{-# OPTIONS --without-K --safe #-}
open import Relation.Binary using (Setoid; _Respects_)
module Data.Vec.Membership.Setoid {c ℓ} (S : Setoid c ℓ) where
open import Function
open import Data.Vec.Base as Vec using (Vec; []; _∷_)
open import Data.Vec.Relation.Unary.Any as Any
using (Any; here; there; index)
open import Data.Product using (∃; _×_; _,_)
open import Relation.Nullary using (¬_)
open import Relation.Unary using (Pred)
open Setoid S renaming (Carrier to A)
infix 4 _∈_ _∉_
_∈_ : A → ∀ {n} → Vec A n → Set _
x ∈ xs = Any (x ≈_) xs
_∉_ : A → ∀ {n} → Vec A n → Set _
x ∉ xs = ¬ x ∈ xs
mapWith∈ : ∀ {b} {B : Set b} {n}
(xs : Vec A n) → (∀ {x} → x ∈ xs → B) → Vec B n
mapWith∈ [] f = []
mapWith∈ (x ∷ xs) f = f (here refl) ∷ mapWith∈ xs (f ∘ there)
_∷=_ : ∀ {n} {xs : Vec A n} {x} → x ∈ xs → A → Vec A n
_∷=_ {xs = xs} x∈xs v = xs Vec.[ index x∈xs ]≔ v
module _ {p} {P : Pred A p} where
find : ∀ {n} {xs : Vec A n} → Any P xs → ∃ λ x → x ∈ xs × P x
find (here px) = (_ , here refl , px)
find (there pxs) with find pxs
... | (x , x∈xs , px) = (x , there x∈xs , px)
lose : P Respects _≈_ → ∀ {x n} {xs : Vec A n} → x ∈ xs → P x → Any P xs
lose resp x∈xs px = Any.map (flip resp px) x∈xs