open import Relation.Binary
open import Relation.Binary.PropositionalEquality using (_≡_)
module Data.AVL.Sets
{k ℓ} {Key : Set k} {_<_ : Rel Key ℓ}
(isStrictTotalOrder : IsStrictTotalOrder _≡_ _<_)
where
open import Category.Functor
import Data.AVL as AVL
open import Data.Bool
open import Data.List as List using (List)
open import Data.Maybe as Maybe
open import Data.Product as Prod using (_×_; _,_; proj₁)
open import Data.Unit
open import Function
open import Level
open RawFunctor (Maybe.functor {f = k ⊔ ℓ})
private
open module S = AVL (const ⊤) isStrictTotalOrder
public using () renaming (Tree to ⟨Set⟩)
empty : ⟨Set⟩
empty = S.empty
singleton : Key → ⟨Set⟩
singleton k = S.singleton k _
insert : Key → ⟨Set⟩ → ⟨Set⟩
insert k = S.insert k _
delete : Key → ⟨Set⟩ → ⟨Set⟩
delete = S.delete
_∈?_ : Key → ⟨Set⟩ → Bool
_∈?_ = S._∈?_
headTail : ⟨Set⟩ → Maybe (Key × ⟨Set⟩)
headTail s = Prod.map proj₁ id <$> S.headTail s
initLast : ⟨Set⟩ → Maybe (⟨Set⟩ × Key)
initLast s = Prod.map id proj₁ <$> S.initLast s
fromList : List Key → ⟨Set⟩
fromList = S.fromList ∘ List.map (λ k → (k , _))
toList : ⟨Set⟩ → List Key
toList = List.map proj₁ ∘ S.toList