module Pandora.Pattern.Functor.Contravariant (Contravariant (..)) where
import Pandora.Core.Functor (type (:.), type (:=))
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
(>&<) :: t b -> (a -> b) -> t a
x >&< f = f >$< x
(>$$<) :: Contravariant u => (a -> b) -> t :. u := a -> t :. u := b
(>$$<) = (>$<) . (>$<)
(>$$$<) :: (Contravariant u, Contravariant v)
=> (a -> b) -> t :. u :. v := b -> t :. u :. v := a
(>$$$<) = (>$<) . (>$<) . (>$<)
(>$$$$<) :: (Contravariant u, Contravariant v, Contravariant w)
=> (a -> b) -> t :. u :. v :. w := a -> t :. u :. v :. w := b
(>$$$$<) = (>$<) . (>$<) . (>$<) . (>$<)
(>&&<) :: Contravariant u => t :. u := a -> (a -> b) -> t :. u := b
x >&&< f = f >$$< x
(>&&&<) :: (Contravariant u, Contravariant v)
=> t :. u :. v := b -> (a -> b) -> t :. u :. v := a
x >&&&< f = f >$$$< x
(>&&&&<) :: (Contravariant u, Contravariant v, Contravariant w)
=> t :. u :. v :. w := a -> (a -> b) -> t :. u :. v :. w := b
x >&&&&< f = f >$$$$< x