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Let us try and repeat this approach in order to compute factorials:
This recurrence relationship can again readily be transformed into a Pico function:
In the above transcript, the function application fac(10) will result in 9 recursive applications, ending when n reaches 1. Backtracking from this level, the necessary arithmetic is performed to compute 10! = 3628800.
Trying this out for other values of the argument, we eventually run into trouble:
We must never forget that in the
physical world, somewhere in our tower of
REP-machines
there is a level at which we will encounter constraints on the values
that we use in our programs. In this case we violated a rule stating
that numbers cannot exceed the range [-1073741824,
1073741823].