On Tue, 18 Nov 2008, Ryan Ingram wrote:
How does this work?
fac n = case n of 0 -> 1 _ -> n * fac (n-1)
ghci> :t fac fac :: (Num t) => t -> t
The first line of "fac" pattern matches on 0. So how does this work over any value of the Num typeclass? I know that the "1" on the rhs of fac are replaced with (fromInteger 1), but what about numeric literals in patterns? Does it turn into a call to (==)?
As far as I know, yes. It is even possible to trap into an error on pattern matching this way if fromInteger generates an 'undefined'.
Should whatever technique is used be extended to other typeclasses too?
It is unusual to do pattern matching on fractions, you mostly need it for recursion on natural numbers. Thus I think the cleanest solution would be to treat natural numbers like strict Peano numbers data PeanoStrict = Zero | Succ !PeanoStrict but with an efficient implementation using GMP integers, maybe using 'views', if they were part of Haskell language. Then you can implement: fac :: Integer -> Integer fac Zero = 1 fac n1@(Succ n) = n1 * fac n I would then give up pattern matching on any numeric type.