On Wed, Oct 17, 2007 at 03:13:23AM +0100, Lennart Augustsson wrote:
If naturals have a perfectly reasonable subtraction then they also have a perfectly reasonable negate; the default is 0-x.
(Oh, subtraction wasn't THAT reasonable, you say. :) )
I suppose I was overextending the use of 'perfectly reasonable' here. :) tangent: if anyone is interested, Although I bet this has been implemented a hundred times over, I have attached my lazy naturals module below just for larks. It is quite efficient as such things go and very lazy. for instance (genericLength xs > 5) will only evaluate up to the 5th element of the list before returning a result. and ((1 `div` 0) > 17) is true, not bottom. Anyone have any comments on my lazy multiplication algorithm? since each number is of the form (x + rx) (an integer, plus the lazy remainder) I just did the multiplicitive expansion (x + rx) * (y + ry) -> x*y + x*ry + y*rx + rx*ry then I simplify to (x + rx) * (y + ry) -> x*y + x*ry + rx*(y + ry) which saves a nice recursive call to * speeding thinsg up signifigantly. but is there a better way? since (+) is lazy, we can still get a good lazy result without evaluating the tails when multiplying... that is nice. also, what do you think n `mod` 0 should be? I can see arguments for it being 'n', 0, or Infinity depending on how you look at it.. hmm.. If anyone wants me to clean this up and package it as a real module, I would be happy to do so. sorry for the tangent. just one of those days. John -- John Meacham - ⑆repetae.net⑆john⑈