On Friday 15 September 2006 12:45, David House wrote:
On 15/09/06, Haihua Lin <HaihuaLin@163.com> wrote:
Is there a way to define it in Haskell?
Note that the function 'fix' (find the fixpoint of a function) already exists in Haskell, and is equivalent to the Y combinator.
It's interesting that most (all?) fixed-point combinators don't typecheck. The Y combinator, and by extension recursion in general, has to be added as a constant to the language.
This actually isn't true. You can define a direct fixed point combinator without relying on nominal recursion in Haskell, but it requires you to define a helper newtype. Don't run this in GHC because it will diverge. Hugs works, however. newtype Mu a = Roll (Mu a -> (a -> a)) unroll (Roll x) = x fix :: (a -> a) -> a -> a fix = \f -> (\x z -> f ((unroll x) x z)) (Roll (\x z -> f ((unroll x) x z))) facF :: (Int -> Int) -> Int -> Int facF f x | x <= 0 = 1 | otherwise = x * (f (x-1)) fac :: Int -> Int fac = fix facF undefined main = print $ fac 5 Rob Dockins Talk softly and drive a Sherman tank. Laugh hard, it's a long way to the bank. -- TMBG