module Pandora.Pattern.Functor.Applicative (Applicative (..)) where
import Pandora.Core.Functor (type (:.:), type (><))
import Pandora.Core.Morphism (identity)
import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$)))
infixl 4 <*>, <*, *>
class Covariant t => Applicative t where
{-# MINIMAL (<*>) #-}
(<*>) :: t (a -> b) -> t a -> t b
apply :: t (a -> b) -> t a -> t b
apply f x = f <*> x
(*>) :: t a -> t b -> t b
x *> y = (identity <$ x) <*> y
(<*) :: t a -> t b -> t a
x <* y = y *> x
forever :: t a -> t b
forever x = x *> forever x
(<**>) :: Applicative u => t :.: u >< (a -> b) -> t :.: u >< a -> t :.: u >< b
f <**> x = (<*>) <$> f <*> x
(<***>) :: (Applicative u, Applicative v) => t :.: u :.: v >< (a -> b)
-> t :.: u :.: v >< a -> t :.: u :.: v >< b
f <***> x = (<**>) <$> f <*> x
(<****>) :: (Applicative u, Applicative v, Applicative w)
=> t :.: u :.: v :.: w >< (a -> b)
-> t :.: u :.: v :.: w >< a
-> t :.: u :.: v :.: w >< b
f <****> x = (<***>) <$> f <*> x