[Haskell-cafe] Stream processors as arrows

[Miguel Mitrofanov]

I'm trying to do Exercise 2.5.2 from John Hughes's "Programming with
Arrows". It asks to make the type SP defined as (notation is slightly
different)

> data SP a b = Inp (a -> SP a b) | Out b (SP a b)

an instance of Arrow, ArrowChoice and ArrowLoop.

Some parts of it are straightforward, e.g.

> arr f = fix $ \sp -> Inp $ \x -> Out (f x) sp

Some are a bit tricky; for "first" I ended up with code

> first = fix first'
>         where first' f sp = Inp $ \(x,z) -> let g = firstL x
>                                                 h = firstR z
>                                             in case sp of Inp _ -> (g . h) f sp
>                                                           Out _ _ -> (h . g) f sp
>               firstL x f (Inp fsp) = f $ fsp x
>               firstL x f sp = first' (firstL x f) sp
>               firstR z f (Out y sp) = Out (y,z) $ f sp
>               firstR z f sp = first' (firstR z f) sp

which is a bit funny.

But the real problem I don't know how to deal with is "loop". My first
attempt was somethig like this:

> loop (Out (y,z) sp) = Out y $ loop' z loop sp
>                       where loop' z f (Inp fsp) = Inp $ \x -> f $ fsp (x,z)
>                             loop' z f (Out (y,z') sp) = Out y $ loop' z' (loop' z f) sp

since I thought it's pointless to make a loop that don't do any
output. But then I ran into trouble:

*StreamProc> process (loop returnA) [1..10]
*** Exception: g:/StreamProc.hs:(26,4)-(28,90): Non-exhaustive patterns in function loop

So I realized that both arr and first are doing input first and output
second, and that causes this error.

I've tried to fix this with

> loop (Inp fsp) = Inp $ \x -> let Out (y,z) sp = fsp (x,z) in Out y $ loop sp

This works as desired:

*StreamProc> process (loop returnA) [1..10]
[1,2,3,4,5,6,7,8,9,10]

But it seems to solve the problem by shifting it one step away from
us. I'm not sure this is enough.

Any advice/suggestions?