module Pandora.Pattern.Functor.Covariant (Covariant (..)) where
import Pandora.Core.Functor (type (:.:), type (><))
import Pandora.Core.Morphism (fix, (.), ($), (!), (?))
infixl 4 <$>, <$, $>
class Covariant (t :: * -> *) where
{-# MINIMAL (<$>) #-}
(<$>) :: (a -> b) -> t a -> t b
comap :: (a -> b) -> t a -> t b
comap f x = f <$> x
(<$) :: a -> t b -> t a
(<$) = comap . (!)
($>) :: t a -> b -> t b
($>) = (?) (<$)
void :: t a -> t ()
void x = () <$ x
loeb :: t (t a -> a) -> t a
loeb tt = fix $ \f -> ($ f) <$> tt
(<&>) :: t a -> (a -> b) -> t b
x <&> f = f <$> x
(<$$>) :: Covariant u => (a -> b) -> t :.: u >< a -> t :.: u >< b
(<$$>) = (<$>) . (<$>)
(<$$$>) :: (Covariant u, Covariant v)
=> (a -> b) -> t :.: u :.: v >< a -> t :.: u :.: v >< b
(<$$$>) = (<$>) . (<$>) . (<$>)
(<$$$$>) :: (Covariant u, Covariant v, Covariant w)
=> (a -> b) -> t :.: u :.: v :.: w >< a -> t :.: u :.: v :.: w >< b
(<$$$$>) = (<$>) . (<$>) . (<$>) . (<$>)
(<&&>) :: Covariant u => t :.: u >< a -> (a -> b) -> t :.: u >< b
x <&&> f = f <$$> x
(<&&&>) :: (Covariant u, Covariant v)
=> t :.: u :.: v >< a -> (a -> b) -> t :.: u :.: v >< b
x <&&&> f = f <$$$> x
(<&&&&>) :: (Covariant u, Covariant v, Covariant w)
=> t :.: u :.: v :.: w >< a -> (a -> b) -> t :.: u :.: v :.: w >< b
x <&&&&> f = f <$$$$> x
instance Covariant ((->) a) where
(<$>) = (.)