------------------------------------------------------------------------
-- The Agda standard library
--
-- Coinductive lists where at least one element satisfies a predicate
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --guardedness #-}
module Codata.Musical.Colist.Relation.Unary.Any where
open import Codata.Musical.Colist.Base
open import Codata.Musical.Notation using (♭)
open import Data.Nat.Base using (ℕ; zero; suc)
open import Function.Base using (_∋_)
open import Level using (Level; _⊔_)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl)
open import Relation.Unary using (Pred)
private
variable
a b p : Level
A : Set a
B : Set b
P : Pred A p
data Any {A : Set a} (P : Pred A p) : Pred (Colist A) (a ⊔ p) where
here : ∀ {x xs} (px : P x) → Any P (x ∷ xs)
there : ∀ {x xs} (pxs : Any P (♭ xs)) → Any P (x ∷ xs)
index : ∀ {xs} → Any P xs → ℕ
index (here px) = zero
index (there p) = suc (index p)
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