------------------------------------------------------------------------
-- An example showing how Container.Tree-sort can be used
------------------------------------------------------------------------

{-# OPTIONS --without-K --safe #-}

module Container.Tree-sort.Example where

open import Container
open import Container.List
open import Equality.Propositional
open import Prelude using (; zero; suc; Bool; true; false)

-- Comparison function for natural numbers.

_≤_ :     Bool
zero   _     = true
suc _  zero  = false
suc m  suc n = m  n

open import Container.Tree-sort _≤_

-- The sort function seems to return an ordered list.

ordered : sort (3  1  2  [])  1  2  3  []
ordered = refl

-- The sort function definitely returns a list which is bag equivalent
-- to the input. This property can be used to establish bag
-- equivalences between concrete lists.

a-bag-equivalence : 1  2  3  [] ≈-bag 3  1  2  []
a-bag-equivalence = sort≈ (3  1  2  [])