module Pandora.Pattern.Functor.Distributive where

import Pandora.Core.Functor (type (:.), type (:=))
import Pandora.Core.Morphism ((%))
import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))
import Pandora.Pattern.Category (identity, (.))

{- |
> Let f :: Distributive g => (a -> g b)

> When providing a new instance, you should ensure it satisfies the two laws:
> * Identity morphism: distribute . distribute ≡ identity
> * Interchange collection: collect f ≡ distribute . comap f
-}

infixl 5 >>-, >>>-, >>>>-, >>>>>-

class Covariant t => Distributive t where
        {-# MINIMAL (>>-) #-}
        -- | Infix and flipped version of 'collect'
        (>>-) :: Covariant u => u a -> (a -> t b) -> t :. u := b

        -- | Prefix version of '>>-'
        collect :: Covariant u => (a -> t b) -> u a -> t :. u := b
        collect f t = t >>- f
        -- | The dual of 'sequence'
        distribute :: Covariant u => u :. t := a -> t :. u := a
        distribute t = t >>- identity

        -- | Infix versions of `collect` with various nesting levels
        (>>>-) :: (Covariant u, Covariant v)
                => u :. v := a -> (a -> t b) -> t :. u :. v := b
        x >>>- f = (collect . collect) f x
        (>>>>-) :: (Covariant u, Covariant v, Covariant w)
                => u :. v :. w := a -> (a -> t b) -> t :. u :. v :. w := b
        x >>>>- f = (collect . collect . collect) f x
        (>>>>>-) :: (Covariant u, Covariant v, Covariant w, Covariant j)
                => u :. v :. w :. j := a -> (a -> t b) -> t :. u :. v :. w :. j := b
        x >>>>>- f = (collect . collect . collect . collect) f x

instance Distributive ((->) e) where
        g >>- f = \e -> (f % e) <$> g