------------------------------------------------------------------------
-- 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 using (These; this; that; these; map₂)
open import Effect.Functor using (RawFunctor)
open import Effect.Applicative using (RawApplicative)
open import Effect.Monad using (RawMonad)
open import Function.Base using (_∘_; flip)
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
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