3 Apr
2002
3 Apr
'02
1:43 a.m.
I've been watching the discussion of the fixed point function with interest. In Antony's example,
factGen = \f -> \n -> if n==0 then 1 else n * f (n-1)
The fixed point of factGen is clearly n! because 0! = 1 and n! = n * (n-1) * (n-2) * .. * 1 = n * ( (n-1)! ) = n * f (n-1) so the factGen transformation simply maps the factorial function back onto itself. What I would like to know is how the 'fix' function could be used to find the fixed point of a function like ( \n -> 2*n ). If it isn't possible, can someone explain the crucial difference between n! and (\n -> 2*n ) which allows n factorial to be found via the fix point method and not zero. Tom