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

    module _ {ks : List A} (uks : Unique ks) (≈₂-dec : Decidable _≈₂_) where
        import Lattice.FiniteValueMap A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A isLattice₂ as FVM

        FiniteHeightType = FVM.FiniteMap ks

        finiteHeightLattice = FVM.IterProdIsomorphism.finiteHeightLattice uks ≈₂-dec height₂ fixedHeight₂
        open FiniteHeightLattice finiteHeightLattice public

        ≈-dec = FVM.≈-dec ks ≈₂-dec