What is tail recursion?

Question

Whilst starting to learn lisp, I\'ve come across the term tail-recursive. What does it mean exactly?

Answer 1

Instead of explaining it with words, here's an example. This is a Scheme version of the factorial function:

(define (factorial x)
  (if (= x 0) 1
      (* x (factorial (- x 1)))))

Here is a version of factorial that is tail-recursive:

(define factorial
  (letrec ((fact (lambda (x accum)
                   (if (= x 0) accum
                       (fact (- x 1) (* accum x))))))
    (lambda (x)
      (fact x 1))))

You will notice in the first version that the recursive call to fact is fed into the multiplication expression, and therefore the state has to be saved on the stack when making the recursive call. In the tail-recursive version there is no other S-expression waiting for the value of the recursive call, and since there is no further work to do, the state doesn't have to be saved on the stack. As a rule, Scheme tail-recursive functions use constant stack space.