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WIP
This commit is contained in:
ajeffrey@roblox.com
parent
51133397cc
commit
ac76424b6d
22 changed files with 335 additions and 306 deletions
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@ -3,9 +3,8 @@
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module Examples.OpSem where
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open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; subst)
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open import Luau.Syntax using (Block; var; nil; local_←_; _∙_; done; return; block_is_end)
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open import Luau.Syntax using (Block; var; val; nil; local_←_; _∙_; done; return; block_is_end)
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open import Luau.Heap using (∅)
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open import Luau.Value using (nil)
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ex1 : ∅ ⊢ (local (var "x") ← nil ∙ return (var "x") ∙ done) ⟶ᴮ (return nil ∙ done) ⊣ ∅
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ex1 : ∅ ⊢ (local (var "x") ← val nil ∙ return (var "x") ∙ done) ⟶ᴮ (return (val nil) ∙ done) ⊣ ∅
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ex1 = subst nil
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@ -4,18 +4,17 @@ module Examples.Run where
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open import Agda.Builtin.Equality using (_≡_; refl)
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open import Agda.Builtin.Bool using (true; false)
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open import Luau.Syntax using (nil; var; _$_; function_is_end; return; _∙_; done; _⟨_⟩; number; binexp; +; <; true; false)
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open import Luau.Value using (nil; number; bool)
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open import Luau.Syntax using (nil; var; _$_; function_is_end; return; _∙_; done; _⟨_⟩; number; binexp; +; <; val; bool)
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open import Luau.Run using (run; return)
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ex1 : (run (function "id" ⟨ var "x" ⟩ is return (var "x") ∙ done end ∙ return (var "id" $ nil) ∙ done) ≡ return nil _)
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ex1 : (run (function "id" ⟨ var "x" ⟩ is return (var "x") ∙ done end ∙ return (var "id" $ val nil) ∙ done) ≡ return nil _)
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ex1 = refl
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ex2 : (run (function "fn" ⟨ var "x" ⟩ is return (number 123.0) ∙ done end ∙ return (var "fn" $ nil) ∙ done) ≡ return (number 123.0) _)
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ex2 : (run (function "fn" ⟨ var "x" ⟩ is return (val (number 123.0)) ∙ done end ∙ return (var "fn" $ val nil) ∙ done) ≡ return (number 123.0) _)
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ex2 = refl
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ex3 : (run (function "fn" ⟨ var "x" ⟩ is return (binexp (number 1.0) + (number 2.0)) ∙ done end ∙ return (var "fn" $ nil) ∙ done) ≡ return (number 3.0) _)
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ex3 : (run (function "fn" ⟨ var "x" ⟩ is return (binexp (val (number 1.0)) + (val (number 2.0))) ∙ done end ∙ return (var "fn" $ val nil) ∙ done) ≡ return (number 3.0) _)
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ex3 = refl
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ex4 : (run (function "fn" ⟨ var "x" ⟩ is return (binexp (number 1.0) < (number 2.0)) ∙ done end ∙ return (var "fn" $ nil) ∙ done) ≡ return (bool true) _)
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ex4 : (run (function "fn" ⟨ var "x" ⟩ is return (binexp (val (number 1.0)) < (val (number 2.0))) ∙ done end ∙ return (var "fn" $ val nil) ∙ done) ≡ return (bool true) _)
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ex4 = refl
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@ -2,7 +2,7 @@ module Examples.Syntax where
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open import Agda.Builtin.Equality using (_≡_; refl)
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open import FFI.Data.String using (_++_)
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open import Luau.Syntax using (var; _$_; return; nil; function_is_end; local_←_; done; _∙_; _⟨_⟩)
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open import Luau.Syntax using (var; _$_; return; val; nil; function_is_end; local_←_; done; _∙_; _⟨_⟩)
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open import Luau.Syntax.ToString using (exprToString; blockToString)
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ex1 : exprToString(function "" ⟨ var "x" ⟩ is return (var "f" $ var "x") ∙ done end) ≡
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@ -11,7 +11,7 @@ ex1 : exprToString(function "" ⟨ var "x" ⟩ is return (var "f" $ var "x") ∙
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"end"
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ex1 = refl
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ex2 : blockToString(local var "x" ← nil ∙ return (var "x") ∙ done) ≡
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ex2 : blockToString(local var "x" ← (val nil) ∙ return (var "x") ∙ done) ≡
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"local x = nil\n" ++
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"return x"
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ex2 = refl
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@ -17,10 +17,9 @@ open import FFI.System.Exit using (exitWith; ExitFailure)
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open import Luau.StrictMode.ToString using (warningToStringᴮ)
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open import Luau.Syntax using (Block; yes; maybe; isAnnotatedᴮ)
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open import Luau.Syntax.FromJSON using (blockFromJSON)
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open import Luau.Syntax.ToString using (blockToString)
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open import Luau.Syntax.ToString using (blockToString; valueToString)
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open import Luau.Run using (run; return; done; error)
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open import Luau.RuntimeError.ToString using (errToStringᴮ)
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open import Luau.Value.ToString using (valueToString)
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open import Properties.StrictMode using (wellTypedProgramsDontGoWrong)
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@ -7,47 +7,33 @@ open import Agda.Builtin.Float using (Float; primFloatPlus; primFloatMinus; prim
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open import Agda.Builtin.Bool using (Bool; true; false)
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open import Utility.Bool using (not; _or_; _and_)
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open import Agda.Builtin.Nat using () renaming (_==_ to _==ᴬ_)
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open import FFI.Data.Maybe using (just)
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open import FFI.Data.Maybe using (Maybe; just; nothing)
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open import Luau.Heap using (Heap; _≡_⊕_↦_; _[_]; function_is_end)
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open import Luau.Substitution using (_[_/_]ᴮ)
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open import Luau.Syntax using (Expr; Stat; Block; nil; addr; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name; fun; arg; binexp; BinaryOperator; +; -; *; /; <; >; ==; ~=; <=; >=; number)
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open import Luau.Value using (addr; val; number; Value; bool)
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open import Luau.Syntax using (Value; Expr; Stat; Block; nil; addr; val; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name; fun; arg; binexp; BinaryOperator; +; -; *; /; <; >; ==; ~=; <=; >=; number; bool)
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open import Luau.RuntimeType using (RuntimeType; valueType)
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open import Properties.Product using (_×_; _,_)
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evalNumOp : Float → BinaryOperator → Float → Value
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evalNumOp x + y = number (primFloatPlus x y)
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evalNumOp x - y = number (primFloatMinus x y)
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evalNumOp x * y = number (primFloatTimes x y)
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evalNumOp x / y = number (primFloatDiv x y)
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evalNumOp x < y = bool (primFloatLess x y)
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evalNumOp x > y = bool (primFloatLess y x)
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evalNumOp x == y = bool (primFloatEquality x y)
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evalNumOp x ~= y = bool (primFloatInequality x y)
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evalNumOp x <= y = bool ((primFloatLess x y) or (primFloatEquality x y))
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evalNumOp x >= y = bool ((primFloatLess y x) or (primFloatEquality x y))
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evalEqOp : Value → Value → Value
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evalEqOp Value.nil Value.nil = bool true
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evalEqOp (addr x) (addr y) = bool (x ==ᴬ y)
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evalEqOp (number x) (number y) = bool (primFloatEquality x y)
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evalEqOp (bool true) (bool y) = bool y
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evalEqOp (bool false) (bool y) = bool (not y)
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evalEqOp _ _ = bool false
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evalNeqOp : Value → Value → Value
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evalNeqOp Value.nil Value.nil = bool false
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evalNeqOp (addr x) (addr y) = bool (not (x ==ᴬ y))
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evalNeqOp (number x) (number y) = bool (primFloatInequality x y)
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evalNeqOp (bool true) (bool y) = bool (not y)
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evalNeqOp (bool false) (bool y) = bool y
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evalNeqOp _ _ = bool true
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coerceToBool : Value → Bool
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coerceToBool Value.nil = false
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coerceToBool (addr x) = true
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coerceToBool (number x) = true
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coerceToBool (bool x) = x
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evalEqOp : Value → Value → Bool
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evalEqOp Value.nil Value.nil = true
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evalEqOp (addr x) (addr y) = (x ==ᴬ y)
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evalEqOp (number x) (number y) = primFloatEquality x y
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evalEqOp (bool true) (bool y) = y
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evalEqOp (bool false) (bool y) = not y
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evalEqOp _ _ = false
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data _⟦_⟧_⟶_ : Value → BinaryOperator → Value → Value → Set where
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+ : ∀ m n → (number m) ⟦ + ⟧ (number n) ⟶ number (primFloatPlus m n)
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- : ∀ m n → (number m) ⟦ - ⟧ (number n) ⟶ number (primFloatMinus m n)
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/ : ∀ m n → (number m) ⟦ / ⟧ (number n) ⟶ number (primFloatTimes m n)
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* : ∀ m n → (number m) ⟦ * ⟧ (number n) ⟶ number (primFloatDiv m n)
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< : ∀ m n → (number m) ⟦ < ⟧ (number n) ⟶ bool (primFloatLess m n)
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> : ∀ m n → (number m) ⟦ > ⟧ (number n) ⟶ bool (primFloatLess n m)
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<= : ∀ m n → (number m) ⟦ <= ⟧ (number n) ⟶ bool ((primFloatLess m n) or (primFloatEquality m n))
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>= : ∀ m n → (number m) ⟦ >= ⟧ (number n) ⟶ bool ((primFloatLess n m) or (primFloatEquality m n))
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== : ∀ v w → v ⟦ == ⟧ w ⟶ bool (evalEqOp v w)
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~= : ∀ v w → v ⟦ ~= ⟧ w ⟶ bool (not (evalEqOp v w))
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data _⊢_⟶ᴮ_⊣_ {a} : Heap a → Block a → Block a → Heap a → Set
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data _⊢_⟶ᴱ_⊣_ {a} : Heap a → Expr a → Expr a → Heap a → Set
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@ -57,7 +43,7 @@ data _⊢_⟶ᴱ_⊣_ where
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H′ ≡ H ⊕ a ↦ (function F is B end) →
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-------------------------------------------
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H ⊢ (function F is B end) ⟶ᴱ (addr a) ⊣ H′
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H ⊢ (function F is B end) ⟶ᴱ val(addr a) ⊣ H′
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app₁ : ∀ {H H′ M M′ N} →
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@ -76,7 +62,7 @@ data _⊢_⟶ᴱ_⊣_ where
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(O ≡ function F is B end) →
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H [ a ] ≡ just(O) →
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-----------------------------------------------------------------------------
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H ⊢ (addr a $ val v) ⟶ᴱ (block (fun F) is (B [ v / name(arg F) ]ᴮ) end) ⊣ H
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H ⊢ (val (addr a) $ val v) ⟶ᴱ (block (fun F) is (B [ v / name(arg F) ]ᴮ) end) ⊣ H
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block : ∀ {H H′ B B′ b} →
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@ -91,24 +77,15 @@ data _⊢_⟶ᴱ_⊣_ where
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done : ∀ {H b} →
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---------------------------------
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H ⊢ (block b is done end) ⟶ᴱ nil ⊣ H
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binOpEquality :
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∀ {H x y} →
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---------------------------------------------------------------------------
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H ⊢ (binexp (val x) == (val y)) ⟶ᴱ (val (evalEqOp x y)) ⊣ H
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binOpInequality :
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∀ {H x y} →
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----------------------------------------------------------------------------
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H ⊢ (binexp (val x) ~= (val y)) ⟶ᴱ (val (evalNeqOp x y)) ⊣ H
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binOpNumbers :
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∀ {H x op y} →
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-----------------------------------------------------------------------
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H ⊢ (binexp (number x) op (number y)) ⟶ᴱ (val (evalNumOp x op y)) ⊣ H
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--------------------------------------------
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H ⊢ (block b is done end) ⟶ᴱ (val nil) ⊣ H
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binOp₀ : ∀ {H op v₁ v₂ w} →
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v₁ ⟦ op ⟧ v₂ ⟶ w →
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--------------------------------------------------
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H ⊢ (binexp (val v₁) op (val v₂)) ⟶ᴱ (val w) ⊣ H
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binOp₁ : ∀ {H H′ x x′ op y} →
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H ⊢ x ⟶ᴱ x′ ⊣ H′ →
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@ -4,14 +4,13 @@ module Luau.Run where
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open import Agda.Builtin.Equality using (_≡_; refl)
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open import Luau.Heap using (Heap; ∅)
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open import Luau.Syntax using (Block; return; _∙_; done)
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open import Luau.Syntax using (Block; val; return; _∙_; done)
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open import Luau.OpSem using (_⊢_⟶*_⊣_; refl; step)
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open import Luau.Value using (val)
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open import Properties.Step using (stepᴮ; step; return; done; error)
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open import Luau.RuntimeError using (RuntimeErrorᴮ)
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data RunResult {a} (H : Heap a) (B : Block a) : Set where
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return : ∀ V {B′ H′} → (H ⊢ B ⟶* (return (val V) ∙ B′) ⊣ H′) → RunResult H B
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return : ∀ v {B′ H′} → (H ⊢ B ⟶* (return (val v) ∙ B′) ⊣ H′) → RunResult H B
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done : ∀ {H′} → (H ⊢ B ⟶* done ⊣ H′) → RunResult H B
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error : ∀ {B′ H′} → (RuntimeErrorᴮ H′ B′) → (H ⊢ B ⟶* B′ ⊣ H′) → RunResult H B
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@ -6,20 +6,29 @@ open import Agda.Builtin.Equality using (_≡_)
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open import Luau.Heap using (Heap; _[_])
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open import FFI.Data.Maybe using (just; nothing)
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open import FFI.Data.String using (String)
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open import Luau.Syntax using (Block; Expr; nil; var; addr; block_is_end; _$_; local_←_; return; done; _∙_; number; binexp)
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open import Luau.Syntax using (BinaryOperator; Block; Expr; nil; var; val; addr; block_is_end; _$_; local_←_; return; done; _∙_; number; binexp; +; -; *; /; <; >; <=; >=)
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open import Luau.RuntimeType using (RuntimeType; valueType; function; number)
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open import Luau.Value using (val)
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open import Properties.Equality using (_≢_)
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data BinOpError : BinaryOperator → RuntimeType → Set where
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+ : ∀ {t} → (t ≢ number) → BinOpError + t
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- : ∀ {t} → (t ≢ number) → BinOpError - t
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* : ∀ {t} → (t ≢ number) → BinOpError * t
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/ : ∀ {t} → (t ≢ number) → BinOpError / t
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< : ∀ {t} → (t ≢ number) → BinOpError < t
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> : ∀ {t} → (t ≢ number) → BinOpError > t
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<= : ∀ {t} → (t ≢ number) → BinOpError <= t
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>= : ∀ {t} → (t ≢ number) → BinOpError >= t
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data RuntimeErrorᴮ {a} (H : Heap a) : Block a → Set
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data RuntimeErrorᴱ {a} (H : Heap a) : Expr a → Set
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data RuntimeErrorᴱ H where
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FunctionMismatch : ∀ v w → (function ≢ valueType v) → RuntimeErrorᴱ H (val v $ val w)
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BinopMismatch₁ : ∀ v w {op} → (number ≢ valueType v) → RuntimeErrorᴱ H (binexp (val v) op (val w))
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BinopMismatch₂ : ∀ v w {op} → (number ≢ valueType w) → RuntimeErrorᴱ H (binexp (val v) op (val w))
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BinOpMismatch₁ : ∀ v w {op} → (BinOpError op (valueType v)) → RuntimeErrorᴱ H (binexp (val v) op (val w))
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BinOpMismatch₂ : ∀ v w {op} → (BinOpError op (valueType w)) → RuntimeErrorᴱ H (binexp (val v) op (val w))
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UnboundVariable : ∀ {x} → RuntimeErrorᴱ H (var x)
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SEGV : ∀ {a} → (H [ a ] ≡ nothing) → RuntimeErrorᴱ H (addr a)
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SEGV : ∀ {a} → (H [ a ] ≡ nothing) → RuntimeErrorᴱ H (val (addr a))
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app₁ : ∀ {M N} → RuntimeErrorᴱ H M → RuntimeErrorᴱ H (M $ N)
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app₂ : ∀ {M N} → RuntimeErrorᴱ H N → RuntimeErrorᴱ H (M $ N)
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block : ∀ {b B} → RuntimeErrorᴮ H B → RuntimeErrorᴱ H (block b is B end)
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@ -4,24 +4,23 @@ module Luau.RuntimeError.ToString where
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open import Agda.Builtin.Float using (primShowFloat)
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open import FFI.Data.String using (String; _++_)
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open import Luau.RuntimeError using (RuntimeErrorᴮ; RuntimeErrorᴱ; local; return; FunctionMismatch; BinopMismatch₁; BinopMismatch₂; UnboundVariable; SEGV; app₁; app₂; block; bin₁; bin₂)
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open import Luau.RuntimeError using (RuntimeErrorᴮ; RuntimeErrorᴱ; local; return; FunctionMismatch; BinOpMismatch₁; BinOpMismatch₂; UnboundVariable; SEGV; app₁; app₂; block; bin₁; bin₂)
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open import Luau.RuntimeType.ToString using (runtimeTypeToString)
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open import Luau.Addr.ToString using (addrToString)
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open import Luau.Syntax.ToString using (exprToString)
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open import Luau.Syntax.ToString using (valueToString; exprToString)
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open import Luau.Var.ToString using (varToString)
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open import Luau.Value.ToString using (valueToString)
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open import Luau.Syntax using (var; addr; binexp; block_is_end; local_←_; return; _∙_; name; _$_)
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open import Luau.Syntax using (var; val; addr; binexp; block_is_end; local_←_; return; _∙_; name; _$_)
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errToStringᴱ : ∀ {a H} M → RuntimeErrorᴱ {a} H M → String
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errToStringᴮ : ∀ {a H} B → RuntimeErrorᴮ {a} H B → String
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errToStringᴱ (var x) (UnboundVariable) = "variable " ++ varToString x ++ " is unbound"
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errToStringᴱ (addr a) (SEGV p) = "address " ++ addrToString a ++ " is unallocated"
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errToStringᴱ (val (addr a)) (SEGV p) = "address " ++ addrToString a ++ " is unallocated"
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errToStringᴱ (M $ N) (FunctionMismatch v w p) = "value " ++ (valueToString v) ++ " is not a function"
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errToStringᴱ (M $ N) (app₁ E) = errToStringᴱ M E
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errToStringᴱ (M $ N) (app₂ E) = errToStringᴱ N E
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errToStringᴱ (binexp M op N) (BinopMismatch₁ v w p) = "value " ++ (valueToString v) ++ " is not a number"
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errToStringᴱ (binexp M op N) (BinopMismatch₂ v w p) = "value " ++ (valueToString w) ++ " is not a number"
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errToStringᴱ (binexp M op N) (BinOpMismatch₁ v w p) = "value " ++ (valueToString v) ++ " is not a number"
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errToStringᴱ (binexp M op N) (BinOpMismatch₂ v w p) = "value " ++ (valueToString w) ++ " is not a number"
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errToStringᴱ (binexp M op N) (bin₁ E) = errToStringᴱ M E
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errToStringᴱ (binexp M op N) (bin₂ E) = errToStringᴱ N E
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errToStringᴱ (block b is B end) (block E) = errToStringᴮ B E ++ "\n in call of function " ++ varToString (name b)
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@ -1,6 +1,6 @@
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module Luau.RuntimeType where
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open import Luau.Value using (Value; nil; addr; number; bool)
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open import Luau.Syntax using (Value; nil; addr; number; bool)
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data RuntimeType : Set where
|
||||
function : RuntimeType
|
||||
|
|
@ -10,6 +10,6 @@ data RuntimeType : Set where
|
|||
|
||||
valueType : Value → RuntimeType
|
||||
valueType nil = nil
|
||||
valueType (addr x) = function
|
||||
valueType (number x) = number
|
||||
valueType (bool _) = boolean
|
||||
valueType (addr a) = function
|
||||
valueType (number n) = number
|
||||
valueType (bool b) = boolean
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ module Luau.StrictMode where
|
|||
|
||||
open import Agda.Builtin.Equality using (_≡_)
|
||||
open import FFI.Data.Maybe using (just; nothing)
|
||||
open import Luau.Syntax using (Expr; Stat; Block; yes; nil; addr; var; binexp; var_∈_; _⟨_⟩∈_; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name)
|
||||
open import Luau.Syntax using (Expr; Stat; Block; BinaryOperator; yes; nil; addr; var; binexp; var_∈_; _⟨_⟩∈_; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name; +; -; *; /; <; >; <=; >=)
|
||||
open import Luau.Type using (Type; strict; bot; top; nil; number; _⇒_; tgt)
|
||||
open import Luau.Heap using (Heap; function_is_end) renaming (_[_] to _[_]ᴴ)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
|
||||
|
|
@ -16,6 +16,16 @@ open import Properties.Product using (_,_)
|
|||
src : Type → Type
|
||||
src = Luau.Type.src strict
|
||||
|
||||
data BinOpWarning : BinaryOperator → Type → Set where
|
||||
+ : ∀ {T} → (T ≢ number) → BinOpWarning + T
|
||||
- : ∀ {T} → (T ≢ number) → BinOpWarning - T
|
||||
* : ∀ {T} → (T ≢ number) → BinOpWarning * T
|
||||
/ : ∀ {T} → (T ≢ number) → BinOpWarning / T
|
||||
< : ∀ {T} → (T ≢ number) → BinOpWarning < T
|
||||
> : ∀ {T} → (T ≢ number) → BinOpWarning > T
|
||||
<= : ∀ {T} → (T ≢ number) → BinOpWarning <= T
|
||||
>= : ∀ {T} → (T ≢ number) → BinOpWarning >= T
|
||||
|
||||
data Warningᴱ (H : Heap yes) {Γ} : ∀ {M T} → (Γ ⊢ᴱ M ∈ T) → Set
|
||||
data Warningᴮ (H : Heap yes) {Γ} : ∀ {B T} → (Γ ⊢ᴮ B ∈ T) → Set
|
||||
|
||||
|
|
@ -51,15 +61,15 @@ data Warningᴱ H {Γ} where
|
|||
-----------------
|
||||
Warningᴱ H (app D₁ D₂)
|
||||
|
||||
BinopMismatch₁ : ∀ {op M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
|
||||
BinOpMismatch₁ : ∀ {op M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
|
||||
|
||||
(T ≢ number) →
|
||||
BinOpWarning op T →
|
||||
------------------------------
|
||||
Warningᴱ H (binexp {op} D₁ D₂)
|
||||
|
||||
BinopMismatch₂ : ∀ {op M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
|
||||
BinOpMismatch₂ : ∀ {op M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
|
||||
|
||||
(U ≢ number) →
|
||||
BinOpWarning op U →
|
||||
------------------------------
|
||||
Warningᴱ H (binexp {op} D₁ D₂)
|
||||
|
||||
|
|
|
|||
|
|
@ -3,8 +3,8 @@
|
|||
module Luau.StrictMode.ToString where
|
||||
|
||||
open import FFI.Data.String using (String; _++_)
|
||||
open import Luau.StrictMode using (Warningᴱ; Warningᴮ; UnallocatedAddress; UnboundVariable; FunctionCallMismatch; FunctionDefnMismatch; BlockMismatch; app₁; app₂; BinopMismatch₁; BinopMismatch₂; bin₁; bin₂; block₁; return; LocalVarMismatch; local₁; local₂; function₁; function₂; heap; expr; block; addr)
|
||||
open import Luau.Syntax using (Expr; yes; var; var_∈_; _⟨_⟩∈_; _$_; addr; number; binexp; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg; name)
|
||||
open import Luau.StrictMode using (Warningᴱ; Warningᴮ; UnallocatedAddress; UnboundVariable; FunctionCallMismatch; FunctionDefnMismatch; BlockMismatch; app₁; app₂; BinOpMismatch₁; BinOpMismatch₂; bin₁; bin₂; block₁; return; LocalVarMismatch; local₁; local₂; function₁; function₂; heap; expr; block; addr)
|
||||
open import Luau.Syntax using (Expr; val; yes; var; var_∈_; _⟨_⟩∈_; _$_; addr; number; binexp; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg; name)
|
||||
open import Luau.Type using (strict)
|
||||
open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_)
|
||||
open import Luau.Addr.ToString using (addrToString)
|
||||
|
|
@ -16,7 +16,7 @@ warningToStringᴱ : ∀ {H Γ T} M → {D : Γ ⊢ᴱ M ∈ T} → Warningᴱ H
|
|||
warningToStringᴮ : ∀ {H Γ T} B → {D : Γ ⊢ᴮ B ∈ T} → Warningᴮ H D → String
|
||||
|
||||
warningToStringᴱ (var x) (UnboundVariable p) = "Unbound variable " ++ varToString x
|
||||
warningToStringᴱ (addr a) (UnallocatedAddress p) = "Unallocated adress " ++ addrToString a
|
||||
warningToStringᴱ (val (addr a)) (UnallocatedAddress p) = "Unallocated adress " ++ addrToString a
|
||||
warningToStringᴱ (M $ N) (FunctionCallMismatch {T = T} {U = U} p) = "Function has type " ++ typeToString T ++ " but argument has type " ++ typeToString U
|
||||
warningToStringᴱ (M $ N) (app₁ W) = warningToStringᴱ M W
|
||||
warningToStringᴱ (M $ N) (app₂ W) = warningToStringᴱ N W
|
||||
|
|
@ -24,8 +24,8 @@ warningToStringᴱ (function f ⟨ var x ∈ T ⟩∈ U is B end) (FunctionDefnM
|
|||
warningToStringᴱ (function f ⟨ var x ∈ T ⟩∈ U is B end) (function₁ W) = warningToStringᴮ B W ++ "\n in function expression " ++ varToString f
|
||||
warningToStringᴱ block var b ∈ T is B end (BlockMismatch {U = U} p) = "Block " ++ varToString b ++ " has type " ++ typeToString T ++ " but body returns " ++ typeToString U
|
||||
warningToStringᴱ block var b ∈ T is B end (block₁ W) = warningToStringᴮ B W ++ "\n in block " ++ varToString b
|
||||
warningToStringᴱ (binexp M op N) (BinopMismatch₁ {T = T} p) = "Binary operator " ++ binOpToString op ++ " lhs has type " ++ typeToString T ++ " not number"
|
||||
warningToStringᴱ (binexp M op N) (BinopMismatch₂ {U = U} p) = "Binary operator " ++ binOpToString op ++ " rhs has type " ++ typeToString U ++ " not number"
|
||||
warningToStringᴱ (binexp M op N) (BinOpMismatch₁ {T = T} p) = "Binary operator " ++ binOpToString op ++ " lhs has type " ++ typeToString T
|
||||
warningToStringᴱ (binexp M op N) (BinOpMismatch₂ {U = U} p) = "Binary operator " ++ binOpToString op ++ " rhs has type " ++ typeToString U
|
||||
warningToStringᴱ (binexp M op N) (bin₁ W) = warningToStringᴱ M W
|
||||
warningToStringᴱ (binexp M op N) (bin₂ W) = warningToStringᴱ N W
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,6 @@
|
|||
module Luau.Substitution where
|
||||
|
||||
open import Luau.Syntax using (Expr; Stat; Block; nil; true; false; addr; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; _⟨_⟩ ; name; fun; arg; number; binexp)
|
||||
open import Luau.Value using (Value; val)
|
||||
open import Luau.Syntax using (Value; Expr; Stat; Block; val; nil; bool; addr; var; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; _⟨_⟩ ; name; fun; arg; number; binexp)
|
||||
open import Luau.Var using (Var; _≡ⱽ_)
|
||||
open import Properties.Dec using (Dec; yes; no)
|
||||
|
||||
|
|
@ -10,12 +9,8 @@ _[_/_]ᴮ : ∀ {a} → Block a → Value → Var → Block a
|
|||
var_[_/_]ᴱwhenever_ : ∀ {a P} → Var → Value → Var → (Dec P) → Expr a
|
||||
_[_/_]ᴮunless_ : ∀ {a P} → Block a → Value → Var → (Dec P) → Block a
|
||||
|
||||
nil [ v / x ]ᴱ = nil
|
||||
true [ v / x ]ᴱ = true
|
||||
false [ v / x ]ᴱ = false
|
||||
val w [ v / x ]ᴱ = val w
|
||||
var y [ v / x ]ᴱ = var y [ v / x ]ᴱwhenever (x ≡ⱽ y)
|
||||
addr a [ v / x ]ᴱ = addr a
|
||||
(number y) [ v / x ]ᴱ = number y
|
||||
(M $ N) [ v / x ]ᴱ = (M [ v / x ]ᴱ) $ (N [ v / x ]ᴱ)
|
||||
function F is C end [ v / x ]ᴱ = function F is C [ v / x ]ᴮunless (x ≡ⱽ name(arg F)) end
|
||||
block b is C end [ v / x ]ᴱ = block b is C [ v / x ]ᴮ end
|
||||
|
|
|
|||
|
|
@ -1,6 +1,7 @@
|
|||
module Luau.Syntax where
|
||||
|
||||
open import Agda.Builtin.Equality using (_≡_)
|
||||
open import Agda.Builtin.Bool using (Bool; true; false)
|
||||
open import Agda.Builtin.Float using (Float)
|
||||
open import Luau.Var using (Var)
|
||||
open import Luau.Addr using (Addr)
|
||||
|
|
@ -45,6 +46,12 @@ data BinaryOperator : Set where
|
|||
<= : BinaryOperator
|
||||
>= : BinaryOperator
|
||||
|
||||
data Value : Set where
|
||||
nil : Value
|
||||
addr : Addr → Value
|
||||
number : Float → Value
|
||||
bool : Bool → Value
|
||||
|
||||
data Block (a : Annotated) : Set
|
||||
data Stat (a : Annotated) : Set
|
||||
data Expr (a : Annotated) : Set
|
||||
|
|
@ -59,25 +66,18 @@ data Stat a where
|
|||
return : Expr a → Stat a
|
||||
|
||||
data Expr a where
|
||||
nil : Expr a
|
||||
true : Expr a
|
||||
false : Expr a
|
||||
var : Var → Expr a
|
||||
addr : Addr → Expr a
|
||||
val : Value → Expr a
|
||||
_$_ : Expr a → Expr a → Expr a
|
||||
function_is_end : FunDec a → Block a → Expr a
|
||||
block_is_end : VarDec a → Block a → Expr a
|
||||
number : Float → Expr a
|
||||
binexp : Expr a → BinaryOperator → Expr a → Expr a
|
||||
|
||||
isAnnotatedᴱ : ∀ {a} → Expr a → Maybe (Expr yes)
|
||||
isAnnotatedᴮ : ∀ {a} → Block a → Maybe (Block yes)
|
||||
|
||||
isAnnotatedᴱ nil = just nil
|
||||
isAnnotatedᴱ (var x) = just (var x)
|
||||
isAnnotatedᴱ (addr a) = just (addr a)
|
||||
isAnnotatedᴱ true = just true
|
||||
isAnnotatedᴱ false = just false
|
||||
isAnnotatedᴱ (val v) = just (val v)
|
||||
isAnnotatedᴱ (M $ N) with isAnnotatedᴱ M | isAnnotatedᴱ N
|
||||
isAnnotatedᴱ (M $ N) | just M′ | just N′ = just (M′ $ N′)
|
||||
isAnnotatedᴱ (M $ N) | _ | _ = nothing
|
||||
|
|
@ -89,7 +89,6 @@ isAnnotatedᴱ (block var b ∈ T is B end) with isAnnotatedᴮ B
|
|||
isAnnotatedᴱ (block var b ∈ T is B end) | just B′ = just (block var b ∈ T is B′ end)
|
||||
isAnnotatedᴱ (block var b ∈ T is B end) | _ = nothing
|
||||
isAnnotatedᴱ (block _ is B end) = nothing
|
||||
isAnnotatedᴱ (number n) = just (number n)
|
||||
isAnnotatedᴱ (binexp M op N) with isAnnotatedᴱ M | isAnnotatedᴱ N
|
||||
isAnnotatedᴱ (binexp M op N) | just M′ | just N′ = just (binexp M′ op N′)
|
||||
isAnnotatedᴱ (binexp M op N) | _ | _ = nothing
|
||||
|
|
|
|||
|
|
@ -2,7 +2,7 @@
|
|||
|
||||
module Luau.Syntax.FromJSON where
|
||||
|
||||
open import Luau.Syntax using (Block; Stat ; Expr; nil; _$_; var; var_∈_; function_is_end; _⟨_⟩; _⟨_⟩∈_; local_←_; return; done; _∙_; maybe; VarDec; number; binexp; BinaryOperator; +; -; *; /; ==; ~=; <; >; <=; >=)
|
||||
open import Luau.Syntax using (Block; Stat ; Expr; _$_; val; nil; bool; number; var; var_∈_; function_is_end; _⟨_⟩; _⟨_⟩∈_; local_←_; return; done; _∙_; maybe; VarDec; binexp; BinaryOperator; +; -; *; /; ==; ~=; <; >; <=; >=)
|
||||
open import Luau.Type.FromJSON using (typeFromJSON)
|
||||
|
||||
open import Agda.Builtin.List using (List; _∷_; [])
|
||||
|
|
@ -53,7 +53,7 @@ blockFromJSON : Value → Either String (Block maybe)
|
|||
blockFromArray : Array → Either String (Block maybe)
|
||||
|
||||
binOpFromJSON (string s) = binOpFromString s
|
||||
binOpFromJSON val = Left "Binary operator not a string"
|
||||
binOpFromJSON _ = Left "Binary operator not a string"
|
||||
|
||||
binOpFromString "Add" = Right +
|
||||
binOpFromString "Sub" = Right -
|
||||
|
|
@ -68,7 +68,7 @@ binOpFromString "CompareGe" = Right >=
|
|||
binOpFromString s = Left ("'" ++ s ++ "' is not a valid operator")
|
||||
|
||||
varDecFromJSON (object arg) = varDecFromObject arg
|
||||
varDecFromJSON val = Left "VarDec not an object"
|
||||
varDecFromJSON _ = Left "VarDec not an object"
|
||||
|
||||
varDecFromObject obj with lookup name obj | lookup type obj
|
||||
varDecFromObject obj | just (string name) | nothing = Right (var name)
|
||||
|
|
@ -80,7 +80,7 @@ varDecFromObject obj | just _ | _ = Left "AstLocal name is not a string"
|
|||
varDecFromObject obj | nothing | _ = Left "AstLocal missing name"
|
||||
|
||||
exprFromJSON (object obj) = exprFromObject obj
|
||||
exprFromJSON val = Left "AstExpr not an object"
|
||||
exprFromJSON _ = Left "AstExpr not an object"
|
||||
|
||||
exprFromObject obj with lookup type obj
|
||||
exprFromObject obj | just (string "AstExprCall") with lookup func obj | lookup args obj
|
||||
|
|
@ -93,7 +93,7 @@ exprFromObject obj | just (string "AstExprCall") | just value | just (array arr)
|
|||
exprFromObject obj | just (string "AstExprCall") | just value | just _ = Left ("AstExprCall args not an array")
|
||||
exprFromObject obj | just (string "AstExprCall") | nothing | _ = Left ("AstExprCall missing func")
|
||||
exprFromObject obj | just (string "AstExprCall") | _ | nothing = Left ("AstExprCall missing args")
|
||||
exprFromObject obj | just (string "AstExprConstantNil") = Right nil
|
||||
exprFromObject obj | just (string "AstExprConstantNil") = Right (val nil)
|
||||
exprFromObject obj | just (string "AstExprFunction") with lookup args obj | lookup body obj | lookup returnAnnotation obj
|
||||
exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just blockValue | rtn with head arr | blockFromJSON blockValue
|
||||
exprFromObject obj | just (string "AstExprFunction") | just (array arr) | just blockValue | rtn | just argValue | Right B with varDecFromJSON argValue
|
||||
|
|
@ -119,12 +119,11 @@ exprFromObject obj | just (string "AstExprLocal") | just x | Right x′ = Right
|
|||
exprFromObject obj | just (string "AstExprLocal") | just x | Left err = Left err
|
||||
exprFromObject obj | just (string "AstExprLocal") | nothing = Left "AstExprLocal missing local"
|
||||
exprFromObject obj | just (string "AstExprConstantNumber") with lookup value obj
|
||||
exprFromObject obj | just (string "AstExprConstantNumber") | just (FFI.Data.Aeson.Value.number x) = Right (number (toFloat x))
|
||||
exprFromObject obj | just (string "AstExprConstantNumber") | just (FFI.Data.Aeson.Value.number x) = Right (val (number (toFloat x)))
|
||||
exprFromObject obj | just (string "AstExprConstantNumber") | just _ = Left "AstExprConstantNumber value is not a number"
|
||||
exprFromObject obj | just (string "AstExprConstantNumber") | nothing = Left "AstExprConstantNumber missing value"
|
||||
exprFromObject obj | just (string "AstExprConstantBool") with lookup value obj
|
||||
exprFromObject obj | just (string "AstExprConstantBool") | just (FFI.Data.Aeson.Value.bool true) = Right Expr.true
|
||||
exprFromObject obj | just (string "AstExprConstantBool") | just (FFI.Data.Aeson.Value.bool false) = Right Expr.false
|
||||
exprFromObject obj | just (string "AstExprConstantBool") | just (FFI.Data.Aeson.Value.bool b) = Right (val (bool b))
|
||||
exprFromObject obj | just (string "AstExprConstantBool") | just _ = Left "AstExprConstantBool value is not a bool"
|
||||
exprFromObject obj | just (string "AstExprConstantBool") | nothing = Left "AstExprConstantBool missing value"
|
||||
exprFromObject obj | just (string "AstExprBinary") with lookup op obj | lookup left obj | lookup right obj
|
||||
|
|
|
|||
|
|
@ -1,7 +1,8 @@
|
|||
module Luau.Syntax.ToString where
|
||||
|
||||
open import Agda.Builtin.Bool using (true; false)
|
||||
open import Agda.Builtin.Float using (primShowFloat)
|
||||
open import Luau.Syntax using (Block; Stat; Expr; VarDec; FunDec; nil; var; var_∈_; addr; _$_; function_is_end; return; local_←_; _∙_; done; block_is_end; _⟨_⟩; _⟨_⟩∈_; number; BinaryOperator; +; -; *; /; <; >; ≡; ≅; ≤; ≥; binexp; true; false)
|
||||
open import Luau.Syntax using (Value; Block; Stat; Expr; VarDec; FunDec; nil; bool; val; var; var_∈_; addr; _$_; function_is_end; return; local_←_; _∙_; done; block_is_end; _⟨_⟩; _⟨_⟩∈_; number; BinaryOperator; +; -; *; /; <; >; ==; ~=; <=; >=; binexp)
|
||||
open import FFI.Data.String using (String; _++_)
|
||||
open import Luau.Addr.ToString using (addrToString)
|
||||
open import Luau.Type.ToString using (typeToString)
|
||||
|
|
@ -24,19 +25,24 @@ binOpToString * = "*"
|
|||
binOpToString / = "/"
|
||||
binOpToString < = "<"
|
||||
binOpToString > = ">"
|
||||
binOpToString ≡ = "=="
|
||||
binOpToString ≅ = "~="
|
||||
binOpToString ≤ = "<="
|
||||
binOpToString ≥ = ">="
|
||||
binOpToString == = "=="
|
||||
binOpToString ~= = "~="
|
||||
binOpToString <= = "<="
|
||||
binOpToString >= = ">="
|
||||
|
||||
valueToString : Value → String
|
||||
valueToString nil = "nil"
|
||||
valueToString (addr a) = addrToString a
|
||||
valueToString (number x) = primShowFloat x
|
||||
valueToString (bool false) = "false"
|
||||
valueToString (bool true) = "true"
|
||||
|
||||
exprToString′ : ∀ {a} → String → Expr a → String
|
||||
statToString′ : ∀ {a} → String → Stat a → String
|
||||
blockToString′ : ∀ {a} → String → Block a → String
|
||||
|
||||
exprToString′ lb nil =
|
||||
"nil"
|
||||
exprToString′ lb (addr a) =
|
||||
addrToString(a)
|
||||
exprToString′ lb (val v) =
|
||||
valueToString(v)
|
||||
exprToString′ lb (var x) =
|
||||
varToString(x)
|
||||
exprToString′ lb (M $ N) =
|
||||
|
|
@ -49,10 +55,7 @@ exprToString′ lb (block b is B end) =
|
|||
"(" ++ varDecToString b ++ "()" ++ lb ++
|
||||
" " ++ (blockToString′ (lb ++ " ") B) ++ lb ++
|
||||
"end)()"
|
||||
exprToString′ lb (number x) = primShowFloat x
|
||||
exprToString′ lb (binexp x op y) = exprToString′ lb x ++ " " ++ binOpToString op ++ " " ++ exprToString′ lb y
|
||||
exprToString′ lb true = "true"
|
||||
exprToString′ lb false = "false"
|
||||
|
||||
statToString′ lb (function F is B end) =
|
||||
"local " ++ funDecToString F ++ lb ++
|
||||
|
|
|
|||
|
|
@ -6,11 +6,10 @@ module Luau.TypeCheck (m : Mode) where
|
|||
|
||||
open import Agda.Builtin.Equality using (_≡_)
|
||||
open import FFI.Data.Maybe using (Maybe; just)
|
||||
open import Luau.Syntax using (Expr; Stat; Block; yes; nil; addr; number; true; false; var; var_∈_; _⟨_⟩∈_; function_is_end; _$_; block_is_end; binexp; local_←_; _∙_; done; return; name)
|
||||
open import Luau.Syntax using (Expr; Stat; Block; BinaryOperator; yes; nil; addr; number; bool; val; var; var_∈_; _⟨_⟩∈_; function_is_end; _$_; block_is_end; binexp; local_←_; _∙_; done; return; name; +; -; *; /; <; >; ==; ~=; <=; >=)
|
||||
open import Luau.Var using (Var)
|
||||
open import Luau.Addr using (Addr)
|
||||
open import Luau.Heap using (Heap; Object; function_is_end) renaming (_[_] to _[_]ᴴ)
|
||||
open import Luau.Value using (addr; val)
|
||||
open import Luau.Type using (Type; Mode; nil; bot; top; number; boolean; _⇒_; tgt)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
|
||||
open import FFI.Data.Vector using (Vector)
|
||||
|
|
@ -24,6 +23,18 @@ orBot : Maybe Type → Type
|
|||
orBot nothing = bot
|
||||
orBot (just T) = T
|
||||
|
||||
tgtBinOp : BinaryOperator → Type
|
||||
tgtBinOp + = number
|
||||
tgtBinOp - = number
|
||||
tgtBinOp * = number
|
||||
tgtBinOp / = number
|
||||
tgtBinOp < = boolean
|
||||
tgtBinOp > = boolean
|
||||
tgtBinOp == = boolean
|
||||
tgtBinOp ~= = boolean
|
||||
tgtBinOp <= = boolean
|
||||
tgtBinOp >= = boolean
|
||||
|
||||
data _⊢ᴮ_∈_ : VarCtxt → Block yes → Type → Set
|
||||
data _⊢ᴱ_∈_ : VarCtxt → Expr yes → Type → Set
|
||||
|
||||
|
|
@ -59,8 +70,8 @@ data _⊢ᴱ_∈_ where
|
|||
|
||||
nil : ∀ {Γ} →
|
||||
|
||||
--------------
|
||||
Γ ⊢ᴱ nil ∈ nil
|
||||
--------------------
|
||||
Γ ⊢ᴱ (val nil) ∈ nil
|
||||
|
||||
var : ∀ {x T Γ} →
|
||||
|
||||
|
|
@ -71,22 +82,17 @@ data _⊢ᴱ_∈_ where
|
|||
addr : ∀ {a Γ} T →
|
||||
|
||||
-----------------
|
||||
Γ ⊢ᴱ (addr a) ∈ T
|
||||
Γ ⊢ᴱ val(addr a) ∈ T
|
||||
|
||||
number : ∀ {n Γ} →
|
||||
|
||||
------------------------
|
||||
Γ ⊢ᴱ (number n) ∈ number
|
||||
---------------------------
|
||||
Γ ⊢ᴱ val(number n) ∈ number
|
||||
|
||||
true : ∀ {Γ} →
|
||||
bool : ∀ {b Γ} →
|
||||
|
||||
-------------------
|
||||
Γ ⊢ᴱ true ∈ boolean
|
||||
|
||||
false : ∀ {Γ} →
|
||||
|
||||
-------------------
|
||||
Γ ⊢ᴱ false ∈ boolean
|
||||
--------------------------
|
||||
Γ ⊢ᴱ val(bool b) ∈ boolean
|
||||
|
||||
app : ∀ {M N T U Γ} →
|
||||
|
||||
|
|
@ -111,8 +117,8 @@ data _⊢ᴱ_∈_ where
|
|||
|
||||
Γ ⊢ᴱ M ∈ T →
|
||||
Γ ⊢ᴱ N ∈ U →
|
||||
----------------------------
|
||||
Γ ⊢ᴱ (binexp M op N) ∈ number
|
||||
----------------------------------
|
||||
Γ ⊢ᴱ (binexp M op N) ∈ tgtBinOp op
|
||||
|
||||
data ⊢ᴼ_ : Maybe(Object yes) → Set where
|
||||
|
||||
|
|
|
|||
|
|
@ -1,20 +1 @@
|
|||
module Luau.Value where
|
||||
|
||||
open import Agda.Builtin.Bool using (Bool; true; false)
|
||||
open import Agda.Builtin.Float using (Float)
|
||||
open import Luau.Addr using (Addr)
|
||||
open import Luau.Syntax using (Block; Expr; nil; addr; number; true; false)
|
||||
open import Luau.Var using (Var)
|
||||
|
||||
data Value : Set where
|
||||
nil : Value
|
||||
addr : Addr → Value
|
||||
number : Float → Value
|
||||
bool : Bool → Value
|
||||
|
||||
val : ∀ {a} → Value → Expr a
|
||||
val nil = nil
|
||||
val (addr a) = addr a
|
||||
val (number x) = number x
|
||||
val (bool false) = false
|
||||
val (bool true) = true
|
||||
|
|
|
|||
|
|
@ -1,14 +1 @@
|
|||
module Luau.Value.ToString where
|
||||
|
||||
open import Agda.Builtin.String using (String)
|
||||
open import Agda.Builtin.Float using (primShowFloat)
|
||||
open import Agda.Builtin.Bool using (true; false)
|
||||
open import Luau.Value using (Value; nil; addr; number; bool)
|
||||
open import Luau.Addr.ToString using (addrToString)
|
||||
|
||||
valueToString : Value → String
|
||||
valueToString nil = "nil"
|
||||
valueToString (addr a) = addrToString a
|
||||
valueToString (number x) = primShowFloat x
|
||||
valueToString (bool false) = "false"
|
||||
valueToString (bool true) = "true"
|
||||
|
|
|
|||
|
|
@ -1,5 +1,7 @@
|
|||
module Properties.Product where
|
||||
|
||||
infixr 5 _×_ _,_
|
||||
|
||||
record Σ {A : Set} (B : A → Set) : Set where
|
||||
|
||||
constructor _,_
|
||||
|
|
|
|||
|
|
@ -3,24 +3,89 @@
|
|||
module Properties.Step where
|
||||
|
||||
open import Agda.Builtin.Equality using (_≡_; refl)
|
||||
open import Agda.Builtin.Float using (primFloatPlus; primFloatMinus; primFloatTimes; primFloatDiv)
|
||||
open import Agda.Builtin.Float using (primFloatPlus; primFloatMinus; primFloatTimes; primFloatDiv; primFloatEquality; primFloatLess)
|
||||
open import Agda.Builtin.Bool using (true; false)
|
||||
open import FFI.Data.Maybe using (just; nothing)
|
||||
open import Luau.Heap using (Heap; _[_]; alloc; ok; function_is_end)
|
||||
open import Luau.Syntax using (Block; Expr; nil; var; addr; true; false; function_is_end; block_is_end; _$_; local_←_; return; done; _∙_; name; fun; arg; number; binexp; +; ==; ~=)
|
||||
open import Luau.OpSem using (_⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; app₁ ; app₂ ; beta; function; block; return; done; local; subst; binOpNumbers; evalNumOp; binOp₁; binOp₂; evalEqOp; evalNeqOp; binOpEquality; binOpInequality)
|
||||
open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinopMismatch₁; BinopMismatch₂; UnboundVariable; SEGV; app₁; app₂; block; local; return; bin₁; bin₂)
|
||||
open import Luau.RuntimeType using (function; number)
|
||||
open import Luau.Syntax using (Block; Expr; nil; var; val; addr; bool; function_is_end; block_is_end; _$_; local_←_; return; done; _∙_; name; fun; arg; number; binexp; +; -; *; /; <; >; <=; >=; ==; ~=)
|
||||
open import Luau.OpSem using (_⟦_⟧_⟶_; _⊢_⟶ᴱ_⊣_; _⊢_⟶ᴮ_⊣_; app₁ ; app₂ ; beta; function; block; return; done; local; subst; binOp₀; binOp₁; binOp₂; +; -; *; /; <; >; <=; >=; ==; ~=; evalEqOp)
|
||||
open import Luau.RuntimeError using (BinOpError; RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinOpMismatch₁; BinOpMismatch₂; UnboundVariable; SEGV; app₁; app₂; block; local; return; bin₁; bin₂; +; -; *; /; <; >; <=; >=)
|
||||
open import Luau.RuntimeType using (valueType; function; number)
|
||||
open import Luau.Substitution using (_[_/_]ᴮ)
|
||||
open import Luau.Value using (nil; addr; val; number; bool)
|
||||
open import Properties.Remember using (remember; _,_)
|
||||
open import Utility.Bool using (not; _or_)
|
||||
|
||||
data BinOpStepResult v op w : Set where
|
||||
step : ∀ x → (v ⟦ op ⟧ w ⟶ x) → BinOpStepResult v op w
|
||||
error₁ : BinOpError op (valueType(v)) → BinOpStepResult v op w
|
||||
error₂ : BinOpError op (valueType(w)) → BinOpStepResult v op w
|
||||
|
||||
binOpStep : ∀ v op w → BinOpStepResult v op w
|
||||
binOpStep nil + w = error₁ (+ (λ ()))
|
||||
binOpStep (addr a) + w = error₁ (+ (λ ()))
|
||||
binOpStep (number m) + nil = error₂ (+ (λ ()))
|
||||
binOpStep (number m) + (addr a) = error₂ (+ (λ ()))
|
||||
binOpStep (number m) + (number n) = step (number (primFloatPlus m n)) (+ m n)
|
||||
binOpStep (number m) + (bool b) = error₂ (+ (λ ()))
|
||||
binOpStep (bool b) + w = error₁ (+ (λ ()))
|
||||
binOpStep nil - w = error₁ (- (λ ()))
|
||||
binOpStep (addr a) - w = error₁ (- (λ ()))
|
||||
binOpStep (number x) - nil = error₂ (- (λ ()))
|
||||
binOpStep (number x) - (addr a) = error₂ (- (λ ()))
|
||||
binOpStep (number x) - (number n) = step (number (primFloatMinus x n)) (- x n)
|
||||
binOpStep (number x) - (bool b) = error₂ (- (λ ()))
|
||||
binOpStep (bool b) - w = error₁ (- (λ ()))
|
||||
binOpStep nil * w = error₁ (* (λ ()))
|
||||
binOpStep (addr a) * w = error₁ (* (λ ()))
|
||||
binOpStep (number m) * nil = error₂ (* (λ ()))
|
||||
binOpStep (number m) * (addr a) = error₂ (* (λ ()))
|
||||
binOpStep (number m) * (number n) = step (number (primFloatDiv m n)) (* m n)
|
||||
binOpStep (number m) * (bool b) = error₂ (* (λ ()))
|
||||
binOpStep (bool b) * w = error₁ (* (λ ()))
|
||||
binOpStep nil / w = error₁ (/ (λ ()))
|
||||
binOpStep (addr a) / w = error₁ (/ (λ ()))
|
||||
binOpStep (number m) / nil = error₂ (/ (λ ()))
|
||||
binOpStep (number m) / (addr a) = error₂ (/ (λ ()))
|
||||
binOpStep (number m) / (number n) = step (number (primFloatTimes m n)) (/ m n)
|
||||
binOpStep (number m) / (bool b) = error₂ (/ (λ ()))
|
||||
binOpStep (bool b) / w = error₁ (/ (λ ()))
|
||||
binOpStep nil < w = error₁ (< (λ ()))
|
||||
binOpStep (addr a) < w = error₁ (< (λ ()))
|
||||
binOpStep (number m) < nil = error₂ (< (λ ()))
|
||||
binOpStep (number m) < (addr a) = error₂ (< (λ ()))
|
||||
binOpStep (number m) < (number n) = step (bool (primFloatLess m n)) (< m n)
|
||||
binOpStep (number m) < (bool b) = error₂ (< (λ ()))
|
||||
binOpStep (bool b) < w = error₁ (< (λ ()))
|
||||
binOpStep nil > w = error₁ (> (λ ()))
|
||||
binOpStep (addr a) > w = error₁ (> (λ ()))
|
||||
binOpStep (number m) > nil = error₂ (> (λ ()))
|
||||
binOpStep (number m) > (addr a) = error₂ (> (λ ()))
|
||||
binOpStep (number m) > (number n) = step (bool (primFloatLess n m)) (> m n)
|
||||
binOpStep (number m) > (bool b) = error₂ (> (λ ()))
|
||||
binOpStep (bool b) > w = error₁ (> (λ ()))
|
||||
binOpStep v == w = step (bool (evalEqOp v w)) (== v w)
|
||||
binOpStep v ~= w = step (bool (not (evalEqOp v w))) (~= v w)
|
||||
binOpStep nil <= w = error₁ (<= (λ ()))
|
||||
binOpStep (addr a) <= w = error₁ (<= (λ ()))
|
||||
binOpStep (number m) <= nil = error₂ (<= (λ ()))
|
||||
binOpStep (number m) <= (addr a) = error₂ (<= (λ ()))
|
||||
binOpStep (number m) <= (number n) = step (bool (primFloatLess m n or primFloatEquality m n)) (<= m n)
|
||||
binOpStep (number m) <= (bool b) = error₂ (<= (λ ()))
|
||||
binOpStep (bool b) <= w = error₁ (<= (λ ()))
|
||||
binOpStep nil >= w = error₁ (>= (λ ()))
|
||||
binOpStep (addr a) >= w = error₁ (>= (λ ()))
|
||||
binOpStep (number m) >= nil = error₂ (>= (λ ()))
|
||||
binOpStep (number m) >= (addr a) = error₂ (>= (λ ()))
|
||||
binOpStep (number m) >= (number n) = step (bool (primFloatLess n m or primFloatEquality m n)) (>= m n)
|
||||
binOpStep (number m) >= (bool b) = error₂ (>= (λ ()))
|
||||
binOpStep (bool b) >= w = error₁ (>= (λ ()))
|
||||
|
||||
data StepResultᴮ {a} (H : Heap a) (B : Block a) : 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
|
||||
return : ∀ V {B′} → (B ≡ (return (val V) ∙ B′)) → StepResultᴮ H B
|
||||
return : ∀ v {B′} → (B ≡ (return (val v) ∙ B′)) → StepResultᴮ H B
|
||||
done : (B ≡ done) → StepResultᴮ H B
|
||||
error : (RuntimeErrorᴮ H B) → StepResultᴮ H B
|
||||
|
||||
|
|
@ -32,12 +97,8 @@ data StepResultᴱ H M where
|
|||
stepᴱ : ∀ {a} H M → StepResultᴱ {a} H M
|
||||
stepᴮ : ∀ {a} H B → StepResultᴮ {a} H B
|
||||
|
||||
stepᴱ H nil = value nil refl
|
||||
stepᴱ H (val v) = value v refl
|
||||
stepᴱ H (var x) = error UnboundVariable
|
||||
stepᴱ H (addr a) = value (addr a) refl
|
||||
stepᴱ H (number x) = value (number x) refl
|
||||
stepᴱ H (true) = value (bool true) refl
|
||||
stepᴱ H (false) = value (bool false) refl
|
||||
stepᴱ H (M $ N) with stepᴱ H M
|
||||
stepᴱ H (M $ N) | step H′ M′ D = step H′ (M′ $ N) (app₁ D)
|
||||
stepᴱ H (_ $ N) | value v refl with stepᴱ H N
|
||||
|
|
@ -46,32 +107,27 @@ stepᴱ H (_ $ _) | value (addr a) refl | value w refl with remember (H [ a ])
|
|||
stepᴱ H (_ $ _) | value (addr a) refl | value w refl | (nothing , p) = error (app₁ (SEGV p))
|
||||
stepᴱ H (_ $ _) | value (addr a) refl | value w refl | (just(function F is B end) , p) = step H (block (fun F) is B [ w / name (arg F) ]ᴮ end) (beta function F is B end w refl p)
|
||||
stepᴱ H (_ $ _) | value nil refl | value w refl = error (FunctionMismatch nil w (λ ()))
|
||||
stepᴱ H (_ $ _) | value (number x) refl | value w refl = error (FunctionMismatch (number x) w (λ ()))
|
||||
stepᴱ H (_ $ _) | value (number m) refl | value w refl = error (FunctionMismatch (number m) w (λ ()))
|
||||
stepᴱ H (_ $ _) | value (bool b) refl | value w refl = error (FunctionMismatch (bool b) w (λ ()))
|
||||
stepᴱ H (M $ N) | value V p | error E = error (app₂ E)
|
||||
stepᴱ H (M $ N) | error E = error (app₁ E)
|
||||
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 v)
|
||||
stepᴱ H (block b is done end) | done refl = step H nil done
|
||||
stepᴱ H (block b is done end) | done refl = step H (val nil) done
|
||||
stepᴱ H (block b is B end) | error E = error (block E)
|
||||
stepᴱ H (function F is C end) with alloc H (function F is C end)
|
||||
stepᴱ H function F is C end | ok a H′ p = step H′ (addr a) (function a p)
|
||||
stepᴱ H function F is C end | ok a H′ p = step H′ (val (addr a)) (function a p)
|
||||
stepᴱ H (binexp M op N) with stepᴱ H M
|
||||
stepᴱ H (binexp M op N) | step H′ M′ s = step H′ (binexp M′ op N) (binOp₁ s)
|
||||
stepᴱ H (binexp M op N) | error E = error (bin₁ E)
|
||||
stepᴱ H (binexp M op N) | value v refl with stepᴱ H N
|
||||
stepᴱ H (binexp M op N) | value v refl | step H′ N′ s = step H′ (binexp (val v) op N′) (binOp₂ s)
|
||||
stepᴱ H (binexp M op N) | value v refl | error E = error (bin₂ E)
|
||||
stepᴱ H (binexp M == N) | value v refl | value w refl = step H (val (evalEqOp v w)) binOpEquality
|
||||
stepᴱ H (binexp M ~= N) | value v refl | value w refl = step H (val (evalNeqOp v w)) binOpInequality
|
||||
stepᴱ H (binexp M op N) | value (number m) refl | value (number n) refl = step H (val (evalNumOp m op n)) binOpNumbers
|
||||
stepᴱ H (binexp M op N) | value nil refl | value w refl = error (BinopMismatch₁ nil w λ ())
|
||||
stepᴱ H (binexp M op N) | value (addr a) refl | value w refl = error (BinopMismatch₁ (addr a) w λ ())
|
||||
stepᴱ H (binexp M op N) | value (bool b) refl | value w refl = error (BinopMismatch₁ (bool b) w λ ())
|
||||
stepᴱ H (binexp M op N) | value v refl | value nil refl = error (BinopMismatch₂ v nil (λ ()))
|
||||
stepᴱ H (binexp M op N) | value v refl | value (addr a) refl = error (BinopMismatch₂ v (addr a) (λ ()))
|
||||
stepᴱ H (binexp M op N) | value v refl | value (bool b) refl = error (BinopMismatch₂ v (bool b) (λ ()))
|
||||
stepᴱ H (binexp M op N) | step H′ M′ s = step H′ (binexp M′ op N) (binOp₁ s)
|
||||
stepᴱ H (binexp M op N) | error E = error (bin₁ E)
|
||||
stepᴱ H (binexp M op N) | value v refl | value w refl with binOpStep v op w
|
||||
stepᴱ H (binexp M op N) | value v refl | value w refl | step x p = step H (val x) (binOp₀ p)
|
||||
stepᴱ H (binexp M op N) | value v refl | value w refl | error₁ E = error (BinOpMismatch₁ v w E)
|
||||
stepᴱ H (binexp M op N) | value v refl | value w refl | error₂ E = error (BinOpMismatch₂ v w E)
|
||||
|
||||
stepᴮ H (function F is C end ∙ B) with alloc H (function F is C end)
|
||||
stepᴮ H (function F is C end ∙ B) | ok a H′ p = step H′ (B [ addr a / name (fun F) ]ᴮ) (function a p)
|
||||
|
|
|
|||
|
|
@ -6,12 +6,11 @@ import Agda.Builtin.Equality.Rewrite
|
|||
open import Agda.Builtin.Equality using (_≡_; refl)
|
||||
open import FFI.Data.Maybe using (Maybe; just; nothing)
|
||||
open import Luau.Heap using (Heap; Object; function_is_end; defn; alloc; ok; next; lookup-not-allocated) renaming (_≡_⊕_↦_ to _≡ᴴ_⊕_↦_; _[_] to _[_]ᴴ; ∅ to ∅ᴴ)
|
||||
open import Luau.StrictMode using (Warningᴱ; Warningᴮ; Warningᴼ; Warningᴴᴱ; Warningᴴᴮ; UnallocatedAddress; UnboundVariable; FunctionCallMismatch; app₁; app₂; BinopMismatch₁; BinopMismatch₂; bin₁; bin₂; BlockMismatch; block₁; return; LocalVarMismatch; local₁; local₂; FunctionDefnMismatch; function₁; function₂; heap; expr; block; addr)
|
||||
open import Luau.StrictMode using (Warningᴱ; Warningᴮ; Warningᴼ; Warningᴴᴱ; Warningᴴᴮ; UnallocatedAddress; UnboundVariable; FunctionCallMismatch; app₁; app₂; BinOpWarning; BinOpMismatch₁; BinOpMismatch₂; bin₁; bin₂; BlockMismatch; block₁; return; LocalVarMismatch; local₁; local₂; FunctionDefnMismatch; function₁; function₂; heap; expr; block; addr; +; -; *; /; <; >; <=; >=)
|
||||
open import Luau.Substitution using (_[_/_]ᴮ; _[_/_]ᴱ; _[_/_]ᴮunless_; var_[_/_]ᴱwhenever_)
|
||||
open import Luau.Syntax using (Expr; yes; var; var_∈_; _⟨_⟩∈_; _$_; addr; number; binexp; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg; name)
|
||||
open import Luau.Syntax using (Expr; yes; var; val; var_∈_; _⟨_⟩∈_; _$_; addr; number; bool; binexp; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg; name; ==; ~=)
|
||||
open import Luau.Type using (Type; strict; nil; _⇒_; bot; tgt; _≡ᵀ_; _≡ᴹᵀ_)
|
||||
open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; _⊢ᴴᴮ_▷_∈_; _⊢ᴴᴱ_▷_∈_; nil; var; addr; app; function; block; done; return; local; orBot)
|
||||
open import Luau.Value using (val; nil; addr; number)
|
||||
open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; _⊢ᴴᴮ_▷_∈_; _⊢ᴴᴱ_▷_∈_; nil; var; addr; app; function; block; done; return; local; orBot; tgtBinOp)
|
||||
open import Luau.Var using (_≡ⱽ_)
|
||||
open import Luau.Addr using (_≡ᴬ_)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_; ⊕-lookup-miss; ⊕-swap; ⊕-over) renaming (_[_] to _[_]ⱽ)
|
||||
|
|
@ -20,9 +19,10 @@ open import Properties.Remember using (remember; _,_)
|
|||
open import Properties.Equality using (_≢_; sym; cong; trans; subst₁)
|
||||
open import Properties.Dec using (Dec; yes; no)
|
||||
open import Properties.Contradiction using (CONTRADICTION)
|
||||
open import Properties.TypeCheck(strict) using (typeOfᴼ; typeOfᴹᴼ; typeOfⱽ; typeOfᴱ; typeOfᴮ; typeOfᴱⱽ; typeCheckᴱ; typeCheckᴮ; typeCheckᴼ; typeCheckᴴᴱ; typeCheckᴴᴮ; mustBeFunction; mustBeNumber)
|
||||
open import Luau.OpSem using (_⊢_⟶*_⊣_; _⊢_⟶ᴮ_⊣_; _⊢_⟶ᴱ_⊣_; app₁; app₂; function; beta; return; block; done; local; subst; binOp₁; binOp₂; binOpEval; refl; step)
|
||||
open import Luau.RuntimeError using (RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinopMismatch₁; BinopMismatch₂; UnboundVariable; SEGV; app₁; app₂; bin₁; bin₂; block; local; return)
|
||||
open import Properties.TypeCheck(strict) using (typeOfᴼ; typeOfᴹᴼ; typeOfⱽ; typeOfᴱ; typeOfᴮ; typeCheckᴱ; typeCheckᴮ; typeCheckᴼ; typeCheckᴴᴱ; typeCheckᴴᴮ; mustBeFunction; mustBeNumber)
|
||||
open import Luau.OpSem using (_⟦_⟧_⟶_; _⊢_⟶*_⊣_; _⊢_⟶ᴮ_⊣_; _⊢_⟶ᴱ_⊣_; app₁; app₂; function; beta; return; block; done; local; subst; binOp₀; binOp₁; binOp₂; refl; step; +; -; *; /; <; >; ==; ~=; <=; >=)
|
||||
open import Luau.RuntimeError using (BinOpError; RuntimeErrorᴱ; RuntimeErrorᴮ; FunctionMismatch; BinOpMismatch₁; BinOpMismatch₂; UnboundVariable; SEGV; app₁; app₂; bin₁; bin₂; block; local; return; +; -; *; /; <; >; <=; >=)
|
||||
open import Luau.RuntimeType using (valueType)
|
||||
|
||||
src = Luau.Type.src strict
|
||||
|
||||
|
|
@ -40,7 +40,7 @@ rednᴱ⊑ (beta O v p q) = refl
|
|||
rednᴱ⊑ (block s) = rednᴮ⊑ s
|
||||
rednᴱ⊑ (return v) = refl
|
||||
rednᴱ⊑ done = refl
|
||||
rednᴱ⊑ (binOpEval m n) = refl
|
||||
rednᴱ⊑ (binOp₀ p) = refl
|
||||
rednᴱ⊑ (binOp₁ s) = rednᴱ⊑ s
|
||||
rednᴱ⊑ (binOp₂ s) = rednᴱ⊑ s
|
||||
|
||||
|
|
@ -78,13 +78,14 @@ data OrWarningᴴᴮ {Γ B T} H (D : Γ ⊢ᴴᴮ H ▷ B ∈ T) A : Set where
|
|||
heap-weakeningᴱ : ∀ H M {H′ Γ} → (H ⊑ H′) → OrWarningᴱ H (typeCheckᴱ H Γ M) (typeOfᴱ H Γ M ≡ typeOfᴱ H′ Γ M)
|
||||
heap-weakeningᴮ : ∀ H B {H′ Γ} → (H ⊑ H′) → OrWarningᴮ H (typeCheckᴮ H Γ B) (typeOfᴮ H Γ B ≡ typeOfᴮ H′ Γ B)
|
||||
|
||||
heap-weakeningᴱ H (nil) h = ok refl
|
||||
heap-weakeningᴱ H (var x) h = ok refl
|
||||
heap-weakeningᴱ H (addr a) refl = ok refl
|
||||
heap-weakeningᴱ H (addr a) (snoc {a = b} defn) with a ≡ᴬ b
|
||||
heap-weakeningᴱ H (addr a) (snoc {a = a} defn) | yes refl = warning (UnallocatedAddress refl)
|
||||
heap-weakeningᴱ H (addr a) (snoc {a = b} p) | no q = ok (cong orBot (cong typeOfᴹᴼ (lookup-not-allocated p q)))
|
||||
heap-weakeningᴱ H (number n) h = ok refl
|
||||
heap-weakeningᴱ H (val nil) h = ok refl
|
||||
heap-weakeningᴱ H (val (addr a)) refl = ok refl
|
||||
heap-weakeningᴱ H (val (addr a)) (snoc {a = b} defn) with a ≡ᴬ b
|
||||
heap-weakeningᴱ H (val (addr a)) (snoc {a = a} defn) | yes refl = warning (UnallocatedAddress refl)
|
||||
heap-weakeningᴱ H (val (addr a)) (snoc {a = b} p) | no q = ok (cong orBot (cong typeOfᴹᴼ (lookup-not-allocated p q)))
|
||||
heap-weakeningᴱ H (val (number n)) h = ok refl
|
||||
heap-weakeningᴱ H (val (bool b)) h = ok refl
|
||||
heap-weakeningᴱ H (binexp M op N) h = ok refl
|
||||
heap-weakeningᴱ H (M $ N) h with heap-weakeningᴱ H M h
|
||||
heap-weakeningᴱ H (M $ N) h | ok p = ok (cong tgt p)
|
||||
|
|
@ -108,6 +109,7 @@ bot-not-obj (function f ⟨ var x ∈ T ⟩∈ U is B end) ()
|
|||
typeOf-val-not-bot : ∀ {H Γ} v → OrWarningᴱ H (typeCheckᴱ H Γ (val v)) (bot ≢ typeOfᴱ H Γ (val v))
|
||||
typeOf-val-not-bot nil = ok (λ ())
|
||||
typeOf-val-not-bot (number n) = ok (λ ())
|
||||
typeOf-val-not-bot (bool b) = ok (λ ())
|
||||
typeOf-val-not-bot {H = H} (addr a) with remember (H [ a ]ᴴ)
|
||||
typeOf-val-not-bot {H = H} (addr a) | (just O , p) = ok (λ q → bot-not-obj O (trans q (cong orBot (cong typeOfᴹᴼ p))))
|
||||
typeOf-val-not-bot {H = H} (addr a) | (nothing , p) = warning (UnallocatedAddress p)
|
||||
|
|
@ -119,17 +121,15 @@ substitutivityᴮ : ∀ {Γ T} H B v x → (just T ≡ typeOfⱽ H v) → (typeO
|
|||
substitutivityᴮ-unless-yes : ∀ {Γ Γ′ T} H B v x y (p : x ≡ y) → (just T ≡ typeOfⱽ H v) → (Γ′ ≡ Γ) → (typeOfᴮ H Γ′ B ≡ typeOfᴮ H Γ (B [ v / x ]ᴮunless (yes p)))
|
||||
substitutivityᴮ-unless-no : ∀ {Γ Γ′ T} H B v x y (p : x ≢ y) → (just T ≡ typeOfⱽ H v) → (Γ′ ≡ Γ ⊕ x ↦ T) → (typeOfᴮ H Γ′ B ≡ typeOfᴮ H Γ (B [ v / x ]ᴮunless (no p)))
|
||||
|
||||
substitutivityᴱ H nil v x p = refl
|
||||
substitutivityᴱ H (var y) v x p with x ≡ⱽ y
|
||||
substitutivityᴱ H (var y) v x p | yes q = substitutivityᴱ-whenever-yes H v x y q p
|
||||
substitutivityᴱ H (var y) v x p | no q = substitutivityᴱ-whenever-no H v x y q p
|
||||
substitutivityᴱ H (addr a) v x p = refl
|
||||
substitutivityᴱ H (number n) v x p = refl
|
||||
substitutivityᴱ H (val w) v x p = refl
|
||||
substitutivityᴱ H (binexp M op N) v x p = refl
|
||||
substitutivityᴱ H (M $ N) v x p = cong tgt (substitutivityᴱ H M v x p)
|
||||
substitutivityᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p = refl
|
||||
substitutivityᴱ H (block var b ∈ T is B end) v x p = refl
|
||||
substitutivityᴱ-whenever-yes H v x x refl q = trans (cong orBot q) (sym (typeOfᴱⱽ v))
|
||||
substitutivityᴱ-whenever-yes H v x x refl q = cong orBot q
|
||||
substitutivityᴱ-whenever-no H v x y p q = cong orBot ( sym (⊕-lookup-miss x y _ _ p))
|
||||
substitutivityᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p with x ≡ⱽ f
|
||||
substitutivityᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p | yes q = substitutivityᴮ-unless-yes H B v x f q p (⊕-over q)
|
||||
|
|
@ -142,6 +142,18 @@ substitutivityᴮ H done v x p = refl
|
|||
substitutivityᴮ-unless-yes H B v x x refl q refl = refl
|
||||
substitutivityᴮ-unless-no H B v x y p q refl = substitutivityᴮ H B v x q
|
||||
|
||||
binOpPreservation : ∀ H {op v w x} → (v ⟦ op ⟧ w ⟶ x) → (tgtBinOp op ≡ typeOfᴱ H ∅ (val x))
|
||||
binOpPreservation H (+ m n) = refl
|
||||
binOpPreservation H (- m n) = refl
|
||||
binOpPreservation H (/ m n) = refl
|
||||
binOpPreservation H (* m n) = refl
|
||||
binOpPreservation H (< m n) = refl
|
||||
binOpPreservation H (> m n) = refl
|
||||
binOpPreservation H (<= m n) = refl
|
||||
binOpPreservation H (>= m n) = refl
|
||||
binOpPreservation H (== v w) = refl
|
||||
binOpPreservation H (~= v w) = refl
|
||||
|
||||
preservationᴱ : ∀ H M {H′ M′} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → OrWarningᴴᴱ H (typeCheckᴴᴱ H ∅ M) (typeOfᴱ H ∅ M ≡ typeOfᴱ H′ ∅ M′)
|
||||
preservationᴮ : ∀ H B {H′ B′} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → OrWarningᴴᴮ H (typeCheckᴴᴮ H ∅ B) (typeOfᴮ H ∅ B ≡ typeOfᴮ H′ ∅ B′)
|
||||
|
||||
|
|
@ -153,14 +165,14 @@ preservationᴱ H (M $ N) (app₁ s) | warning (heap W) = warning (heap W)
|
|||
preservationᴱ H (M $ N) (app₂ p s) with heap-weakeningᴱ H M (rednᴱ⊑ s)
|
||||
preservationᴱ H (M $ N) (app₂ p s) | ok q = ok (cong tgt q)
|
||||
preservationᴱ H (M $ N) (app₂ p s) | warning W = warning (expr (app₁ W))
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) with remember (typeOfⱽ H v)
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) with S ≡ᵀ U | T ≡ᵀ typeOfᴮ H (x ↦ S) B
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | yes refl | yes refl = ok (cong tgt (cong orBot (cong typeOfᴹᴼ p)))
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | yes refl | no r = warning (heap (addr a p (FunctionDefnMismatch r)))
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | no r | _ = warning (expr (FunctionCallMismatch (λ s → r (trans (trans (sym (cong src (cong orBot (cong typeOfᴹᴼ p)))) (trans s (typeOfᴱⱽ v))) (cong orBot q)))))
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) with typeOf-val-not-bot v
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) | ok r = CONTRADICTION (r (sym (trans (typeOfᴱⱽ v) (cong orBot q))))
|
||||
preservationᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) | warning W = warning (expr (app₂ W))
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) with remember (typeOfⱽ H v)
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) with S ≡ᵀ U | T ≡ᵀ typeOfᴮ H (x ↦ S) B
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | yes refl | yes refl = ok (cong tgt (cong orBot (cong typeOfᴹᴼ p)))
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | yes refl | no r = warning (heap (addr a p (FunctionDefnMismatch r)))
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (just U , q) | no r | _ = warning (expr (FunctionCallMismatch (λ s → r (trans (trans (sym (cong src (cong orBot (cong typeOfᴹᴼ p)))) s) (cong orBot q)))))
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) with typeOf-val-not-bot v
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) | ok r = CONTRADICTION (r (sym (cong orBot q)))
|
||||
preservationᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ S ⟩∈ T is B end) v refl p) | (nothing , q) | warning W = warning (expr (app₂ W))
|
||||
preservationᴱ H (block var b ∈ T is B end) (block s) = ok refl
|
||||
preservationᴱ H (block var b ∈ T is return M ∙ B end) (return v) with T ≡ᵀ typeOfᴱ H ∅ (val v)
|
||||
preservationᴱ H (block var b ∈ T is return M ∙ B end) (return v) | yes p = ok p
|
||||
|
|
@ -168,7 +180,7 @@ preservationᴱ H (block var b ∈ T is return M ∙ B end) (return v) | no p =
|
|||
preservationᴱ H (block var b ∈ T is done end) (done) with T ≡ᵀ nil
|
||||
preservationᴱ H (block var b ∈ T is done end) (done) | yes p = ok p
|
||||
preservationᴱ H (block var b ∈ T is done end) (done) | no p = warning (expr (BlockMismatch p))
|
||||
preservationᴱ H (binexp M op N) (binOpEval m n) = ok refl
|
||||
preservationᴱ H (binexp M op N) (binOp₀ s) = ok (binOpPreservation H s)
|
||||
preservationᴱ H (binexp M op N) (binOp₁ s) = ok refl
|
||||
preservationᴱ H (binexp M op N) (binOp₂ s) = ok refl
|
||||
|
||||
|
|
@ -178,9 +190,9 @@ preservationᴮ H (local var x ∈ T ← M ∙ B) (local s) | warning W = warnin
|
|||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) with remember (typeOfⱽ H v)
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just U , p) with T ≡ᵀ U
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just T , p) | yes refl = ok (substitutivityᴮ H B v x (sym p))
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just U , p) | no q = warning (block (LocalVarMismatch (λ r → q (trans r (trans (typeOfᴱⱽ v) (cong orBot p))))))
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (just U , p) | no q = warning (block (LocalVarMismatch (λ r → q (trans r (cong orBot p)))))
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) with typeOf-val-not-bot v
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) | ok q = CONTRADICTION (q (sym (trans (typeOfᴱⱽ v) (cong orBot p))))
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) | ok q = CONTRADICTION (q (sym (cong orBot p)))
|
||||
preservationᴮ H (local var x ∈ T ← M ∙ B) (subst v) | (nothing , p) | warning W = warning (block (local₁ W))
|
||||
preservationᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) with heap-weakeningᴮ H B (snoc defn)
|
||||
preservationᴮ H (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) (function a defn) | ok r = ok (trans r (substitutivityᴮ _ B (addr a) f refl))
|
||||
|
|
@ -200,7 +212,7 @@ reflect-substitutionᴮ-unless-no : ∀ {Γ Γ′ T} H B v x y (r : x ≢ y) →
|
|||
reflect-substitutionᴱ H (var y) v x p W with x ≡ⱽ y
|
||||
reflect-substitutionᴱ H (var y) v x p W | yes r = reflect-substitutionᴱ-whenever-yes H v x y r p W
|
||||
reflect-substitutionᴱ H (var y) v x p W | no r = reflect-substitutionᴱ-whenever-no H v x y r p W
|
||||
reflect-substitutionᴱ H (addr a) v x p (UnallocatedAddress r) = UnallocatedAddress r
|
||||
reflect-substitutionᴱ H (val (addr a)) v x p (UnallocatedAddress r) = UnallocatedAddress r
|
||||
reflect-substitutionᴱ H (M $ N) v x p (FunctionCallMismatch q) = FunctionCallMismatch (λ s → q (trans (cong src (sym (substitutivityᴱ H M v x p))) (trans s (substitutivityᴱ H N v x p))))
|
||||
reflect-substitutionᴱ H (M $ N) v x p (app₁ W) = app₁ (reflect-substitutionᴱ H M v x p W)
|
||||
reflect-substitutionᴱ H (M $ N) v x p (app₂ W) = app₂ (reflect-substitutionᴱ H N v x p W)
|
||||
|
|
@ -212,8 +224,8 @@ reflect-substitutionᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p (
|
|||
reflect-substitutionᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p (function₁ W) | no r = function₁ (reflect-substitutionᴮ-unless-no H B v x y r p (⊕-swap r) W)
|
||||
reflect-substitutionᴱ H (block var b ∈ T is B end) v x p (BlockMismatch q) = BlockMismatch (λ r → q (trans r (substitutivityᴮ H B v x p)))
|
||||
reflect-substitutionᴱ H (block var b ∈ T is B end) v x p (block₁ W) = block₁ (reflect-substitutionᴮ H B v x p W)
|
||||
reflect-substitutionᴱ H (binexp M op N) x v p (BinopMismatch₁ q) = BinopMismatch₁ (λ r → q (trans (sym (substitutivityᴱ H M x v p)) r))
|
||||
reflect-substitutionᴱ H (binexp M op N) x v p (BinopMismatch₂ q) = BinopMismatch₂ (λ r → q (trans (sym (substitutivityᴱ H N x v p)) r))
|
||||
reflect-substitutionᴱ H (binexp M op N) x v p (BinOpMismatch₁ q) = BinOpMismatch₁ (subst₁ (BinOpWarning op) (sym (substitutivityᴱ H M x v p)) q)
|
||||
reflect-substitutionᴱ H (binexp M op N) x v p (BinOpMismatch₂ q) = BinOpMismatch₂ (subst₁ (BinOpWarning op) (sym (substitutivityᴱ H N x v p)) q)
|
||||
reflect-substitutionᴱ H (binexp M op N) x v p (bin₁ W) = bin₁ (reflect-substitutionᴱ H M x v p W)
|
||||
reflect-substitutionᴱ H (binexp M op N) x v p (bin₂ W) = bin₂ (reflect-substitutionᴱ H N x v p W)
|
||||
|
||||
|
|
@ -244,19 +256,19 @@ reflect-weakeningᴱ : ∀ H M {H′ Γ} → (H ⊑ H′) → Warningᴱ H′ (t
|
|||
reflect-weakeningᴮ : ∀ H B {H′ Γ} → (H ⊑ H′) → Warningᴮ H′ (typeCheckᴮ H′ Γ B) → Warningᴮ H (typeCheckᴮ H Γ B)
|
||||
|
||||
reflect-weakeningᴱ H (var x) h (UnboundVariable p) = (UnboundVariable p)
|
||||
reflect-weakeningᴱ H (addr a) h (UnallocatedAddress p) = UnallocatedAddress (lookup-⊑-nothing a h p)
|
||||
reflect-weakeningᴱ H (val (addr a)) h (UnallocatedAddress p) = UnallocatedAddress (lookup-⊑-nothing a h p)
|
||||
reflect-weakeningᴱ H (M $ N) h (FunctionCallMismatch p) with heap-weakeningᴱ H M h | heap-weakeningᴱ H N h
|
||||
reflect-weakeningᴱ H (M $ N) h (FunctionCallMismatch p) | ok q₁ | ok q₂ = FunctionCallMismatch (λ r → p (trans (cong src (sym q₁)) (trans r q₂)))
|
||||
reflect-weakeningᴱ H (M $ N) h (FunctionCallMismatch p) | warning W | _ = app₁ W
|
||||
reflect-weakeningᴱ H (M $ N) h (FunctionCallMismatch p) | _ | warning W = app₂ W
|
||||
reflect-weakeningᴱ H (M $ N) h (app₁ W) = app₁ (reflect-weakeningᴱ H M h W)
|
||||
reflect-weakeningᴱ H (M $ N) h (app₂ W) = app₂ (reflect-weakeningᴱ H N h W)
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinopMismatch₁ p) with heap-weakeningᴱ H M h
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinopMismatch₁ p) | ok q = BinopMismatch₁ (λ r → p (trans (sym q) r))
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinopMismatch₁ p) | warning W = bin₁ W
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinopMismatch₂ p) with heap-weakeningᴱ H N h
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinopMismatch₂ p) | ok q = BinopMismatch₂ (λ r → p (trans (sym q) r))
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinopMismatch₂ p) | warning W = bin₂ W
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinOpMismatch₁ p) with heap-weakeningᴱ H M h
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinOpMismatch₁ p) | ok q = BinOpMismatch₁ (subst₁ (BinOpWarning op) (sym q) p)
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinOpMismatch₁ p) | warning W = bin₁ W
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinOpMismatch₂ p) with heap-weakeningᴱ H N h
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinOpMismatch₂ p) | ok q = BinOpMismatch₂ (subst₁ (BinOpWarning op) (sym q) p)
|
||||
reflect-weakeningᴱ H (binexp M op N) h (BinOpMismatch₂ p) | warning W = bin₂ W
|
||||
reflect-weakeningᴱ H (binexp M op N) h (bin₁ W′) = bin₁ (reflect-weakeningᴱ H M h W′)
|
||||
reflect-weakeningᴱ H (binexp M op N) h (bin₂ W′) = bin₂ (reflect-weakeningᴱ H N h W′)
|
||||
reflect-weakeningᴱ H (function f ⟨ var y ∈ T ⟩∈ U is B end) h (FunctionDefnMismatch p) with heap-weakeningᴮ H B h
|
||||
|
|
@ -307,20 +319,20 @@ reflectᴱ H (M $ N) (app₂ p s) (app₁ W′) = expr (app₁ (reflect-weakenin
|
|||
reflectᴱ H (M $ N) (app₂ p s) (app₂ W′) with reflectᴱ H N s W′
|
||||
reflectᴱ H (M $ N) (app₂ p s) (app₂ W′) | heap W = heap W
|
||||
reflectᴱ H (M $ N) (app₂ p s) (app₂ W′) | expr W = expr (app₂ W)
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) with remember (typeOfⱽ H v)
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (just S , r) with S ≡ᵀ T
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (just T , r) | yes refl = heap (addr a p (FunctionDefnMismatch (λ s → q (trans s (substitutivityᴮ H B v x (sym r))))))
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (just S , r) | no s = expr (FunctionCallMismatch (λ t → s (trans (cong orBot (sym r)) (trans (sym (typeOfᴱⱽ v)) (trans (sym t) (cong src (cong orBot (cong typeOfᴹᴼ p))))))))
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (nothing , r) with typeOf-val-not-bot v
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (nothing , r) | ok s = CONTRADICTION (s (trans (cong orBot (sym r)) (sym (typeOfᴱⱽ v))))
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (nothing , r) | warning W = expr (app₂ W)
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) with remember (typeOfⱽ H v)
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (just S , q) with S ≡ᵀ T
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (just T , q) | yes refl = heap (addr a p (function₁ (reflect-substitutionᴮ H B v x (sym q) W′)))
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (just S , q) | no r = expr (FunctionCallMismatch (λ s → r (trans (cong orBot (sym q)) (trans (sym (typeOfᴱⱽ v)) (trans (sym s) (cong src (cong orBot (cong typeOfᴹᴼ p))))))))
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (nothing , q) with typeOf-val-not-bot v
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (nothing , q) | ok r = CONTRADICTION (r (trans (cong orBot (sym q)) (sym (typeOfᴱⱽ v))))
|
||||
reflectᴱ H (addr a $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (nothing , q) | warning W = expr (app₂ W)
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) with remember (typeOfⱽ H v)
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (just S , r) with S ≡ᵀ T
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (just T , r) | yes refl = heap (addr a p (FunctionDefnMismatch (λ s → q (trans s (substitutivityᴮ H B v x (sym r))))))
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (just S , r) | no s = expr (FunctionCallMismatch (λ t → s (trans (cong orBot (sym r)) (trans (sym t) (cong src (cong orBot (cong typeOfᴹᴼ p)))))))
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (nothing , r) with typeOf-val-not-bot v
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (nothing , r) | ok s = CONTRADICTION (s (cong orBot (sym r)))
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (BlockMismatch q) | (nothing , r) | warning W = expr (app₂ W)
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) with remember (typeOfⱽ H v)
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (just S , q) with S ≡ᵀ T
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (just T , q) | yes refl = heap (addr a p (function₁ (reflect-substitutionᴮ H B v x (sym q) W′)))
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (just S , q) | no r = expr (FunctionCallMismatch (λ s → r (trans (cong orBot (sym q)) (trans (sym s) (cong src (cong orBot (cong typeOfᴹᴼ p)))))))
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (nothing , q) with typeOf-val-not-bot v
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (nothing , q) | ok r = CONTRADICTION (r (cong orBot (sym q)))
|
||||
reflectᴱ H (val (addr a) $ N) (beta (function f ⟨ var x ∈ T ⟩∈ U is B end) v refl p) (block₁ W′) | (nothing , q) | warning W = expr (app₂ W)
|
||||
reflectᴱ H (block var b ∈ T is B end) (block s) (BlockMismatch p) with preservationᴮ H B s
|
||||
reflectᴱ H (block var b ∈ T is B end) (block s) (BlockMismatch p) | ok q = expr (BlockMismatch (λ r → p (trans r q)))
|
||||
reflectᴱ H (block var b ∈ T is B end) (block s) (BlockMismatch p) | warning (heap W) = heap W
|
||||
|
|
@ -330,24 +342,25 @@ reflectᴱ H (block var b ∈ T is B end) (block s) (block₁ W′) | heap W = h
|
|||
reflectᴱ H (block var b ∈ T is B end) (block s) (block₁ W′) | block W = expr (block₁ W)
|
||||
reflectᴱ H (block var b ∈ T is B end) (return v) W′ = expr (block₁ (return W′))
|
||||
reflectᴱ H (function f ⟨ var x ∈ T ⟩∈ U is B end) (function a defn) (UnallocatedAddress ())
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₁ p) with preservationᴱ H M s
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₁ p) | ok q = expr (BinopMismatch₁ (λ r → p (trans (sym q) r)))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₁ p) | warning (heap W) = heap W
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₁ p) | warning (expr W) = expr (bin₁ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₂ p) with heap-weakeningᴱ H N (rednᴱ⊑ s)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₂ p) | ok q = expr (BinopMismatch₂ (λ r → p (trans (sym q) r)))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinopMismatch₂ p) | warning W = expr (bin₂ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₀ ()) (UnallocatedAddress p)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₁ p) with preservationᴱ H M s
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₁ p) | ok q = expr (BinOpMismatch₁ (subst₁ (BinOpWarning op) (sym q) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₁ p) | warning (heap W) = heap W
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₁ p) | warning (expr W) = expr (bin₁ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₂ p) with heap-weakeningᴱ H N (rednᴱ⊑ s)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₂ p) | ok q = expr (BinOpMismatch₂ ((subst₁ (BinOpWarning op) (sym q) p)))
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (BinOpMismatch₂ p) | warning W = expr (bin₂ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (bin₁ W′) with reflectᴱ H M s W′
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (bin₁ W′) | heap W = heap W
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (bin₁ W′) | expr W = expr (bin₁ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₁ s) (bin₂ W′) = expr (bin₂ (reflect-weakeningᴱ H N (rednᴱ⊑ s) W′))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₁ p) with heap-weakeningᴱ H M (rednᴱ⊑ s)
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₁ p) | ok q = expr (BinopMismatch₁ (λ r → p (trans (sym q) r)))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₁ p) | warning W = expr (bin₁ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₂ p) with preservationᴱ H N s
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₂ p) | ok q = expr (BinopMismatch₂ (λ r → p (trans (sym q) r)))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₂ p) | warning (heap W) = heap W
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinopMismatch₂ p) | warning (expr W) = expr (bin₂ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₁ p) with heap-weakeningᴱ H M (rednᴱ⊑ s)
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₁ p) | ok q = expr (BinOpMismatch₁ (subst₁ (BinOpWarning op) (sym q) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₁ p) | warning W = expr (bin₁ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₂ p) with preservationᴱ H N s
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₂ p) | ok q = expr (BinOpMismatch₂ (subst₁ (BinOpWarning op) (sym q) p))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₂ p) | warning (heap W) = heap W
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (BinOpMismatch₂ p) | warning (expr W) = expr (bin₂ W)
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (bin₁ W′) = expr (bin₁ (reflect-weakeningᴱ H M (rednᴱ⊑ s) W′))
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (bin₂ W′) with reflectᴱ H N s W′
|
||||
reflectᴱ H (binexp M op N) (binOp₂ s) (bin₂ W′) | heap W = heap W
|
||||
|
|
@ -364,9 +377,9 @@ reflectᴮ H (local var x ∈ T ← M ∙ B) (local s) (local₂ W′) = block (
|
|||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ with remember (typeOfⱽ H v)
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (just S , p) with S ≡ᵀ T
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (just T , p) | yes refl = block (local₂ (reflect-substitutionᴮ H B v x (sym p) W′))
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (just S , p) | no q = block (LocalVarMismatch (λ r → q (trans (cong orBot (sym p)) (trans (sym (typeOfᴱⱽ v)) (sym r)))))
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (just S , p) | no q = block (LocalVarMismatch (λ r → q (trans (cong orBot (sym p)) (sym r))))
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (nothing , p) with typeOf-val-not-bot v
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (nothing , p) | ok r = CONTRADICTION (r (trans (cong orBot (sym p)) (sym (typeOfᴱⱽ v))))
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (nothing , p) | ok r = CONTRADICTION (r (cong orBot (sym p)))
|
||||
reflectᴮ H (local var x ∈ T ← M ∙ B) (subst v) W′ | (nothing , p) | warning W = block (local₁ W)
|
||||
reflectᴮ H (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) (function a defn) W′ = block (function₂ (reflect-weakeningᴮ H B (snoc defn) (reflect-substitutionᴮ _ B (addr a) f refl W′)))
|
||||
reflectᴮ H (return M ∙ B) (return s) (return W′) with reflectᴱ H M s W′
|
||||
|
|
@ -395,7 +408,7 @@ reflectᴴᴱ H (block var b ∈ T is B end) (block s) (heap W′) | heap W = he
|
|||
reflectᴴᴱ H (block var b ∈ T is B end) (block s) (heap W′) | block W = expr (block₁ W)
|
||||
reflectᴴᴱ H (block var b ∈ T is return N ∙ B end) (return v) (heap W′) = heap W′
|
||||
reflectᴴᴱ H (block var b ∈ T is done end) done (heap W′) = heap W′
|
||||
reflectᴴᴱ H (binexp M op N) (binOpEval m n) (heap W′) = heap W′
|
||||
reflectᴴᴱ H (binexp M op N) (binOp₀ s) (heap W′) = heap W′
|
||||
reflectᴴᴱ H (binexp M op N) (binOp₁ s) (heap W′) with reflectᴴᴱ H M s (heap W′)
|
||||
reflectᴴᴱ H (binexp M op N) (binOp₁ s) (heap W′) | heap W = heap W
|
||||
reflectᴴᴱ H (binexp M op N) (binOp₁ s) (heap W′) | expr W = expr (bin₁ W)
|
||||
|
|
@ -422,19 +435,29 @@ reflect* : ∀ H B {H′ B′} → (H ⊢ B ⟶* B′ ⊣ H′) → Warningᴴ
|
|||
reflect* H B refl W = W
|
||||
reflect* H B (step s t) W = reflectᴴᴮ H B s (reflect* _ _ t W)
|
||||
|
||||
runtimeBinOpWarning : ∀ H {op} v → BinOpError op (valueType v) → BinOpWarning op (orBot (typeOfⱽ H v))
|
||||
runtimeBinOpWarning H v (+ p) = + (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (- p) = - (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (* p) = * (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (/ p) = / (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (< p) = < (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (> p) = > (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (<= p) = <= (λ q → p (mustBeNumber H ∅ v q))
|
||||
runtimeBinOpWarning H v (>= p) = >= (λ q → p (mustBeNumber H ∅ v q))
|
||||
|
||||
runtimeWarningᴱ : ∀ H M → RuntimeErrorᴱ H M → Warningᴱ H (typeCheckᴱ H ∅ M)
|
||||
runtimeWarningᴮ : ∀ H B → RuntimeErrorᴮ H B → Warningᴮ H (typeCheckᴮ H ∅ B)
|
||||
|
||||
runtimeWarningᴱ H (var x) UnboundVariable = UnboundVariable refl
|
||||
runtimeWarningᴱ H (addr a) (SEGV p) = UnallocatedAddress p
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runtimeWarningᴱ H (val (addr a)) (SEGV p) = UnallocatedAddress p
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runtimeWarningᴱ H (M $ N) (FunctionMismatch v w p) with typeOf-val-not-bot w
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runtimeWarningᴱ H (M $ N) (FunctionMismatch v w p) | ok q = FunctionCallMismatch (λ r → p (mustBeFunction H ∅ v (λ r′ → q (trans r′ r))))
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runtimeWarningᴱ H (M $ N) (FunctionMismatch v w p) | warning W = app₂ W
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runtimeWarningᴱ H (M $ N) (app₁ err) = app₁ (runtimeWarningᴱ H M err)
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runtimeWarningᴱ H (M $ N) (app₂ err) = app₂ (runtimeWarningᴱ H N err)
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||||
runtimeWarningᴱ H (block var b ∈ T is B end) (block err) = block₁ (runtimeWarningᴮ H B err)
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runtimeWarningᴱ H (binexp M op N) (BinopMismatch₁ v w p) = BinopMismatch₁ (λ q → p (mustBeNumber H ∅ v (sym q)))
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runtimeWarningᴱ H (binexp M op N) (BinopMismatch₂ v w p) = BinopMismatch₂ (λ q → p (mustBeNumber H ∅ w (sym q)))
|
||||
runtimeWarningᴱ H (binexp M op N) (BinOpMismatch₁ v w p) = BinOpMismatch₁ (runtimeBinOpWarning H v p)
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runtimeWarningᴱ H (binexp M op N) (BinOpMismatch₂ v w p) = BinOpMismatch₂ (runtimeBinOpWarning H w p)
|
||||
runtimeWarningᴱ H (binexp M op N) (bin₁ err) = bin₁ (runtimeWarningᴱ H M err)
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||||
runtimeWarningᴱ H (binexp M op N) (bin₂ err) = bin₂ (runtimeWarningᴱ H N err)
|
||||
|
||||
|
|
|
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|
|
@ -8,14 +8,13 @@ open import Agda.Builtin.Equality using (_≡_; refl)
|
|||
open import Agda.Builtin.Bool using (Bool; true; false)
|
||||
open import FFI.Data.Maybe using (Maybe; just; nothing)
|
||||
open import FFI.Data.Either using (Either)
|
||||
open import Luau.TypeCheck(m) using (_⊢ᴱ_∈_; _⊢ᴮ_∈_; ⊢ᴼ_; ⊢ᴴ_; _⊢ᴴᴱ_▷_∈_; _⊢ᴴᴮ_▷_∈_; nil; var; addr; number; true; false; app; function; block; binexp; done; return; local; nothing; orBot)
|
||||
open import Luau.Syntax using (Block; Expr; yes; nil; var; addr; number; true; false; binexp; _$_; function_is_end; block_is_end; _∙_; return; done; local_←_; _⟨_⟩; _⟨_⟩∈_; var_∈_; name; fun; arg)
|
||||
open import Luau.TypeCheck(m) using (_⊢ᴱ_∈_; _⊢ᴮ_∈_; ⊢ᴼ_; ⊢ᴴ_; _⊢ᴴᴱ_▷_∈_; _⊢ᴴᴮ_▷_∈_; nil; var; addr; number; bool; app; function; block; binexp; done; return; local; nothing; orBot; tgtBinOp)
|
||||
open import Luau.Syntax using (Block; Expr; Value; BinaryOperator; yes; nil; addr; number; bool; val; var; binexp; _$_; function_is_end; block_is_end; _∙_; return; done; local_←_; _⟨_⟩; _⟨_⟩∈_; var_∈_; name; fun; arg; +; -; *; /; <; >; ==; ~=; <=; >=)
|
||||
open import Luau.Type using (Type; nil; top; bot; number; boolean; _⇒_; tgt)
|
||||
open import Luau.RuntimeType using (RuntimeType; nil; number; function; valueType)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _↦_; _⊕_↦_; _⋒_; _⊝_) renaming (_[_] to _[_]ⱽ)
|
||||
open import Luau.Addr using (Addr)
|
||||
open import Luau.Var using (Var; _≡ⱽ_)
|
||||
open import Luau.Value using (Value; nil; addr; number; bool; val)
|
||||
open import Luau.Heap using (Heap; Object; function_is_end) renaming (_[_] to _[_]ᴴ)
|
||||
open import Properties.Contradiction using (CONTRADICTION)
|
||||
open import Properties.Dec using (yes; no)
|
||||
|
|
@ -42,29 +41,18 @@ typeOfⱽ H (number n) = just number
|
|||
typeOfᴱ : Heap yes → VarCtxt → (Expr yes) → Type
|
||||
typeOfᴮ : Heap yes → VarCtxt → (Block yes) → Type
|
||||
|
||||
typeOfᴱ H Γ nil = nil
|
||||
typeOfᴱ H Γ (var x) = orBot(Γ [ x ]ⱽ)
|
||||
typeOfᴱ H Γ (addr a) = orBot(typeOfᴹᴼ (H [ a ]ᴴ))
|
||||
typeOfᴱ H Γ (number n) = number
|
||||
typeOfᴱ H Γ true = boolean
|
||||
typeOfᴱ H Γ false = boolean
|
||||
typeOfᴱ H Γ (val v) = orBot(typeOfⱽ H v)
|
||||
typeOfᴱ H Γ (M $ N) = tgt(typeOfᴱ H Γ M)
|
||||
typeOfᴱ H Γ (function f ⟨ var x ∈ S ⟩∈ T is B end) = S ⇒ T
|
||||
typeOfᴱ H Γ (block var b ∈ T is B end) = T
|
||||
typeOfᴱ H Γ (binexp M op N) = number
|
||||
typeOfᴱ H Γ (binexp M op N) = tgtBinOp op
|
||||
|
||||
typeOfᴮ H Γ (function f ⟨ var x ∈ S ⟩∈ T is C end ∙ B) = typeOfᴮ H (Γ ⊕ f ↦ (S ⇒ T)) B
|
||||
typeOfᴮ H Γ (local var x ∈ T ← M ∙ B) = typeOfᴮ H (Γ ⊕ x ↦ T) B
|
||||
typeOfᴮ H Γ (return M ∙ B) = typeOfᴱ H Γ M
|
||||
typeOfᴮ H Γ done = nil
|
||||
|
||||
typeOfᴱⱽ : ∀ {H Γ} v → (typeOfᴱ H Γ (val v) ≡ orBot(typeOfⱽ H v))
|
||||
typeOfᴱⱽ nil = refl
|
||||
typeOfᴱⱽ (bool true) = refl
|
||||
typeOfᴱⱽ (bool false) = refl
|
||||
typeOfᴱⱽ (addr a) = refl
|
||||
typeOfᴱⱽ (number n) = refl
|
||||
|
||||
mustBeFunction : ∀ H Γ v → (bot ≢ src (typeOfᴱ H Γ (val v))) → (function ≡ valueType(v))
|
||||
mustBeFunction H Γ nil p = CONTRADICTION (p refl)
|
||||
mustBeFunction H Γ (addr a) p = refl
|
||||
|
|
@ -72,12 +60,12 @@ mustBeFunction H Γ (number n) p = CONTRADICTION (p refl)
|
|||
mustBeFunction H Γ (bool true) p = CONTRADICTION (p refl)
|
||||
mustBeFunction H Γ (bool false) p = CONTRADICTION (p refl)
|
||||
|
||||
mustBeNumber : ∀ H Γ v → (number ≡ typeOfᴱ H Γ (val v)) → (number ≡ valueType(v))
|
||||
mustBeNumber : ∀ H Γ v → (typeOfᴱ H Γ (val v) ≡ number) → (valueType(v) ≡ number)
|
||||
mustBeNumber H Γ nil ()
|
||||
mustBeNumber H Γ (addr a) p with remember (H [ a ]ᴴ)
|
||||
mustBeNumber H Γ (addr a) p | (just O , q) with trans p (cong orBot (cong typeOfᴹᴼ q))
|
||||
mustBeNumber H Γ (addr a) p | (just O , q) with trans (cong orBot (cong typeOfᴹᴼ (sym q))) p
|
||||
mustBeNumber H Γ (addr a) p | (just function f ⟨ var x ∈ T ⟩∈ U is B end , q) | ()
|
||||
mustBeNumber H Γ (addr a) p | (nothing , q) with trans p (cong orBot (cong typeOfᴹᴼ q))
|
||||
mustBeNumber H Γ (addr a) p | (nothing , q) with trans (cong orBot (cong typeOfᴹᴼ (sym q))) p
|
||||
mustBeNumber H Γ (addr a) p | nothing , q | ()
|
||||
mustBeNumber H Γ (number n) p = refl
|
||||
mustBeNumber H Γ (bool true) ()
|
||||
|
|
@ -86,12 +74,11 @@ mustBeNumber H Γ (bool false) ()
|
|||
typeCheckᴱ : ∀ H Γ M → (Γ ⊢ᴱ M ∈ (typeOfᴱ H Γ M))
|
||||
typeCheckᴮ : ∀ H Γ B → (Γ ⊢ᴮ B ∈ (typeOfᴮ H Γ B))
|
||||
|
||||
typeCheckᴱ H Γ nil = nil
|
||||
typeCheckᴱ H Γ (var x) = var refl
|
||||
typeCheckᴱ H Γ (addr a) = addr (orBot (typeOfᴹᴼ (H [ a ]ᴴ)))
|
||||
typeCheckᴱ H Γ (number n) = number
|
||||
typeCheckᴱ H Γ true = true
|
||||
typeCheckᴱ H Γ false = false
|
||||
typeCheckᴱ H Γ (val nil) = nil
|
||||
typeCheckᴱ H Γ (val (addr a)) = addr (orBot (typeOfᴹᴼ (H [ a ]ᴴ)))
|
||||
typeCheckᴱ H Γ (val (number n)) = number
|
||||
typeCheckᴱ H Γ (val (bool b)) = bool
|
||||
typeCheckᴱ H Γ (M $ N) = app (typeCheckᴱ H Γ M) (typeCheckᴱ H Γ N)
|
||||
typeCheckᴱ H Γ (function f ⟨ var x ∈ T ⟩∈ U is B end) = function (typeCheckᴮ H (Γ ⊕ x ↦ T) B)
|
||||
typeCheckᴱ H Γ (block var b ∈ T is B end) = block (typeCheckᴮ H Γ B)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue