module Pandora.Pattern.Functor.Invariant where {- | > When providing a new instance, you should ensure it satisfies: > Identity morphisms: invmap identity identity = identity > Interpreted of morphisms: invmap g j . invmap f h = invmap (g . f) (h . j) -} infixl 4 <$< class Invariant (t :: * -> *) where {-# MINIMAL (<$<) #-} (<$<) :: (a -> b) -> (b -> a) -> t a -> t b -- | Prefix version of '<$<' invmap :: (a -> b) -> (b -> a) -> t a -> t b invmap a -> b f b -> a g t a x = (a -> b f (a -> b) -> (b -> a) -> t a -> t b forall (t :: * -> *) a b. Invariant t => (a -> b) -> (b -> a) -> t a -> t b <$< b -> a g) t a x