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