[Haskell-beginners] Re: (->) instance for ArrowApply and laziness

[aditya siram]

Thank you. This was incredibly helpful.
-deech

On 4/2/10, Heinrich Apfelmus <apfelmus at quantentunnel.de> wrote:
> aditya siram wrote:
>> Hi all,
>> Could someone help me understand how the (->) instance for ArrowApply
>> works? It looks like this:
>>> instance ArrowLoop (->) where
>>>         loop f b = let (c,d) = f (b,d) in c
>>
>> This models recursion for arrows and I need help understanding how it
>> does that. I have a strong feeling it has to do with the magic value
>> 'd'. I've read the Patterson tutorial but I still don't grok it.
>
> It's similar to how  fix  works:
>
>   http://en.wikibooks.org/wiki/Haskell/Fix_and_recursion
>
> Here various definitions of the factorial as example:
>
> 1) Definition
>
>     factorial n = product [1..n]
>
> 2) Recursive definition
>
>     factorial 0 = 1
>     factorial n = n * factorial (n-1)
>
> 3) Recursion with the fixed point combinator  fix
>
>     fix f = let knot = f knot in knot
>
>     factorial = fix fac
>         where
>         fac f 0 = 1
>         fac f n = n * f (n-1)
>
> 4) Recursion with  loop
>
>     factorial = loop helper
>         where
>         fac f 0 = 1
>         fac f n = n * f (n-1)
>
>         helper (n,knot) = (knot n, fac knot)
>
>
> Regards,
> Heinrich Apfelmus
>
> --
> http://apfelmus.nfshost.com
>
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