module Pandora.Pattern.Functor.Bindable where

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

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

{- |
> When providing a new instance, you should ensure it satisfies :
> * 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
	a -> t b
f =<< t a
x = t a
x t a -> (a -> t b) -> t b
forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b
>>= a -> t b
f
	-- | Prefix and flipped version of '>>=', the dual of 'extend'
	bind :: (a -> t b) -> t a -> t b
	bind a -> t b
f t a
t = t a
t t a -> (a -> t b) -> t b
forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b
>>= a -> t b
f
	-- | Merge effects/contexts, the dual of 'duplicate'
	join :: t :. t := a -> t a
	join (t :. t) := a
t = (t :. t) := a
t ((t :. t) := a) -> (t a -> t a) -> t a
forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b
>>= \t a
x -> t a
x
	-- | Left-to-right Kleisli composition
	(>=>) :: (a -> t b) -> (b -> t c) -> (a -> t c)
	a -> t b
f >=> b -> t c
g = \a
x -> a -> t b
f a
x t b -> (b -> t c) -> t c
forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b
>>= b -> t c
g
	-- | Right-to-left Kleisli composition
	(<=<) :: (b -> t c) -> (a -> t b) -> (a -> t c)
	b -> t c
g <=< a -> t b
f  = a -> t b
f (a -> t b) -> (b -> t c) -> a -> t c
forall (t :: * -> *) a b c.
Bindable t =>
(a -> t b) -> (b -> t c) -> a -> t c
>=> b -> t c
g

	($>>=) :: Covariant u => u :. t := a -> (a -> t b) -> u :. t := b
	(u :. t) := a
x $>>= a -> t b
f = (t a -> (a -> t b) -> t b
forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b
>>= a -> t b
f) (t a -> t b) -> ((u :. t) := a) -> (u :. t) := b
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> (u :. t) := a
x