module Pandora.Pattern.Functor.Contravariant (Contravariant (..)) where
import Pandora.Core.Morphism ((.), (!), (?))
infixl 4 >$<, $<, >$
class Contravariant (t :: * -> *) where
{-# MINIMAL (>$<) #-}
(>$<) :: (a -> b) -> t b -> t a
contramap :: (a -> b) -> t b -> t a
contramap f x = f >$< x
(>$) :: b -> t b -> t a
(>$) = contramap . (!)
($<) :: t b -> b -> t a
($<) = (?) (>$)
full :: t () -> t a
full x = () >$ x
(>$$$<) :: (Contravariant u, Contravariant v) => (a -> b) -> t (u (v b)) -> t (u (v a))
(>$$$<) = (>$<) . (>$<) . (>$<)