[Haskell-cafe] Computing sums

[Andrew Coppin]

Luke Palmer wrote:
> On Sat, Feb 20, 2010 at 3:30 AM, Andrew Coppin
> <andrewcoppin at btinternet.com> wrote:
>   
>> Have I just invented arrows?
>>     
>
> No... you have a data type which is *an* Arrow (probably/almost).

Well, OK, that's kind of what I meant. ;-)

> The
> pure implementation bugs me because of its use of undefined.  Might
> still be okay though.  I would be more comfortable if it could not
> output until it has *some* input;

Yes, this irritates me also.

> i.e.
>
> data Property' a b = forall s. Property' s (a -> s -> (b,s))
>   

Hmm. I hadn't thought of that. I will work though the consequences and 
see what happens...

> Anyway, for yours: try to implement (.) :: Property b c -> Property a
> b -> Property a c, and first :: Property a b -> Property (a,c) (b,c).
> Then you will have an arrow.
>   

(.) = flip (>==>)

first p = p >==< pure id

> This is a Causal Commutative Arrow, even, similar to the kinds of
> things that are done in Yampa.  It might be more recognizable as the
> non-recursive version of:
>
>   newtype Property a b = Property b (a -> Property a b)
>   

...OK, I'm lost...