{-# OPTIONS --without-K --safe #-}
open import Relation.Binary
module Data.List.Membership.Setoid {c ℓ} (S : Setoid c ℓ) where
open import Function using (_∘_; id; flip)
open import Data.Fin using (Fin; zero; suc)
open import Data.List.Base as List using (List; []; _∷_; length; lookup)
open import Data.List.Relation.Unary.Any
using (Any; index; map; here; there)
open import Data.Product as Prod using (∃; _×_; _,_)
open import Relation.Unary using (Pred)
open import Relation.Nullary using (¬_)
open Setoid S renaming (Carrier to A)
infix 4 _∈_ _∉_
_∈_ : A → List A → Set _
x ∈ xs = Any (x ≈_) xs
_∉_ : A → List A → Set _
x ∉ xs = ¬ x ∈ xs
open Data.List.Relation.Unary.Any using (_∷=_; _─_) public
mapWith∈ : ∀ {b} {B : Set b}
(xs : List A) → (∀ {x} → x ∈ xs → B) → List B
mapWith∈ [] f = []
mapWith∈ (x ∷ xs) f = f (here refl) ∷ mapWith∈ xs (f ∘ there)
module _ {p} {P : Pred A p} where
find : ∀ {xs} → Any P xs → ∃ λ x → x ∈ xs × P x
find (here px) = (_ , here refl , px)
find (there pxs) = Prod.map id (Prod.map there id) (find pxs)
lose : P Respects _≈_ → ∀ {x xs} → x ∈ xs → P x → Any P xs
lose resp x∈xs px = map (flip resp px) x∈xs
map-with-∈ = mapWith∈
{-# WARNING_ON_USAGE map-with-∈
"Warning: map-with-∈ was deprecated in v0.16.
Please use mapWith∈ instead."
#-}