Proposal: Add Compositor class as superclass of Arrow

[Conal Elliott]

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.html


On 10/13/07, Ashley Yakeley <ashley at semantic.org> wrote:
>
> 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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