-- The Agda standard library
-- Base definitions for the left-biased universe-sensitive functor and
-- monad instances for These.
-- To minimize the universe level of the RawFunctor, we require that
-- elements of B are "lifted" to a copy of B at a higher universe level
-- (a ⊔ b).
-- See the Data.Product.Effectful.Examples for how this is done in a
-- Product-based similar setting.

{-# OPTIONS --cubical-compatible --safe #-}

open import Level

module Data.These.Effectful.Left.Base {a} (A : Set a) (b : Level) where

open import Data.These.Base
open import Effect.Functor
open import Effect.Applicative
open import Effect.Monad
open import Function

Theseₗ : Set (a  b)  Set (a  b)
Theseₗ B = These A B

functor : RawFunctor Theseₗ
functor = record { _<$>_ = map₂ }

-- Get access to other monadic functions

module _ {F} (App : RawApplicative {a  b} {a  b} F) where

  open RawApplicative App

  sequenceA :  {A}  Theseₗ (F A)  F (Theseₗ A)
  sequenceA (this a)    = pure (this a)
  sequenceA (that b)    = that <$> b
  sequenceA (these a b) = these a <$> b

  mapA :  {A B}  (A  F B)  Theseₗ A  F (Theseₗ B)
  mapA f = sequenceA  map₂ f

  forA :  {A B}  Theseₗ A  (A  F B)  F (Theseₗ B)
  forA = flip mapA

module _ {M} (Mon : RawMonad {a  b} {a  b} M) where

  private App = RawMonad.rawApplicative Mon

  sequenceM :  {A}  Theseₗ (M A)  M (Theseₗ A)
  sequenceM = sequenceA App

  mapM :  {A B}  (A  M B)  Theseₗ A  M (Theseₗ B)
  mapM = mapA App

  forM :  {A B}  Theseₗ A  (A  M B)  M (Theseₗ B)
  forM = forA App