------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties of lists made up entirely of decidably unique elements
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
open import Data.List.Base using ([]; _∷_; deduplicate)
import Data.List.Relation.Unary.Unique.DecSetoid as Unique
open import Data.List.Relation.Unary.All.Properties using (all-filter)
open import Data.List.Relation.Unary.Unique.Setoid.Properties
open import Level
open import Relation.Binary.Bundles using (DecSetoid)
module Data.List.Relation.Unary.Unique.DecSetoid.Properties where
private
variable
a ℓ : Level
------------------------------------------------------------------------
-- deduplicate
module _ (DS : DecSetoid a ℓ) where
open DecSetoid DS renaming (setoid to S)
open Unique DS
deduplicate-! : ∀ xs → Unique (deduplicate _≟_ xs)
deduplicate-! [] = []
deduplicate-! (x ∷ xs) = all-filter _ (deduplicate _≟_ xs) ∷ filter⁺ S _ (deduplicate-! xs)
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