Class 15: Recursion with Lists

Held Tuesday, September 24, 2002

Summary

Today we investigate recursion over lists with a number of experiments.

Assignments

• Read Recursion with Natural Numbers.

Notes:

• Are there any final questions on homework 3?
• Any food choices other than pop-tarts for tomorrow?
• I'm still trying to find time to grade homework 2.
• Yes, I plan to have today's lab take two days.

Overview

• Reflections on Recursion
• Lab: Repetition with Recursion

Reflection

• I find it useful to think about the pattern one uses to design certain kinds of procedures.
• Here's the pattern of a typical recursive procedure:

  (define proc
    (lambda (val)
      (if (base-case-test)
          (base-case val)
          (combine (partof val)
                   (proc (update val))))))
  

• When the value you're working with is a list and your base case is the null list, the form is somewhat simpler:

  (define proc
    (lambda (lst)
      (if (null? lst)
          null-case
          (combine (onestep (car val))
                   (proc (cdr val))))))
  

• You may even find that there are some boolean procedures that don't even need an if. For example, here's one implementation of member that works on the principle that val is a member of lst if the list is not empty and val is the first element of lst or val is a member of the remainder of lst.

  (define member?
    (lambda (val lst)
      (and (not (null? lst))
           (or (equal? val (car lst))
               (member? val (cdr lst))))))
  

Lab

• Start working on the lab.
• Depending on how things go today, we may continue it tomorrow.