------------------------------------------------------------------------
-- The Agda standard library
--
-- A non-empty fresh list
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
module Data.List.Fresh.NonEmpty where
open import Data.List.Fresh as List# using (List#; []; cons; fresh)
open import Data.Maybe.Base using (Maybe; nothing; just)
open import Data.Nat.Base using (ℕ; suc)
open import Data.Product.Base using (_×_; _,_)
open import Level using (Level; _⊔_)
open import Relation.Binary.Core using (Rel)
private
variable
a r : Level
A : Set a
R : Rel A r
------------------------------------------------------------------------
-- Definition
infixr 5 _∷#⁺_
record List#⁺ (A : Set a) (R : Rel A r) : Set (a ⊔ r) where
constructor _∷#⁺_
field
head : A
tail : List# A R
{rel} : fresh A R head tail
open List#⁺
------------------------------------------------------------------------
-- Operations
uncons : List#⁺ A R → A × List# A R
uncons (x ∷#⁺ xs) = x , xs
[_] : A → List#⁺ A R
[ x ] = x ∷#⁺ []
length : List#⁺ A R → ℕ
length (x ∷#⁺ xs) = suc (List#.length xs)
-- Conversion
toList# : List#⁺ A R → List# A R
toList# l = cons (l .head) (l .tail) (l .rel)
fromList# : List# A R → Maybe (List#⁺ A R)
fromList# [] = nothing
fromList# (cons a as ps) = just (record { head = a ; tail = as ; rel = ps })
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