On Mon, May 3, 2010 at 10:13 PM, Ivan Miljenovic
<ivan.miljeno...@gmail.com> wrote:
> On 4 May 2010 13:30, Luke Palmer <lrpal...@gmail.com> wrote:
>> Here is a contrived example of what I am referring to:
>>
>> prefac f 0 = 1
>> prefac f n = n * f (n-1)
>>
>> fac = (\x -> x x) (\x -> prefac (x x))
>
> I can't work out how this works (or should work rather); is it meant
> to be using church numerals or something (assuming that they have been
> made an instance of Num so that - and * work)?
No they're just integers. fac is a beta expansion of fix prefac.
Obseve the magic:
(\x -> x x) (\x -> prefac (x x)) 2
(\x -> prefac (x x)) (\x -> prefac (x x)) 2
prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) 2
2 * ((\x -> prefac (x x)) (\x -> prefac (x x)) (2-1)
2 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) (2-1)
2 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) 1
2 * (1 * ((\x -> prefac (x x)) (\x -> prefac (x x))) (1-1))
2 * (1 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) (1-1))
2 * (1 * prefac ((\x -> prefac (x x)) (\x -> prefac (x x))) 0)
2 * (1 * 1)
2
Luke
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