Idiomatic naming conventions

5 files changed, 297 insertions, 271 deletions

diff --git a/tests/lean/hashmap_on_disk/Base/Primitives.lean b/tests/lean/hashmap_on_disk/Base/Primitives.lean
index 79958d94..b3f3a1a0 100644
--- a/tests/lean/hashmap_on_disk/Base/Primitives.lean
+++ b/tests/lean/hashmap_on_disk/Base/Primitives.lean
@@ -9,69 +9,69 @@ 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
+-- TODO: use syntactic conventions and capitalize Error, Result, etc.
+
+inductive Error where
+   | assertionFailure: Error
+   | integerOverflow: Error
+   | arrayOutOfBounds: Error
+   | maximumSizeExceeded: Error
+   | panic: Error
 deriving Repr, BEq
 
-open error
+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 is_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) (_: is_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 : (o : Result α) → Result { x : α // o = ret x }
   | .ret x => .ret ⟨x, rfl⟩
   | .fail e   => .fail e
 
 macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
-  `(doElem| let ⟨$e, $h⟩ ← result.attach $f)
+  `(doElem| let ⟨$e, $h⟩ ← Result.attach $f)
 
 -- Silly example of the kind of reasoning that this notation enables
 #eval do
@@ -99,8 +99,8 @@ macro "let" h:ident " : " e:term " <-- " f:term : doElem =>
 -- 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
+-- 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
@@ -134,7 +134,7 @@ macro_rules
 -- 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
@@ -150,7 +150,7 @@ def USize.checked_sub (n: USize) (m: USize): result USize :=
   else
     fail integerOverflow
 
-def USize.checked_add (n: USize) (m: USize): result USize :=
+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
@@ -161,7 +161,7 @@ def USize.checked_add (n: USize) (m: USize): result USize :=
   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
@@ -171,7 +171,7 @@ def USize.checked_rem (n: USize) (m: USize): result USize :=
   else
     .fail integerOverflow
 
-def USize.checked_mul (n: USize) (m: USize): result USize :=
+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
@@ -182,7 +182,7 @@ def USize.checked_mul (n: USize) (m: USize): result USize :=
   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
@@ -209,7 +209,7 @@ run_cmd
     end $typeName
   ))
 
-def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineInteger dst ] (x: src): result dst :=
+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
@@ -230,9 +230,9 @@ def scalar_cast { src: Type } (dst: Type) [ MachineInteger src ] [ MachineIntege
 
 -- 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 +240,20 @@ 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 +272,12 @@ 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 +295,13 @@ 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 +311,25 @@ 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
@@ -364,7 +364,7 @@ def assertImpl : CommandElab := fun (_stx: Syntax) => do
   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?
+    -- How to evaluate the term and compare the Result to true?
     pure ())
   -- logInfo (Expr.dbgToString (``true))
   -- throwError "TODO: assert"
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
index 3466e7e0..a514c58a 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Clauses/Template.lean
@@ -6,7 +6,7 @@ import HashmapMain.Types
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: termination measure -/
 @[simp]
 def hashmap_hash_map_allocate_slots_loop_terminates (T : Type)
-  (slots : vec (hashmap_list_t T)) (n : USize) :=
+  (slots : Vec (hashmap_list_t T)) (n : USize) :=
   (slots, n)
 
 syntax "hashmap_hash_map_allocate_slots_loop_decreases" term+ : tactic
@@ -15,16 +15,17 @@ macro_rules
 | `(tactic| hashmap_hash_map_allocate_slots_loop_decreases $slots $n) =>
   `(tactic| sorry)
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear]: termination measure -/
+/- [hashmap_main::hashmap::HashMap::{0}::clear_slots]: termination measure -/
 @[simp]
-def hashmap_hash_map_clear_loop_terminates (T : Type)
-  (slots : vec (hashmap_list_t T)) (i : USize) :=
+def hashmap_hash_map_clear_slots_loop_terminates (T : Type)
+  (slots : Vec (hashmap_list_t T)) (i : USize) :=
   (slots, i)
 
-syntax "hashmap_hash_map_clear_loop_decreases" term+ : tactic
+syntax "hashmap_hash_map_clear_slots_loop_decreases" term+ : tactic
 
 macro_rules
-| `(tactic| hashmap_hash_map_clear_loop_decreases $slots $i) =>`(tactic| sorry)
+| `(tactic| hashmap_hash_map_clear_slots_loop_decreases $slots $i) =>
+  `(tactic| sorry)
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: termination measure -/
 @[simp]
@@ -53,7 +54,7 @@ $ls) =>`(tactic| sorry)
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements]: termination measure -/
 @[simp]
 def hashmap_hash_map_move_elements_loop_terminates (T : Type)
-  (ntable : hashmap_hash_map_t T) (slots : vec (hashmap_list_t T)) (i : USize)
+  (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T)) (i : USize)
   :=
   (ntable, slots, i)
 
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
index 1abc9f8d..ee50f126 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Funs.lean
@@ -3,35 +3,35 @@
 import Base.Primitives
 import HashmapMain.Types
 import HashmapMain.Opaque
-import HashmapMain.Clauses.Clauses
+import HashmapMain.Clauses.Template
 
 section variable (opaque_defs: OpaqueDefs)
 
 /- [hashmap_main::hashmap::hash_key] -/
-def hashmap_hash_key_fwd (k : USize) : result USize :=
-  result.ret k
+def hashmap_hash_key_fwd (k : USize) : Result USize := Result.ret k
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
 def hashmap_hash_map_allocate_slots_loop_fwd
-  (T : Type) (slots : vec (hashmap_list_t T)) (n : USize) :
-  (result (vec (hashmap_list_t T)))
+  (T : Type) (slots : Vec (hashmap_list_t T)) (n : USize) :
+  (Result (Vec (hashmap_list_t T)))
   :=
   if n > (USize.ofNatCore 0 (by intlit))
   then
     do
       let slots0 <-
-        vec_push_back (hashmap_list_t T) slots hashmap_list_t.HashmapListNil
-      let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit))
+        vec_push_back (hashmap_list_t T) slots hashmap_list_t.HashmapListNil 
+      let n0 <- USize.checked_sub n (USize.ofNatCore 1 (by intlit)) 
       hashmap_hash_map_allocate_slots_loop_fwd T slots0 n0
-  else result.ret slots
+  else Result.ret slots
 termination_by hashmap_hash_map_allocate_slots_loop_fwd slots n =>
-  hashmap_hash_map_allocate_slots_loop_terminates T slots n
+                                                                  hashmap_hash_map_allocate_slots_loop_terminates
+                                                                  T slots n 
 decreasing_by hashmap_hash_map_allocate_slots_loop_decreases slots n
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
 def hashmap_hash_map_allocate_slots_fwd
-  (T : Type) (slots : vec (hashmap_list_t T)) (n : USize) :
-  result (vec (hashmap_list_t T))
+  (T : Type) (slots : Vec (hashmap_list_t T)) (n : USize) :
+  Result (Vec (hashmap_list_t T))
   :=
   hashmap_hash_map_allocate_slots_loop_fwd T slots n
 
@@ -39,14 +39,14 @@ def hashmap_hash_map_allocate_slots_fwd
 def hashmap_hash_map_new_with_capacity_fwd
   (T : Type) (capacity : USize) (max_load_dividend : USize)
   (max_load_divisor : USize) :
-  result (hashmap_hash_map_t T)
+  Result (hashmap_hash_map_t T)
   :=
   do
-    let v := vec_new (hashmap_list_t T)
-    let slots <- hashmap_hash_map_allocate_slots_fwd T v capacity
-    let i <- USize.checked_mul capacity max_load_dividend
-    let i0 <- USize.checked_div i max_load_divisor
-    result.ret
+    let v := vec_new (hashmap_list_t T) 
+    let slots <- hashmap_hash_map_allocate_slots_fwd T v capacity 
+    let i <- USize.checked_mul capacity max_load_dividend 
+    let i0 <- USize.checked_div i max_load_divisor 
+    Result.ret
       {
         hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
         hashmap_hash_map_max_load_factor := (max_load_dividend,
@@ -56,37 +56,45 @@ def hashmap_hash_map_new_with_capacity_fwd
       }
 
 /- [hashmap_main::hashmap::HashMap::{0}::new] -/
-def hashmap_hash_map_new_fwd (T : Type) : result (hashmap_hash_map_t T) :=
+def hashmap_hash_map_new_fwd (T : Type) : Result (hashmap_hash_map_t T) :=
   hashmap_hash_map_new_with_capacity_fwd T (USize.ofNatCore 32 (by intlit))
     (USize.ofNatCore 4 (by intlit)) (USize.ofNatCore 5 (by intlit))
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap_hash_map_clear_loop_fwd_back
-  (T : Type) (slots : vec (hashmap_list_t T)) (i : USize) :
-  (result (vec (hashmap_list_t T)))
+/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
+def hashmap_hash_map_clear_slots_loop_fwd_back
+  (T : Type) (slots : Vec (hashmap_list_t T)) (i : USize) :
+  (Result (Vec (hashmap_list_t T)))
   :=
-  let i0 := vec_len (hashmap_list_t T) slots
+  let i0 := vec_len (hashmap_list_t T) slots 
   if i < i0
   then
     do
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) 
       let slots0 <-
         vec_index_mut_back (hashmap_list_t T) slots i
-          hashmap_list_t.HashmapListNil
-      hashmap_hash_map_clear_loop_fwd_back T slots0 i1
-  else result.ret slots
-termination_by hashmap_hash_map_clear_loop_fwd_back slots i =>
-  hashmap_hash_map_clear_loop_terminates T slots i
-decreasing_by hashmap_hash_map_clear_loop_decreases slots i
+          hashmap_list_t.HashmapListNil 
+      hashmap_hash_map_clear_slots_loop_fwd_back T slots0 i1
+  else Result.ret slots
+termination_by hashmap_hash_map_clear_slots_loop_fwd_back slots i =>
+                                                                    hashmap_hash_map_clear_slots_loop_terminates
+                                                                    T slots i 
+decreasing_by hashmap_hash_map_clear_slots_loop_decreases slots i
+
+/- [hashmap_main::hashmap::HashMap::{0}::clear_slots] -/
+def hashmap_hash_map_clear_slots_fwd_back
+  (T : Type) (slots : Vec (hashmap_list_t T)) :
+  Result (Vec (hashmap_list_t T))
+  :=
+  hashmap_hash_map_clear_slots_loop_fwd_back T slots
+    (USize.ofNatCore 0 (by intlit))
 
 /- [hashmap_main::hashmap::HashMap::{0}::clear] -/
 def hashmap_hash_map_clear_fwd_back
-  (T : Type) (self : hashmap_hash_map_t T) : result (hashmap_hash_map_t T) :=
+  (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
   do
     let v <-
-      hashmap_hash_map_clear_loop_fwd_back T self.hashmap_hash_map_slots
-        (USize.ofNatCore 0 (by intlit))
-    result.ret
+      hashmap_hash_map_clear_slots_fwd_back T self.hashmap_hash_map_slots 
+    Result.ret
       {
         hashmap_hash_map_num_entries := (USize.ofNatCore 0 (by intlit)),
         hashmap_hash_map_max_load_factor := self.hashmap_hash_map_max_load_factor,
@@ -96,78 +104,80 @@ def hashmap_hash_map_clear_fwd_back
 
 /- [hashmap_main::hashmap::HashMap::{0}::len] -/
 def hashmap_hash_map_len_fwd
-  (T : Type) (self : hashmap_hash_map_t T) : result USize :=
-  result.ret self.hashmap_hash_map_num_entries
+  (T : Type) (self : hashmap_hash_map_t T) : Result USize :=
+  Result.ret self.hashmap_hash_map_num_entries
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
 def hashmap_hash_map_insert_in_list_loop_fwd
   (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) :
-  (result Bool)
+  (Result Bool)
   :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey cvalue tl =>
     if ckey = key
-    then result.ret false
+    then Result.ret false
     else hashmap_hash_map_insert_in_list_loop_fwd T key value tl
-  | hashmap_list_t.HashmapListNil => result.ret true
+  | hashmap_list_t.HashmapListNil => Result.ret true
+  
 termination_by hashmap_hash_map_insert_in_list_loop_fwd key value ls =>
-  hashmap_hash_map_insert_in_list_loop_terminates T key value ls
+   hashmap_hash_map_insert_in_list_loop_terminates T key value ls 
 decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
 def hashmap_hash_map_insert_in_list_fwd
-  (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) : result Bool :=
+  (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) : Result Bool :=
   hashmap_hash_map_insert_in_list_loop_fwd T key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
 def hashmap_hash_map_insert_in_list_loop_back
   (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) :
-  (result (hashmap_list_t T))
+  (Result (hashmap_list_t T))
   :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey cvalue tl =>
     if ckey = key
-    then result.ret (hashmap_list_t.HashmapListCons ckey value tl)
+    then Result.ret (hashmap_list_t.HashmapListCons ckey value tl)
     else
       do
-        let tl0 <- hashmap_hash_map_insert_in_list_loop_back T key value tl
-        result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
+        let tl0 <- hashmap_hash_map_insert_in_list_loop_back T key value tl 
+        Result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
   | hashmap_list_t.HashmapListNil =>
-    let l := hashmap_list_t.HashmapListNil
-    result.ret (hashmap_list_t.HashmapListCons key value l)
+    let l := hashmap_list_t.HashmapListNil 
+    Result.ret (hashmap_list_t.HashmapListCons key value l)
+  
 termination_by hashmap_hash_map_insert_in_list_loop_back key value ls =>
-  hashmap_hash_map_insert_in_list_loop_terminates T key value ls
+   hashmap_hash_map_insert_in_list_loop_terminates T key value ls 
 decreasing_by hashmap_hash_map_insert_in_list_loop_decreases key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
 def hashmap_hash_map_insert_in_list_back
   (T : Type) (key : USize) (value : T) (ls : hashmap_list_t T) :
-  result (hashmap_list_t T)
+  Result (hashmap_list_t T)
   :=
   hashmap_hash_map_insert_in_list_loop_back T key value ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] -/
 def hashmap_hash_map_insert_no_resize_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) (value : T) :
-  result (hashmap_hash_map_t T)
+  Result (hashmap_hash_map_t T)
   :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let inserted <- hashmap_hash_map_insert_in_list_fwd T key value l
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+    let inserted <- hashmap_hash_map_insert_in_list_fwd T key value l 
     if inserted
     then
       do
         let i0 <- USize.checked_add self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit))
-        let l0 <- hashmap_hash_map_insert_in_list_back T key value l
+          (USize.ofNatCore 1 (by intlit)) 
+        let l0 <- hashmap_hash_map_insert_in_list_back T key value l 
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        result.ret
+            hash_mod l0 
+        Result.ret
           {
             hashmap_hash_map_num_entries := i0,
             hashmap_hash_map_max_load_factor := self.hashmap_hash_map_max_load_factor,
@@ -176,11 +186,11 @@ def hashmap_hash_map_insert_no_resize_fwd_back
           }
     else
       do
-        let l0 <- hashmap_hash_map_insert_in_list_back T key value l
+        let l0 <- hashmap_hash_map_insert_in_list_back T key value l 
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        result.ret
+            hash_mod l0 
+        Result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
             hashmap_hash_map_max_load_factor := self.hashmap_hash_map_max_load_factor,
@@ -189,84 +199,85 @@ def hashmap_hash_map_insert_no_resize_fwd_back
           }
 
 /- [core::num::u32::{9}::MAX] -/
-def core_num_u32_max_body : result UInt32 :=
-  result.ret (UInt32.ofNatCore 4294967295 (by intlit))
+def core_num_u32_max_body : Result UInt32 :=
+  Result.ret (UInt32.ofNatCore 4294967295 (by intlit))
 def core_num_u32_max_c : UInt32 := eval_global core_num_u32_max_body (by simp)
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
 def hashmap_hash_map_move_elements_from_list_loop_fwd_back
   (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
-  (result (hashmap_hash_map_t T))
+  (Result (hashmap_hash_map_t T))
   :=
   match ls with
   | hashmap_list_t.HashmapListCons k v tl =>
     do
-      let ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T ntable k v
+      let ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T ntable k v 
       hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable0 tl
-  | hashmap_list_t.HashmapListNil => result.ret ntable
+  | hashmap_list_t.HashmapListNil => Result.ret ntable
+  
 termination_by hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls
-  =>
-  hashmap_hash_map_move_elements_from_list_loop_terminates T ntable ls
+              => hashmap_hash_map_move_elements_from_list_loop_terminates T
+                ntable ls 
 decreasing_by hashmap_hash_map_move_elements_from_list_loop_decreases ntable ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
 def hashmap_hash_map_move_elements_from_list_fwd_back
   (T : Type) (ntable : hashmap_hash_map_t T) (ls : hashmap_list_t T) :
-  result (hashmap_hash_map_t T)
+  Result (hashmap_hash_map_t T)
   :=
   hashmap_hash_map_move_elements_from_list_loop_fwd_back T ntable ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
 def hashmap_hash_map_move_elements_loop_fwd_back
-  (T : Type) (ntable : hashmap_hash_map_t T) (slots : vec (hashmap_list_t T))
+  (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
   (i : USize) :
-  (result ((hashmap_hash_map_t T) × (vec (hashmap_list_t T))))
+  (Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T))))
   :=
-  let i0 := vec_len (hashmap_list_t T) slots
+  let i0 := vec_len (hashmap_list_t T) slots 
   if i < i0
   then
     do
-      let l <- vec_index_mut_fwd (hashmap_list_t T) slots i
+      let l <- vec_index_mut_fwd (hashmap_list_t T) slots i 
       let ls :=
-        mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.HashmapListNil
+        mem_replace_fwd (hashmap_list_t T) l hashmap_list_t.HashmapListNil 
       let ntable0 <-
-        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls
-      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit))
+        hashmap_hash_map_move_elements_from_list_fwd_back T ntable ls 
+      let i1 <- USize.checked_add i (USize.ofNatCore 1 (by intlit)) 
       let l0 :=
-        mem_replace_back (hashmap_list_t T) l hashmap_list_t.HashmapListNil
-      let slots0 <- vec_index_mut_back (hashmap_list_t T) slots i l0
+        mem_replace_back (hashmap_list_t T) l hashmap_list_t.HashmapListNil 
+      let slots0 <- vec_index_mut_back (hashmap_list_t T) slots i l0 
       hashmap_hash_map_move_elements_loop_fwd_back T ntable0 slots0 i1
-  else result.ret (ntable, slots)
+  else Result.ret (ntable, slots)
 termination_by hashmap_hash_map_move_elements_loop_fwd_back ntable slots i =>
-  hashmap_hash_map_move_elements_loop_terminates T ntable slots i
+   hashmap_hash_map_move_elements_loop_terminates T ntable slots i 
 decreasing_by hashmap_hash_map_move_elements_loop_decreases ntable slots i
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
 def hashmap_hash_map_move_elements_fwd_back
-  (T : Type) (ntable : hashmap_hash_map_t T) (slots : vec (hashmap_list_t T))
+  (T : Type) (ntable : hashmap_hash_map_t T) (slots : Vec (hashmap_list_t T))
   (i : USize) :
-  result ((hashmap_hash_map_t T) × (vec (hashmap_list_t T)))
+  Result ((hashmap_hash_map_t T) × (Vec (hashmap_list_t T)))
   :=
   hashmap_hash_map_move_elements_loop_fwd_back T ntable slots i
 
 /- [hashmap_main::hashmap::HashMap::{0}::try_resize] -/
 def hashmap_hash_map_try_resize_fwd_back
-  (T : Type) (self : hashmap_hash_map_t T) : result (hashmap_hash_map_t T) :=
+  (T : Type) (self : hashmap_hash_map_t T) : Result (hashmap_hash_map_t T) :=
   do
-    let max_usize <- scalar_cast USize core_num_u32_max_c
-    let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit))
-    let (i, i0) := self.hashmap_hash_map_max_load_factor
-    let i1 <- USize.checked_div n1 i
+    let max_usize <- scalar_cast USize core_num_u32_max_c 
+    let capacity := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let n1 <- USize.checked_div max_usize (USize.ofNatCore 2 (by intlit)) 
+    let (i, i0) := self.hashmap_hash_map_max_load_factor 
+    let i1 <- USize.checked_div n1 i 
     if capacity <= i1
     then
       do
-        let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit))
-        let ntable <- hashmap_hash_map_new_with_capacity_fwd T i2 i i0
+        let i2 <- USize.checked_mul capacity (USize.ofNatCore 2 (by intlit)) 
+        let ntable <- hashmap_hash_map_new_with_capacity_fwd T i2 i i0 
         let (ntable0, _) <-
           hashmap_hash_map_move_elements_fwd_back T ntable
-            self.hashmap_hash_map_slots (USize.ofNatCore 0 (by intlit))
-        result.ret
+            self.hashmap_hash_map_slots (USize.ofNatCore 0 (by intlit)) 
+        Result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
             hashmap_hash_map_max_load_factor := (i, i0),
@@ -274,7 +285,7 @@ def hashmap_hash_map_try_resize_fwd_back
             hashmap_hash_map_slots := ntable0.hashmap_hash_map_slots
           }
     else
-      result.ret
+      Result.ret
         {
           hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
           hashmap_hash_map_max_load_factor := (i, i0),
@@ -285,143 +296,149 @@ def hashmap_hash_map_try_resize_fwd_back
 /- [hashmap_main::hashmap::HashMap::{0}::insert] -/
 def hashmap_hash_map_insert_fwd_back
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) (value : T) :
-  result (hashmap_hash_map_t T)
+  Result (hashmap_hash_map_t T)
   :=
   do
-    let self0 <- hashmap_hash_map_insert_no_resize_fwd_back T self key value
-    let i <- hashmap_hash_map_len_fwd T self0
+    let self0 <- hashmap_hash_map_insert_no_resize_fwd_back T self key value 
+    let i <- hashmap_hash_map_len_fwd T self0 
     if i > self0.hashmap_hash_map_max_load
     then hashmap_hash_map_try_resize_fwd_back T self0
-    else result.ret self0
+    else Result.ret self0
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
 def hashmap_hash_map_contains_key_in_list_loop_fwd
-  (T : Type) (key : USize) (ls : hashmap_list_t T) : (result Bool) :=
+  (T : Type) (key : USize) (ls : hashmap_list_t T) : (Result Bool) :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey t tl =>
     if ckey = key
-    then result.ret true
+    then Result.ret true
     else hashmap_hash_map_contains_key_in_list_loop_fwd T key tl
-  | hashmap_list_t.HashmapListNil => result.ret false
+  | hashmap_list_t.HashmapListNil => Result.ret false
+  
 termination_by hashmap_hash_map_contains_key_in_list_loop_fwd key ls =>
-  hashmap_hash_map_contains_key_in_list_loop_terminates T key ls
+   hashmap_hash_map_contains_key_in_list_loop_terminates T key ls 
 decreasing_by hashmap_hash_map_contains_key_in_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
 def hashmap_hash_map_contains_key_in_list_fwd
-  (T : Type) (key : USize) (ls : hashmap_list_t T) : result Bool :=
+  (T : Type) (key : USize) (ls : hashmap_list_t T) : Result Bool :=
   hashmap_hash_map_contains_key_in_list_loop_fwd T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::contains_key] -/
 def hashmap_hash_map_contains_key_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result Bool :=
+  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result Bool :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
     hashmap_hash_map_contains_key_in_list_fwd T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
 def hashmap_hash_map_get_in_list_loop_fwd
-  (T : Type) (key : USize) (ls : hashmap_list_t T) : (result T) :=
+  (T : Type) (key : USize) (ls : hashmap_list_t T) : (Result T) :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey cvalue tl =>
     if ckey = key
-    then result.ret cvalue
+    then Result.ret cvalue
     else hashmap_hash_map_get_in_list_loop_fwd T key tl
-  | hashmap_list_t.HashmapListNil => result.fail error.panic
+  | hashmap_list_t.HashmapListNil => Result.fail Error.panic
+  
 termination_by hashmap_hash_map_get_in_list_loop_fwd key ls =>
-  hashmap_hash_map_get_in_list_loop_terminates T key ls
+                                                              hashmap_hash_map_get_in_list_loop_terminates
+                                                              T key ls 
 decreasing_by hashmap_hash_map_get_in_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
 def hashmap_hash_map_get_in_list_fwd
-  (T : Type) (key : USize) (ls : hashmap_list_t T) : result T :=
+  (T : Type) (key : USize) (ls : hashmap_list_t T) : Result T :=
   hashmap_hash_map_get_in_list_loop_fwd T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::get] -/
 def hashmap_hash_map_get_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result T :=
+  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result T :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+      vec_index_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
     hashmap_hash_map_get_in_list_fwd T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
 def hashmap_hash_map_get_mut_in_list_loop_fwd
-  (T : Type) (ls : hashmap_list_t T) (key : USize) : (result T) :=
+  (T : Type) (ls : hashmap_list_t T) (key : USize) : (Result T) :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey cvalue tl =>
     if ckey = key
-    then result.ret cvalue
+    then Result.ret cvalue
     else hashmap_hash_map_get_mut_in_list_loop_fwd T tl key
-  | hashmap_list_t.HashmapListNil => result.fail error.panic
+  | hashmap_list_t.HashmapListNil => Result.fail Error.panic
+  
 termination_by hashmap_hash_map_get_mut_in_list_loop_fwd ls key =>
-  hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
+                                                                  hashmap_hash_map_get_mut_in_list_loop_terminates
+                                                                  T ls key 
 decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
 def hashmap_hash_map_get_mut_in_list_fwd
-  (T : Type) (ls : hashmap_list_t T) (key : USize) : result T :=
+  (T : Type) (ls : hashmap_list_t T) (key : USize) : Result T :=
   hashmap_hash_map_get_mut_in_list_loop_fwd T ls key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
 def hashmap_hash_map_get_mut_in_list_loop_back
   (T : Type) (ls : hashmap_list_t T) (key : USize) (ret0 : T) :
-  (result (hashmap_list_t T))
+  (Result (hashmap_list_t T))
   :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey cvalue tl =>
     if ckey = key
-    then result.ret (hashmap_list_t.HashmapListCons ckey ret0 tl)
+    then Result.ret (hashmap_list_t.HashmapListCons ckey ret0 tl)
     else
       do
-        let tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0
-        result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
-  | hashmap_list_t.HashmapListNil => result.fail error.panic
+        let tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T tl key ret0 
+        Result.ret (hashmap_list_t.HashmapListCons ckey cvalue tl0)
+  | hashmap_list_t.HashmapListNil => Result.fail Error.panic
+  
 termination_by hashmap_hash_map_get_mut_in_list_loop_back ls key ret0 =>
-  hashmap_hash_map_get_mut_in_list_loop_terminates T ls key
+   hashmap_hash_map_get_mut_in_list_loop_terminates T ls key 
 decreasing_by hashmap_hash_map_get_mut_in_list_loop_decreases ls key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
 def hashmap_hash_map_get_mut_in_list_back
   (T : Type) (ls : hashmap_list_t T) (key : USize) (ret0 : T) :
-  result (hashmap_list_t T)
+  Result (hashmap_list_t T)
   :=
   hashmap_hash_map_get_mut_in_list_loop_back T ls key ret0
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
 def hashmap_hash_map_get_mut_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result T :=
+  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result T :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
     hashmap_hash_map_get_mut_in_list_fwd T l key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
 def hashmap_hash_map_get_mut_back
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) (ret0 : T) :
-  result (hashmap_hash_map_t T)
+  Result (hashmap_hash_map_t T)
   :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let l0 <- hashmap_hash_map_get_mut_in_list_back T l key ret0
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+    let l0 <- hashmap_hash_map_get_mut_in_list_back T l key ret0 
     let v <-
       vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-        hash_mod l0
-    result.ret
+        hash_mod l0 
+    Result.ret
       {
         hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
         hashmap_hash_map_max_load_factor := self.hashmap_hash_map_max_load_factor,
@@ -431,33 +448,36 @@ def hashmap_hash_map_get_mut_back
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
 def hashmap_hash_map_remove_from_list_loop_fwd
-  (T : Type) (key : USize) (ls : hashmap_list_t T) : (result (Option T)) :=
+  (T : Type) (key : USize) (ls : hashmap_list_t T) : (Result (Option T)) :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey t tl =>
     if ckey = key
     then
       let mv_ls :=
         mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.HashmapListCons ckey
-          t tl) hashmap_list_t.HashmapListNil
+          t tl) hashmap_list_t.HashmapListNil 
       match mv_ls with
       | hashmap_list_t.HashmapListCons i cvalue tl0 =>
-        result.ret (Option.some cvalue)
-      | hashmap_list_t.HashmapListNil => result.fail error.panic
+        Result.ret (Option.some cvalue)
+      | hashmap_list_t.HashmapListNil => Result.fail Error.panic
+      
     else hashmap_hash_map_remove_from_list_loop_fwd T key tl
-  | hashmap_list_t.HashmapListNil => result.ret Option.none
+  | hashmap_list_t.HashmapListNil => Result.ret Option.none
+  
 termination_by hashmap_hash_map_remove_from_list_loop_fwd key ls =>
-  hashmap_hash_map_remove_from_list_loop_terminates T key ls
+                                                                   hashmap_hash_map_remove_from_list_loop_terminates
+                                                                   T key ls 
 decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
 def hashmap_hash_map_remove_from_list_fwd
-  (T : Type) (key : USize) (ls : hashmap_list_t T) : result (Option T) :=
+  (T : Type) (key : USize) (ls : hashmap_list_t T) : Result (Option T) :=
   hashmap_hash_map_remove_from_list_loop_fwd T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
 def hashmap_hash_map_remove_from_list_loop_back
   (T : Type) (key : USize) (ls : hashmap_list_t T) :
-  (result (hashmap_list_t T))
+  (Result (hashmap_list_t T))
   :=
   match ls with
   | hashmap_list_t.HashmapListCons ckey t tl =>
@@ -465,64 +485,68 @@ def hashmap_hash_map_remove_from_list_loop_back
     then
       let mv_ls :=
         mem_replace_fwd (hashmap_list_t T) (hashmap_list_t.HashmapListCons ckey
-          t tl) hashmap_list_t.HashmapListNil
+          t tl) hashmap_list_t.HashmapListNil 
       match mv_ls with
-      | hashmap_list_t.HashmapListCons i cvalue tl0 => result.ret tl0
-      | hashmap_list_t.HashmapListNil => result.fail error.panic
+      | hashmap_list_t.HashmapListCons i cvalue tl0 => Result.ret tl0
+      | hashmap_list_t.HashmapListNil => Result.fail Error.panic
+      
     else
       do
-        let tl0 <- hashmap_hash_map_remove_from_list_loop_back T key tl
-        result.ret (hashmap_list_t.HashmapListCons ckey t tl0)
-  | hashmap_list_t.HashmapListNil => result.ret hashmap_list_t.HashmapListNil
+        let tl0 <- hashmap_hash_map_remove_from_list_loop_back T key tl 
+        Result.ret (hashmap_list_t.HashmapListCons ckey t tl0)
+  | hashmap_list_t.HashmapListNil => Result.ret hashmap_list_t.HashmapListNil
+  
 termination_by hashmap_hash_map_remove_from_list_loop_back key ls =>
-  hashmap_hash_map_remove_from_list_loop_terminates T key ls
+                                                                    hashmap_hash_map_remove_from_list_loop_terminates
+                                                                    T key ls 
 decreasing_by hashmap_hash_map_remove_from_list_loop_decreases key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
 def hashmap_hash_map_remove_from_list_back
   (T : Type) (key : USize) (ls : hashmap_list_t T) :
-  result (hashmap_list_t T)
+  Result (hashmap_list_t T)
   :=
   hashmap_hash_map_remove_from_list_loop_back T key ls
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove] -/
 def hashmap_hash_map_remove_fwd
-  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : result (Option T) :=
+  (T : Type) (self : hashmap_hash_map_t T) (key : USize) : Result (Option T) :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let x <- hashmap_hash_map_remove_from_list_fwd T key l
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+    let x <- hashmap_hash_map_remove_from_list_fwd T key l 
     match x with
-    | Option.none => result.ret Option.none
+    | Option.none => Result.ret Option.none
     | Option.some x0 =>
       do
         let _ <- USize.checked_sub self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit))
-        result.ret (Option.some x0)
+          (USize.ofNatCore 1 (by intlit)) 
+        Result.ret (Option.some x0)
+    
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove] -/
 def hashmap_hash_map_remove_back
   (T : Type) (self : hashmap_hash_map_t T) (key : USize) :
-  result (hashmap_hash_map_t T)
+  Result (hashmap_hash_map_t T)
   :=
   do
-    let hash <- hashmap_hash_key_fwd key
-    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots
-    let hash_mod <- USize.checked_rem hash i
+    let hash <- hashmap_hash_key_fwd key 
+    let i := vec_len (hashmap_list_t T) self.hashmap_hash_map_slots 
+    let hash_mod <- USize.checked_rem hash i 
     let l <-
-      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod
-    let x <- hashmap_hash_map_remove_from_list_fwd T key l
+      vec_index_mut_fwd (hashmap_list_t T) self.hashmap_hash_map_slots hash_mod 
+    let x <- hashmap_hash_map_remove_from_list_fwd T key l 
     match x with
     | Option.none =>
       do
-        let l0 <- hashmap_hash_map_remove_from_list_back T key l
+        let l0 <- hashmap_hash_map_remove_from_list_back T key l 
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        result.ret
+            hash_mod l0 
+        Result.ret
           {
             hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries,
             hashmap_hash_map_max_load_factor := self.hashmap_hash_map_max_load_factor,
@@ -532,101 +556,102 @@ def hashmap_hash_map_remove_back
     | Option.some x0 =>
       do
         let i0 <- USize.checked_sub self.hashmap_hash_map_num_entries
-          (USize.ofNatCore 1 (by intlit))
-        let l0 <- hashmap_hash_map_remove_from_list_back T key l
+          (USize.ofNatCore 1 (by intlit)) 
+        let l0 <- hashmap_hash_map_remove_from_list_back T key l 
         let v <-
           vec_index_mut_back (hashmap_list_t T) self.hashmap_hash_map_slots
-            hash_mod l0
-        result.ret
+            hash_mod l0 
+        Result.ret
           {
             hashmap_hash_map_num_entries := i0,
             hashmap_hash_map_max_load_factor := self.hashmap_hash_map_max_load_factor,
             hashmap_hash_map_max_load := self.hashmap_hash_map_max_load,
             hashmap_hash_map_slots := v
           }
+    
 
 /- [hashmap_main::hashmap::test1] -/
-def hashmap_test1_fwd : result Unit :=
+def hashmap_test1_fwd : Result Unit :=
   do
-    let hm <- hashmap_hash_map_new_fwd UInt64
+    let hm <- hashmap_hash_map_new_fwd UInt64 
     let hm0 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm
-        (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit))
+        (USize.ofNatCore 0 (by intlit)) (UInt64.ofNatCore 42 (by intlit)) 
     let hm1 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm0
-        (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit))
+        (USize.ofNatCore 128 (by intlit)) (UInt64.ofNatCore 18 (by intlit)) 
     let hm2 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm1
-        (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit))
+        (USize.ofNatCore 1024 (by intlit)) (UInt64.ofNatCore 138 (by intlit)) 
     let hm3 <-
       hashmap_hash_map_insert_fwd_back UInt64 hm2
-        (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit))
+        (USize.ofNatCore 1056 (by intlit)) (UInt64.ofNatCore 256 (by intlit)) 
     let i <-
-      hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit))
+      hashmap_hash_map_get_fwd UInt64 hm3 (USize.ofNatCore 128 (by intlit)) 
     if not (i = (UInt64.ofNatCore 18 (by intlit)))
-    then result.fail error.panic
+    then Result.fail Error.panic
     else
       do
         let hm4 <-
           hashmap_hash_map_get_mut_back UInt64 hm3
             (USize.ofNatCore 1024 (by intlit))
-            (UInt64.ofNatCore 56 (by intlit))
+            (UInt64.ofNatCore 56 (by intlit)) 
         let i0 <-
           hashmap_hash_map_get_fwd UInt64 hm4
-            (USize.ofNatCore 1024 (by intlit))
+            (USize.ofNatCore 1024 (by intlit)) 
         if not (i0 = (UInt64.ofNatCore 56 (by intlit)))
-        then result.fail error.panic
+        then Result.fail Error.panic
         else
           do
             let x <-
               hashmap_hash_map_remove_fwd UInt64 hm4
-                (USize.ofNatCore 1024 (by intlit))
+                (USize.ofNatCore 1024 (by intlit)) 
             match x with
-            | Option.none => result.fail error.panic
+            | Option.none => Result.fail Error.panic
             | Option.some x0 =>
               if not (x0 = (UInt64.ofNatCore 56 (by intlit)))
-              then result.fail error.panic
+              then Result.fail Error.panic
               else
                 do
                   let hm5 <-
                     hashmap_hash_map_remove_back UInt64 hm4
-                      (USize.ofNatCore 1024 (by intlit))
+                      (USize.ofNatCore 1024 (by intlit)) 
                   let i1 <-
                     hashmap_hash_map_get_fwd UInt64 hm5
-                      (USize.ofNatCore 0 (by intlit))
+                      (USize.ofNatCore 0 (by intlit)) 
                   if not (i1 = (UInt64.ofNatCore 42 (by intlit)))
-                  then result.fail error.panic
+                  then Result.fail Error.panic
                   else
                     do
                       let i2 <-
                         hashmap_hash_map_get_fwd UInt64 hm5
-                          (USize.ofNatCore 128 (by intlit))
+                          (USize.ofNatCore 128 (by intlit)) 
                       if not (i2 = (UInt64.ofNatCore 18 (by intlit)))
-                      then result.fail error.panic
+                      then Result.fail Error.panic
                       else
                         do
                           let i3 <-
                             hashmap_hash_map_get_fwd UInt64 hm5
-                              (USize.ofNatCore 1056 (by intlit))
+                              (USize.ofNatCore 1056 (by intlit)) 
                           if not (i3 = (UInt64.ofNatCore 256 (by intlit)))
-                          then result.fail error.panic
-                          else result.ret ()
+                          then Result.fail Error.panic
+                          else Result.ret ()
+            
 
 /- Unit test for [hashmap_main::hashmap::test1] -/
 #assert (hashmap_test1_fwd = .ret ())
 
 /- [hashmap_main::insert_on_disk] -/
 def insert_on_disk_fwd
-  (key : USize) (value : UInt64) (st : state) : result (state × Unit) :=
+  (key : USize) (value : UInt64) (st : State) : Result (State × Unit) :=
   do
-    let (st0, hm) <- opaque_defs.hashmap_utils_deserialize_fwd st
-    let hm0 <- hashmap_hash_map_insert_fwd_back UInt64 hm key value
-    let (st1, _) <- opaque_defs.hashmap_utils_serialize_fwd hm0 st0
-    result.ret (st1, ())
+    let (st0, hm) <- opaque_defs.hashmap_utils_deserialize_fwd st 
+    let hm0 <- hashmap_hash_map_insert_fwd_back UInt64 hm key value 
+    let (st1, _) <- opaque_defs.hashmap_utils_serialize_fwd hm0 st0 
+    Result.ret (st1, ())
 
 /- [hashmap_main::main] -/
-def main_fwd : result Unit :=
-  result.ret ()
+def main_fwd : Result Unit := Result.ret ()
 
 /- Unit test for [hashmap_main::main] -/
 #assert (main_fwd = .ret ())
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean b/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean
index ce618a6c..3531e6e0 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Opaque.lean
@@ -7,9 +7,9 @@ structure OpaqueDefs where
   
   /- [hashmap_main::hashmap_utils::deserialize] -/
   hashmap_utils_deserialize_fwd
-    : state -> result (state × (hashmap_hash_map_t UInt64))
+    : State -> Result (State × (hashmap_hash_map_t UInt64))
   
   /- [hashmap_main::hashmap_utils::serialize] -/
   hashmap_utils_serialize_fwd
-    : hashmap_hash_map_t UInt64 -> state -> result (state × Unit)
+    : hashmap_hash_map_t UInt64 -> State -> Result (State × Unit)
   
diff --git a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean b/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
index 2a3ea462..40f9b7e9 100644
--- a/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
+++ b/tests/lean/hashmap_on_disk/HashmapMain/Types.lean
@@ -13,7 +13,7 @@ structure hashmap_hash_map_t (T : Type) where
   hashmap_hash_map_num_entries : USize
   hashmap_hash_map_max_load_factor : (USize × USize)
   hashmap_hash_map_max_load : USize
-  hashmap_hash_map_slots : vec (hashmap_list_t T)
+  hashmap_hash_map_slots : Vec (hashmap_list_t T)
 
-/- The state type used in the state-error monad -/ axiom state : Type
+/- The state type used in the state-error monad -/ axiom State : Type