Homework 8: Tail Recursion

Assigned: Friday, November 15, 2002
Due: Wednesday, November 20, 2002
No extensions!

Summary: In this assignment, you will consider a few of the more problematic issues in tail recursion.

Purposes: To give you more experience working with tail recursion and higher-order procedures.

Collaboration: Although you may certainly discuss this assignment with anyone, you should each turn in your own solution.

Assignment:

1. Consider the efficient exponent procedure we wrote in class. Rewrite that procedure to be tail recursive.

2. Rewrite insert-right to be tail recursive.

3. Here's a non-tail-recursive version of append.

(define append
  (lambda (list-one list-two)
    (if (null? list-one) list-two
        (cons (car list-one)
              (append (cdr list-one) list-two)))))

a. Write your own tail-recursive version.

b. Determine experimentally which of the three versions (built-in, given above, tail-recursive) is fastest.