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30 lines
1.4 KiB
Agda
30 lines
1.4 KiB
Agda
module Luau.Substitution where
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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 (Value; val)
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open import Luau.Var using (Var; _≡ⱽ_)
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open import Properties.Dec using (Dec; yes; no)
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_[_/_]ᴱ : Expr → Value → Var → Expr
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_[_/_]ᴮ : Block → Value → Var → Block
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var_[_/_]ᴱwhenever_ : ∀ {P} → Var → Value → Var → (Dec P) → Expr
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_[_/_]ᴮunless_ : ∀ {P} → Block → Value → Var → (Dec P) → Block
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nil [ v / x ]ᴱ = nil
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var y [ v / x ]ᴱ = var y [ v / x ]ᴱwhenever (x ≡ⱽ y)
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addr a [ v / x ]ᴱ = addr a
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(M $ N) [ v / x ]ᴱ = (M [ v / x ]ᴱ) $ (N [ v / x ]ᴱ)
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function⟨ y ⟩ C end [ v / x ]ᴱ = function⟨ y ⟩ C [ v / x ]ᴮunless (x ≡ⱽ y) end
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block b is C end [ v / x ]ᴱ = block b is C [ v / x ]ᴮ end
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(function f ⟨ y ⟩ C end ∙ B) [ v / x ]ᴮ = function f ⟨ y ⟩ (C [ v / x ]ᴮunless (x ≡ⱽ y)) end ∙ (B [ v / x ]ᴮunless (x ≡ⱽ f))
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(local y ← M ∙ B) [ v / x ]ᴮ = local y ← (M [ v / x ]ᴱ) ∙ (B [ v / x ]ᴮunless (x ≡ⱽ y))
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(return M ∙ B) [ v / x ]ᴮ = return (M [ v / x ]ᴱ) ∙ (B [ v / x ]ᴮ)
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done [ v / x ]ᴮ = done
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var y [ v / x ]ᴱwhenever yes p = val v
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var y [ v / x ]ᴱwhenever no p = var y
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B [ v / x ]ᴮunless yes p = B
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B [ v / x ]ᴮunless no p = B [ v / x ]ᴮ
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