------------------------------------------------------------------------
-- The Agda standard library
--
-- A categorical view of List⁺
------------------------------------------------------------------------

module Data.List.NonEmpty.Categorical where

open import Agda.Builtin.List
import Data.List.Categorical as List
open import Data.List.NonEmpty
open import Data.Product using (uncurry)
open import Category.Functor
open import Category.Applicative
open import Category.Monad
open import Category.Comonad
open import Function

------------------------------------------------------------------------
-- List⁺ applicative functor

functor : ∀ {f} → RawFunctor {f} List⁺
functor = record
  { _<$>_ = map
  }

applicative : ∀ {f} → RawApplicative {f} List⁺
applicative = record
  { pure = [_]
  ; _⊛_  = λ fs as → concatMap (λ f → map f as) fs
  }

------------------------------------------------------------------------
-- List⁺ monad

monad : ∀ {f} → RawMonad {f} List⁺
monad = record
  { return = [_]
  ; _>>=_  = flip concatMap
  }

------------------------------------------------------------------------
-- List⁺ comonad

comonad : ∀ {f} → RawComonad {f} List⁺
comonad = record
  { extract = head
  ; extend  = λ f → uncurry (extend f) ∘′ uncons
  } where

  extend : ∀ {A B} → (List⁺ A → B) → A → List A → List⁺ B
  extend f x xs@[]       = f (x ∷ xs) ∷ []
  extend f x xs@(y ∷ ys) = f (x ∷ xs) ∷⁺ extend f y ys


------------------------------------------------------------------------
-- Get access to other monadic functions

module _ {f F} (App : RawApplicative {f} F) where

  open RawApplicative App

  sequenceA : ∀ {A} → List⁺ (F A) → F (List⁺ A)
  sequenceA (x ∷ xs) = _∷_ <$> x ⊛ List.sequenceA App xs

  mapA : ∀ {a} {A : Set a} {B} → (A → F B) → List⁺ A → F (List⁺ B)
  mapA f = sequenceA ∘ map f

  forA : ∀ {a} {A : Set a} {B} → List⁺ A → (A → F B) → F (List⁺ B)
  forA = flip mapA

module _ {m M} (Mon : RawMonad {m} M) where

  private App = RawMonad.rawIApplicative Mon

  sequenceM = sequenceA App
  mapM = mapA App
  forM = forA App

------------------------------------------------------------------------
-- List⁺ monad transformer

monadT : ∀ {f} → RawMonadT {f} (_∘′ List⁺)
monadT M = record
  { return = pure ∘′ [_]
  ; _>>=_  = λ mas f → mas >>= λ as → concat <$> mapM M f as
  } where open RawMonad M