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https://github.com/luau-lang/luau.git
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WIP
This commit is contained in:
ajeffrey@roblox.com
parent
1f4d77bac9
commit
8e52542526
12 changed files with 374 additions and 192 deletions
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@ -1,6 +1,9 @@
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{-# OPTIONS --rewriting #-}
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module FFI.Data.Aeson where
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open import Agda.Builtin.Equality using (_≡_)
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open import Agda.Builtin.Equality.Rewrite using ()
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open import Agda.Builtin.Bool using (Bool)
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open import Agda.Builtin.String using (String)
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@ -42,6 +45,8 @@ postulate lookup-insert : ∀ {A} k v (m : KeyMap A) → (lookup k (insert k v m
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postulate lookup-empty : ∀ {A} k → (lookup {A} k empty ≡ nothing)
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postulate singleton-insert-empty : ∀ {A} k (v : A) → (singleton k v ≡ insert k v empty)
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{-# REWRITE lookup-insert lookup-empty singleton-insert-empty #-}
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data Value : Set where
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object : KeyMap Value → Value
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array : Vector Value → Value
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@ -1,6 +1,9 @@
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{-# OPTIONS --rewriting #-}
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module FFI.Data.Vector where
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open import Agda.Builtin.Equality using (_≡_)
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open import Agda.Builtin.Equality.Rewrite using ()
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open import Agda.Builtin.Int using (Int; pos; negsuc)
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open import Agda.Builtin.Nat using (Nat)
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open import FFI.Data.Bool using (Bool; false; true)
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@ -33,6 +36,8 @@ postulate length-empty : ∀ {A} → (length (empty {A}) ≡ 0)
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postulate lookup-snoc : ∀ {A} (x : A) (v : Vector A) → (lookup (snoc v x) (length v) ≡ just x)
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postulate lookup-snoc-empty : ∀ {A} (x : A) → (lookup (snoc empty x) 0 ≡ just x)
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{-# REWRITE length-empty lookup-snoc lookup-snoc-empty #-}
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head : ∀ {A} → (Vector A) → (Maybe A)
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head vec with null vec
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head vec | false = just (unsafeHead vec)
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@ -1,3 +1,5 @@
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{-# OPTIONS --rewriting #-}
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module Luau.AddrCtxt where
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open import Luau.Type using (Type)
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@ -1,3 +1,5 @@
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{-# OPTIONS --rewriting #-}
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module Luau.Heap where
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open import Agda.Builtin.Equality using (_≡_)
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@ -37,13 +39,3 @@ next = length
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allocated : ∀ {a} → Heap a → HeapValue a → Heap a
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allocated = snoc
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-- next-emp : (length empty ≡ 0)
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next-emp = FFI.Data.Vector.length-empty
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-- lookup-next : ∀ V H → (lookup (allocated H V) (next H) ≡ just V)
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lookup-next = FFI.Data.Vector.lookup-snoc
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-- lookup-next-emp : ∀ V → (lookup (allocated emp V) 0 ≡ just V)
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lookup-next-emp = FFI.Data.Vector.lookup-snoc-empty
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@ -1,3 +1,5 @@
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{-# OPTIONS --rewriting #-}
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module Luau.OpSem where
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open import Agda.Builtin.Equality using (_≡_)
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@ -1,3 +1,5 @@
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{-# OPTIONS --rewriting #-}
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module Luau.RuntimeError where
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open import Agda.Builtin.Equality using (_≡_)
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@ -1,81 +1,108 @@
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{-# OPTIONS --rewriting #-}
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module Luau.StrictMode where
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open import Agda.Builtin.Equality using (_≡_)
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open import FFI.Data.Maybe using (just; nothing)
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open import Luau.Syntax using (Expr; Stat; Block; yes; nil; addr; var; var_∈_; _⟨_⟩∈_; function_is_end; _$_; block_is_end; local_←_; _∙_; done; return; name)
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open import Luau.Type using (Type; strict; bot; top; nil; _⇒_; tgt)
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open import Luau.Heap using (Heap) renaming (_[_] to _[_]ᴴ)
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open import Luau.Heap using (Heap; function_is_end) renaming (_[_] to _[_]ᴴ)
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open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
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open import Luau.TypeCheck(strict) using (_⊢ᴮ_∋_∈_⊣_; _⊢ᴱ_∋_∈_⊣_; var; addr; app; block; return; local; function)
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open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; var; addr; app; block; return; local; function)
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open import Properties.Equality using (_≢_)
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open import Properties.TypeCheck(strict) using (typeOfᴴ)
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open import Properties.TypeCheck(strict) using (typeOfᴴ; typeCheckᴮ)
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src : Type → Type
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src = Luau.Type.src strict
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data Warningᴱ (H : Heap yes) {Γ S} : ∀ {M T Δ} → (Γ ⊢ᴱ S ∋ M ∈ T ⊣ Δ) → Set
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data Warningᴮ (H : Heap yes) {Γ S} : ∀ {B T Δ} → (Γ ⊢ᴮ S ∋ B ∈ T ⊣ Δ) → Set
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data Warningᴱ (H : Heap yes) {Γ} : ∀ {M T} → (Γ ⊢ᴱ M ∈ T) → Set
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data Warningᴮ (H : Heap yes) {Γ} : ∀ {B T} → (Γ ⊢ᴮ B ∈ T) → Set
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data Warningᴱ H {Γ S} where
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data Warningᴱ H {Γ} where
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bot : ∀ {M T Δ} {D : Γ ⊢ᴱ S ∋ M ∈ T ⊣ Δ} →
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BadlyTypedFunctionAddress : ∀ a f {x S T U B} →
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(T ≡ bot) →
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------------
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Warningᴱ H D
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(H [ a ]ᴴ ≡ just (function f ⟨ var x ∈ T ⟩∈ U is B end)) →
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Warningᴮ H (typeCheckᴮ H (x ↦ T) B) →
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--------------------------------------------------------
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Warningᴱ H (addr a S)
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addr : ∀ a T →
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UnallocatedAddress : ∀ a {T} →
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(T ≢ typeOfᴴ(H [ a ]ᴴ)) →
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-------------------------
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(H [ a ]ᴴ ≡ nothing) →
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--------------------------------------------------------
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Warningᴱ H (addr a T)
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app₁ : ∀ {M N T U Δ₁ Δ₂} {D₁ : Γ ⊢ᴱ (U ⇒ S) ∋ M ∈ T ⊣ Δ₁} {D₂ : Γ ⊢ᴱ (src T) ∋ N ∈ U ⊣ Δ₂} →
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app₀ : ∀ {M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
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(src T ≢ U) →
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-----------------
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Warningᴱ H (app D₁ D₂)
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app₁ : ∀ {M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
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Warningᴱ H D₁ →
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-----------------
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Warningᴱ H (app D₁ D₂)
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app₂ : ∀ {M N T U Δ₁ Δ₂} {D₁ : Γ ⊢ᴱ (U ⇒ S) ∋ M ∈ T ⊣ Δ₁} {D₂ : Γ ⊢ᴱ (src T) ∋ N ∈ U ⊣ Δ₂} →
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app₂ : ∀ {M N T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴱ N ∈ U} →
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Warningᴱ H D₂ →
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-----------------
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Warningᴱ H(app D₁ D₂)
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Warningᴱ H (app D₁ D₂)
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block : ∀ b {B T Δ} {D : Γ ⊢ᴮ S ∋ B ∈ T ⊣ Δ} →
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function₀ : ∀ f {x B T U V} {D : (Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V} →
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(U ≢ V) →
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-------------------------
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Warningᴱ H (function f {U = U} D)
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function₁ : ∀ f {x B T U V} {D : (Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V} →
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Warningᴮ H D →
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-------------------------
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Warningᴱ H (function f {U = U} D)
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block : ∀ b {B T} {D : Γ ⊢ᴮ B ∈ T} →
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Warningᴮ H D →
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-----------------
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Warningᴱ H(block b D)
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Warningᴱ H (block b D)
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data Warningᴮ H {Γ S} where
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data Warningᴮ H {Γ} where
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disagree : ∀ {B T Δ} {D : Γ ⊢ᴮ S ∋ B ∈ T ⊣ Δ} →
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(S ≢ T) →
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-----------
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Warningᴮ H D
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return : ∀ {M B T U Δ₁ Δ₂} {D₁ : Γ ⊢ᴱ S ∋ M ∈ T ⊣ Δ₁} {D₂ : Γ ⊢ᴮ nil ∋ B ∈ U ⊣ Δ₂} →
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return : ∀ {M B T U} {D₁ : Γ ⊢ᴱ M ∈ T} {D₂ : Γ ⊢ᴮ B ∈ U} →
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Warningᴱ H D₁ →
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------------------
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Warningᴮ H (return D₁ D₂)
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local₁ : ∀ {x M B T U V Δ₁ Δ₂} {D₁ : Γ ⊢ᴱ T ∋ M ∈ U ⊣ Δ₁} {D₂ : (Γ ⊕ x ↦ T) ⊢ᴮ S ∋ B ∈ V ⊣ Δ₂} →
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local₀ : ∀ {x M B T U V} {D₁ : Γ ⊢ᴱ M ∈ U} {D₂ : (Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V} →
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(T ≢ U) →
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--------------------
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Warningᴮ H (local D₁ D₂)
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local₁ : ∀ {x M B T U V} {D₁ : Γ ⊢ᴱ M ∈ U} {D₂ : (Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V} →
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Warningᴱ H D₁ →
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--------------------
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Warningᴮ H (local D₁ D₂)
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-- data Warningᴴ {H} : ∀ {V T} → (H ▷ V ∈ T) → Set where
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local₂ : ∀ {x M B T U V} {D₁ : Γ ⊢ᴱ M ∈ U} {D₂ : (Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V} →
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-- nothing :
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Warningᴮ H D₂ →
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--------------------
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Warningᴮ H (local D₁ D₂)
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-- -----------------
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-- Warningᴴ(nothing)
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function₁ : ∀ f {x B C T U V W} {D₁ : (Γ ⊕ x ↦ T) ⊢ᴮ C ∈ V} {D₂ : (Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ B ∈ W} →
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-- function : ∀ f {x B T U V W} {D : (x ↦ T) ⊢ᴮ U ∋ B ∈ V ⊣ (x ↦ W)} →
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Warningᴮ H D₁ →
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--------------------
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Warningᴮ H (function f D₁ D₂)
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-- Warningᴮ(D) →
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-- --------------------
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-- Warningᴴ(function f D)
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function₂ : ∀ f {x B C T U V W} {D₁ : (Γ ⊕ x ↦ T) ⊢ᴮ C ∈ V} {D₂ : (Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ B ∈ W} →
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Warningᴮ H D₂ →
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--------------------
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Warningᴮ H (function f D₁ D₂)
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@ -1,3 +1,5 @@
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{-# OPTIONS --rewriting #-}
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open import Luau.Type using (Mode)
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module Luau.TypeCheck (m : Mode) where
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@ -17,70 +19,138 @@ open import FFI.Data.Maybe using (Maybe; just; nothing)
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src : Type → Type
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src = Luau.Type.src m
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data _⊢ᴮ_∋_∈_⊣_ : VarCtxt → Type → Block yes → Type → VarCtxt → Set
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data _⊢ᴱ_∋_∈_⊣_ : VarCtxt → Type → Expr yes → Type → VarCtxt → Set
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data _⊢ᴮ_∈_ : VarCtxt → Block yes → Type → Set
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data _⊢ᴱ_∈_ : VarCtxt → Expr yes → Type → Set
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data _⊢ᴮ_∋_∈_⊣_ where
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data _⊢ᴮ_∈_ where
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done : ∀ {S Γ} →
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done : ∀ {Γ} →
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----------------------
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Γ ⊢ᴮ S ∋ done ∈ nil ⊣ ∅
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---------------
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Γ ⊢ᴮ done ∈ nil
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return : ∀ {M B S T U Γ Δ₁ Δ₂} →
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return : ∀ {M B T U Γ} →
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Γ ⊢ᴱ S ∋ M ∈ T ⊣ Δ₁ →
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Γ ⊢ᴮ nil ∋ B ∈ U ⊣ Δ₂ →
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---------------------------------
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Γ ⊢ᴮ S ∋ return M ∙ B ∈ T ⊣ Δ₁
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Γ ⊢ᴱ M ∈ T →
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Γ ⊢ᴮ B ∈ U →
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---------------------
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Γ ⊢ᴮ return M ∙ B ∈ T
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local : ∀ {x M B S T U V Γ Δ₁ Δ₂} →
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local : ∀ {x M B T U V Γ} →
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Γ ⊢ᴱ T ∋ M ∈ U ⊣ Δ₁ →
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(Γ ⊕ x ↦ T) ⊢ᴮ S ∋ B ∈ V ⊣ Δ₂ →
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----------------------------------------------------------
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Γ ⊢ᴮ S ∋ local var x ∈ T ← M ∙ B ∈ V ⊣ (Δ₁ ⋒ (Δ₂ ⊝ x))
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Γ ⊢ᴱ M ∈ U →
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(Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V →
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--------------------------------
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Γ ⊢ᴮ local var x ∈ T ← M ∙ B ∈ V
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function : ∀ {f x B C S T U V W Γ Δ₁ Δ₂} →
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function : ∀ f {x B C T U V W Γ} →
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(Γ ⊕ x ↦ T) ⊢ᴮ U ∋ C ∈ V ⊣ Δ₁ →
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(Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ S ∋ B ∈ W ⊣ Δ₂ →
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---------------------------------------------------------------------------------
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Γ ⊢ᴮ S ∋ function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B ∈ W ⊣ ((Δ₁ ⊝ x) ⋒ (Δ₂ ⊝ f))
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(Γ ⊕ x ↦ T) ⊢ᴮ C ∈ V →
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(Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ B ∈ W →
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-------------------------------------------------
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Γ ⊢ᴮ function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B ∈ W
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data _⊢ᴱ_∋_∈_⊣_ where
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data _⊢ᴱ_∈_ where
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nil : ∀ {S Γ} →
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nil : ∀ {Γ} →
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----------------------
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Γ ⊢ᴱ S ∋ nil ∈ nil ⊣ ∅
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--------------
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Γ ⊢ᴱ nil ∈ nil
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var : ∀ x {S T Γ} →
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var : ∀ x {T Γ} →
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T ≡ Γ [ x ]ⱽ →
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----------------------------
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Γ ⊢ᴱ S ∋ var x ∈ T ⊣ (x ↦ S)
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--------------
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Γ ⊢ᴱ var x ∈ T
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addr : ∀ a T {S Γ} →
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addr : ∀ a T {Γ} →
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-------------------------
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Γ ⊢ᴱ S ∋ (addr a) ∈ T ⊣ ∅
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-----------------
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Γ ⊢ᴱ (addr a) ∈ T
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app : ∀ {M N S T U Γ Δ₁ Δ₂} →
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app : ∀ {M N T U Γ} →
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Γ ⊢ᴱ (U ⇒ S) ∋ M ∈ T ⊣ Δ₁ →
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Γ ⊢ᴱ (src T) ∋ N ∈ U ⊣ Δ₂ →
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--------------------------------------
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Γ ⊢ᴱ S ∋ (M $ N) ∈ (tgt T) ⊣ (Δ₁ ⋒ Δ₂)
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Γ ⊢ᴱ M ∈ T →
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Γ ⊢ᴱ N ∈ U →
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----------------------
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Γ ⊢ᴱ (M $ N) ∈ (tgt T)
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function : ∀ {f x B S T U V Γ Δ} →
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function : ∀ f {x B T U V Γ} →
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(Γ ⊕ x ↦ T) ⊢ᴮ U ∋ B ∈ V ⊣ Δ →
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-----------------------------------------------------------------------
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Γ ⊢ᴱ S ∋ (function f ⟨ var x ∈ T ⟩∈ U is B end) ∈ (T ⇒ U) ⊣ (Δ ⊝ x)
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(Γ ⊕ x ↦ T) ⊢ᴮ B ∈ V →
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-----------------------------------------------------
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Γ ⊢ᴱ (function f ⟨ var x ∈ T ⟩∈ U is B end) ∈ (T ⇒ U)
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block : ∀ b {B S T Γ Δ} →
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block : ∀ b {B T Γ} →
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Γ ⊢ᴮ S ∋ B ∈ T ⊣ Δ →
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----------------------------------------------------
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Γ ⊢ᴱ S ∋ (block b is B end) ∈ T ⊣ Δ
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Γ ⊢ᴮ B ∈ T →
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---------------------------
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Γ ⊢ᴱ (block b is B end) ∈ T
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-- data _⊢ᴮ_∋_∈_⊣_ : VarCtxt → Type → Block yes → Type → VarCtxt → Set
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-- data _⊢ᴱ_∋_∈_⊣_ : VarCtxt → Type → Expr yes → Type → VarCtxt → Set
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-- data _⊢ᴮ_∋_∈_⊣_ where
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-- done : ∀ {S Γ} →
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-- ----------------------
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-- Γ ⊢ᴮ S ∋ done ∈ nil ⊣ ∅
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-- return : ∀ {M B S T U Γ Δ₁ Δ₂} →
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-- Γ ⊢ᴱ S ∋ M ∈ T ⊣ Δ₁ →
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-- Γ ⊢ᴮ nil ∋ B ∈ U ⊣ Δ₂ →
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-- ---------------------------------
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-- Γ ⊢ᴮ S ∋ return M ∙ B ∈ T ⊣ Δ₁
|
||||
|
||||
-- local : ∀ {x M B S T U V Γ Δ₁ Δ₂} →
|
||||
|
||||
-- Γ ⊢ᴱ T ∋ M ∈ U ⊣ Δ₁ →
|
||||
-- (Γ ⊕ x ↦ T) ⊢ᴮ S ∋ B ∈ V ⊣ Δ₂ →
|
||||
-- ----------------------------------------------------------
|
||||
-- Γ ⊢ᴮ S ∋ local var x ∈ T ← M ∙ B ∈ V ⊣ (Δ₁ ⋒ (Δ₂ ⊝ x))
|
||||
|
||||
-- function : ∀ {f x B C S T U V W Γ Δ₁ Δ₂} →
|
||||
|
||||
-- (Γ ⊕ x ↦ T) ⊢ᴮ U ∋ C ∈ V ⊣ Δ₁ →
|
||||
-- (Γ ⊕ f ↦ (T ⇒ U)) ⊢ᴮ S ∋ B ∈ W ⊣ Δ₂ →
|
||||
-- ---------------------------------------------------------------------------------
|
||||
-- Γ ⊢ᴮ S ∋ function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B ∈ W ⊣ ((Δ₁ ⊝ x) ⋒ (Δ₂ ⊝ f))
|
||||
|
||||
-- data _⊢ᴱ_∋_∈_⊣_ where
|
||||
|
||||
-- nil : ∀ {S Γ} →
|
||||
|
||||
-- ----------------------
|
||||
-- Γ ⊢ᴱ S ∋ nil ∈ nil ⊣ ∅
|
||||
|
||||
-- var : ∀ x {S T Γ} →
|
||||
|
||||
-- T ≡ Γ [ x ]ⱽ →
|
||||
-- ----------------------------
|
||||
-- Γ ⊢ᴱ S ∋ var x ∈ T ⊣ (x ↦ S)
|
||||
|
||||
-- addr : ∀ a T {S Γ} →
|
||||
|
||||
-- -------------------------
|
||||
-- Γ ⊢ᴱ S ∋ (addr a) ∈ T ⊣ ∅
|
||||
|
||||
-- app : ∀ {M N S T U Γ Δ₁ Δ₂} →
|
||||
|
||||
-- Γ ⊢ᴱ (U ⇒ S) ∋ M ∈ T ⊣ Δ₁ →
|
||||
-- Γ ⊢ᴱ (src T) ∋ N ∈ U ⊣ Δ₂ →
|
||||
-- --------------------------------------
|
||||
-- Γ ⊢ᴱ S ∋ (M $ N) ∈ (tgt T) ⊣ (Δ₁ ⋒ Δ₂)
|
||||
|
||||
-- function : ∀ {f x B S T U V Γ Δ} →
|
||||
|
||||
-- (Γ ⊕ x ↦ T) ⊢ᴮ U ∋ B ∈ V ⊣ Δ →
|
||||
-- -----------------------------------------------------------------------
|
||||
-- Γ ⊢ᴱ S ∋ (function f ⟨ var x ∈ T ⟩∈ U is B end) ∈ (T ⇒ U) ⊣ (Δ ⊝ x)
|
||||
|
||||
-- block : ∀ b {B S T Γ Δ} →
|
||||
|
||||
-- Γ ⊢ᴮ S ∋ B ∈ T ⊣ Δ →
|
||||
-- ----------------------------------------------------
|
||||
-- Γ ⊢ᴱ S ∋ (block b is B end) ∈ T ⊣ Δ
|
||||
|
|
|
|||
|
|
@ -1,3 +1,5 @@
|
|||
{-# OPTIONS --rewriting #-}
|
||||
|
||||
module Luau.VarCtxt where
|
||||
|
||||
open import Agda.Builtin.Equality using (_≡_)
|
||||
|
|
@ -34,10 +36,3 @@ x ↦ T = singleton (fromString x) T
|
|||
|
||||
_⊕_↦_ : VarCtxt → Var → Type → VarCtxt
|
||||
Γ ⊕ x ↦ T = insert (fromString x) T Γ
|
||||
|
||||
-- ⊕-[] : ∀ (Γ : VarCtxt) x T → (((Γ ⊕ x ↦ T) [ x ]) ≡ T)
|
||||
⊕-[] = λ (Γ : VarCtxt) x T → cong orBot (lookup-insert (fromString x) T Γ)
|
||||
|
||||
-- ∅-[] : ∀ x → ∅ [ x ] ≡ bot
|
||||
∅-[] = λ (x : Var) → cong orBot (lookup-empty (fromString x))
|
||||
|
||||
|
|
|
|||
|
|
@ -1,3 +1,5 @@
|
|||
{-# OPTIONS --rewriting #-}
|
||||
|
||||
module Properties.Step where
|
||||
|
||||
open import Agda.Builtin.Equality using (_≡_; refl)
|
||||
|
|
|
|||
|
|
@ -5,102 +5,188 @@ module Properties.StrictMode where
|
|||
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; HeapValue; function_is_end; defn; alloc; ok; next; lookup-next) renaming (_≡_⊕_↦_ to _≡ᴴ_⊕_↦_; _[_] to _[_]ᴴ)
|
||||
open import Luau.StrictMode using (Warningᴱ; Warningᴮ; bot; disagree; addr; app₁; app₂; block; return; local₁)
|
||||
open import Luau.Substitution using (_[_/_]ᴮ; _[_/_]ᴱ)
|
||||
open import Luau.Syntax using (Expr; yes; var_∈_; _⟨_⟩∈_; _$_; addr; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg)
|
||||
open import Luau.Heap using (Heap; HeapValue; function_is_end; defn; alloc; ok; next) renaming (_≡_⊕_↦_ to _≡ᴴ_⊕_↦_; _[_] to _[_]ᴴ)
|
||||
open import Luau.StrictMode using (Warningᴱ; Warningᴮ; BadlyTypedFunctionAddress; UnallocatedAddress; app₀; app₁; app₂; block; return; local₀; local₁; local₂; function₀; function₁; function₂)
|
||||
open import Luau.Substitution using (_[_/_]ᴮ; _[_/_]ᴱ; _[_/_]ᴮunless_; var_[_/_]ᴱwhenever_)
|
||||
open import Luau.Syntax using (Expr; yes; var; var_∈_; _⟨_⟩∈_; _$_; addr; nil; function_is_end; block_is_end; done; return; local_←_; _∙_; fun; arg)
|
||||
open import Luau.Type using (Type; strict; nil; _⇒_; bot; tgt)
|
||||
open import Luau.TypeCheck(strict) using (_⊢ᴮ_∋_∈_⊣_; _⊢ᴱ_∋_∈_⊣_; nil; var; addr; app; function; block; done; return; local)
|
||||
open import Luau.TypeCheck(strict) using (_⊢ᴮ_∈_; _⊢ᴱ_∈_; nil; var; addr; app; function; block; done; return; local)
|
||||
open import Luau.Value using (val; nil; addr)
|
||||
open import Luau.Var using (_≡ⱽ_)
|
||||
open import Luau.Addr using (_≡ᴬ_)
|
||||
open import Luau.AddrCtxt using (AddrCtxt)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_; ∅-[]) renaming (_[_] to _[_]ⱽ)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _⋒_; _↦_; _⊕_↦_; _⊝_) renaming (_[_] to _[_]ⱽ)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅)
|
||||
open import Properties.Remember using (remember; _,_)
|
||||
open import Properties.Equality using (sym; cong; trans; subst₁)
|
||||
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 (typeOfᴴ; typeOfᴱ; typeOfᴮ; typeCheckᴱ; typeCheckᴮ)
|
||||
open import Properties.TypeCheck(strict) using (declaredTypeᴴ; typeOfⱽ; typeOfᴴ; typeOfᴱ; typeOfᴮ; typeOfᴱⱽ; typeCheckᴱ; typeCheckᴮ)
|
||||
open import Luau.OpSem using (_⊢_⟶ᴮ_⊣_; _⊢_⟶ᴱ_⊣_; app; function; beta; return; block; done; local; subst)
|
||||
|
||||
{-# REWRITE lookup-next #-}
|
||||
|
||||
src = Luau.Type.src strict
|
||||
|
||||
_≡ᵀ_ : ∀ (T U : Type) → Dec(T ≡ U)
|
||||
_≡ᵀ_ = {!!}
|
||||
|
||||
data _⊑_ (H : Heap yes) : Heap yes → Set where
|
||||
refl : (H ⊑ H)
|
||||
snoc : ∀ {H′ H″ a V} → (H ⊑ H′) → (H″ ≡ᴴ H′ ⊕ a ↦ V) → (H ⊑ H″)
|
||||
|
||||
warning-⊑ : ∀ {H H′ Γ Δ S T M} {D : Γ ⊢ᴱ S ∋ M ∈ T ⊣ Δ} → (H ⊑ H′) → (Warningᴱ H′ D) → Warningᴱ H D
|
||||
warning-⊑ : ∀ {H H′ Γ T M} {D : Γ ⊢ᴱ M ∈ T} → (H ⊑ H′) → (Warningᴱ H′ D) → Warningᴱ H D
|
||||
warning-⊑ = {!!}
|
||||
|
||||
data TypeOfᴱ-⊑-Result H H′ Γ M : Set where
|
||||
ok : (typeOfᴱ H Γ M ≡ typeOfᴱ H′ Γ M) → TypeOfᴱ-⊑-Result H H′ Γ M
|
||||
warning : (∀ {S} → Warningᴱ H (typeCheckᴱ H Γ S M)) → TypeOfᴱ-⊑-Result H H′ Γ M
|
||||
data LookupResult (H : Heap yes) a V : Set where
|
||||
just : (H [ a ]ᴴ ≡ just V) → LookupResult H a V
|
||||
nothing : (H [ a ]ᴴ ≡ nothing) → LookupResult H a V
|
||||
|
||||
data TypeOfᴮ-⊑-Result H H′ Γ B : Set where
|
||||
ok : (typeOfᴮ H Γ B ≡ typeOfᴮ H′ Γ B) → TypeOfᴮ-⊑-Result H H′ Γ B
|
||||
warning : (∀ {S} → Warningᴮ H (typeCheckᴮ H Γ S B)) → TypeOfᴮ-⊑-Result H H′ Γ B
|
||||
lookup-⊑-just : ∀ {H H′ V} a → (H ⊑ H′) → (H′ [ a ]ᴴ ≡ just V) → LookupResult H a V
|
||||
lookup-⊑-just = {!!}
|
||||
|
||||
typeOfᴱ-⊑ : ∀ {H H′ Γ M} → (H ⊑ H′) → (TypeOfᴱ-⊑-Result H H′ Γ M)
|
||||
typeOfᴱ-⊑ = {!!}
|
||||
lookup-⊑-nothing : ∀ {H H′} a → (H ⊑ H′) → (H′ [ a ]ᴴ ≡ nothing) → (H [ a ]ᴴ ≡ nothing)
|
||||
lookup-⊑-nothing = {!!}
|
||||
|
||||
typeOfᴮ-⊑ : ∀ {H H′ Γ B} → (H ⊑ H′) → (TypeOfᴮ-⊑-Result H H′ Γ B)
|
||||
typeOfᴮ-⊑ = {!!}
|
||||
data OrWarningᴱ {Γ M T} (H : Heap yes) (D : Γ ⊢ᴱ M ∈ T) A : Set where
|
||||
ok : A → OrWarningᴱ H D A
|
||||
warning : Warningᴱ H D → OrWarningᴱ H D A
|
||||
|
||||
blah : ∀ {H H′ Γ S S′ M} → (H ⊑ H′) → (S ≡ S′) → (Warningᴱ H′ (typeCheckᴱ H′ Γ S′ M)) → (Warningᴱ H (typeCheckᴱ H Γ S M))
|
||||
blah = {!!}
|
||||
|
||||
bloz : ∀ {H Γ S S′ M} → (S ≡ S′) → (Warningᴱ H (typeCheckᴱ H Γ S′ M)) → (Warningᴱ H (typeCheckᴱ H Γ S M))
|
||||
bloz = {!!}
|
||||
data OrWarningᴮ {Γ B T} (H : Heap yes) (D : Γ ⊢ᴮ B ∈ T) A : Set where
|
||||
ok : A → OrWarningᴮ H D A
|
||||
warning : Warningᴮ H D → OrWarningᴮ H D A
|
||||
|
||||
redn-⊑ : ∀ {H H′ M M′} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → (H ⊑ H′)
|
||||
redn-⊑ = {!!}
|
||||
|
||||
⊕-overwrite : ∀ {Γ x y T U} → (x ≡ y) → ((Γ ⊕ x ↦ T) ⊕ y ↦ U) ≡ (Γ ⊕ y ↦ U)
|
||||
⊕-overwrite = {!!}
|
||||
|
||||
⊕-swap : ∀ {Γ x y T U} → (x ≢ y) → ((Γ ⊕ x ↦ T) ⊕ y ↦ U) ≡ ((Γ ⊕ y ↦ U) ⊕ x ↦ T)
|
||||
⊕-swap = {!!}
|
||||
|
||||
substitutivityᴱ : ∀ {Γ T H M v x} → (T ≡ typeOfᴱ H Γ (val v)) → (typeOfᴱ H (Γ ⊕ x ↦ T) M ≡ typeOfᴱ H Γ (M [ v / x ]ᴱ))
|
||||
substitutivityᴮ : ∀ {Γ T H B v x} → (T ≡ typeOfᴱ H Γ (val v)) → (typeOfᴮ H (Γ ⊕ x ↦ T) B ≡ typeOfᴮ H Γ (B [ v / x ]ᴮ))
|
||||
|
||||
substitutivityᴱ = {!!}
|
||||
substitutivityᴮ = {!!}
|
||||
|
||||
preservationᴱ : ∀ {H H′ M M′ Γ} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → (typeOfᴱ H Γ M ≡ typeOfᴱ H′ Γ M′)
|
||||
preservationᴮ : ∀ {H H′ B B′ Γ} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → (typeOfᴮ H Γ B ≡ typeOfᴮ H′ Γ B′)
|
||||
heap-weakeningᴱ : ∀ {H H′ M Γ} → (H ⊑ H′) → OrWarningᴱ H (typeCheckᴱ H Γ M) (typeOfᴱ H Γ M ≡ typeOfᴱ H′ Γ M)
|
||||
heap-weakeningᴮ : ∀ {H H′ B Γ} → (H ⊑ H′) → OrWarningᴮ H (typeCheckᴮ H Γ B) (typeOfᴮ H Γ B ≡ typeOfᴮ H′ Γ B)
|
||||
|
||||
preservationᴱ (function {F = f ⟨ var x ∈ S ⟩∈ T} defn) = refl
|
||||
preservationᴱ (app s) = cong tgt (preservationᴱ s)
|
||||
preservationᴱ (beta {F = f ⟨ var x ∈ S ⟩∈ T} p) = trans (cong tgt (cong typeOfᴴ p)) {!!}
|
||||
preservationᴱ (block s) = preservationᴮ s
|
||||
preservationᴱ (return p) = refl
|
||||
preservationᴱ done = refl
|
||||
heap-weakeningᴱ = {!!}
|
||||
heap-weakeningᴮ = {!!}
|
||||
|
||||
preservationᴮ (local {x = var x ∈ T} {B = B} s) with typeOfᴮ-⊑ {B = B} (redn-⊑ s)
|
||||
preservationᴮ (local {x = var x ∈ T} s) | ok p = p
|
||||
preservationᴮ (local {x = var x ∈ T} s) | warning W = {!!}
|
||||
preservationᴮ (subst {x = var x ∈ T} {B = B}) = substitutivityᴮ {B = B} {!!}
|
||||
preservationᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} {B = B} defn) with typeOfᴮ-⊑ {B = B} (snoc refl defn)
|
||||
preservationᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} {B = B} defn) | ok r = trans r (substitutivityᴮ {T = S ⇒ T} {B = B} refl)
|
||||
preservationᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} {B = B} defn) | warning W = {!!}
|
||||
preservationᴮ (return s) = preservationᴱ s
|
||||
preservationᴱ : ∀ {H H′ M M′ Γ} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → OrWarningᴱ H (typeCheckᴱ H Γ M) (typeOfᴱ H Γ M ≡ typeOfᴱ H′ Γ M′)
|
||||
preservationᴮ : ∀ {H H′ B B′ Γ} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → OrWarningᴮ H (typeCheckᴮ H Γ B) (typeOfᴮ H Γ B ≡ typeOfᴮ H′ Γ B′)
|
||||
|
||||
reflectᴱ : ∀ {H H′ M M′ S} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → Warningᴱ H′ (typeCheckᴱ H′ ∅ S M′) → Warningᴱ H (typeCheckᴱ H ∅ S M)
|
||||
reflectᴮ : ∀ {H H′ B B′ S} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → Warningᴮ H′ (typeCheckᴮ H′ ∅ S B′) → Warningᴮ H (typeCheckᴮ H ∅ S B)
|
||||
preservationᴱ (function {F = f ⟨ var x ∈ S ⟩∈ T} defn) = ok refl
|
||||
preservationᴱ (app s) with preservationᴱ s
|
||||
preservationᴱ (app s) | ok p = ok (cong tgt p)
|
||||
preservationᴱ (app s) | warning W = warning (app₁ W)
|
||||
preservationᴱ (beta {F = f ⟨ var x ∈ S ⟩∈ T} p) = {!!} -- ok (trans (cong tgt (cong typeOfᴴ p)) {!!})
|
||||
preservationᴱ (block s) with preservationᴮ s
|
||||
preservationᴱ (block s) | ok p = ok p
|
||||
preservationᴱ (block {b = b} s) | warning W = warning (block b W)
|
||||
preservationᴱ (return p) = ok refl
|
||||
preservationᴱ done = ok refl
|
||||
|
||||
reflectᴱ s W with redn-⊑ s
|
||||
reflectᴱ (function {F = f ⟨ var x ∈ S ⟩∈ T} defn) (addr a _ r) | p = CONTRADICTION (r refl)
|
||||
reflectᴱ (app s) (bot x) | p = {!x!}
|
||||
reflectᴱ (app s) (app₁ W) | p with typeOfᴱ-⊑ p
|
||||
reflectᴱ (app s) (app₁ W) | p | ok q = app₁ (bloz (cong (λ ∙ → ∙ ⇒ _) q) (reflectᴱ s W))
|
||||
reflectᴱ (app s) (app₁ W) | p | warning W′ = app₂ W′
|
||||
reflectᴱ (app s) (app₂ W) | p = app₂ (blah p (cong src (preservationᴱ s)) W)
|
||||
reflectᴱ (beta s) (bot x₁) | p = {!!}
|
||||
reflectᴱ (beta {F = f ⟨ var x ∈ T ⟩∈ U} q) (block _ (disagree x₁)) | p = {!!}
|
||||
reflectᴱ (beta {F = f ⟨ var x ∈ T ⟩∈ U} q) (block _ (local₁ W)) | p = app₂ (bloz (cong src (cong typeOfᴴ q)) W)
|
||||
reflectᴱ (block s) (bot x₁) | p = {!!}
|
||||
reflectᴱ (block s) (block b W) | p = block b (reflectᴮ s W)
|
||||
reflectᴱ (return q) W | p = block _ (return W)
|
||||
reflectᴱ done (bot x) | p = {!!}
|
||||
preservationᴮ (local {x = var x ∈ T} s) with heap-weakeningᴮ (redn-⊑ s)
|
||||
preservationᴮ (local {x = var x ∈ T} s) | ok p = ok p
|
||||
preservationᴮ (local {x = var x ∈ T} s) | warning W = warning (local₂ W)
|
||||
preservationᴮ (subst {x = var x ∈ T} {B = B}) = ok (substitutivityᴮ {B = B} {!!})
|
||||
preservationᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} {B = B} defn) with heap-weakeningᴮ (snoc refl defn)
|
||||
preservationᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} {B = B} defn) | ok r = ok (trans r (substitutivityᴮ {T = S ⇒ T} {B = B} refl))
|
||||
preservationᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} {B = B} defn) | warning W = warning (function₂ f W)
|
||||
preservationᴮ (return s) with preservationᴱ s
|
||||
preservationᴮ (return s) | ok p = ok p
|
||||
preservationᴮ (return s) | warning W = warning (return W)
|
||||
|
||||
reflectᴮ s = {!!}
|
||||
reflect-substitutionᴱ : ∀ {H Γ Γ′ T} M v x → (T ≡ typeOfⱽ H v) → (Γ′ ≡ Γ ⊕ x ↦ T) → Warningᴱ H (typeCheckᴱ H Γ (M [ v / x ]ᴱ)) → Warningᴱ H (typeCheckᴱ H Γ′ M)
|
||||
reflect-substitutionᴱ-whenever-yes : ∀ {H Γ Γ′ T} v x y (p : x ≡ y) → (typeOfᴱ H Γ (val v) ≡ T) → (Γ′ ≡ Γ ⊕ x ↦ T) → Warningᴱ H (typeCheckᴱ H Γ (var y [ v / x ]ᴱwhenever yes p)) → Warningᴱ H (typeCheckᴱ H Γ′ (var y))
|
||||
reflect-substitutionᴱ-whenever-no : ∀ {H Γ Γ′ T} v x y (p : x ≢ y) → (typeOfᴱ H Γ (val v) ≡ T) → (Γ′ ≡ Γ ⊕ x ↦ T) → Warningᴱ H (typeCheckᴱ H Γ (var y [ v / x ]ᴱwhenever no p)) → Warningᴱ H (typeCheckᴱ H Γ′ (var y))
|
||||
reflect-substitutionᴮ : ∀ {H Γ Γ′ T} B v x → (T ≡ typeOfⱽ H v) → (Γ′ ≡ Γ ⊕ x ↦ T) → Warningᴮ H (typeCheckᴮ H Γ (B [ v / x ]ᴮ)) → Warningᴮ H (typeCheckᴮ H Γ′ B)
|
||||
reflect-substitutionᴮ-unless-yes : ∀ {H Γ Γ′ T} B v x y (r : x ≡ y) → (T ≡ typeOfⱽ H v) → (Γ′ ≡ Γ) → Warningᴮ H (typeCheckᴮ H Γ (B [ v / x ]ᴮunless yes r)) → Warningᴮ H (typeCheckᴮ H Γ′ B)
|
||||
|
||||
reflect-substitutionᴱ (var y) v x refl q W with x ≡ⱽ y
|
||||
reflect-substitutionᴱ (var y) v x refl q W | yes r = reflect-substitutionᴱ-whenever-yes v x y r (typeOfᴱⱽ v) q W
|
||||
reflect-substitutionᴱ (var y) v x refl q W | no r = reflect-substitutionᴱ-whenever-no v x y r (typeOfᴱⱽ v) q W
|
||||
reflect-substitutionᴱ (addr a) v x p q (BadlyTypedFunctionAddress a f r W) = BadlyTypedFunctionAddress a f r W
|
||||
reflect-substitutionᴱ (addr a) v x p q (UnallocatedAddress a r) = UnallocatedAddress a r
|
||||
reflect-substitutionᴱ (M $ N) v x p q (app₀ r) = {!!}
|
||||
reflect-substitutionᴱ (M $ N) v x p q (app₁ W) = app₁ (reflect-substitutionᴱ M v x p q W)
|
||||
reflect-substitutionᴱ (M $ N) v x p q (app₂ W) = app₂ (reflect-substitutionᴱ N v x p q W)
|
||||
reflect-substitutionᴱ (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p q (function₀ f r) = {!!}
|
||||
reflect-substitutionᴱ (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p refl (function₁ f W) with (x ≡ⱽ y)
|
||||
reflect-substitutionᴱ (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p refl (function₁ f W) | yes r = function₁ f (reflect-substitutionᴮ-unless-yes B v x y r p (⊕-overwrite r) W)
|
||||
reflect-substitutionᴱ (function f ⟨ var y ∈ T ⟩∈ U is B end) v x p refl (function₁ f W) | no r = function₁ f (reflect-substitutionᴮ B v x p (⊕-swap r) W)
|
||||
reflect-substitutionᴱ (block b is B end) v x p q (block b W) = block b (reflect-substitutionᴮ B v x p q W)
|
||||
|
||||
reflect-substitutionᴱ-whenever-no v x y r refl refl ()
|
||||
reflect-substitutionᴱ-whenever-yes (addr a) x x refl refl refl (BadlyTypedFunctionAddress a f p W) = {!!}
|
||||
reflect-substitutionᴱ-whenever-yes (addr a) x x refl refl refl (UnallocatedAddress a p) = {!!}
|
||||
|
||||
reflect-substitutionᴮ (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p q (function₁ f W) = {!!}
|
||||
reflect-substitutionᴮ (function f ⟨ var y ∈ T ⟩∈ U is C end ∙ B) v x p q (function₂ f W) = {!!}
|
||||
reflect-substitutionᴮ (local var y ∈ T ← M ∙ B) v x p q (local₀ r) = {!!}
|
||||
reflect-substitutionᴮ (local var y ∈ T ← M ∙ B) v x p q (local₁ W) = local₁ (reflect-substitutionᴱ M v x p q W)
|
||||
reflect-substitutionᴮ (local var y ∈ T ← M ∙ B) v x p q (local₂ W) = {!!}
|
||||
reflect-substitutionᴮ (return M ∙ B) v x p q (return W) = return (reflect-substitutionᴱ M v x p q W)
|
||||
|
||||
reflect-substitutionᴮ-unless-yes B v x y r p refl W = W
|
||||
|
||||
reflect-weakeningᴱ : ∀ {H H′ Γ M} → (H ⊑ H′) → Warningᴱ H′ (typeCheckᴱ H′ Γ M) → Warningᴱ H (typeCheckᴱ H Γ M)
|
||||
reflect-weakeningᴮ : ∀ {H H′ Γ B} → (H ⊑ H′) → Warningᴮ H′ (typeCheckᴮ H′ Γ B) → Warningᴮ H (typeCheckᴮ H Γ B)
|
||||
|
||||
reflect-weakeningᴱ h (BadlyTypedFunctionAddress a f p W) with lookup-⊑-just a h p
|
||||
reflect-weakeningᴱ h (BadlyTypedFunctionAddress a f p W) | just q = BadlyTypedFunctionAddress a f q (reflect-weakeningᴮ h W)
|
||||
reflect-weakeningᴱ h (BadlyTypedFunctionAddress a f p W) | nothing q = UnallocatedAddress a q
|
||||
reflect-weakeningᴱ h (UnallocatedAddress a p) = UnallocatedAddress a (lookup-⊑-nothing a h p)
|
||||
reflect-weakeningᴱ h (app₀ p) with heap-weakeningᴱ h | heap-weakeningᴱ h
|
||||
reflect-weakeningᴱ h (app₀ p) | ok q₁ | ok q₂ = app₀ (λ r → p (trans (cong src (sym q₁)) (trans r q₂)))
|
||||
reflect-weakeningᴱ h (app₀ p) | warning W | _ = app₁ W
|
||||
reflect-weakeningᴱ h (app₀ p) | _ | warning W = app₂ W
|
||||
reflect-weakeningᴱ h (app₁ W) = app₁ (reflect-weakeningᴱ h W)
|
||||
reflect-weakeningᴱ h (app₂ W) = app₂ (reflect-weakeningᴱ h W)
|
||||
reflect-weakeningᴱ h (function₀ f p) with heap-weakeningᴮ h
|
||||
reflect-weakeningᴱ h (function₀ f p) | ok q = function₀ f (λ r → p (trans r q))
|
||||
reflect-weakeningᴱ h (function₀ f p) | warning W = function₁ f W
|
||||
reflect-weakeningᴱ h (function₁ f W) = function₁ f (reflect-weakeningᴮ h W)
|
||||
reflect-weakeningᴱ h (block b W) = block b (reflect-weakeningᴮ h W)
|
||||
|
||||
reflect-weakeningᴮ h (return W) = return (reflect-weakeningᴱ h W)
|
||||
reflect-weakeningᴮ h (local₀ p) with heap-weakeningᴱ h
|
||||
reflect-weakeningᴮ h (local₀ p) | ok q = local₀ (λ r → p (trans r q))
|
||||
reflect-weakeningᴮ h (local₀ p) | warning W = local₁ W
|
||||
reflect-weakeningᴮ h (local₁ W) = local₁ (reflect-weakeningᴱ h W)
|
||||
reflect-weakeningᴮ h (local₂ W) = local₂ (reflect-weakeningᴮ h W)
|
||||
reflect-weakeningᴮ h (function₁ f W) = function₁ f (reflect-weakeningᴮ h W)
|
||||
reflect-weakeningᴮ h (function₂ f W) = function₂ f (reflect-weakeningᴮ h W)
|
||||
|
||||
reflectᴱ : ∀ {H H′ M M′} → (H ⊢ M ⟶ᴱ M′ ⊣ H′) → Warningᴱ H′ (typeCheckᴱ H′ ∅ M′) → Warningᴱ H (typeCheckᴱ H ∅ M)
|
||||
reflectᴮ : ∀ {H H′ B B′} → (H ⊢ B ⟶ᴮ B′ ⊣ H′) → Warningᴮ H′ (typeCheckᴮ H′ ∅ B′) → Warningᴮ H (typeCheckᴮ H ∅ B)
|
||||
|
||||
reflectᴱ (function {F = f ⟨ var x ∈ S ⟩∈ T} defn) (BadlyTypedFunctionAddress a f refl W) = function₁ f (reflect-weakeningᴮ (snoc refl defn) W)
|
||||
reflectᴱ (app s) (app₀ p) with preservationᴱ s | heap-weakeningᴱ (redn-⊑ s)
|
||||
reflectᴱ (app s) (app₀ p) | ok q | ok q′ = app₀ (λ r → p (trans (trans (cong src (sym q)) r) q′))
|
||||
reflectᴱ (app s) (app₀ p) | warning W | _ = app₁ W
|
||||
reflectᴱ (app s) (app₀ p) | _ | warning W = app₂ W
|
||||
reflectᴱ (app s) (app₁ W) = app₁ (reflectᴱ s W)
|
||||
reflectᴱ (app s) (app₂ W) = app₂ (reflect-weakeningᴱ (redn-⊑ s) W)
|
||||
reflectᴱ (beta {a = a} {F = f ⟨ var x ∈ T ⟩∈ U} q) (block f (local₀ p)) = app₀ (λ r → p (trans (sym (cong src (cong declaredTypeᴴ q))) r))
|
||||
reflectᴱ (beta {a = a} {F = f ⟨ var x ∈ T ⟩∈ U} q) (block f (local₁ W)) = app₂ W
|
||||
reflectᴱ (beta {a = a} {F = f ⟨ var x ∈ T ⟩∈ U} q) (block f (local₂ {T = T′} W)) = app₁ (BadlyTypedFunctionAddress a f q W)
|
||||
reflectᴱ (block s) (block b W) = block b (reflectᴮ s W)
|
||||
reflectᴱ (return q) W = block _ (return W)
|
||||
|
||||
reflectᴮ (local s) (local₀ p) with preservationᴱ s
|
||||
reflectᴮ (local s) (local₀ p) | ok q = local₀ (λ r → p (trans r q))
|
||||
reflectᴮ (local s) (local₀ p) | warning W = local₁ W
|
||||
reflectᴮ (local s) (local₁ W) = local₁ (reflectᴱ s W)
|
||||
reflectᴮ (local s) (local₂ W) = local₂ (reflect-weakeningᴮ (redn-⊑ s) W)
|
||||
reflectᴮ (subst {H = H} {x = var x ∈ T} {v = v}) W with T ≡ᵀ (typeOfᴱ H ∅ (val v))
|
||||
reflectᴮ (subst {x = var x ∈ T} {v = v}) W | yes refl = local₂ (reflect-substitutionᴮ _ v x (typeOfᴱⱽ v) refl W)
|
||||
reflectᴮ (subst {x = var x ∈ T} {v = v}) W | no p = local₀ p
|
||||
reflectᴮ (function {F = f ⟨ var x ∈ S ⟩∈ T} defn) W = function₂ f (reflect-weakeningᴮ (snoc refl defn) (reflect-substitutionᴮ _ _ f refl refl W))
|
||||
reflectᴮ (return s) (return W) = return (reflectᴱ s W)
|
||||
|
||||
-- reflectᴱ (function {F = f ⟨ var x ∈ S ⟩∈ T} defn) (bot ())
|
||||
-- reflectᴱ (function defn) (addr a T q) = CONTRADICTION (q refl)
|
||||
|
|
@ -168,12 +254,6 @@ reflectᴮ s = {!!}
|
|||
-- progressᴮ H h (function D₁ D₂) q with alloc H _
|
||||
-- progressᴮ H h (function D₁ D₂) q | ok a H′ r = step (function r)
|
||||
|
||||
import FFI.Data.Aeson
|
||||
{-# REWRITE FFI.Data.Aeson.singleton-insert-empty #-}
|
||||
|
||||
_≡ᵀ_ : (T U : Type) → Dec (T ≡ U)
|
||||
_≡ᵀ_ = {!!}
|
||||
|
||||
-- data LookupResult {Σ V S} (D : Σ ▷ V ∈ S) : Set where
|
||||
|
||||
-- function : ∀ f {x B T U W} →
|
||||
|
|
|
|||
|
|
@ -1,3 +1,5 @@
|
|||
{-# OPTIONS --rewriting #-}
|
||||
|
||||
open import Luau.Type using (Mode)
|
||||
|
||||
module Properties.TypeCheck (m : Mode) where
|
||||
|
|
@ -5,13 +7,14 @@ module Properties.TypeCheck (m : Mode) where
|
|||
open import Agda.Builtin.Equality using (_≡_; refl)
|
||||
open import FFI.Data.Maybe using (Maybe; just; nothing)
|
||||
open import FFI.Data.Either using (Either)
|
||||
open import Luau.TypeCheck(m) using (_⊢ᴱ_∋_∈_⊣_; _⊢ᴮ_∋_∈_⊣_; nil; var; addr; app; function; block; done; return; local)
|
||||
open import Luau.TypeCheck(m) using (_⊢ᴱ_∈_; _⊢ᴮ_∈_; nil; var; addr; app; function; block; done; return; local)
|
||||
open import Luau.Syntax using (Block; Expr; yes; nil; var; addr; _$_; function_is_end; block_is_end; _∙_; return; done; local_←_; _⟨_⟩; _⟨_⟩∈_; var_∈_; name; fun; arg)
|
||||
open import Luau.Type using (Type; nil; top; bot; _⇒_; tgt)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _↦_; _⊕_↦_; _⋒_; _⊝_; ⊕-[]) renaming (_[_] to _[_]ⱽ)
|
||||
open import Luau.VarCtxt using (VarCtxt; ∅; _↦_; _⊕_↦_; _⋒_; _⊝_) renaming (_[_] to _[_]ⱽ)
|
||||
open import Luau.AddrCtxt using (AddrCtxt) renaming (_[_] to _[_]ᴬ)
|
||||
open import Luau.Addr using (Addr)
|
||||
open import Luau.Var using (Var; _≡ⱽ_)
|
||||
open import Luau.Value using (Value; nil; addr; val)
|
||||
open import Luau.Heap using (Heap; HeapValue; function_is_end) renaming (_[_] to _[_]ᴴ)
|
||||
open import Properties.Dec using (yes; no)
|
||||
open import Properties.Equality using (_≢_; sym; trans; cong)
|
||||
|
|
@ -20,16 +23,20 @@ open import Properties.Remember using (remember; _,_)
|
|||
src : Type → Type
|
||||
src = Luau.Type.src m
|
||||
|
||||
typeOfᴴ : Maybe(HeapValue yes) → Type
|
||||
typeOfᴴ nothing = bot
|
||||
typeOfᴴ (just function f ⟨ var x ∈ S ⟩∈ T is B end) = (S ⇒ T)
|
||||
declaredTypeᴴ : Maybe(HeapValue yes) → Type
|
||||
declaredTypeᴴ nothing = bot
|
||||
declaredTypeᴴ (just function f ⟨ var x ∈ S ⟩∈ T is B end) = (S ⇒ T)
|
||||
|
||||
typeOfⱽ : Heap yes → Value → Type
|
||||
typeOfⱽ H nil = nil
|
||||
typeOfⱽ H (addr a) = declaredTypeᴴ (H [ a ]ᴴ)
|
||||
|
||||
typeOfᴱ : Heap yes → VarCtxt → (Expr yes) → Type
|
||||
typeOfᴮ : Heap yes → VarCtxt → (Block yes) → Type
|
||||
|
||||
typeOfᴱ H Γ nil = nil
|
||||
typeOfᴱ H Γ (var x) = Γ [ x ]ⱽ
|
||||
typeOfᴱ H Γ (addr a) = typeOfᴴ (H [ a ]ᴴ)
|
||||
typeOfᴱ H Γ (addr a) = declaredTypeᴴ (H [ a ]ᴴ)
|
||||
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 b is B end) = typeOfᴮ H Γ B
|
||||
|
|
@ -39,32 +46,25 @@ 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
|
||||
|
||||
contextOfᴱ : Heap yes → VarCtxt → Type → (Expr yes) → VarCtxt
|
||||
contextOfᴮ : Heap yes → VarCtxt → Type → (Block yes) → VarCtxt
|
||||
typeOfᴴ : Heap yes → Maybe(HeapValue yes) → Type
|
||||
typeOfᴴ H nothing = bot
|
||||
typeOfᴴ H (just function f ⟨ var x ∈ S ⟩∈ T is B end) = (S ⇒ typeOfᴮ H (x ↦ S) B)
|
||||
|
||||
contextOfᴱ H Γ S nil = ∅
|
||||
contextOfᴱ H Γ S (var x) = (x ↦ S)
|
||||
contextOfᴱ H Γ S (addr a) = ∅
|
||||
contextOfᴱ H Γ S (M $ N) = (contextOfᴱ H Γ (U ⇒ S) M) ⋒ (contextOfᴱ H Γ (src T) N) where T = typeOfᴱ H Γ M; U = typeOfᴱ H Γ N
|
||||
contextOfᴱ H Γ S (function f ⟨ var x ∈ T ⟩∈ U is B end) = (contextOfᴮ H (Γ ⊕ x ↦ T) U B) ⊝ x
|
||||
contextOfᴱ H Γ S (block b is B end) = (contextOfᴮ H Γ S B)
|
||||
typeOfᴱⱽ : ∀ {H Γ} v → (typeOfᴱ H Γ (val v) ≡ typeOfⱽ H v)
|
||||
typeOfᴱⱽ nil = refl
|
||||
typeOfᴱⱽ (addr a) = refl
|
||||
|
||||
contextOfᴮ H Γ S (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) = ((contextOfᴮ H (Γ ⊕ x ↦ T) U C) ⊝ x) ⋒ ((contextOfᴮ H (Γ ⊕ f ↦ (T ⇒ U)) S B) ⊝ f)
|
||||
contextOfᴮ H Γ S (local var x ∈ T ← M ∙ B) = (contextOfᴱ H Γ T M) ⋒ ((contextOfᴮ H (Γ ⊕ x ↦ T)S B) ⊝ x)
|
||||
contextOfᴮ H Γ S (return M ∙ B) = (contextOfᴱ H Γ S M)
|
||||
contextOfᴮ H Γ S done = ∅
|
||||
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 S M → (Γ ⊢ᴱ S ∋ M ∈ (typeOfᴱ H Γ M) ⊣ (contextOfᴱ H Γ S M))
|
||||
typeCheckᴮ : ∀ H Γ S B → (Γ ⊢ᴮ S ∋ B ∈ (typeOfᴮ H Γ B) ⊣ (contextOfᴮ H Γ S B))
|
||||
typeCheckᴱ H Γ nil = nil
|
||||
typeCheckᴱ H Γ (var x) = var x refl
|
||||
typeCheckᴱ H Γ (addr a) = addr a (declaredTypeᴴ (H [ a ]ᴴ))
|
||||
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 f (typeCheckᴮ H (Γ ⊕ x ↦ T) B)
|
||||
typeCheckᴱ H Γ (block b is B end) = block b (typeCheckᴮ H Γ B)
|
||||
|
||||
typeCheckᴱ H Γ S nil = nil
|
||||
typeCheckᴱ H Γ S (var x) = var x refl
|
||||
typeCheckᴱ H Γ S (addr a) = addr a (typeOfᴴ (H [ a ]ᴴ))
|
||||
typeCheckᴱ H Γ S (M $ N) = app (typeCheckᴱ H Γ (typeOfᴱ H Γ N ⇒ S) M) (typeCheckᴱ H Γ (src (typeOfᴱ H Γ M)) N)
|
||||
typeCheckᴱ H Γ S (function f ⟨ var x ∈ T ⟩∈ U is B end) = function(typeCheckᴮ H (Γ ⊕ x ↦ T) U B)
|
||||
typeCheckᴱ H Γ S (block b is B end) = block b (typeCheckᴮ H Γ S B)
|
||||
|
||||
typeCheckᴮ H Γ S (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) = function(typeCheckᴮ H (Γ ⊕ x ↦ T) U C) (typeCheckᴮ H (Γ ⊕ f ↦ (T ⇒ U)) S B)
|
||||
typeCheckᴮ H Γ S (local var x ∈ T ← M ∙ B) = local (typeCheckᴱ H Γ T M) (typeCheckᴮ H (Γ ⊕ x ↦ T) S B)
|
||||
typeCheckᴮ H Γ S (return M ∙ B) = return (typeCheckᴱ H Γ S M) (typeCheckᴮ H Γ nil B)
|
||||
typeCheckᴮ H Γ S done = done
|
||||
typeCheckᴮ H Γ (function f ⟨ var x ∈ T ⟩∈ U is C end ∙ B) = function f (typeCheckᴮ H (Γ ⊕ x ↦ T) C) (typeCheckᴮ H (Γ ⊕ f ↦ (T ⇒ U)) B)
|
||||
typeCheckᴮ H Γ (local var x ∈ T ← M ∙ B) = local (typeCheckᴱ H Γ M) (typeCheckᴮ H (Γ ⊕ x ↦ T) B)
|
||||
typeCheckᴮ H Γ (return M ∙ B) = return (typeCheckᴱ H Γ M) (typeCheckᴮ H Γ B)
|
||||
typeCheckᴮ H Γ done = done
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue