[Haskell-cafe] Re: Arrow without `>>>'

[Peter Gavin]

Valery V. Vorotyntsev wrote:
> On 1/23/08, David Menendez <dave at zednenem.com> wrote:
>> On Jan 23, 2008 12:20 PM, Valery V. Vorotyntsev <valery.vv at gmail.com> wrote:
>>> I've built GHC from darcs, and...
>>> Could anybody tell me, what's the purpose of Arrow[1] not having `>>>'
>>> method?
>> It's derived from the Category superclass.
> 
> Yes, it is.
> 
> The right question: how to build `arrows' in such circumstances?
> 
> Here go 2 changes I made to `CoState.hs' accompanied by the
> error messages. :) Unfortunately, I'm not arrow-capable enough to
> make _proper_ changes to the code and satisfy GHC... Any help?
> 

Well, without looking at your code, generally all you have to do is

1) move the definition of (>>>) to Category and rename it to (.) after flipping 
the arguments.
2) define the id method of Category which is just (arr id) or returnA.

So essentially

instance Arrow (Foo a) where
   a >>> b = compose a b
   pure f = ...
   first a = ...

becomes

instance Arrow (Foo a) where
   pure f = ...
   first a = ...

instance Category (Foo a) where
   id = arr id
   a . b = compose b a

That's it.  It's too bad there's no way to do this automatically in the 
libraries, but it could be noted in the API docs.

Pete

> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Change #1:
> 
> $ darcs w Control/Arrow/Transformer/CoState.hs
> What's new in "Control/Arrow/Transformer/CoState.hs":
> 
> {
> hunk ./Control/Arrow/Transformer/CoState.hs 23
> +import Control.Category ((>>>))
> }
> 
> --------------------------------------------------
> Error #1:
> 
> Control/Arrow/Transformer/CoState.hs:29:7:
>     `>>>' is not a (visible) method of class `Arrow'
> Failed, modules loaded: Control.Arrow.Operations.
> 
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Change #2:
> 
> $ darcs diff -u Control/Arrow/Transformer/CoState.hs
> --- old-arrows/Control/Arrow/Transformer/CoState.hs     2008-01-24
> 14:54:29.852296559 +0200
> +++ new-arrows/Control/Arrow/Transformer/CoState.hs     2008-01-24
> 14:54:29.852296559 +0200
> @@ -20,12 +20,13 @@
> 
>  import Control.Arrow
>  import Control.Arrow.Operations
> +import Control.Category ((>>>))
> 
>   newtype CoStateArrow s a b c = CST (a (s -> b) (s -> c))
> 
>   instance Arrow a => Arrow (CoStateArrow s a) where
>         arr f = CST (arr (f .))
> -       CST f >>> CST g = CST (f >>> g)
> +--     CST f >>> CST g = CST (f >>> g)
>         first (CST f) = CST (arr unzipMap >>> first f >>> arr zipMap)
> 
>   zipMap :: (s -> a, s -> b) -> (s -> (a,b))
> 
> --------------------------------------------------
> Error#2:
> 
> Control/Arrow/Transformer/CoState.hs:27:0:
>     Could not deduce (Control.Category.Category (CoStateArrow s a))
>       from the context (Arrow a)
>       arising from the superclasses of an instance declaration
>                    at Control/Arrow/Transformer/CoState.hs:27:0
>     Possible fix:
>       add (Control.Category.Category
>              (CoStateArrow s a)) to the context of
>         the instance declaration
>       or add an instance declaration for
>          (Control.Category.Category (CoStateArrow s a))
>     In the instance declaration for `Arrow (CoStateArrow s a)'
> Failed, modules loaded: Control.Arrow.Operations.
> 
> Thank you.
>