In Scheme, how do you use lambda to create a recursive function?

Question

I\'m in a Scheme class and I was curious about writing a recursive function without using define. The main problem, of course, is that you cannot call a function within itse

Answer 1

The expression (lambda (x) (x x)) creates a function that, when evaluated with one argument (which must be a function), applies that function with itself as an argument.

Your given expression evaluates to a function that takes one numeric argument and returns the factorial of that argument. To try it:

(let ((factorial ((lambda (x) (x x))
                  (lambda (fact-gen)
                    (lambda (n)
                      (if (zero? n)
                          1
                          (* n ((fact-gen fact-gen) (sub1 n)))))))))
  (display (factorial 5)))

There are several layers in your example, it's worthwhile to work through step by step and carefully examine what each does.

Answer 2

Basically what you have is a form similar to the Y combinator. If you refactored out the factorial specific code so that any recursive function could be implemented, then the remaining code would be the Y combinator.

I have gone through these steps myself for better understanding.
https://gist.github.com/z5h/238891

If you don't like what I've written, just do some googleing for Y Combinator (the function).