (by intlit))
 
 /- [loops::sum_with_mut_borrows] -/
 def sum_with_mut_borrows_loop_fwd
-  (max : UInt32) (mi : UInt32) (ms : UInt32) : (result UInt32) :=
-  if mi < max
+  (max : UInt32) (mi : UInt32) (ms : UInt32) : (Result UInt32) :=
+  if h: mi < max
   then
     do
-      let ms0 <- UInt32.checked_add ms mi
-      let mi0 <- UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
+      let ms0 ← UInt32.checked_add ms mi
+      let mi0 ← UInt32.checked_add mi (UInt32.ofNatCore 1 (by intlit))
       sum_with_mut_borrows_loop_fwd max mi0 ms0
   else UInt32.checked_mul ms (UInt32.ofNatCore 2 (by intlit))
 termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
@@ -36,18 +36,18 @@ termination_by sum_with_mut_borrows_loop_fwd max mi ms =>
 decreasing_by sum_with_mut_borrows_loop_decreases max mi ms
 
 /- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_fwd (max : UInt32) : result UInt32 :=
+def sum_with_mut_borrows_fwd (max : UInt32) : Result UInt32 :=
   sum_with_mut_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
     (UInt32.ofNatCore 0 (by intlit))
 
 /- [loops::sum_with_shared_borrows] -/
 def sum_with_shared_borrows_loop_fwd
-  (max : UInt32) (i : UInt32) (s : UInt32) : (result UInt32) :=
-  if i < max
+  (max : UInt32) (i : UInt32) (s : UInt32) : (Result UInt32) :=
+  if h: i < max
   then
     do
-      let i0 <- UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
-      let s0 <- UInt32.checked_add s i0
+      let i0 ← UInt32.checked_add i (UInt32.ofNatCore 1 (by intlit))
+      let s0 ← UInt32.checked_add s i0
       sum_with_shared_borrows_loop_fwd max i0 s0
   else UInt32.checked_mul s (UInt32.ofNatCore 2 (by intlit))
 termination_by sum_with_shared_borrows_loop_fwd max i s =>
@@ -55,271 +55,272 @@ termination_by sum_with_shared_borrows_loop_fwd max i s =>
 decreasing_by sum_with_shared_borrows_loop_decreases max i s
 
 /- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_fwd (max : UInt32) : result UInt32 :=
+def sum_with_shared_borrows_fwd (max : UInt32) : Result UInt32 :=
   sum_with_shared_borrows_loop_fwd max (UInt32.ofNatCore 0 (by intlit))
     (UInt32.ofNatCore 0 (by intlit))
 
 /- [loops::clear] -/
-def clear_loop_fwd_back (v : vec UInt32) (i : USize) : (result (vec UInt32)) :=
+def clear_loop_fwd_back (v : Vec UInt32) (i : USize) : (Result (Vec UInt32)) :=
   let i0 := vec_len UInt32 v
-  if i < i0
+  if h: i < i0
   then
     do
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
-      let v0 <- vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit))
+      let i1 ← USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let v0 ← vec_index_mut_back UInt32 v i (UInt32.ofNatCore 0 (by intlit))
       clear_loop_fwd_back v0 i1
-  else result.ret v
+  else Result.ret v
 termination_by clear_loop_fwd_back v i => clear_loop_terminates v i
 decreasing_by clear_loop_decreases v i
 
 /- [loops::clear] -/
-def clear_fwd_back (v : vec UInt32) : result (vec UInt32) :=
+def clear_fwd_back (v : Vec UInt32) : Result (Vec UInt32) :=
   clear_loop_fwd_back v (USize.ofNatCore 0 (by intlit))
 
 /- [loops::list_mem] -/
-def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (result Bool) :=
-  match ls with
+def list_mem_loop_fwd (x : UInt32) (ls : list_t UInt32) : (Result Bool) :=
+  match h: ls with
   | list_t.ListCons y tl =>
-    if y = x
-    then result.ret true
+    if h: y = x
+    then Result.ret true
     else list_mem_loop_fwd x tl
-  | list_t.ListNil => result.ret false
+  | list_t.ListNil => Result.ret false
 termination_by list_mem_loop_fwd x ls => list_mem_loop_terminates x ls
 decreasing_by list_mem_loop_decreases x ls
 
 /- [loops::list_mem] -/
-def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : result Bool :=
+def list_mem_fwd (x : UInt32) (ls : list_t UInt32) : Result Bool :=
   list_mem_loop_fwd x ls
 
 /- [loops::list_nth_mut_loop] -/
 def list_nth_mut_loop_loop_fwd
-  (T : Type) (ls : list_t T) (i : UInt32) : (result T) :=
-  match ls with
+  (T : Type) (ls : list_t T) (i : UInt32) : (Result T) :=
+  match h: ls with
   | list_t.ListCons x tl =>
-    if i = (UInt32.ofNatCore 0 (by intlit))
-    then result.ret x
+    if h: i = (UInt32.ofNatCore 0 (by intlit))
+    then Result.ret x
     else
       do
-        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
         list_nth_mut_loop_loop_fwd T tl i0
-  | list_t.ListNil => result.fail error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_loop_fwd ls i =>
   list_nth_mut_loop_loop_terminates T ls i
 decreasing_by list_nth_mut_loop_loop_decreases ls i
 
 /- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+def list_nth_mut_loop_fwd (T : Type) (ls : list_t T) (i : UInt32) : Result T :=
   list_nth_mut_loop_loop_fwd T ls i
 
 /- [loops::list_nth_mut_loop] -/
 def list_nth_mut_loop_loop_back
-  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (result (list_t T)) :=
-  match ls with
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : (Result (list_t T)) :=
+  match h: ls with
   | list_t.ListCons x tl =>
-    if i = (UInt32.ofNatCore 0 (by intlit))
-    then result.ret (list_t.ListCons ret0 tl)
+    if h: i = (UInt32.ofNatCore 0 (by intlit))
+    then Result.ret (list_t.ListCons ret0 tl)
     else
       do
-        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        let tl0 <- list_nth_mut_loop_loop_back T tl i0 ret0
-        result.ret (list_t.ListCons x tl0)
-  | list_t.ListNil => result.fail error.panic
+        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+        Result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_loop_back ls i ret0 =>
   list_nth_mut_loop_loop_terminates T ls i
 decreasing_by list_nth_mut_loop_loop_decreases ls i
 
 /- [loops::list_nth_mut_loop] -/
 def list_nth_mut_loop_back
-  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) :=
   list_nth_mut_loop_loop_back T ls i ret0
 
 /- [loops::list_nth_shared_loop] -/
 def list_nth_shared_loop_loop_fwd
-  (T : Type) (ls : list_t T) (i : UInt32) : (result T) :=
-  match ls with
+  (T : Type) (ls : list_t T) (i : UInt32) : (Result T) :=
+  match h: ls with
   | list_t.ListCons x tl =>
-    if i = (UInt32.ofNatCore 0 (by intlit))
-    then result.ret x
+    if h: i = (UInt32.ofNatCore 0 (by intlit))
+    then Result.ret x
     else
       do
-        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
         list_nth_shared_loop_loop_fwd T tl i0
-  | list_t.ListNil => result.fail error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_loop_loop_fwd ls i =>
   list_nth_shared_loop_loop_terminates T ls i
 decreasing_by list_nth_shared_loop_loop_decreases ls i
 
 /- [loops::list_nth_shared_loop] -/
 def list_nth_shared_loop_fwd
-  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  (T : Type) (ls : list_t T) (i : UInt32) : Result T :=
   list_nth_shared_loop_loop_fwd T ls i
 
 /- [loops::get_elem_mut] -/
-def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (result USize) :=
-  match ls with
+def get_elem_mut_loop_fwd (x : USize) (ls : list_t USize) : (Result USize) :=
+  match h: ls with
   | list_t.ListCons y tl =>
-    if y = x
-    then result.ret y
+    if h: y = x
+    then Result.ret y
     else get_elem_mut_loop_fwd x tl
-  | list_t.ListNil => result.fail error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by get_elem_mut_loop_fwd x ls => get_elem_mut_loop_terminates x ls
 decreasing_by get_elem_mut_loop_decreases x ls
 
 /- [loops::get_elem_mut] -/
-def get_elem_mut_fwd (slots : vec (list_t USize)) (x : USize) : result USize :=
+def get_elem_mut_fwd (slots : Vec (list_t USize)) (x : USize) : Result USize :=
   do
-    let l <-
+    let l ←
       vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
     get_elem_mut_loop_fwd x l
 
 /- [loops::get_elem_mut] -/
 def get_elem_mut_loop_back
-  (x : USize) (ls : list_t USize) (ret0 : USize) : (result (list_t USize)) :=
-  match ls with
+  (x : USize) (ls : list_t USize) (ret0 : USize) : (Result (list_t USize)) :=
+  match h: ls with
   | list_t.ListCons y tl =>
-    if y = x
-    then result.ret (list_t.ListCons ret0 tl)
+    if h: y = x
+    then Result.ret (list_t.ListCons ret0 tl)
     else
       do
-        let tl0 <- get_elem_mut_loop_back x tl ret0
-        result.ret (list_t.ListCons y tl0)
-  | list_t.ListNil => result.fail error.panic
+        let tl0 ← get_elem_mut_loop_back x tl ret0
+        Result.ret (list_t.ListCons y tl0)
+  | list_t.ListNil => Result.fail Error.panic
 termination_by get_elem_mut_loop_back x ls ret0 =>
   get_elem_mut_loop_terminates x ls
 decreasing_by get_elem_mut_loop_decreases x ls
 
 /- [loops::get_elem_mut] -/
 def get_elem_mut_back
-  (slots : vec (list_t USize)) (x : USize) (ret0 : USize) :
-  result (vec (list_t USize))
+  (slots : Vec (list_t USize)) (x : USize) (ret0 : USize) :
+  Result (Vec (list_t USize))
   :=
   do
-    let l <-
+    let l ←
       vec_index_mut_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
-    let l0 <- get_elem_mut_loop_back x l ret0
+    let l0 ← get_elem_mut_loop_back x l ret0
     vec_index_mut_back (list_t USize) slots (USize.ofNatCore 0 (by intlit)) l0
 
 /- [loops::get_elem_shared] -/
 def get_elem_shared_loop_fwd
-  (x : USize) (ls : list_t USize) : (result USize) :=
-  match ls with
+  (x : USize) (ls : list_t USize) : (Result USize) :=
+  match h: ls with
   | list_t.ListCons y tl =>
-    if y = x
-    then result.ret y
+    if h: y = x
+    then Result.ret y
     else get_elem_shared_loop_fwd x tl
-  | list_t.ListNil => result.fail error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by get_elem_shared_loop_fwd x ls =>
   get_elem_shared_loop_terminates x ls
 decreasing_by get_elem_shared_loop_decreases x ls
 
 /- [loops::get_elem_shared] -/
 def get_elem_shared_fwd
-  (slots : vec (list_t USize)) (x : USize) : result USize :=
+  (slots : Vec (list_t USize)) (x : USize) : Result USize :=
   do
-    let l <- vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
+    let l ←
+      vec_index_fwd (list_t USize) slots (USize.ofNatCore 0 (by intlit))
     get_elem_shared_loop_fwd x l
 
 /- [loops::id_mut] -/
-def id_mut_fwd (T : Type) (ls : list_t T) : result (list_t T) :=
-  result.ret ls
+def id_mut_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
+  Result.ret ls
 
 /- [loops::id_mut] -/
 def id_mut_back
-  (T : Type) (ls : list_t T) (ret0 : list_t T) : result (list_t T) :=
-  result.ret ret0
+  (T : Type) (ls : list_t T) (ret0 : list_t T) : Result (list_t T) :=
+  Result.ret ret0
 
 /- [loops::id_shared] -/
-def id_shared_fwd (T : Type) (ls : list_t T) : result (list_t T) :=
-  result.ret ls
+def id_shared_fwd (T : Type) (ls : list_t T) : Result (list_t T) :=
+  Result.ret ls
 
 /- [loops::list_nth_mut_loop_with_id] -/
 def list_nth_mut_loop_with_id_loop_fwd
-  (T : Type) (i : UInt32) (ls : list_t T) : (result T) :=
-  match ls with
+  (T : Type) (i : UInt32) (ls : list_t T) : (Result T) :=
+  match h: ls with
   | list_t.ListCons x tl =>
-    if i = (UInt32.ofNatCore 0 (by intlit))
-    then result.ret x
+    if h: i = (UInt32.ofNatCore 0 (by intlit))
+    then Result.ret x
     else
       do
-        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
         list_nth_mut_loop_with_id_loop_fwd T i0 tl
-  | list_t.ListNil => result.fail error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_with_id_loop_fwd i ls =>
   list_nth_mut_loop_with_id_loop_terminates T i ls
 decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
 
 /- [loops::list_nth_mut_loop_with_id] -/
 def list_nth_mut_loop_with_id_fwd
-  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  (T : Type) (ls : list_t T) (i : UInt32) : Result T :=
   do
-    let ls0 <- id_mut_fwd T ls
+    let ls0 ← id_mut_fwd T ls
     list_nth_mut_loop_with_id_loop_fwd T i ls0
 
 /- [loops::list_nth_mut_loop_with_id] -/
 def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (result (list_t T)) :=
-  match ls with
+  (T : Type) (i : UInt32) (ls : list_t T) (ret0 : T) : (Result (list_t T)) :=
+  match h: ls with
   | list_t.ListCons x tl =>
-    if i = (UInt32.ofNatCore 0 (by intlit))
-    then result.ret (list_t.ListCons ret0 tl)
+    if h: i = (UInt32.ofNatCore 0 (by intlit))
+    then Result.ret (list_t.ListCons ret0 tl)
     else
       do
-        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-        let tl0 <- list_nth_mut_loop_with_id_loop_back T i0 tl ret0
-        result.ret (list_t.ListCons x tl0)
-  | list_t.ListNil => result.fail error.panic
+        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        Result.ret (list_t.ListCons x tl0)
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_with_id_loop_back i ls ret0 =>
   list_nth_mut_loop_with_id_loop_terminates T i ls
 decreasing_by list_nth_mut_loop_with_id_loop_decreases i ls
 
 /- [loops::list_nth_mut_loop_with_id] -/
 def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : result (list_t T) :=
+  (T : Type) (ls : list_t T) (i : UInt32) (ret0 : T) : Result (list_t T) :=
   do
-    let ls0 <- id_mut_fwd T ls
-    let l <- list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+    let ls0 ← id_mut_fwd T ls
+    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
     id_mut_back T ls l
 
 /- [loops::list_nth_shared_loop_with_id] -/
 def list_nth_shared_loop_with_id_loop_fwd
-  (T : Type) (i : UInt32) (ls : list_t T) : (result T) :=
-  match ls with
+  (T : Type) (i : UInt32) (ls : list_t T) : (Result T) :=
+  match h: ls with
   | list_t.ListCons x tl =>
-    if i = (UInt32.ofNatCore 0 (by intlit))
-    then result.ret x
+    if h: i = (UInt32.ofNatCore 0 (by intlit))
+    then Result.ret x
     else
       do
-        let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+        let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
         list_nth_shared_loop_with_id_loop_fwd T i0 tl
-  | list_t.ListNil => result.fail error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_loop_with_id_loop_fwd i ls =>
   list_nth_shared_loop_with_id_loop_terminates T i ls
 decreasing_by list_nth_shared_loop_with_id_loop_decreases i ls
 
 /- [loops::list_nth_shared_loop_with_id] -/
 def list_nth_shared_loop_with_id_fwd
-  (T : Type) (ls : list_t T) (i : UInt32) : result T :=
+  (T : Type) (ls : list_t T) (i : UInt32) : Result T :=
   do
-    let ls0 <- id_shared_fwd T ls
+    let ls0 ← id_shared_fwd T ls
     list_nth_shared_loop_with_id_loop_fwd T i ls0
 
 /- [loops::list_nth_mut_loop_pair] -/
 def list_nth_mut_loop_pair_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_pair_loop_fwd ls0 ls1 i =>
   list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
@@ -327,28 +328,28 @@ decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_loop_pair] -/
 def list_nth_mut_loop_pair_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_mut_loop_pair] -/
 def list_nth_mut_loop_pair_loop_back'a
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  (result (list_t T))
+  (Result (list_t T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (list_t.ListCons ret0 tl0)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (list_t.ListCons ret0 tl0)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl00 <- list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x0 tl00)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          Result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret0 =>
   list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
@@ -356,28 +357,28 @@ decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_loop_pair] -/
 def list_nth_mut_loop_pair_back'a
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  result (list_t T)
+  Result (list_t T)
   :=
   list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
 
 /- [loops::list_nth_mut_loop_pair] -/
 def list_nth_mut_loop_pair_loop_back'b
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  (result (list_t T))
+  (Result (list_t T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (list_t.ListCons ret0 tl1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (list_t.ListCons ret0 tl1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl10 <- list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x1 tl10)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          Result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret0 =>
   list_nth_mut_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
@@ -385,27 +386,27 @@ decreasing_by list_nth_mut_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_loop_pair] -/
 def list_nth_mut_loop_pair_back'b
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  result (list_t T)
+  Result (list_t T)
   :=
   list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
 
 /- [loops::list_nth_shared_loop_pair] -/
 def list_nth_shared_loop_pair_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_loop_pair_loop_fwd ls0 ls1 i =>
   list_nth_shared_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
@@ -413,27 +414,27 @@ decreasing_by list_nth_shared_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_shared_loop_pair] -/
 def list_nth_shared_loop_pair_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_mut_loop_pair_merge] -/
 def list_nth_mut_loop_pair_merge_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
   list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -441,31 +442,31 @@ decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_loop_pair_merge] -/
 def list_nth_mut_loop_pair_merge_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_mut_loop_pair_merge] -/
 def list_nth_mut_loop_pair_merge_loop_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) :
-  (result ((list_t T) × (list_t T)))
+  (Result ((list_t T) × (list_t T)))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
       then
         let (t, t0) := ret0
-        result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
+        Result.ret (list_t.ListCons t tl0, list_t.ListCons t0 tl1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let (tl00, tl10) <-
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let (tl00, tl10) ←
             list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          Result.ret (list_t.ListCons x0 tl00, list_t.ListCons x1 tl10)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
   list_nth_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -473,27 +474,27 @@ decreasing_by list_nth_mut_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_loop_pair_merge] -/
 def list_nth_mut_loop_pair_merge_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : (T × T)) :
-  result ((list_t T) × (list_t T))
+  Result ((list_t T) × (list_t T))
   :=
   list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
 
 /- [loops::list_nth_shared_loop_pair_merge] -/
 def list_nth_shared_loop_pair_merge_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
   list_nth_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -501,27 +502,27 @@ decreasing_by list_nth_shared_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_shared_loop_pair_merge] -/
 def list_nth_shared_loop_pair_merge_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_mut_shared_loop_pair] -/
 def list_nth_mut_shared_loop_pair_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i =>
   list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
@@ -529,28 +530,29 @@ decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_shared_loop_pair] -/
 def list_nth_mut_shared_loop_pair_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_mut_shared_loop_pair] -/
 def list_nth_mut_shared_loop_pair_loop_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  (result (list_t T))
+  (Result (list_t T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (list_t.ListCons ret0 tl0)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (list_t.ListCons ret0 tl0)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl00 <- list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x0 tl00)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret0 =>
   list_nth_mut_shared_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
@@ -558,27 +560,27 @@ decreasing_by list_nth_mut_shared_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_shared_loop_pair] -/
 def list_nth_mut_shared_loop_pair_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  result (list_t T)
+  Result (list_t T)
   :=
   list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
 
 /- [loops::list_nth_mut_shared_loop_pair_merge] -/
 def list_nth_mut_shared_loop_pair_merge_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i =>
   list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -586,29 +588,29 @@ decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_shared_loop_pair_merge] -/
 def list_nth_mut_shared_loop_pair_merge_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_mut_shared_loop_pair_merge] -/
 def list_nth_mut_shared_loop_pair_merge_loop_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  (result (list_t T))
+  (Result (list_t T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (list_t.ListCons ret0 tl0)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (list_t.ListCons ret0 tl0)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl00 <-
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl00 ←
             list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x0 tl00)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          Result.ret (list_t.ListCons x0 tl00)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
   list_nth_mut_shared_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -616,27 +618,27 @@ decreasing_by list_nth_mut_shared_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_mut_shared_loop_pair_merge] -/
 def list_nth_mut_shared_loop_pair_merge_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  result (list_t T)
+  Result (list_t T)
   :=
   list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
 
 /- [loops::list_nth_shared_mut_loop_pair] -/
 def list_nth_shared_mut_loop_pair_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i =>
   list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
@@ -644,28 +646,29 @@ decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_shared_mut_loop_pair] -/
 def list_nth_shared_mut_loop_pair_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_shared_mut_loop_pair] -/
 def list_nth_shared_mut_loop_pair_loop_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  (result (list_t T))
+  (Result (list_t T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (list_t.ListCons ret0 tl1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (list_t.ListCons ret0 tl1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl10 <- list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x1 tl10)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret0 =>
   list_nth_shared_mut_loop_pair_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
@@ -673,27 +676,27 @@ decreasing_by list_nth_shared_mut_loop_pair_loop_decreases ls0 ls1 i
 /- [loops::list_nth_shared_mut_loop_pair] -/
 def list_nth_shared_mut_loop_pair_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  result (list_t T)
+  Result (list_t T)
   :=
   list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
 
 /- [loops::list_nth_shared_mut_loop_pair_merge] -/
 def list_nth_shared_mut_loop_pair_merge_loop_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  (result (T × T))
+  (Result (T × T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (x0, x1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (x0, x1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
           list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i =>
   list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -701,29 +704,29 @@ decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_shared_mut_loop_pair_merge] -/
 def list_nth_shared_mut_loop_pair_merge_fwd
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) :
-  result (T × T)
+  Result (T × T)
   :=
   list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
 
 /- [loops::list_nth_shared_mut_loop_pair_merge] -/
 def list_nth_shared_mut_loop_pair_merge_loop_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  (result (list_t T))
+  (Result (list_t T))
   :=
-  match ls0 with
+  match h: ls0 with
   | list_t.ListCons x0 tl0 =>
-    match ls1 with
+    match h: ls1 with
     | list_t.ListCons x1 tl1 =>
-      if i = (UInt32.ofNatCore 0 (by intlit))
-      then result.ret (list_t.ListCons ret0 tl1)
+      if h: i = (UInt32.ofNatCore 0 (by intlit))
+      then Result.ret (list_t.ListCons ret0 tl1)
       else
         do
-          let i0 <- UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
-          let tl10 <-
+          let i0 ← UInt32.checked_sub i (UInt32.ofNatCore 1 (by intlit))
+          let tl10 ←
             list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          result.ret (list_t.ListCons x1 tl10)
-    | list_t.ListNil => result.fail error.panic
-  | list_t.ListNil => result.fail error.panic
+          Result.ret (list_t.ListCons x1 tl10)
+    | list_t.ListNil => Result.fail Error.panic
+  | list_t.ListNil => Result.fail Error.panic
 termination_by list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret0 =>
   list_nth_shared_mut_loop_pair_merge_loop_terminates T ls0 ls1 i
 decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
@@ -731,7 +734,7 @@ decreasing_by list_nth_shared_mut_loop_pair_merge_loop_decreases ls0 ls1 i
 /- [loops::list_nth_shared_mut_loop_pair_merge] -/
 def list_nth_shared_mut_loop_pair_merge_back
   (T : Type) (ls0 : list_t T) (ls1 : list_t T) (i : UInt32) (ret0 : T) :
-  result (list_t T)
+  Result (list_t T)
   :=
   list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0