Track untyped v typed syntax

prototyping/Examples/OpSem.agda

@@ -1,7 +1,7 @@
 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)
+open import Luau.Syntax using (Block; no; var; nil; local_←_; _∙_; done; return; block_is_end)
 open import Luau.Heap using (∅)
 
 ex1 : ∅ ⊢ (local (var "x") ← nil ∙ return (var "x") ∙ done) ⟶ᴮ (return nil ∙ done) ⊣ ∅

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; _$_; function_⟨_⟩_end; return; _∙_; done)
+open import Luau.Syntax using (nil; var; _$_; function_is_end; return; _∙_; done; _⟨_⟩)
 open import Luau.Value using (nil)
 open import Luau.Run using (run; return)
 open import Luau.Heap using (lookup-next; next-emp; lookup-next-emp)
@@ -11,5 +11,5 @@ open import Luau.Heap using (lookup-next; next-emp; lookup-next-emp)
 import Agda.Builtin.Equality.Rewrite
 {-# REWRITE lookup-next next-emp lookup-next-emp #-}
 
-ex1 : (run (function "id" ⟨ var "x" ⟩ return (var "x") ∙ done end ∙ return (var "id" $ nil) ∙ done) ≡ return nil _)
+ex1 : (run (function "id" ⟨ var "x" ⟩ is return (var "x") ∙ done end ∙ return (var "id" $ nil) ∙ done) ≡ return nil _)
 ex1 = refl

prototyping/Examples/Syntax.agda

@@ -2,18 +2,21 @@ module Examples.Syntax where
 
 open import Agda.Builtin.Equality using (_≡_; refl)
 open import FFI.Data.String using (_++_)
-open import Luau.Syntax using (var; _$_; return; nil; function_⟨_⟩_end; done; _∙_)
+open import Luau.Syntax using (var; _$_; return; nil; function_is_end; local_←_; done; _∙_; _⟨_⟩; anon⟨_⟩)
 open import Luau.Syntax.ToString using (exprToString; blockToString)
 
-ex1 : exprToString(var "f" $ var "x") ≡
+ex1 : exprToString(function anon⟨ var "x" ⟩ is return (var "f" $ var "x") ∙ done end) ≡
-  "f(x)"
+  "function (x)\n" ++
+  "  return f(x)\n" ++
+  "end"
 ex1 = refl
 
-ex2 : blockToString(return nil ∙ done) ≡
+ex2 : blockToString(local var "x" ← nil ∙ return (var "x") ∙ done) ≡
-  "return nil"
+  "local x = nil\n" ++
+  "return x"
 ex2 = refl
 
-ex3 : blockToString(function "f" ⟨ var "x" ⟩ return (var "x") ∙ done end ∙ return (var "f") ∙ done) ≡
+ex3 : blockToString(function "f" ⟨ var "x" ⟩ is return (var "x") ∙ done end ∙ return (var "f") ∙ done) ≡
   "local function f(x)\n" ++
   "  return x\n" ++
   "end\n" ++

prototyping/Interpreter.agda

@@ -18,7 +18,7 @@ open import Luau.Run using (run; return; done; error)
 open import Luau.RuntimeError.ToString using (errToStringᴮ)
 open import Luau.Value.ToString using (valueToString)
 
-runBlock : Block → IO ⊤
+runBlock : ∀ {a} → Block a → IO ⊤
 runBlock block with run block
 runBlock block | return V D = putStrLn (valueToString V)
 runBlock block | done D = putStrLn "nil"

prototyping/Luau/Heap.agda

@@ -5,36 +5,37 @@ open import FFI.Data.Maybe using (Maybe; just)
 open import FFI.Data.Vector using (Vector; length; snoc; empty)
 open import Luau.Addr using (Addr)
 open import Luau.Var using (Var)
-open import Luau.Syntax using (Block; Expr; VarDec; nil; addr; function⟨_⟩_end)
+open import Luau.Syntax using (Block; Expr; Annotated; FunDec; nil; addr; function_is_end)
 
-data HeapValue : Set where
+data HeapValue (a : Annotated) : Set where
-  function_⟨_⟩_end : Var → VarDec → Block → HeapValue
+  function_is_end : FunDec a → Block a → HeapValue a
 
-Heap = Vector HeapValue
+Heap : Annotated → Set
+Heap a = Vector (HeapValue a)
 
-data _≡_⊕_↦_ : Heap → Heap → Addr → HeapValue → Set where
+data _≡_⊕_↦_ {a} : Heap a → Heap a → Addr → HeapValue a → Set where
 
   defn : ∀ {H val} →
 
     -----------------------------------
     (snoc H val) ≡ H ⊕ (length H) ↦ val
 
-_[_] : Heap → Addr → Maybe HeapValue
+_[_] : ∀ {a} → Heap a → Addr → Maybe (HeapValue a)
 _[_] = FFI.Data.Vector.lookup
 
-∅ : Heap
+∅ : ∀ {a} → Heap a
 ∅ = empty
 
-data AllocResult (H : Heap) (V : HeapValue) : Set where
+data AllocResult a (H : Heap a) (V : HeapValue a) : Set where
-  ok : ∀ a H′ → (H′ ≡ H ⊕ a ↦ V) → AllocResult H V
+  ok : ∀ b H′ → (H′ ≡ H ⊕ b ↦ V) → AllocResult a H V
 
-alloc : ∀ H V → AllocResult H V
+alloc : ∀ {a} H V → AllocResult a H V
 alloc H V = ok (length H) (snoc H V) defn
 
-next : Heap → Addr
+next : ∀ {a} → Heap a → Addr
 next = length
 
-allocated : Heap → HeapValue → Heap
+allocated : ∀ {a} → Heap a → HeapValue a → Heap a
 allocated = snoc
 
 -- next-emp : (length empty ≡ 0)

prototyping/Luau/OpSem.agda

@@ -2,13 +2,13 @@ module Luau.OpSem where
 
 open import Agda.Builtin.Equality using (_≡_)
 open import FFI.Data.Maybe using (just)
-open import Luau.Heap using (Heap; _≡_⊕_↦_; _[_]; function_⟨_⟩_end)
+open import Luau.Heap using (Heap; _≡_⊕_↦_; _[_]; function_is_end)
 open import Luau.Substitution using (_[_/_]ᴮ)
-open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; function⟨_⟩_end; _$_; block_is_end; local_←_; _∙_; done; function_⟨_⟩_end; return; name)
+open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name; fun; arg; namify)
 open import Luau.Value using (addr; val)
 
-data _⊢_⟶ᴮ_⊣_ : Heap → Block → Block → Heap → Set
+data _⊢_⟶ᴮ_⊣_ {a} : Heap a → Block a → Block a → Heap a → Set
-data _⊢_⟶ᴱ_⊣_ : Heap → Expr → Expr → Heap → Set
+data _⊢_⟶ᴱ_⊣_ {a} : Heap a → Expr a → Expr a → Heap a → Set
 
 data _⊢_⟶ᴱ_⊣_  where
 
@@ -17,11 +17,11 @@ data _⊢_⟶ᴱ_⊣_  where
     -------------------
     H ⊢ nil ⟶ᴱ nil ⊣ H
 
-  function : ∀ {H H′ a x B} →
+  function : ∀ {H H′ a F B} →
 
-    H′ ≡ H ⊕ a ↦ (function "anon" ⟨ x ⟩ B end) →
+    H′ ≡ H ⊕ a ↦ (function (namify F) is B end) →
     -------------------------------------------
-    H ⊢ (function⟨ x ⟩ B end) ⟶ᴱ (addr a) ⊣ H′
+    H ⊢ (function F is B end) ⟶ᴱ (addr a) ⊣ H′
 
   app : ∀ {H H′ M M′ N} →
   
@@ -29,11 +29,11 @@ data _⊢_⟶ᴱ_⊣_  where
     -----------------------------
     H ⊢ (M $ N) ⟶ᴱ (M′ $ N) ⊣ H′
 
-  beta : ∀ {H M a f x B} →
+  beta : ∀ {H M a F B} →
   
-    H [ a ] ≡ just(function f ⟨ x ⟩ B end) →
+    H [ a ] ≡ just(function F is B end) →
     -----------------------------------------------------
-    H ⊢ (addr a $ M) ⟶ᴱ (block f is local x ← M ∙ B end) ⊣ H
+    H ⊢ (addr a $ M) ⟶ᴱ (block (fun F) is local (arg F) ← M ∙ B end) ⊣ H
 
   block : ∀ {H H′ B B′ b} →
  
@@ -64,11 +64,11 @@ data _⊢_⟶ᴮ_⊣_  where
     ------------------------------------------------------
     H ⊢ (local x ← val v ∙ B) ⟶ᴮ (B [ v / name x ]ᴮ) ⊣ H
 
-  function : ∀ {H H′ a f x B C} →
+  function : ∀ {H H′ a F B C} →
   
-    H′ ≡ H ⊕ a ↦ (function f ⟨ x ⟩ C end) →
+    H′ ≡ H ⊕ a ↦ (function F is C end) →
     --------------------------------------------------------------
-    H ⊢ (function f ⟨ x ⟩ C end ∙ B) ⟶ᴮ (B [ addr a / f ]ᴮ) ⊣ H′
+    H ⊢ (function F is C end ∙ B) ⟶ᴮ (B [ addr a / fun F ]ᴮ) ⊣ H′
 
   return : ∀ {H H′ M M′ B} →
   
@@ -76,7 +76,7 @@ data _⊢_⟶ᴮ_⊣_  where
     --------------------------------------------
     H ⊢ (return M ∙ B) ⟶ᴮ (return M′ ∙ B) ⊣ H′
 
-data _⊢_⟶*_⊣_ : Heap → Block → Block → Heap → Set where
+data _⊢_⟶*_⊣_ {a} : Heap a → Block a → Block a → Heap a → Set where
 
   refl : ∀ {H B} →
 

prototyping/Luau/Run.agda

@@ -8,13 +8,13 @@ open import Luau.Value using (val)
 open import Properties.Step using (stepᴮ; step; return; done; error)
 open import Luau.RuntimeError using (RuntimeErrorᴮ)
 
-data RunResult (H : Heap) (B : Block) : Set where
+data RunResult {a} (H : Heap a) (B : Block a) : Set where
   return : ∀ V {B′ H′} → (H ⊢ B ⟶* (return (val V) ∙ B′) ⊣ H′) → RunResult H B
   done : ∀ {H′} → (H ⊢ B ⟶* done ⊣ H′) → RunResult H B
   error : ∀ {B′ H′} → (RuntimeErrorᴮ H′ B′) → (H ⊢ B ⟶* B′ ⊣ H′) → RunResult H B
 
 {-# TERMINATING #-}
-run′ : ∀ H B → RunResult H B
+run′ : ∀ {a} H B → RunResult {a} H B
 run′ H B with stepᴮ H B
 run′ H B | step H′ B′ D with run′ H′ B′
 run′ H B | step H′ B′ D | return V D′  = return V (step D D′)
@@ -24,5 +24,5 @@ run′ H _ | return V refl = return V refl
 run′ H _ | done refl = done refl
 run′ H B | error E = error E refl
 
-run : ∀ B → RunResult ∅ B
+run : ∀ {a} B → RunResult {a} ∅ B
 run = run′ ∅

prototyping/Luau/RuntimeError.agda

@@ -3,10 +3,10 @@ module Luau.RuntimeError where
 open import Agda.Builtin.Equality using (_≡_)
 open import Luau.Heap using (Heap; _[_])
 open import FFI.Data.Maybe using (just; nothing)
-open import Luau.Syntax using (Block; Expr; nil; var; addr; function⟨_⟩_end; block_is_end; _$_; local_←_; function_⟨_⟩_end; return; done; _∙_)
+open import Luau.Syntax using (Block; Expr; nil; var; addr; block_is_end; _$_; local_←_; return; done; _∙_)
 
-data RuntimeErrorᴮ (H : Heap) : Block → Set
+data RuntimeErrorᴮ {a} (H : Heap a) : Block a → Set
-data RuntimeErrorᴱ (H : Heap) : Expr → Set
+data RuntimeErrorᴱ {a} (H : Heap a) : Expr a → Set
 
 data RuntimeErrorᴱ H where
   NilIsNotAFunction : ∀ {M} → RuntimeErrorᴱ H (nil $ M)

prototyping/Luau/RuntimeError/ToString.agda

@@ -6,8 +6,8 @@ open import Luau.Addr.ToString using (addrToString)
 open import Luau.Var.ToString using (varToString)
 open import Luau.Syntax using (name)
 
-errToStringᴱ : ∀ {H B} → RuntimeErrorᴱ H B → String
+errToStringᴱ : ∀ {a H B} → RuntimeErrorᴱ {a} H B → String
-errToStringᴮ : ∀ {H B} → RuntimeErrorᴮ H B → String
+errToStringᴮ : ∀ {a H B} → RuntimeErrorᴮ {a} H B → String
 
 errToStringᴱ NilIsNotAFunction = "nil is not a function"
 errToStringᴱ (UnboundVariable x) = "variable " ++ varToString x ++ " is unbound"

prototyping/Luau/Substitution.agda

@@ -1,23 +1,23 @@
 module Luau.Substitution where
 
-open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; function⟨_⟩_end; _$_; block_is_end; local_←_; _∙_; done; function_⟨_⟩_end; return; name)
+open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; _⟨_⟩ ; name; fun; arg; namify)
 open import Luau.Value using (Value; val)
 open import Luau.Var using (Var; _≡ⱽ_)
 open import Properties.Dec using (Dec; yes; no)
 
-_[_/_]ᴱ : Expr → Value → Var → Expr
+_[_/_]ᴱ : ∀ {a} → Expr a → Value → Var → Expr a
-_[_/_]ᴮ : Block → Value → Var → Block
+_[_/_]ᴮ : ∀ {a} → Block a → Value → Var → Block a
-var_[_/_]ᴱwhenever_ : ∀ {P} → Var → Value → Var → (Dec P) → Expr
+var_[_/_]ᴱwhenever_ : ∀ {a P} → Var → Value → Var → (Dec P) → Expr a
-_[_/_]ᴮunless_ : ∀ {P} → Block → Value → Var → (Dec P) → Block
+_[_/_]ᴮunless_ : ∀ {a P} → Block a → Value → Var → (Dec P) → Block a
 
 nil [ v / x ]ᴱ = nil
 var y [ v / x ]ᴱ = var y [ v / x ]ᴱwhenever (x ≡ⱽ y)
 addr a [ v / x ]ᴱ = addr a
 (M $ N) [ v / x ]ᴱ = (M [ v / x ]ᴱ) $ (N [ v / x ]ᴱ)
-function⟨ y ⟩ C end [ v / x ]ᴱ = function⟨ y ⟩ C [ v / x ]ᴮunless (x ≡ⱽ name y) end
+function F is C end [ v / x ]ᴱ = function F is C [ v / x ]ᴮunless (x ≡ⱽ name(arg(namify F))) end
 block b is C end [ v / x ]ᴱ = block b is C [ v / x ]ᴮ end
 
-(function f ⟨ y ⟩ C end ∙ B) [ v / x ]ᴮ = function f ⟨ y ⟩ (C [ v / x ]ᴮunless (x ≡ⱽ name y)) end ∙ (B [ v / x ]ᴮunless (x ≡ⱽ f))
+(function F is C end ∙ B) [ v / x ]ᴮ = function F is (C [ v / x ]ᴮunless (x ≡ⱽ name(arg F))) end ∙ (B [ v / x ]ᴮunless (x ≡ⱽ fun F))
 (local y ← M ∙ B) [ v / x ]ᴮ = local y ← (M [ v / x ]ᴱ) ∙ (B [ v / x ]ᴮunless (x ≡ⱽ name y))
 (return M ∙ B) [ v / x ]ᴮ = return (M [ v / x ]ᴱ) ∙ (B [ v / x ]ᴮ)
 done [ v / x ]ᴮ = done

prototyping/Luau/Syntax.agda

@@ -1,37 +1,63 @@
 module Luau.Syntax where
 
-open import Luau.Var using (Var)
+open import Agda.Builtin.Equality using (_≡_)
+open import Properties.Dec using (⊥)
+open import Luau.Var using (Var; anon)
 open import Luau.Addr using (Addr)
 open import Luau.Type using (Type)
 
 infixr 5 _∙_
 
-data VarDec : Set where
+data Annotated : Set where
-  var : Var → VarDec
+  maybe : Annotated
-  var_∈_ : Var → Type → VarDec
+  yes : Annotated
 
-name : VarDec → Var
+data VarDec : Annotated → Set where
+  var : Var → VarDec maybe
+  var_∈_ : ∀ {a} → Var → Type → VarDec a
+
+name : ∀ {a} → VarDec a → Var
 name (var x) = x
 name (var x ∈ T) = x
 
-data Block : Set
+data FunDec : Annotated → Set where
-data Stat : Set
+  _⟨_⟩∈_ : ∀ {a} → Var → VarDec a → Type → FunDec a
-data Expr : Set
+  _⟨_⟩ : Var → VarDec maybe → FunDec maybe
 
-data Block where
+data AnonFunDec : Annotated → Set where
-  _∙_ : Stat → Block → Block
+  anon⟨_⟩∈_ : ∀ {a} → VarDec a → Type → AnonFunDec a
-  done : Block
+  anon⟨_⟩ : VarDec maybe → AnonFunDec maybe
 
-data Stat where
+fun : ∀ {a} → FunDec a → Var
-  function_⟨_⟩_end : Var → VarDec → Block → Stat
+fun (f ⟨ x ⟩∈ T) = f
-  local_←_ : VarDec → Expr → Stat
+fun (f ⟨ x ⟩) = f
-  return : Expr → Stat
 
-data Expr where
+arg : ∀ {a} → FunDec a → VarDec a
-  nil : Expr
+arg (f ⟨ x ⟩∈ T) = x
-  var : Var → Expr
+arg (f ⟨ x ⟩) = x
-  addr : Addr → Expr
+
-  _$_ : Expr → Expr → Expr
+namify : ∀ {a} → AnonFunDec a → FunDec a
-  function⟨_⟩_end : VarDec → Block → Expr
+namify (anon⟨ x ⟩∈ T) = anon ⟨ x ⟩∈ T
-  block_is_end : Var → Block → Expr
+namify anon⟨ x ⟩ = anon ⟨ x ⟩
+
+data Block (a : Annotated) : Set
+data Stat (a : Annotated) : Set
+data Expr (a : Annotated) : Set
+
+data Block a where
+  _∙_ : Stat a → Block a → Block a
+  done : Block a
+
+data Stat a where
+  function_is_end : FunDec a → Block a → Stat a
+  local_←_ : VarDec a → Expr a → Stat a
+  return : Expr a → Stat a
+
+data Expr a where
+  nil : Expr a
+  var : Var → Expr a
+  addr : Addr → Expr a
+  _$_ : Expr a → Expr a → Expr a
+  function_is_end : AnonFunDec a → Block a → Expr a
+  block_is_end : Var → Block a → Expr a
 

prototyping/Luau/Syntax/FromJSON.agda

@@ -1,6 +1,6 @@
 module Luau.Syntax.FromJSON where
 
-open import Luau.Syntax using (Block; Stat ; Expr; nil; _$_; var; function⟨_⟩_end; local_←_; function_⟨_⟩_end; return; done; _∙_)
+open import Luau.Syntax using (Block; Stat ; Expr; nil; _$_; var; function_is_end; anon⟨_⟩; _⟨_⟩; local_←_; return; done; _∙_; maybe)
 
 open import Agda.Builtin.List using (List; _∷_; [])
 
@@ -31,12 +31,12 @@ lookupIn (key ∷ keys) obj with lookup (fromString key) obj
 lookupIn (key ∷ keys) obj | nothing = lookupIn keys obj
 lookupIn (key ∷ keys) obj | just value = (key , value)
 
-exprFromJSON : Value → Either String Expr
+exprFromJSON : Value → Either String (Expr maybe)
-exprFromObject : Object → Either String Expr
+exprFromObject : Object → Either String (Expr maybe)
-statFromJSON : Value → Either String Stat
+statFromJSON : Value → Either String (Stat maybe)
-statFromObject : Object → Either String Stat
+statFromObject : Object → Either String (Stat maybe)
-blockFromJSON : Value → Either String Block
+blockFromJSON : Value → Either String (Block maybe)
-blockFromArray : Array → Either String Block
+blockFromArray : Array → Either String (Block maybe)
 
 exprFromJSON (object obj) = exprFromObject obj
 exprFromJSON val = Left "AstExpr not an object"
@@ -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⟨ var x ⟩ B end)
+exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just value | just (string x) | Right B = Right (function anon⟨ var x ⟩ is 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
@@ -89,7 +89,7 @@ statFromObject obj | just(string "AstStatLocal") | just(_) | nothing = Left "Ast
 statFromObject obj | just(string "AstStatLocal") | nothing | _ = Left "AstStatLocal missing vars"
 statFromObject obj | just(string "AstStatLocalFunction") with lookup name obj | lookup func obj
 statFromObject obj | just(string "AstStatLocalFunction") | just (string f) | just value with exprFromJSON value
-statFromObject obj | just(string "AstStatLocalFunction") | just (string f) | just value | Right (function⟨ x ⟩ B end) = Right (function f ⟨ x ⟩ B end)
+statFromObject obj | just(string "AstStatLocalFunction") | just (string f) | just value | Right (function anon⟨ x ⟩ is B end) = Right (function f ⟨ x ⟩ is B end)
 statFromObject obj | just(string "AstStatLocalFunction") | just (string f) | just value | Left err = Left err
 statFromObject obj | just(string "AstStatLocalFunction") | just _ | just _ | Right _ = Left "AstStatLocalFunction func is not an AstExprFunction"
 statFromObject obj | just(string "AstStatLocalFunction") | just _ | just _ =  Left "AstStatLocalFunction name is not a string"

prototyping/Luau/Syntax/ToString.agda

@@ -1,18 +1,26 @@
 module Luau.Syntax.ToString where
 
-open import Luau.Syntax using (Block; Stat; Expr; VarDec; nil; var; var_∈_; addr; _$_; function⟨_⟩_end; return; function_⟨_⟩_end ;local_←_; _∙_; done; block_is_end)
+open import Luau.Syntax using (Block; Stat; Expr; VarDec; FunDec; AnonFunDec; nil; var; var_∈_; addr; _$_; function_is_end; return; local_←_; _∙_; done; block_is_end; _⟨_⟩; _⟨_⟩∈_; anon⟨_⟩; anon⟨_⟩∈_)
 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 : ∀ {a} → VarDec a → String
 varDecToString (var x) = varToString x
 varDecToString (var x ∈ T) =  varToString x ++ " : " ++ typeToString T
 
-exprToString′ : String → Expr → String
+funDecToString : ∀ {a} → FunDec a → String
-statToString′ : String → Stat → String
+funDecToString (f ⟨ x ⟩∈ T) = varToString f ++ "(" ++ varDecToString x ++ "): " ++ typeToString T
-blockToString′ : String → Block → String
+funDecToString (f ⟨ x ⟩) = varToString f ++ "(" ++ varDecToString x ++ ")"
+
+anonFunDecToString : ∀ {a} → AnonFunDec a → String
+anonFunDecToString (anon⟨ x ⟩∈ T) = "(" ++ varDecToString x ++ "): " ++ typeToString T
+anonFunDecToString anon⟨ x ⟩ =  "(" ++ varDecToString x ++ ")"
+
+exprToString′ : ∀ {a} → String → Expr a → String
+statToString′ : ∀ {a} → String → Stat a → String
+blockToString′ : ∀ {a} → String → Block a → String
 
 exprToString′ lb nil =
   "nil"
@@ -22,8 +30,8 @@ exprToString′ lb (var x) =
   varToString(x)
 exprToString′ lb (M $ N) =
   (exprToString′ lb M) ++ "(" ++ (exprToString′ lb N) ++ ")"
-exprToString′ lb (function⟨ x ⟩ B end) =
+exprToString′ lb (function F is B end) =
-  "function(" ++ varDecToString x ++ ")" ++ lb ++
+  "function " ++ anonFunDecToString F ++ lb ++
   "  " ++ (blockToString′ (lb ++ "  ") B) ++ lb ++
   "end"
 exprToString′ lb (block b is B end) =
@@ -31,8 +39,8 @@ exprToString′ lb (block b is B end) =
   "  " ++ (blockToString′ (lb ++ "  ") B) ++ lb ++
   "end)()"
 
-statToString′ lb (function f ⟨ x ⟩ B end) =
+statToString′ lb (function F is B end) =
-  "local function " ++ f ++ "(" ++ varDecToString x ++ ")" ++ lb ++
+  "local function " ++ funDecToString F ++ lb ++
   "  " ++ (blockToString′ (lb ++ "  ") B) ++ lb ++
   "end"
 statToString′ lb (local x ← M) =
@@ -44,11 +52,11 @@ blockToString′ lb (S ∙ done) = statToString′ lb S
 blockToString′ lb (S ∙ B) = statToString′ lb S ++ lb ++ blockToString′ lb B
 blockToString′ lb (done) = ""
 
-exprToString : Expr → String
+exprToString : ∀ {a} → Expr a → String
 exprToString = exprToString′ "\n"
 
-statToString : Stat → String
+statToString : ∀ {a} → Stat a → String
 statToString = statToString′ "\n"
 
-blockToString : Block → String
+blockToString : ∀ {a} → Block a → String
 blockToString = blockToString′ "\n"

prototyping/Luau/TypeCheck.agda

@@ -2,10 +2,10 @@ module Luau.TypeCheck where
 
 open import Agda.Builtin.Equality using (_≡_)
 open import FFI.Data.Maybe using (Maybe; just)
-open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; var_∈_; function⟨_⟩_end; _$_; block_is_end; local_←_; _∙_; done; function_⟨_⟩_end; return; name)
+open import Luau.Syntax using (Expr; Stat; Block; yes; nil; addr; var; var_∈_; _⟨_⟩∈_; anon⟨_⟩∈_; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name)
 open import Luau.Var using (Var)
 open import Luau.Addr using (Addr)
-open import Luau.Heap using (Heap; HeapValue; function_⟨_⟩_end) renaming (_[_] to _[_]ᴴ)
+open import Luau.Heap using (Heap; HeapValue; function_is_end) renaming (_[_] to _[_]ᴴ)
 open import Luau.Value using (addr; val)
 open import Luau.Type using (Type; nil; any; _⇒_; src; tgt)
 open import Luau.AddrCtxt using (AddrCtxt) renaming (_[_] to _[_]ᴬ)
@@ -13,8 +13,8 @@ open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) re
 open import FFI.Data.Vector using (Vector)
 open import FFI.Data.Maybe using (Maybe; just; nothing)
 
-data _▷_⊢ᴮ_∋_∈_⊣_ : AddrCtxt → VarCtxt → Type → Block → Type → VarCtxt → Set
+data _▷_⊢ᴮ_∋_∈_⊣_ : AddrCtxt → VarCtxt → Type → Block yes → Type → VarCtxt → Set
-data _▷_⊢ᴱ_∋_∈_⊣_ : AddrCtxt → VarCtxt → Type → Expr → Type → VarCtxt → Set
+data _▷_⊢ᴱ_∋_∈_⊣_ : AddrCtxt → VarCtxt → Type → Expr yes → Type → VarCtxt → Set
 
 data _▷_⊢ᴮ_∋_∈_⊣_ where
 
@@ -41,7 +41,7 @@ data _▷_⊢ᴮ_∋_∈_⊣_ where
     Σ ▷ (Γ ⊕ x ↦ T) ⊢ᴮ any ∋ C ∈ U ⊣ Δ₁ →
     Σ ▷ (Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ S ∋ B ∈ V ⊣ Δ₂ →
     ---------------------------------------------------------------------------
-    Σ ▷ Γ ⊢ᴮ S ∋ function f ⟨ var x ∈ T ⟩ C end ∙ B ∈ V ⊣ ((Δ₁ ⊝ x) ⋒ (Δ₂ ⊝ f))
+    Σ ▷ Γ ⊢ᴮ S ∋ function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B ∈ V ⊣ ((Δ₁ ⊝ x) ⋒ (Δ₂ ⊝ f))
 
 data _▷_⊢ᴱ_∋_∈_⊣_  where
 
@@ -69,11 +69,11 @@ data _▷_⊢ᴱ_∋_∈_⊣_  where
     --------------------------------------
     Σ ▷ Γ ⊢ᴱ S ∋ (M $ N) ∈ (tgt T) ⊣ (Δ₁ ⋒ Δ₂)
 
-  function : ∀ {Σ x B S T U Γ Δ} →
+  function : ∀ {Σ x B S T U V Γ Δ} →
 
-    Σ ▷ (Γ ⊕ x ↦ T) ⊢ᴮ any ∋ B ∈ U ⊣ Δ →
+    Σ ▷ (Γ ⊕ x ↦ T) ⊢ᴮ U ∋ B ∈ V ⊣ Δ →
-    --------------------------------------------------------------
+    ----------------------------------------------------------------------
-    Σ ▷ Γ ⊢ᴱ S ∋ (function⟨ var x ∈ T ⟩ B end) ∈ (T ⇒ U) ⊣ (Δ ⊝ x)
+    Σ ▷ Γ ⊢ᴱ S ∋ (function anon⟨ var x ∈ T ⟩∈ U is B end) ∈ (T ⇒ U) ⊣ (Δ ⊝ x)
 
   block : ∀ {Σ b B S T Γ Δ} →
 
@@ -81,19 +81,19 @@ data _▷_⊢ᴱ_∋_∈_⊣_  where
     ----------------------------------------------------
     Σ ▷ Γ ⊢ᴱ S ∋ (block b is B end) ∈ T ⊣ Δ
 
-data _▷_∈_ (Σ : AddrCtxt) : (Maybe HeapValue) → (Maybe Type) → Set where
+data _▷_∈_ (Σ : AddrCtxt) : Maybe (HeapValue yes) → (Maybe Type) → Set where
 
   nothing :
 
     ---------------------
     Σ ▷ nothing ∈ nothing
 
-  function : ∀ {f x B T} →
+  function : ∀ {f x B T U V W} →
 
-    Σ ▷ ∅ ⊢ᴱ any ∋ (function⟨ x ⟩ B end) ∈ T ⊣ ∅ →
+    Σ ▷ (x ↦ T) ⊢ᴮ U ∋ B ∈ V ⊣ (x ↦ W) →
-    ------------------------------------------------
+    --------------------------------------------------------------
-    Σ ▷ just (function f ⟨ x ⟩ B end) ∈ just T
+    Σ ▷ just (function f ⟨ var x ∈ T ⟩∈ U is B end) ∈ just (T ⇒ U)
 
-data _▷_✓ (Σ : AddrCtxt) (H : Heap) : Set where
+data _▷_✓ (Σ : AddrCtxt) (H : Heap yes) : Set where
 
-  defn : (∀ a → Σ ▷ (H [ a ]ᴴ) ∈ (Σ [ a ]ᴬ)) → (Σ ▷ H ✓)
+   defn : (∀ a → Σ ▷ (H [ a ]ᴴ) ∈ (Σ [ a ]ᴬ)) → (Σ ▷ H ✓)

prototyping/Luau/Value.agda

@@ -1,14 +1,14 @@
 module Luau.Value where
 
 open import Luau.Addr using (Addr)
-open import Luau.Syntax using (Block; Expr; nil; addr; function⟨_⟩_end)
+open import Luau.Syntax using (Block; Expr; nil; addr)
 open import Luau.Var using (Var)
 
 data Value : Set where
   nil : Value
   addr : Addr → Value
 
-val : Value → Expr
+val : ∀ {a} → Value → Expr a
 val nil = nil
 val (addr a) = addr a
 

prototyping/Luau/Var.agda

@@ -14,3 +14,5 @@ a ≡ⱽ b with primStringEquality a b
 a ≡ⱽ b | false = no p where postulate p : (a ≡ b) → ⊥
 a ≡ⱽ b | true = yes primTrustMe
 
+anon : Var
+anon = "(anonymous)"

prototyping/PrettyPrinter.agda

@@ -15,7 +15,7 @@ open import Luau.Syntax using (Block)
 open import Luau.Syntax.FromJSON using (blockFromJSON)
 open import Luau.Syntax.ToString using (blockToString)
 
-runBlock : Block → IO ⊤
+runBlock : ∀ {a} → Block a → IO ⊤
 runBlock block = putStrLn (blockToString block)
 
 runJSON : Value → IO ⊤

prototyping/Properties.agda

@@ -3,4 +3,3 @@ module Properties where
 import Properties.Dec
 import Properties.Remember
 import Properties.Step
-import Properties.TypeCheck

prototyping/Properties/Step.agda

@@ -2,16 +2,16 @@ module Properties.Step where
 
 open import Agda.Builtin.Equality using (_≡_; refl)
 open import FFI.Data.Maybe using (just; nothing)
-open import Luau.Heap using (Heap; _[_]; alloc; ok; function_⟨_⟩_end)
+open import Luau.Heap using (Heap; _[_]; alloc; ok; function_is_end)
-open import Luau.Syntax using (Block; Expr; nil; var; addr; function⟨_⟩_end; block_is_end; _$_; local_←_; function_⟨_⟩_end; return; done; _∙_; name)
+open import Luau.Syntax using (Block; Expr; nil; var; addr; function_is_end; block_is_end; _$_; local_←_; return; done; _∙_; name; fun; arg; namify)
 open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; app ; beta; function; block; return; done; local; subst)
 open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; NilIsNotAFunction; UnboundVariable; SEGV; app; block; local; return)
 open import Luau.Substitution using (_[_/_]ᴮ)
 open import Luau.Value using (nil; addr; val)
 open import Properties.Remember using (remember; _,_)
 
-data StepResultᴮ (H : Heap) (B : Block) : Set
+data StepResultᴮ {a} (H : Heap a) (B : Block a) : Set
-data StepResultᴱ (H : Heap) (M : Expr) : Set
+data StepResultᴱ {a} (H : Heap a) (M : Expr a) : Set
 
 data StepResultᴮ H B where
   step : ∀ H′ B′ → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → StepResultᴮ H B
@@ -24,8 +24,8 @@ data StepResultᴱ H M where
   value : ∀ V → (M ≡ val V) → StepResultᴱ H M
   error : (RuntimeErrorᴱ H M) → StepResultᴱ H M
 
-stepᴱ : ∀ H M → StepResultᴱ H M
+stepᴱ : ∀ {a} H M → StepResultᴱ {a} H M
-stepᴮ : ∀ H B → StepResultᴮ H B
+stepᴮ : ∀ {a} H B → StepResultᴮ {a} H B
 
 stepᴱ H nil = value nil refl
 stepᴱ H (var x) = error (UnboundVariable x)
@@ -35,18 +35,18 @@ stepᴱ H (M $ N) | step H′ M′ D = step H′ (M′ $ N) (app D)
 stepᴱ H (nil $ N) | value nil refl = error NilIsNotAFunction
 stepᴱ H (addr a $ N) | value (addr a) refl with remember (H [ a ])
 stepᴱ H (addr a $ N) | value (addr a) refl | (nothing , p) = error (app (SEGV a p))
-stepᴱ H (addr a $ N) | value (addr a) refl | (just(function f ⟨ x ⟩ B end) , p) = step H (block f is local x ← N ∙ B end) (beta p)
+stepᴱ H (addr a $ N) | value (addr a) refl | (just(function F is B end) , p) = step H (block fun F is (local arg F ← N) ∙ B end) (beta p)
 stepᴱ H (M $ N) | error E = error (app E)
-stepᴱ H (function⟨ x ⟩ B end) with alloc H (function "anon" ⟨ x ⟩ B end)
-stepᴱ H (function⟨ x ⟩ B end) | ok a H′ p = step H′ (addr a) (function p)
 stepᴱ H (block b is B end) with stepᴮ H B
 stepᴱ H (block b is B end) | step H′ B′ D = step H′ (block b is B′ end) (block D)
 stepᴱ H (block b is (return _ ∙ B′) end) | return V refl = step H (val V) return
 stepᴱ H (block b is done end) | done refl = step H nil done
 stepᴱ H (block b is B end) | error E = error (block b E)
+stepᴱ H (function F is C end) with alloc H (function (namify F) is C end)
+stepᴱ H function F is C end | ok a H′ p = step H′ (addr a) (function p)
 
-stepᴮ H (function f ⟨ x ⟩ C end ∙ B) with alloc H (function f ⟨ x ⟩ C end)
+stepᴮ H (function F is C end ∙ B) with alloc H (function F is C end)
-stepᴮ H (function f ⟨ x ⟩ C end ∙ B) | ok a H′ p = step H′ (B [ addr a / f ]ᴮ) (function p)
+stepᴮ H (function F is C end ∙ B) | ok a H′ p = step H′ (B [ addr a / fun F ]ᴮ) (function p)
 stepᴮ H (local x ← M ∙ B) with stepᴱ H M
 stepᴮ H (local x ← M ∙ B) | step H′ M′ D = step H′ (local x ← M′ ∙ B) (local D)
 stepᴮ H (local x ← _ ∙ B) | value V refl = step H (B [ V / name x ]ᴮ) subst