Thank you. This was incredibly helpful.
-deech
On 4/2/10, Heinrich Apfelmus
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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