------------------------------------------------------------------------
-- The Agda standard library
--
-- Left-biased universe-sensitive functor and monad instances for the
-- Product type.
--
-- 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.
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
open import Algebra
open import Level
module Data.Product.Effectful.Left
{a e} (A : RawMonoid a e) (b : Level) where
open import Data.Product.Base using (_,_; map₁; map₂; zip; uncurry)
import Data.Product.Effectful.Left.Base as Base using (Productₗ; functor)
open import Effect.Applicative using (RawApplicative)
open import Effect.Monad using (RawMonad; RawMonadT; mkRawMonad)
open import Function.Base using (id; flip; _∘_; _∘′_)
open RawMonoid A
------------------------------------------------------------------------
-- Re-export the base contents publically
open Base Carrier b public
------------------------------------------------------------------------
-- Basic records
applicative : RawApplicative Productₗ
applicative = record
{ rawFunctor = functor
; pure = ε ,_
; _<*>_ = zip _∙_ id
}
monad : RawMonad Productₗ
monad = record
{ rawApplicative = applicative
; _>>=_ = uncurry λ w₁ a f → map₁ (w₁ ∙_) (f a)
}
-- The monad instance also requires some mucking about with universe levels.
monadT : ∀ {ℓ} → RawMonadT {g₁ = ℓ} (_∘′ Productₗ)
monadT M = record
{ lift = (ε ,_) <$>_
; rawMonad = mkRawMonad _
(pure ∘′ (ε ,_))
(λ ma f → ma >>= uncurry λ a x → map₁ (a ∙_) <$> f x)
} where open RawMonad M
------------------------------------------------------------------------
-- Get access to other monadic functions
module TraversableA {F} (App : RawApplicative {a ⊔ b} {a ⊔ b} F) where
open RawApplicative App
sequenceA : ∀ {A} → Productₗ (F A) → F (Productₗ A)
sequenceA (x , fa) = (x ,_) <$> fa
mapA : ∀ {A B} → (A → F B) → Productₗ A → F (Productₗ B)
mapA f = sequenceA ∘ map₂ f
forA : ∀ {A B} → Productₗ A → (A → F B) → F (Productₗ B)
forA = flip mapA
module TraversableM {M} (Mon : RawMonad {a ⊔ b} {a ⊔ b} M) where
open RawMonad Mon
open TraversableA rawApplicative public
renaming
( sequenceA to sequenceM
; mapA to mapM
; forA to forM
)
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