From 4828b77847ee981f5c6a1bbad7f8e6ed0e58eb0f Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Thu, 4 Apr 2024 16:08:32 +0200
Subject: Rename Result.ret as Result.ok in the backends

---
 backends/lean/Base/Primitives/Alloc.lean      |   4 +-
 backends/lean/Base/Primitives/ArraySlice.lean |  54 +++++-----
 backends/lean/Base/Primitives/Base.lean       |  30 +++---
 backends/lean/Base/Primitives/Scalar.lean     | 144 +++++++++++++-------------
 backends/lean/Base/Primitives/Vec.lean        |  26 ++---
 5 files changed, 128 insertions(+), 130 deletions(-)

(limited to 'backends/lean/Base/Primitives')

diff --git a/backends/lean/Base/Primitives/Alloc.lean b/backends/lean/Base/Primitives/Alloc.lean
index 1f470fe1..15fe1ff9 100644
--- a/backends/lean/Base/Primitives/Alloc.lean
+++ b/backends/lean/Base/Primitives/Alloc.lean
@@ -11,8 +11,8 @@ namespace boxed -- alloc.boxed
 
 namespace Box -- alloc.boxed.Box
 
-def deref (T : Type) (x : T) : Result T := ret x
-def deref_mut (T : Type) (x : T) : Result (T × (T → Result T)) := ret (x, λ x => ret x)
+def deref (T : Type) (x : T) : Result T := ok x
+def deref_mut (T : Type) (x : T) : Result (T × (T → Result T)) := ok (x, λ x => ok x)
 
 /-- Trait instance -/
 def coreopsDerefInst (Self : Type) :
diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean
index e1a39d40..ef658e1b 100644
--- a/backends/lean/Base/Primitives/ArraySlice.lean
+++ b/backends/lean/Base/Primitives/ArraySlice.lean
@@ -50,7 +50,7 @@ abbrev Array.slice {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i
 def Array.index_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) : Result α :=
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
-  | some x => ret x
+  | some x => ok x
 
 -- For initialization
 def Array.repeat (α : Type u) (n : Usize) (x : α) : Array α n :=
@@ -69,7 +69,7 @@ theorem Array.repeat_spec {α : Type u} (n : Usize) (x : α) :
 @[pspec]
 theorem Array.index_usize_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x, v.index_usize α n i = ret x ∧ x = v.val.index i.val := by
+  ∃ x, v.index_usize α n i = ok x ∧ x = v.val.index i.val := by
   simp only [index_usize]
   -- TODO: dependent rewrite
   have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
@@ -79,12 +79,12 @@ def Array.update_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (x:
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
   | some _ =>
-    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+    ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
 
 @[pspec]
 theorem Array.update_usize_spec {α : Type u} {n : Usize} (v: Array α n) (i: Usize) (x : α)
   (hbound : i.val < v.length) :
-  ∃ nv, v.update_usize α n i x = ret nv ∧
+  ∃ nv, v.update_usize α n i x = ok nv ∧
   nv.val = v.val.update i.val x
   := by
   simp only [update_usize]
@@ -96,12 +96,12 @@ theorem Array.update_usize_spec {α : Type u} {n : Usize} (v: Array α n) (i: Us
 def Array.index_mut_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) :
   Result (α × (α -> Result (Array α n))) := do
   let x ← index_usize α n v i
-  ret (x, update_usize α n v i)
+  ok (x, update_usize α n v i)
 
 @[pspec]
 theorem Array.index_mut_usize_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x back, v.index_mut_usize α n i = ret (x, back) ∧
+  ∃ x back, v.index_mut_usize α n i = ok (x, back) ∧
   x = v.val.index i.val ∧
   back = update_usize α n v i := by
   simp only [index_mut_usize, Bind.bind, bind]
@@ -148,7 +148,7 @@ abbrev Slice.slice {α : Type u} [Inhabited α] (s : Slice α) (i j : Int) : Lis
 def Slice.index_usize (α : Type u) (v: Slice α) (i: Usize) : Result α :=
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
-  | some x => ret x
+  | some x => ok x
 
 /- In the theorems below: we don't always need the `∃ ..`, but we use one
    so that `progress` introduces an opaque variable and an equality. This
@@ -158,7 +158,7 @@ def Slice.index_usize (α : Type u) (v: Slice α) (i: Usize) : Result α :=
 @[pspec]
 theorem Slice.index_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x, v.index_usize α i = ret x ∧ x = v.val.index i.val := by
+  ∃ x, v.index_usize α i = ok x ∧ x = v.val.index i.val := by
   simp only [index_usize]
   -- TODO: dependent rewrite
   have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
@@ -168,12 +168,12 @@ def Slice.update_usize (α : Type u) (v: Slice α) (i: Usize) (x: α) : Result (
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
   | some _ =>
-    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+    ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
 
 @[pspec]
 theorem Slice.update_usize_spec {α : Type u} (v: Slice α) (i: Usize) (x : α)
   (hbound : i.val < v.length) :
-  ∃ nv, v.update_usize α i x = ret nv ∧
+  ∃ nv, v.update_usize α i x = ok nv ∧
   nv.val = v.val.update i.val x
   := by
   simp only [update_usize]
@@ -185,12 +185,12 @@ theorem Slice.update_usize_spec {α : Type u} (v: Slice α) (i: Usize) (x : α)
 def Slice.index_mut_usize (α : Type u) (v: Slice α) (i: Usize) :
   Result (α × (α → Result (Slice α))) := do
   let x ← Slice.index_usize α v i
-  ret (x, Slice.update_usize α v i)
+  ok (x, Slice.update_usize α v i)
 
 @[pspec]
 theorem Slice.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x back, v.index_mut_usize α i = ret (x, back) ∧
+  ∃ x back, v.index_mut_usize α i = ok (x, back) ∧
   x = v.val.index i.val ∧
   back = Slice.update_usize α v i := by
   simp only [index_mut_usize, Bind.bind, bind]
@@ -204,30 +204,30 @@ theorem Slice.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i
    `progress` tactic), meaning `Array.to_slice` should be considered as opaque.
    All what the spec theorem reveals is that the "representative" lists are the same. -/
 def Array.to_slice (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) :=
-  ret ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩
+  ok ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩
 
 @[pspec]
 theorem Array.to_slice_spec {α : Type u} {n : Usize} (v : Array α n) :
-  ∃ s, to_slice α n v = ret s ∧ v.val = s.val := by simp [to_slice]
+  ∃ s, to_slice α n v = ok s ∧ v.val = s.val := by simp [to_slice]
 
 def Array.from_slice (α : Type u) (n : Usize) (_ : Array α n) (s : Slice α) : Result (Array α n) :=
   if h: s.val.len = n.val then
-    ret ⟨ s.val, by simp [← List.len_eq_length, *] ⟩
+    ok ⟨ s.val, by simp [← List.len_eq_length, *] ⟩
   else fail panic
 
 @[pspec]
 theorem Array.from_slice_spec {α : Type u} {n : Usize} (a : Array α n) (ns : Slice α) (h : ns.val.len = n.val) :
-  ∃ na, from_slice α n a ns = ret na ∧ na.val = ns.val
+  ∃ na, from_slice α n a ns = ok na ∧ na.val = ns.val
   := by simp [from_slice, *]
 
 def Array.to_slice_mut (α : Type u) (n : Usize) (a : Array α n) :
   Result (Slice α × (Slice α → Result (Array α n))) := do
   let s ← Array.to_slice α n a
-  ret (s, Array.from_slice α n a)
+  ok (s, Array.from_slice α n a)
 
 @[pspec]
 theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) :
-  ∃ s back, to_slice_mut α n v = ret (s, back) ∧
+  ∃ s back, to_slice_mut α n v = ok (s, back) ∧
   v.val = s.val ∧
   back = Array.from_slice α n v
   := by simp [to_slice_mut, to_slice]
@@ -235,7 +235,7 @@ theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) :
 def Array.subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) : Result (Slice α) :=
   -- TODO: not completely sure here
   if r.start.val < r.end_.val ∧ r.end_.val ≤ a.val.len then
-    ret ⟨ a.val.slice r.start.val r.end_.val,
+    ok ⟨ a.val.slice r.start.val r.end_.val,
           by
             simp [← List.len_eq_length]
             have := a.val.slice_len_le r.start.val r.end_.val
@@ -246,7 +246,7 @@ def Array.subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize)
 @[pspec]
 theorem Array.subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize)
   (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ a.val.len) :
-  ∃ s, subslice α n a r = ret s ∧
+  ∃ s, subslice α n a r = ok s ∧
   s.val = a.val.slice r.start.val r.end_.val ∧
   (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → s.val.index i = a.val.index (r.start.val + i))
   := by
@@ -270,7 +270,7 @@ def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range
       . scalar_tac
     let na := s_beg.append (s.val.append s_end)
     have : na.len = a.val.len := by simp [*]
-    ret ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩
+    ok ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩
   else
     fail panic
 
@@ -282,7 +282,7 @@ def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range
 @[pspec]
 theorem Array.update_subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize) (s : Slice α)
   (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : s.length = r.end_.val - r.start.val) :
-  ∃ na, update_subslice α n a r s = ret na ∧
+  ∃ na, update_subslice α n a r s = ok na ∧
   (∀ i, 0 ≤ i → i < r.start.val → na.index_s i = a.index_s i) ∧
   (∀ i, r.start.val ≤ i → i < r.end_.val → na.index_s i = s.index_s (i - r.start.val)) ∧
   (∀ i, r.end_.val ≤ i → i < n.val → na.index_s i = a.index_s i) := by
@@ -306,7 +306,7 @@ theorem Array.update_subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a :
 def Slice.subslice (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slice α) :=
   -- TODO: not completely sure here
   if r.start.val < r.end_.val ∧ r.end_.val ≤ s.length then
-    ret ⟨ s.val.slice r.start.val r.end_.val,
+    ok ⟨ s.val.slice r.start.val r.end_.val,
           by
             simp [← List.len_eq_length]
             have := s.val.slice_len_le r.start.val r.end_.val
@@ -317,7 +317,7 @@ def Slice.subslice (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slic
 @[pspec]
 theorem Slice.subslice_spec {α : Type u} [Inhabited α] (s : Slice α) (r : Range Usize)
   (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ s.val.len) :
-  ∃ ns, subslice α s r = ret ns ∧
+  ∃ ns, subslice α s r = ok ns ∧
   ns.val = s.slice r.start.val r.end_.val ∧
   (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index_s i = s.index_s (r.start.val + i))
   := by
@@ -344,14 +344,14 @@ def Slice.update_subslice (α : Type u) (s : Slice α) (r : Range Usize) (ss : S
       . scalar_tac
     let ns := s_beg.append (ss.val.append s_end)
     have : ns.len = s.val.len := by simp [*]
-    ret ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩
+    ok ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩
   else
     fail panic
 
 @[pspec]
 theorem Slice.update_subslice_spec {α : Type u} [Inhabited α] (a : Slice α) (r : Range Usize) (ss : Slice α)
   (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : ss.length = r.end_.val - r.start.val) :
-  ∃ na, update_subslice α a r ss = ret na ∧
+  ∃ na, update_subslice α a r ss = ok na ∧
   (∀ i, 0 ≤ i → i < r.start.val → na.index_s i = a.index_s i) ∧
   (∀ i, r.start.val ≤ i → i < r.end_.val → na.index_s i = ss.index_s (i - r.start.val)) ∧
   (∀ i, r.end_.val ≤ i → i < a.length → na.index_s i = a.index_s i) := by
@@ -393,7 +393,7 @@ def core.slice.index.Slice.index
   let x ← inst.get i slice
   match x with
   | none => fail panic
-  | some x => ret x
+  | some x => ok x
 
 /- [core::slice::index::Range:::get]: forward function -/
 def core.slice.index.RangeUsize.get (T : Type) (i : Range Usize) (slice : Slice T) :
diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean
index 0c64eca1..4c5b2795 100644
--- a/backends/lean/Base/Primitives/Base.lean
+++ b/backends/lean/Base/Primitives/Base.lean
@@ -41,7 +41,7 @@ deriving Repr, BEq
 open Error
 
 inductive Result (α : Type u) where
-  | ret (v: α): Result α
+  | ok (v: α): Result α
   | fail (e: Error): Result α
   | div
 deriving Repr, BEq
@@ -56,31 +56,31 @@ instance Result_Nonempty (α : Type u) : Nonempty (Result α) :=
 
 /- HELPERS -/
 
-def ret? {α: Type u} (r: Result α): Bool :=
+def ok? {α: Type u} (r: Result α): Bool :=
   match r with
-  | ret _ => true
+  | ok _ => true
   | fail _ | div => false
 
 def div? {α: Type u} (r: Result α): Bool :=
   match r with
   | div => true
-  | ret _ | fail _ => false
+  | ok _ | fail _ => false
 
 def massert (b:Bool) : Result Unit :=
-  if b then ret () else fail assertionFailure
+  if b then ok () else fail assertionFailure
 
 macro "prove_eval_global" : tactic => `(tactic| first | apply Eq.refl | decide)
 
-def eval_global {α: Type u} (x: Result α) (_: ret? x := by prove_eval_global) : α :=
+def eval_global {α: Type u} (x: Result α) (_: ok? x := by prove_eval_global) : α :=
   match x with
   | fail _ | div => by contradiction
-  | ret x => x
+  | ok x => x
 
 /- DO-DSL SUPPORT -/
 
 def bind {α : Type u} {β : Type v} (x: Result α) (f: α → Result β) : Result β :=
   match x with
-  | ret v  => f v
+  | ok v  => f v
   | fail v => fail v
   | div => div
 
@@ -88,11 +88,11 @@ def bind {α : Type u} {β : Type v} (x: Result α) (f: α → Result β) : Resu
 instance : Bind Result where
   bind := bind
 
--- Allows using return x in do-blocks
+-- Allows using pure x in do-blocks
 instance : Pure Result where
-  pure := fun x => ret x
+  pure := fun x => ok x
 
-@[simp] theorem bind_ret (x : α) (f : α → Result β) : bind (.ret x) f = f x := by simp [bind]
+@[simp] theorem bind_ok (x : α) (f : α → Result β) : bind (.ok x) f = f x := by simp [bind]
 @[simp] theorem bind_fail (x : Error) (f : α → Result β) : bind (.fail x) f = .fail x := by simp [bind]
 @[simp] theorem bind_div (f : α → Result β) : bind .div f = .div := by simp [bind]
 
@@ -103,14 +103,14 @@ instance : Pure Result where
 -- 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 } :=
+def Result.attach {α: Type} (o : Result α): Result { x : α // o = ok x } :=
   match o with
-  | ret x => ret ⟨x, rfl⟩
+  | ok x => ok ⟨x, rfl⟩
   | fail e => fail e
   | div => div
 
-@[simp] theorem bind_tc_ret (x : α) (f : α → Result β) :
-  (do let y ← .ret x; f y) = f x := by simp [Bind.bind, bind]
+@[simp] theorem bind_tc_ok (x : α) (f : α → Result β) :
+  (do let y ← .ok x; f y) = f x := by simp [Bind.bind, bind]
 
 @[simp] theorem bind_tc_fail (x : Error) (f : α → Result β) :
   (do let y ← fail x; f y) = fail x := by simp [Bind.bind, bind]
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 3d90f1a5..c298ba92 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -339,7 +339,7 @@ def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
     -- ```
     -- then normalization blocks (for instance, some proofs which use reflexivity fail).
     -- However, the version below doesn't block reduction (TODO: investigate):
-    return Scalar.ofIntCore x (Scalar.check_bounds_prop h)
+    ok (Scalar.ofIntCore x (Scalar.check_bounds_prop h))
   else fail integerOverflow
 
 def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
@@ -573,7 +573,7 @@ instance {ty} : HAnd (Scalar ty) (Scalar ty) (Scalar ty) where
 theorem Scalar.add_spec {ty} {x y : Scalar ty}
   (hmin : Scalar.min ty ≤ ↑x + y.val)
   (hmax : ↑x + ↑y ≤ Scalar.max ty) :
-  (∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y) := by
+  (∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y) := by
   -- Applying the unfoldings only on the left
   conv => congr; ext; lhs; unfold HAdd.hAdd instHAddScalarResult; simp [add, tryMk]
   split
@@ -582,7 +582,7 @@ theorem Scalar.add_spec {ty} {x y : Scalar ty}
 
 theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   (hmax : ↑x + ↑y ≤ Scalar.max ty) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   have hmin : Scalar.min ty ≤ ↑x + ↑y := by
     have hx := x.hmin
     have hy := y.hmin
@@ -591,57 +591,57 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
 
 /- Fine-grained theorems -/
 @[pspec] theorem Usize.add_spec {x y : Usize} (hmax : ↑x + ↑y ≤ Usize.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *]
 
 @[pspec] theorem U8.add_spec {x y : U8} (hmax : ↑x + ↑y ≤ U8.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *]
 
 @[pspec] theorem U16.add_spec {x y : U16} (hmax : ↑x + ↑y ≤ U16.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *]
 
 @[pspec] theorem U32.add_spec {x y : U32} (hmax : ↑x + ↑y ≤ U32.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *]
 
 @[pspec] theorem U64.add_spec {x y : U64} (hmax : ↑x + ↑y ≤ U64.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *]
 
 @[pspec] theorem U128.add_spec {x y : U128} (hmax : ↑x + ↑y ≤ U128.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by
   apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *]
 
 @[pspec] theorem Isize.add_spec {x y : Isize}
   (hmin : Isize.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ Isize.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y :=
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y :=
   Scalar.add_spec hmin hmax
 
 @[pspec] theorem I8.add_spec {x y : I8}
   (hmin : I8.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I8.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y :=
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y :=
   Scalar.add_spec hmin hmax
 
 @[pspec] theorem I16.add_spec {x y : I16}
   (hmin : I16.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I16.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y :=
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y :=
   Scalar.add_spec hmin hmax
 
 @[pspec] theorem I32.add_spec {x y : I32}
   (hmin : I32.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I32.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y :=
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y :=
   Scalar.add_spec hmin hmax
 
 @[pspec] theorem I64.add_spec {x y : I64}
   (hmin : I64.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I64.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y :=
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y :=
   Scalar.add_spec hmin hmax
 
 @[pspec] theorem I128.add_spec {x y : I128}
   (hmin : I128.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I128.max) :
-  ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y :=
+  ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y :=
   Scalar.add_spec hmin hmax
 
 -- Generic theorem - shouldn't be used much
@@ -649,7 +649,7 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
 theorem Scalar.sub_spec {ty} {x y : Scalar ty}
   (hmin : Scalar.min ty ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ Scalar.max ty) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   conv => congr; ext; lhs; simp [HSub.hSub, sub, tryMk, Sub.sub]
   split
   . simp [pure]
@@ -658,7 +658,7 @@ theorem Scalar.sub_spec {ty} {x y : Scalar ty}
 
 theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned)
   {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   have : ↑x - ↑y ≤ Scalar.max ty := by
     have hx := x.hmin
     have hxm := x.hmax
@@ -669,64 +669,64 @@ theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned)
 
 /- Fine-grained theorems -/
 @[pspec] theorem Usize.sub_spec {x y : Usize} (hmin : Usize.min ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned]
 
 @[pspec] theorem U8.sub_spec {x y : U8} (hmin : U8.min ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned]
 
 @[pspec] theorem U16.sub_spec {x y : U16} (hmin : U16.min ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned]
 
 @[pspec] theorem U32.sub_spec {x y : U32} (hmin : U32.min ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned]
 
 @[pspec] theorem U64.sub_spec {x y : U64} (hmin : U64.min ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned]
 
 @[pspec] theorem U128.sub_spec {x y : U128} (hmin : U128.min ≤ ↑x - ↑y) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned]
 
 @[pspec] theorem Isize.sub_spec {x y : Isize} (hmin : Isize.min ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ Isize.max) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y :=
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y :=
   Scalar.sub_spec hmin hmax
 
 @[pspec] theorem I8.sub_spec {x y : I8} (hmin : I8.min ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ I8.max) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y :=
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y :=
   Scalar.sub_spec hmin hmax
 
 @[pspec] theorem I16.sub_spec {x y : I16} (hmin : I16.min ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ I16.max) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y :=
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y :=
   Scalar.sub_spec hmin hmax
 
 @[pspec] theorem I32.sub_spec {x y : I32} (hmin : I32.min ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ I32.max) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y :=
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y :=
   Scalar.sub_spec hmin hmax
 
 @[pspec] theorem I64.sub_spec {x y : I64} (hmin : I64.min ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ I64.max) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y :=
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y :=
   Scalar.sub_spec hmin hmax
 
 @[pspec] theorem I128.sub_spec {x y : I128} (hmin : I128.min ≤ ↑x - ↑y)
   (hmax : ↑x - ↑y ≤ I128.max) :
-  ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y :=
+  ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y :=
   Scalar.sub_spec hmin hmax
 
 -- Generic theorem - shouldn't be used much
 theorem Scalar.mul_spec {ty} {x y : Scalar ty}
   (hmin : Scalar.min ty ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ Scalar.max ty) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   conv => congr; ext; lhs; simp [HMul.hMul]
   simp [mul, tryMk]
   split
@@ -736,7 +736,7 @@ theorem Scalar.mul_spec {ty} {x y : Scalar ty}
 
 theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   (hmax : ↑x * ↑y ≤ Scalar.max ty) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   have : Scalar.min ty ≤ ↑x * ↑y := by
     have hx := x.hmin
     have hy := y.hmin
@@ -745,57 +745,57 @@ theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
 
 /- Fine-grained theorems -/
 @[pspec] theorem Usize.mul_spec {x y : Usize} (hmax : ↑x * ↑y ≤ Usize.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned]
 
 @[pspec] theorem U8.mul_spec {x y : U8} (hmax : ↑x * ↑y ≤ U8.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned]
 
 @[pspec] theorem U16.mul_spec {x y : U16} (hmax : ↑x * ↑y ≤ U16.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned]
 
 @[pspec] theorem U32.mul_spec {x y : U32} (hmax : ↑x * ↑y ≤ U32.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned]
 
 @[pspec] theorem U64.mul_spec {x y : U64} (hmax : ↑x * ↑y ≤ U64.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned]
 
 @[pspec] theorem U128.mul_spec {x y : U128} (hmax : ↑x * ↑y ≤ U128.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by
   apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned]
 
 @[pspec] theorem Isize.mul_spec {x y : Isize} (hmin : Isize.min ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ Isize.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y :=
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y :=
   Scalar.mul_spec hmin hmax
 
 @[pspec] theorem I8.mul_spec {x y : I8} (hmin : I8.min ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ I8.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y :=
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y :=
   Scalar.mul_spec hmin hmax
 
 @[pspec] theorem I16.mul_spec {x y : I16} (hmin : I16.min ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ I16.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y :=
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y :=
   Scalar.mul_spec hmin hmax
 
 @[pspec] theorem I32.mul_spec {x y : I32} (hmin : I32.min ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ I32.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y :=
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y :=
   Scalar.mul_spec hmin hmax
 
 @[pspec] theorem I64.mul_spec {x y : I64} (hmin : I64.min ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ I64.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y :=
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y :=
   Scalar.mul_spec hmin hmax
 
 @[pspec] theorem I128.mul_spec {x y : I128} (hmin : I128.min ≤ ↑x * ↑y)
   (hmax : ↑x * ↑y ≤ I128.max) :
-  ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y :=
+  ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y :=
   Scalar.mul_spec hmin hmax
 
 -- Generic theorem - shouldn't be used much
@@ -804,15 +804,14 @@ theorem Scalar.div_spec {ty} {x y : Scalar ty}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : Scalar.min ty ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ Scalar.max ty) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := by
   simp [HDiv.hDiv, div, Div.div]
   simp [tryMk, *]
-  simp [pure]
   rfl
 
 theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty}
   (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   have h : Scalar.min ty = 0 := by cases ty <;> simp [ScalarTy.isSigned, min] at *
   have hx := x.hmin
   have hy := y.hmin
@@ -828,69 +827,69 @@ theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
 
 /- Fine-grained theorems -/
 @[pspec] theorem Usize.div_spec (x : Usize) {y : Usize} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U8.div_spec (x : U8) {y : U8} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U16.div_spec (x : U16) {y : U16} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U32.div_spec (x : U32) {y : U32} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U64.div_spec (x : U64) {y : U64} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U128.div_spec (x : U128) {y : U128} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by
+  ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by
   apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem Isize.div_spec (x : Isize) {y : Isize}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : Isize.min ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ Isize.max):
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
   Scalar.div_spec hnz hmin hmax
 
 @[pspec] theorem I8.div_spec (x : I8) {y : I8}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I8.min ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ I8.max):
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
   Scalar.div_spec hnz hmin hmax
 
 @[pspec] theorem I16.div_spec (x : I16) {y : I16}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I16.min ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ I16.max):
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
   Scalar.div_spec hnz hmin hmax
 
 @[pspec] theorem I32.div_spec (x : I32) {y : I32}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I32.min ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ I32.max):
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
   Scalar.div_spec hnz hmin hmax
 
 @[pspec] theorem I64.div_spec (x : I64) {y : I64}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I64.min ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ I64.max):
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
   Scalar.div_spec hnz hmin hmax
 
 @[pspec] theorem I128.div_spec (x : I128) {y : I128}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I128.min ≤ scalar_div ↑x ↑y)
   (hmax : scalar_div ↑x ↑y ≤ I128.max):
-  ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
+  ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y :=
   Scalar.div_spec hnz hmin hmax
 
 -- Generic theorem - shouldn't be used much
@@ -899,15 +898,14 @@ theorem Scalar.rem_spec {ty} {x y : Scalar ty}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : Scalar.min ty ≤ scalar_rem ↑x ↑y)
   (hmax : scalar_rem ↑x ↑y ≤ Scalar.max ty) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := by
   simp [HMod.hMod, rem]
   simp [tryMk, *]
-  simp [pure]
   rfl
 
 theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty}
   (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   have h : Scalar.min ty = 0 := by cases ty <;> simp [ScalarTy.isSigned, min] at *
   have hx := x.hmin
   have hy := y.hmin
@@ -923,62 +921,62 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
   simp [*]
 
 @[pspec] theorem Usize.rem_spec (x : Usize) {y : Usize} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U8.rem_spec (x : U8) {y : U8} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U16.rem_spec (x : U16) {y : U16} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U32.rem_spec (x : U32) {y : U32} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U64.rem_spec (x : U64) {y : U64} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem U128.rem_spec (x : U128) {y : U128} (hnz : ↑y ≠ (0 : Int)) :
-  ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by
+  ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by
   apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *]
 
 @[pspec] theorem I8.rem_spec (x : I8) {y : I8}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I8.min ≤ scalar_rem ↑x ↑y)
   (hmax : scalar_rem ↑x ↑y ≤ I8.max):
-  ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
+  ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
   Scalar.rem_spec hnz hmin hmax
 
 @[pspec] theorem I16.rem_spec (x : I16) {y : I16}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I16.min ≤ scalar_rem ↑x ↑y)
   (hmax : scalar_rem ↑x ↑y ≤ I16.max):
-  ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
+  ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
   Scalar.rem_spec hnz hmin hmax
 
 @[pspec] theorem I32.rem_spec (x : I32) {y : I32}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I32.min ≤ scalar_rem ↑x ↑y)
   (hmax : scalar_rem ↑x ↑y ≤ I32.max):
-  ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
+  ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
   Scalar.rem_spec hnz hmin hmax
 
 @[pspec] theorem I64.rem_spec (x : I64) {y : I64}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I64.min ≤ scalar_rem ↑x ↑y)
   (hmax : scalar_rem ↑x ↑y ≤ I64.max):
-  ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
+  ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
   Scalar.rem_spec hnz hmin hmax
 
 @[pspec] theorem I128.rem_spec (x : I128) {y : I128}
   (hnz : ↑y ≠ (0 : Int))
   (hmin : I128.min ≤ scalar_rem ↑x ↑y)
   (hmax : scalar_rem ↑x ↑y ≤ I128.max):
-  ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
+  ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y :=
   Scalar.rem_spec hnz hmin hmax
 
 -- ofIntCore
@@ -1152,6 +1150,6 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
     | isFalse h => isFalse (Scalar.ne_of_val_ne h)
 
 @[simp] theorem Scalar.neq_to_neq_val {ty} : ∀ {i j : Scalar ty}, (¬ i = j) ↔ ¬ i.val = j.val := by
-  intro i j; cases i; cases j; simp
+  simp [eq_equiv]
 
 end Primitives
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index 65249c12..dbe5c8dd 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -61,34 +61,34 @@ def Vec.push (α : Type u) (v : Vec α) (x : α) : Result (Vec α)
       simp [Usize.max] at *
       have hm := Usize.refined_max.property
       cases h <;> cases hm <;> simp [U32.max, U64.max] at * <;> try linarith
-    return ⟨ List.concat v.val x, by simp at *; assumption ⟩
+    ok ⟨ List.concat v.val x, by simp at *; assumption ⟩
   else
     fail maximumSizeExceeded
 
 -- This shouldn't be used
 def Vec.insert_fwd (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
   if i.val < v.length then
-    .ret ()
+    ok ()
   else
-    .fail arrayOutOfBounds
+    fail arrayOutOfBounds
 
 -- This is actually the backward function
 def Vec.insert (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
   if i.val < v.length then
-    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+    ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
   else
-    .fail arrayOutOfBounds
+    fail arrayOutOfBounds
 
 @[pspec]
 theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α)
   (hbound : i.val < v.length) :
-  ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by
+  ∃ nv, v.insert α i x = ok nv ∧ nv.val = v.val.update i.val x := by
   simp [insert, *]
 
 def Vec.index_usize {α : Type u} (v: Vec α) (i: Usize) : Result α :=
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
-  | some x => ret x
+  | some x => ok x
 
 /- In the theorems below: we don't always need the `∃ ..`, but we use one
    so that `progress` introduces an opaque variable and an equality. This
@@ -98,7 +98,7 @@ def Vec.index_usize {α : Type u} (v: Vec α) (i: Usize) : Result α :=
 @[pspec]
 theorem Vec.index_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x, v.index_usize i = ret x ∧ x = v.val.index i.val := by
+  ∃ x, v.index_usize i = ok x ∧ x = v.val.index i.val := by
   simp only [index_usize]
   -- TODO: dependent rewrite
   have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
@@ -108,12 +108,12 @@ def Vec.update_usize {α : Type u} (v: Vec α) (i: Usize) (x: α) : Result (Vec
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
   | some _ =>
-    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+    ok ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
 
 @[pspec]
 theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
   (hbound : i.val < v.length) :
-  ∃ nv, v.update_usize i x = ret nv ∧
+  ∃ nv, v.update_usize i x = ok nv ∧
   nv.val = v.val.update i.val x
   := by
   simp only [update_usize]
@@ -125,15 +125,15 @@ theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
 def Vec.index_mut_usize {α : Type u} (v: Vec α) (i: Usize) :
   Result (α × (α → Result (Vec α))) :=
   match Vec.index_usize v i with
-  | ret x =>
-    ret (x, Vec.update_usize v i)
+  | ok x =>
+    ok (x, Vec.update_usize v i)
   | fail e => fail e
   | div => div
 
 @[pspec]
 theorem Vec.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x back, v.index_mut_usize i = ret (x, back) ∧
+  ∃ x back, v.index_mut_usize i = ok (x, back) ∧
   x = v.val.index i.val ∧
   -- Backward function
   back = v.update_usize i
-- 
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