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93 lines
2.8 KiB
Agda
93 lines
2.8 KiB
Agda
module Luau.OpSem where
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open import Agda.Builtin.Equality using (_≡_)
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open import FFI.Data.Maybe using (just)
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open import Luau.Heap using (Heap; _≡_⊕_↦_; lookup; function_⟨_⟩_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⟨_⟩_end; _$_; block_is_end; local_←_; _∙_; done; function_⟨_⟩_end; return)
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open import Luau.Value using (addr; val)
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data _⊢_⟶ᴮ_⊣_ : Heap → Block → Block → Heap → Set
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data _⊢_⟶ᴱ_⊣_ : Heap → Expr → Expr → Heap → Set
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data _⊢_⟶ᴱ_⊣_ where
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nil : ∀ {H} →
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-------------------
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H ⊢ nil ⟶ᴱ nil ⊣ H
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function : ∀ {H H′ a x B} →
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H′ ≡ H ⊕ a ↦ (function "anon" ⟨ x ⟩ B end) →
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-------------------------------------------
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H ⊢ (function⟨ x ⟩ B end) ⟶ᴱ (addr a) ⊣ H′
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app : ∀ {H H′ M M′ N} →
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H ⊢ M ⟶ᴱ M′ ⊣ H′ →
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-----------------------------
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H ⊢ (M $ N) ⟶ᴱ (M′ $ N) ⊣ H′
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beta : ∀ {H M a f x B} →
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(lookup H a) ≡ just(function f ⟨ x ⟩ B end) →
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-----------------------------------------------------
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H ⊢ (addr a $ M) ⟶ᴱ (block f is local x ← M ∙ B end) ⊣ H
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block : ∀ {H H′ B B′ b} →
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H ⊢ B ⟶ᴮ B′ ⊣ H′ →
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----------------------------------------------------
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H ⊢ (block b is B end) ⟶ᴱ (block b is B′ end) ⊣ H′
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return : ∀ {H V B b} →
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--------------------------------------------------------
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H ⊢ (block b is return (val V) ∙ B end) ⟶ᴱ (val V) ⊣ H
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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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data _⊢_⟶ᴮ_⊣_ where
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local : ∀ {H H′ x M M′ B} →
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H ⊢ M ⟶ᴱ M′ ⊣ H′ →
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-------------------------------------------------
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H ⊢ (local x ← M ∙ B) ⟶ᴮ (local x ← M′ ∙ B) ⊣ H′
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subst : ∀ {H x v B} →
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-------------------------------------------------
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H ⊢ (local x ← val v ∙ B) ⟶ᴮ (B [ v / x ]ᴮ) ⊣ H
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function : ∀ {H H′ a f x B C} →
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H′ ≡ H ⊕ a ↦ (function f ⟨ x ⟩ C end) →
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--------------------------------------------------------------
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H ⊢ (function f ⟨ x ⟩ C end ∙ B) ⟶ᴮ (B [ addr a / f ]ᴮ) ⊣ H′
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return : ∀ {H H′ M M′ B} →
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H ⊢ M ⟶ᴱ M′ ⊣ H′ →
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--------------------------------------------
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H ⊢ (return M ∙ B) ⟶ᴮ (return M′ ∙ B) ⊣ H′
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data _⊢_⟶*_⊣_ : Heap → Block → Block → Heap → Set where
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refl : ∀ {H B} →
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----------------
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H ⊢ B ⟶* B ⊣ H
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step : ∀ {H H′ H″ B B′ B″} →
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H ⊢ B ⟶ᴮ B′ ⊣ H′ →
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H′ ⊢ B′ ⟶* B″ ⊣ H″ →
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------------------
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H ⊢ B ⟶* B″ ⊣ H″
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