module Main where

open import IO
open import Level
open import Data.Nat.Show using (show)
open import Data.List using (List; _∷_; [])
open import Data.String using (String) renaming (_≟_ to _≟ˢ_)
open import Data.Unit using (⊤; tt) renaming (_≟_ to _≟ᵘ_)
open import Data.List.Relation.Unary.All using (_∷_; [])
open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; subst; refl; trans)
open import Relation.Nullary using (¬_)

open import Utils using (Unique; push; empty)

xyzw : List String
xyzw = "x" ∷ "y" ∷ "z" ∷ "w" ∷ []

xyzw-Unique : Unique xyzw
xyzw-Unique = push ((λ ()) ∷ (λ ()) ∷ (λ ()) ∷ []) (push ((λ ()) ∷ (λ ()) ∷ []) (push ((λ ()) ∷ []) (push [] empty)))

open import Lattice using (IsFiniteHeightLattice; FiniteHeightLattice)
open import Lattice.AboveBelow ⊤ _≡_ (record { ≈-refl = refl; ≈-sym = sym; ≈-trans = trans }) _≟ᵘ_  as AB renaming (≈-dec to ≈ᵘ-dec)
open AB.Plain renaming (finiteHeightLattice to finiteHeightLatticeᵘ)
open import Lattice.Bundles.FiniteValueMap String AB.AboveBelow _≟ˢ_ renaming (finiteHeightLattice to finiteHeightLatticeᵐ)

fhlᵘ = finiteHeightLatticeᵘ (Data.Unit.tt)

fhlⁱᵖ = finiteHeightLatticeᵐ fhlᵘ xyzw-Unique ≈ᵘ-dec

main = run {0ℓ} (putStrLn (show (FiniteHeightLattice.height fhlⁱᵖ)))