module Pandora.Pattern.Functor.Bindable (Bindable (..)) where

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

infixl 1 >>=
infixr 1 =<<, <=<, >=>

{- |
> When providing a new instance, you should ensure it satisfies the one law:
> * Interchange: t >>= f = join (f <$> t)
-}

class Covariant t => Bindable t where
        {-# MINIMAL (>>=) #-}
        -- | Infix and flipped version of 'bind', the dual of '=>>'
        (>>=) :: t a -> (a -> t b) -> t b

        -- | Flipped version of '>>=', the dual of '<<='
        (=<<) :: (a -> t b) -> t a -> t b
        (=<<) = (%) (>>=)
        -- | Prefix and flipped version of '>>=', the dual of 'extend'
        bind :: (a -> t b) -> t a -> t b
        bind f t = t >>= f
        -- | Merge effects/contexts, the dual of 'duplicate'
        join :: t :. t := a -> t a
        join t = t >>= identity
        -- | Left-to-right Kleisli composition
        (>=>) :: (a -> t b) -> (b -> t c) -> (a -> t c)
        f >=> g = \x -> f x >>= g
        -- | Right-to-left Kleisli composition
        (<=<) :: (b -> t c) -> (a -> t b) -> (a -> t c)
        (<=<) = (%) (>=>)

instance Bindable ((->) e) where
        f >>= g = \x -> g (f x) x