44 lines
1.6 KiB
Agda
44 lines
1.6 KiB
Agda
{-# OPTIONS --rewriting #-}
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module Luau.VarCtxt where
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open import Agda.Builtin.Equality using (_≡_)
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open import Luau.Type using (Type; _∪_; _∩_)
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open import Luau.Var using (Var)
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open import FFI.Data.Aeson using (KeyMap; Key; empty; unionWith; singleton; insert; delete; lookup; toString; fromString; lookup-insert; lookup-insert-not; lookup-empty; to-from; insert-swap; insert-over)
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open import FFI.Data.Maybe using (Maybe; just; nothing)
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open import Properties.Equality using (_≢_; cong; sym; trans)
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VarCtxt : Set
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VarCtxt = KeyMap Type
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∅ : VarCtxt
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∅ = empty
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_⋒_ : VarCtxt → VarCtxt → VarCtxt
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_⋒_ = unionWith _∩_
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_⋓_ : VarCtxt → VarCtxt → VarCtxt
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_⋓_ = unionWith _∪_
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_[_] : VarCtxt → Var → Maybe Type
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Γ [ x ] = lookup (fromString x) Γ
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_⊝_ : VarCtxt → Var → VarCtxt
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Γ ⊝ x = delete (fromString x) Γ
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_↦_ : Var → Type → VarCtxt
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x ↦ T = singleton (fromString x) T
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_⊕_↦_ : VarCtxt → Var → Type → VarCtxt
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Γ ⊕ x ↦ T = insert (fromString x) T Γ
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⊕-over : ∀ {Γ x y T U} → (x ≡ y) → ((Γ ⊕ x ↦ T) ⊕ y ↦ U) ≡ (Γ ⊕ y ↦ U)
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⊕-over p = insert-over _ _ _ _ _ (cong fromString (sym p))
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⊕-swap : ∀ {Γ x y T U} → (x ≢ y) → ((Γ ⊕ x ↦ T) ⊕ y ↦ U) ≡ ((Γ ⊕ y ↦ U) ⊕ x ↦ T)
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⊕-swap p = insert-swap _ _ _ _ _ (λ q → p (trans (sym (to-from _)) (trans (cong toString (sym q) ) (to-from _))) )
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⊕-lookup-miss : ∀ x y T Γ → (x ≢ y) → (Γ [ y ] ≡ (Γ ⊕ x ↦ T) [ y ])
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⊕-lookup-miss x y T Γ p = lookup-insert-not (fromString x) (fromString y) T Γ λ q → p (trans (sym (to-from x)) (trans (cong toString q) (to-from y)))
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