agda-spa/Lattice/Bundles/FiniteValueMap.agda

open import Relation.Binary.PropositionalEquality using (_≡_)
open import Relation.Binary.Definitions using (Decidable)

module Lattice.Bundles.FiniteValueMap (A B : Set) (≡-dec-A : Decidable (_≡_ {_} {A})) where

open import Lattice
open import Data.List using (List)
open import Data.Nat using (ℕ)
open import Utils using (Unique)

module FromFiniteHeightLattice (fhB : FiniteHeightLattice B)
                               {ks : List A} (uks : Unique ks)
                               (≈₂-dec : Decidable (FiniteHeightLattice._≈_ fhB)) where

    open Lattice.FiniteHeightLattice fhB using () renaming
        ( _≈_ to _≈₂_; _⊔_ to _⊔₂_; _⊓_ to _⊓₂_
        ; height to height₂
        ; isLattice to isLattice₂
        ; fixedHeight to fixedHeight₂
        )

    import Lattice.FiniteMap
    module FM = Lattice.FiniteMap ≡-dec-A isLattice₂
    open FM.WithKeys ks public

    import Lattice.FiniteValueMap
    module FVM = Lattice.FiniteValueMap ≡-dec-A isLattice₂
    open FVM.IterProdIsomorphism.WithUniqueKeysAndFixedHeight uks ≈₂-dec height₂ fixedHeight₂ public

    ≈-dec = ≈₂-dec⇒≈-dec ≈₂-dec