diff --git a/prototyping/Examples/OpSem.agda b/prototyping/Examples/OpSem.agda
index 25d79139..4b8c2d6d 100644
--- a/prototyping/Examples/OpSem.agda
+++ b/prototyping/Examples/OpSem.agda
@@ -1,11 +1,9 @@
 module Examples.OpSem where
 
 open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; subst)
-open import Luau.Syntax using (var; nil; local_←_; _∙_; done; return; block_is_end; untyped)
+open import Luau.Syntax using (var; nil; local_←_; _∙_; done; return; block_is_end)
 open import Luau.Heap using (emp)
 
-x = var "x"
-
-ex1 : emp ⊢ (local (untyped "x") ← nil ∙ return x ∙ done) ⟶ᴮ (return nil ∙ done) ⊣ emp
+ex1 : emp ⊢ (local (var "x") ← nil ∙ return (var "x") ∙ done) ⟶ᴮ (return nil ∙ done) ⊣ emp
 ex1 = subst
 
diff --git a/prototyping/Examples/Run.agda b/prototyping/Examples/Run.agda
index 9703bd40..90a56a09 100644
--- a/prototyping/Examples/Run.agda
+++ b/prototyping/Examples/Run.agda
@@ -3,7 +3,7 @@
 module Examples.Run where
 
 open import Agda.Builtin.Equality using (_≡_; refl)
-open import Luau.Syntax using (nil; var; _$_; function_⟨_⟩_end; return; _∙_; done; untyped)
+open import Luau.Syntax using (nil; var; _$_; function_⟨_⟩_end; return; _∙_; done)
 open import Luau.Value using (nil)
 open import Luau.Run using (run; return)
 open import Luau.Heap using (emp; lookup-next; next-emp; lookup-next-emp)
@@ -11,8 +11,5 @@ open import Luau.Heap using (emp; lookup-next; next-emp; lookup-next-emp)
 import Agda.Builtin.Equality.Rewrite
 {-# REWRITE lookup-next next-emp lookup-next-emp #-}
 
-x = var "x"
-id = var "id"
-
-ex1 : (run (function "id" ⟨ untyped "x" ⟩ return x ∙ done end ∙ return (id $ nil) ∙ done) ≡ return nil _)
+ex1 : (run (function "id" ⟨ var "x" ⟩ return (var "x") ∙ done end ∙ return (var "id" $ nil) ∙ done) ≡ return nil _)
 ex1 = refl
diff --git a/prototyping/Examples/Syntax.agda b/prototyping/Examples/Syntax.agda
index 9ea1026c..e1e3a403 100644
--- a/prototyping/Examples/Syntax.agda
+++ b/prototyping/Examples/Syntax.agda
@@ -2,13 +2,10 @@ module Examples.Syntax where
 
 open import Agda.Builtin.Equality using (_≡_; refl)
 open import FFI.Data.String using (_++_)
-open import Luau.Syntax using (var; _$_; return; nil; function_⟨_⟩_end; done; _∙_; untyped)
+open import Luau.Syntax using (var; _$_; return; nil; function_⟨_⟩_end; done; _∙_)
 open import Luau.Syntax.ToString using (exprToString; blockToString)
 
-f = var "f"
-x = var "x"
-
-ex1 : exprToString(f $ x) ≡
+ex1 : exprToString(var "f" $ var "x") ≡
   "f(x)"
 ex1 = refl
 
@@ -16,7 +13,7 @@ ex2 : blockToString(return nil ∙ done) ≡
   "return nil"
 ex2 = refl
 
-ex3 : blockToString(function "f" ⟨ untyped "x" ⟩ return x ∙ done end ∙ return f ∙ done) ≡
+ex3 : blockToString(function "f" ⟨ var "x" ⟩ return (var "x") ∙ done end ∙ return (var "f") ∙ done) ≡
   "local function f(x)\n" ++
   "  return x\n" ++
   "end\n" ++
diff --git a/prototyping/Luau/Syntax.agda b/prototyping/Luau/Syntax.agda
index 9182e586..af9eefa2 100644
--- a/prototyping/Luau/Syntax.agda
+++ b/prototyping/Luau/Syntax.agda
@@ -7,12 +7,12 @@ open import Luau.Type using (Type)
 infixr 5 _∙_
 
 data VarDec : Set where
-  untyped : Var → VarDec
-  typed_∈_ : Var → Type → VarDec
+  var : Var → VarDec
+  var_∈_ : Var → Type → VarDec
 
 name : VarDec → Var
-name (untyped x) = x
-name (typed x ∈ T) = x
+name (var x) = x
+name (var x ∈ T) = x
 
 data Block : Set
 data Stat : Set
diff --git a/prototyping/Luau/Syntax/FromJSON.agda b/prototyping/Luau/Syntax/FromJSON.agda
index 311c6465..f09ea887 100644
--- a/prototyping/Luau/Syntax/FromJSON.agda
+++ b/prototyping/Luau/Syntax/FromJSON.agda
@@ -1,6 +1,6 @@
 module Luau.Syntax.FromJSON where
 
-open import Luau.Syntax using (Block; Stat ; Expr; nil; _$_; var; function⟨_⟩_end; local_←_; function_⟨_⟩_end; return; done; _∙_; untyped)
+open import Luau.Syntax using (Block; Stat ; Expr; nil; _$_; var; function⟨_⟩_end; local_←_; function_⟨_⟩_end; return; done; _∙_)
 
 open import Agda.Builtin.List using (List; _∷_; [])
 
@@ -55,7 +55,7 @@ exprFromObject obj | just (string "AstExprCall") | _ | nothing  = Left ("AstExpr
 exprFromObject obj | just (string "AstExprConstantNil") = Right nil
 exprFromObject obj | just (string "AstExprFunction") with lookup args obj | lookup body obj
 exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value with head arr | blockFromJSON value
-exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value | just (string x) | Right B = Right (function⟨ untyped x ⟩ B end)
+exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value | just (string x) | Right B = Right (function⟨ var x ⟩ B end)
 exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value | just _ | Right B = Left "AstExprFunction args not a string array"
 exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value | nothing | Right B = Left "Unsupported AstExprFunction empty args"
 exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value | _ | Left err = Left err
@@ -78,7 +78,7 @@ statFromObject obj with lookup type obj
 statFromObject obj | just(string "AstStatLocal") with lookup vars obj | lookup values obj
 statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) with head(arr1) | head(arr2)
 statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) | just(string x) | just(value) with exprFromJSON(value)
-statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) | just(string x) | just(value) | Right M = Right (local untyped x ← M)
+statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) | just(string x) | just(value) | Right M = Right (local (var x) ← M)
 statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) | just(string x) | just(value) | Left err = Left err
 statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) | just(string x) | nothing = Left "AstStatLocal empty values"
 statFromObject obj | just(string "AstStatLocal") | just(array arr1) | just(array arr2) | just(_) | _ = Left "AstStatLocal vars not a string array"
diff --git a/prototyping/Luau/Syntax/ToString.agda b/prototyping/Luau/Syntax/ToString.agda
index 635c2f6c..8d533d31 100644
--- a/prototyping/Luau/Syntax/ToString.agda
+++ b/prototyping/Luau/Syntax/ToString.agda
@@ -1,14 +1,14 @@
 module Luau.Syntax.ToString where
 
-open import Luau.Syntax using (Block; Stat; Expr; VarDec; nil; var; addr; _$_; function⟨_⟩_end; return; function_⟨_⟩_end ;local_←_; _∙_; done; block_is_end; typed_∈_; untyped)
+open import Luau.Syntax using (Block; Stat; Expr; VarDec; nil; var; var_∈_; addr; _$_; function⟨_⟩_end; return; function_⟨_⟩_end ;local_←_; _∙_; done; block_is_end)
 open import FFI.Data.String using (String; _++_)
 open import Luau.Addr.ToString using (addrToString)
 open import Luau.Type.ToString using (typeToString)
 open import Luau.Var.ToString using (varToString)
 
 varDecToString : VarDec → String
-varDecToString (untyped x) = varToString x
-varDecToString (typed x ∈ T) =  varToString x ++ " : " ++ typeToString T
+varDecToString (var x) = varToString x
+varDecToString (var x ∈ T) =  varToString x ++ " : " ++ typeToString T
 
 exprToString′ : String → Expr → String
 statToString′ : String → Stat → String
diff --git a/prototyping/Properties.agda b/prototyping/Properties.agda
index a3c685d1..a8b59f30 100644
--- a/prototyping/Properties.agda
+++ b/prototyping/Properties.agda
@@ -1,3 +1,5 @@
 module Properties where
 
 import Properties.Dec
+import Properties.Remember
+import Properties.Step