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

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