http://hackage.haskell.org/trac/ghc/ticket/1773 (darcs patch attached to ticket) The Compositor class has two members: class Compositor comp where identity :: comp a a (>>>) :: comp a b -> comp b c -> comp a c with the obvious monoid. Since all Arrows are Compositors, make Compositor a superclass of Arrow. A number of useful types are Compositors but not Arrows: 1. Bijections data Bijection a b = MkBijection (a -> b) (b -> a) 2. Codecs, i.e. encoder/decoder pairs such as charset converters data Codec base derived = MkCodec { encode :: derived -> base, decode :: base -> Maybe derived -- or other Monad } utf8 :: Codec [Word8] String xml :: Codec String XML 3. Lenses These make updatable sections of data structures. data Lens s t = MkLens { lensGet :: s -> t, lensPutback :: t -> s -> s } See http://www.cis.upenn.edu/~bcpierce/papers/lenses-etapsslides.pdf 4. Reified proofs of type identity These are useful if you use GADTs and type-witnesses a lot. newtype SameType a a' = MkSameType (forall f. f a -> f a') Proposal period: two weeks, until 10-27