Class 08: Conditionals

Held Friday, February 2, 2001

Summary

Today we begin to learn how to tell Scheme to make decisions. The procedures used to make decisions are called conditionals.

Due

• HW1: Web Pages

Notes

• No readings for the weekend! Monday is a catch-up day in which we'll work on the lab and discuss some of the more confusing problems.
  • I'll try to leave most of the refletion for Monday.
  • You should still try to work on the labs (at least a little) over the weekend.
• Be sure to make fun of Grinnell seniors for their inability to count.
  • The 100 days party is 107 days before graduation.
  • Only 1 in 7 years can the 100 days party be precisely 100 days before graduation. This year was one of them, and they blew it!
• Are there questions on the reading on Boolean values or the reading on conditional evaluation?
• Since Scheme ignores whitespace, you have a lot of freedom in how you format your code. Please please please try to format your code so that it's readable (no long lines, indent like DrScheme tells you to, ...).
• I've received homework 1 from many of you. If you'd like to check out what your colleagues did, here are some URLs:
  • http://www.cs.grinnell.edu/~schriebe/hub.html (Makinen, Martin, and Schrieber): Reviews of introductory computer science courses (and how easy it is to find info on the courses at various institutions).
  • http://www.cs.grinnell.edu/~walkerxh/hmwk1.html (Eilert, Heinz, Walker): Reflections on starting CS.
  • http://www.cs.grinnell.edu/~nusswarr/hw1/ (DeVilder, Gamboa, and Nuss-Warren): Basic programming strategies.
  • http://www.cs.grinnell.edu/~waymouth/website/index.html (Kase and Waymouth): Scheme commands.
  • http://www.math.grin.edu/~farrow/index2.html (Farrow and Hodgman): An introduction to Scheme.
  • http://www.math.grinnell.edu/~hernanda/index.html (Hernández and Ipatova): Exploring Scheme and CS.
• I'll set up a page with links to these sites (and my comments on the sites, unless anyone objects).

Overview

• A problem: Turning numbers into letters.
  • In English
  • In conditional-less Scheme
• Making life easier: Conditionals

A Problem

• Suppose that for fairness's sake, I'd like a program that converts numeric grades to letter grades.
• We'll look at two related grading schemes.
  • 94-100: A, 90-93: B, 87-89: B+, 84-86: B, ...
  • 10:A+ 9:A, 8:A-, 7:B+, 6:B, 5:B-, 4:C+ 3:C 2:C- 1:D 0:F
• How might you explain to someone how to turn a number into a grade?
• In either schema, can you write a procedure that turns a number into a grade, using only the Scheme you already know?

First Solution: Use if

• As you may have noted from your narrative, we are often tempted to describe the procedure in terms of the word if. For example, if the grade is at least 94, then give the student an A, otherwise, if the grade is between 90 and 93, ...
• In Scheme, you can write such expressions as

  (if condition 
      success-expression 
      failure-expression)
  

• Note that if does not behave according to Marie's evaluation pattern (in which all the arguments to a procedure are computed before the procedure is applied).
  • In particular, only one of the success-expression and failure-expression is computed.
  • Given the Scheme that you know right now, the only effect is on efficiency.
  • Later, you'll see that this decision affects other things, too.
• For example

  (if (>= grade 94) 'A 'F)
  

• We can nest these conditions.

  (if (>= grade 94) 
      'A
      (if (<= 90 grade 93)
          'Aminus
          (if (<= 87 grade 90)
              ...)))
  

Another Solution

• As you may have noticed, the code is somewhat hard to read (and awfully indented). Another alternative is to use Scheme's cond, which more closely resembles a table.
• Here's what a cond expression looks like

  (cond 
    ((condition1) exp1)
    ((condition2) exp2)
    ((condition3) exp3)
    ...
    (else default-exp))
  

• In this case, the conditions are evaluted one-by-one until one holds true. The value of the corresponding expression is the then returned.
• For our problem, this format seems particularly appropriate.

  (cond
    ((>= grade 94) 'A)
    ((<= 90 grade 93) 'Aminus)
    ...)