46 lines
1.5 KiB
Agda
46 lines
1.5 KiB
Agda
open import Lattice
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open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym; trans; cong; subst)
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open import Relation.Binary.Definitions using (Decidable)
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open import Agda.Primitive using (Level) renaming (_⊔_ to _⊔ℓ_)
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module Lattice.MapSet {a : Level} {A : Set a} (≡-dec-A : Decidable (_≡_ {a} {A})) where
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open import Data.List using (List; map)
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open import Data.Product using (_,_; proj₁)
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open import Function using (_∘_)
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open import Lattice.Unit using (⊤; tt) renaming (_≈_ to _≈₂_; _⊔_ to _⊔₂_; _⊓_ to _⊓₂_; isLattice to ⊤-isLattice)
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import Lattice.Map
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private module UnitMap = Lattice.Map ≡-dec-A ⊤-isLattice
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open UnitMap
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using (Map; Expr; ⟦_⟧)
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renaming
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( Expr-Provenance to Expr-Provenanceᵐ
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)
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open UnitMap
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using
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( _⊆_; _≈_; ≈-equiv; _⊔_; _⊓_; _∪_ ; _∩_ ; `_; empty; forget
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; isUnionSemilattice; isIntersectSemilattice; isLattice; lattice
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; Provenance
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; ⊔-preserves-∈k₁
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; ⊔-preserves-∈k₂
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)
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renaming (_∈k_ to _∈_) public
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open Provenance public
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MapSet : Set a
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MapSet = Map
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to-List : MapSet → List A
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to-List = map proj₁ ∘ proj₁
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insert : A → MapSet → MapSet
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insert k = UnitMap.insert k tt
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singleton : A → MapSet
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singleton k = UnitMap.insert k tt empty
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Expr-Provenance : ∀ (k : A) (e : Expr) → k ∈ ⟦ e ⟧ → Provenance k tt e
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Expr-Provenance k e k∈e = let (tt , (prov , _)) = Expr-Provenanceᵐ k e k∈e in prov
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