While we're at it, how about one or more classes in between
Category/Compositor and Arrow? One example is DeepArrow (see wiki page [1]
and haddock docs [2]). Sample instances: functions and transformers of
typed type representations, UIs, code, and pairs of same. I've currently
structured DeepArrow as a subclass of Arrow, but most of my instances do not
have arr. Any real arrow (including arr) is a DeepArrow (or almost), as the
haddock docs mention.
DeepArrow could benefit from suggestions (perhaps refactoring), and I would
appreciate such input. In any case, I imagine there's some rich, useful
structure between Category & Arrow, and now would be a great time to explore
it before settling on a new class hierarchy.
Cheers, - Conal
[1] http://haskell.org/haskellwiki/DeepArrow
[2]
http://darcs.haskell.org/packages/DeepArrow/doc/html/Control-Arrow-DeepArrow...
On 10/13/07, Ashley Yakeley
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
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