43 lines
1.6 KiB
Agda
43 lines
1.6 KiB
Agda
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl)
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open import Relation.Binary.Definitions using (Decidable)
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open import Relation.Binary.Core using (Rel)
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open import Relation.Nullary using (Dec; yes; no)
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open import Agda.Primitive using (Level; _⊔_)
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module Map {a b : Level} (A : Set a) (B : Set b)
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(≡-dec-A : Decidable (_≡_ {a} {A}))
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where
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open import Data.Nat using (ℕ)
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open import Data.String using (String; _++_)
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open import Data.List using (List; []; _∷_)
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open import Data.List.Membership.Propositional using ()
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open import Data.Product using (_×_; _,_; Σ)
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open import Data.Unit using (⊤)
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open import Data.Empty using (⊥)
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Map : Set (a ⊔ b)
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Map = List (A × B)
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insert : (B → B → B) → A → B → Map → Map
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insert f k v [] = (k , v) ∷ []
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insert f k v (x@(k' , v') ∷ xs) with ≡-dec-A k k'
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... | yes _ = (k , f v v') ∷ xs
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... | no _ = x ∷ insert f k v xs
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foldr : ∀ {c} {C : Set c} → (A → B → C → C) -> C -> Map -> C
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foldr f b [] = b
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foldr f b ((k , v) ∷ xs) = f k v (foldr f b xs)
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_∈_ : (A × B) → Map → Set (a ⊔ b)
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_∈_ p m = Data.List.Membership.Propositional._∈_ p m
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subset : ∀ (_≈_ : B → B → Set b) → Map → Map → Set (a ⊔ b)
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subset _≈_ m₁ m₂ = ∀ (k : A) (v : B) → (k , v) ∈ m₁ → Σ B (λ v' → v ≈ v' × ((k , v') ∈ m₂))
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lift : ∀ (_≈_ : B → B → Set b) → Map → Map → Set (a ⊔ b)
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lift _≈_ m₁ m₂ = (m₁ ⊆ m₂) × (m₂ ⊆ m₁)
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where
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_⊆_ : Map → Map → Set (a ⊔ b)
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_⊆_ = subset _≈_
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