Class 16: More Recursion with Lists

Held Friday, February 16, 2001

Summary

Today we continue our exploration of recursion over lists through experimentation and reflection.

Due

• Homework 2: A Simple CGI Story.

Assignments

• Read Recursion with Natural Numbers.
• Homework 3: A Simple Database CGI.

Notes

• On the days when homeworks are due, I get a lot of email whose title is simply "Homework" or "Homework 2" or whatever. I file those away until I'm ready to grade. If you need help on a homework, please title your message Help on Homework or something similar.
• Many of you clearly did not finish HW2 (or at least didn't get it working).
  • You need to start earlier.
  • You may have an extension until Monday.
  • However, you do still have other work to do for the course.
• I'll do my best to get HW2 graded over the weekend. I again plan to post my comments publically.
• You have two assignments for next Friday, a lab writeup and a homework.
• Some people were confused about the take home: I'm distributing it next Friday.

Overview

• Recursively-defined types
• Squaring a list of values
• Lab: Repetition with Recursion
• Reflection

Recursively Defined Data

• You may not have gotten this idea from the readings, but we define more than procedures recursively: We also define some data recursively.
• Lists: A list is either
  • the empty list (base case)
  • the cons of a value and a list (recursive case)
• Natural numbers: A natural number is either
  • the value 0 (base case)
  • one plus a natural number
• ...

Squaring Values

• Let's talk together about the problem of squaring all the values in a list.
  • My one-on-one discussions have suggested some ways to look at the problem that may help others of you who had difficulties.
• Here's the problem: We need to square every element in a list and create a new list of those squares.
• Remember that the basic point of recursion is to
• break up the problem into a small subproblem and a big subproblem (but still smaller than the original problem),
• solve the small problem,
• assume you can solve the big subproblem
• Let's begin with the recursive case.
  • Suppose you know how to create a list containing the square of every element but the first.
  • How can you use that result to create a list containing the square of every element?
• Now let's consider the base case. For recursion over lists, the empty list, the typical base case involves an empty list or the singleton list.
  • What is the result of squaring every value in the empty list?
  • It may help to think about the kind of valur our procedure is supposed to return (is it a number, a symbol, a string, a list, or something else).

Reflection

Patterns

• Let's try to identify some patterns of recursion over lists.
  • That is, the general structure of kinds of Scheme procedures that work on lists.
• Here's one category of recursion that we did a few times: apply some operation to every element of a list.
• How do we express the general form of that category?
• What other kinds of things do you do to lists?
• What is the general form for those things?

Problems

• What things are likely to be difficult or wrong in one of your recursive procedures?
• I see many people having trouble with the base case. It may help to think about what kind of thing the procedure should return.
• I know that you sometimes write procedures that run forever (I do, too; I wrote one yesterday). Make sure that when you do the recursive call, you're using something closer to the base case.