functors

2 files changed, 35 insertions, 0 deletions

diff --git a/functor/h4.hs b/functor/h4.hs
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+++ b/functor/h4.hs
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+-- Haskell only has covariant functors of the following form:
+--  class Functor f where
+--      fmap:: (a->b) -> f a -> f b
+-- Contra/Co-variant : 
+--  http://www.reddit.com/r/haskell/comments/1cht4v/what_does_coalgebra_mean_in_the_context_of/c9gzulr
+
+class Contravariant f where
+    contramap :: (a->b) -> f b -> f a
+
+data Cont a = Cont (a -> Int)
+
+instance Contravariant Cont where
+    contramap f (Cont x) = Cont (x.f)
+
+-- The following however is covariant
+data H t = H1 t | H2 ((t -> Int) -> Int)
+
+instance Functor H where
+    fmap f (H1 x) = H1 (f x)
+    fmap f (H2 g) = H2 (\h -> g (h . f))
+
diff --git a/functor/h5.hs b/functor/h5.hs
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+++ b/functor/h5.hs
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+-- The composition of two Functors is also a Functor.
+
+import Data.Functor
+
+newtype Comp f g a = Comp { unComp :: f (g a) }
+
+compose :: f (g a) -> Comp f g a
+compose = Comp
+
+decompose :: Comp f g a -> f (g a)
+decompose = unComp
+
+instance (Functor f, Functor g) => Functor (Comp f g) where
+  fmap f = compose . fmap (fmap f) . decompose