Fundamentals of Computer Science I: Media Computing (CS151.01 2008S)

Laboratory: Starting Scheme

Summary: In this laboratory, you will begin to type Scheme expressions, using DrScheme. Scheme is the language in which we will express many of our algorithms this semester, and DrScheme is the environment in which we will write those.


Many of the fundamental ideas of computer science are best learned by reading, writing, and executing small computer programs that illustrate them. One of our most important tools for this course, therefore, is a program-development environment, a computer program designed specifically to make it easier to read, write, and execute other computer programs. In this class, we will often use a programming environment named DrScheme, along with the DrFu extensions. As you may recall from the introductory Linux laboratory, DrFu is a locally-developed environment that applies the interface of DrScheme to programming for GIMP.

In the previous lab, we examined GIMP. In this lab, we will look at the other two parts of the equation: the Scheme language and the DrScheme environment.


If you successfully completed the Linux laboratory, you should have an icon for DrFu at the bottom of your screen. (The icon is currently a hastily scrawled red lambda with a pen near the top, but that may change.) Click on that icon to start DrFu. A few GIMP windows should appear. A DrScheme opening screen should also appear. After you wait a little bit, you should see a DrScheme editing window appear. You will do most of your work in this window.


Exercise 1: Discovering DrScheme's Interactions Pane

Short Version

  • The lower text area is called the interactions pane.
  • You type Scheme commands there and DrScheme responds.
  • Type the first few examples from the reading.
    • (sqrt 144)
    • (+ 3 4)
    • (+ 3 (* 4 5))
    • (* (+ 3 4) 5)
    • (string-append "Hello" " " "Sam")

Detailed Version

As you may remember from the reading on DrScheme, the DrScheme window has two panes, one for definitions and one for interaction. Just as in the reading, we'll begin by considering the interactions panel.

The best way to understand the interactions pane is to use it. So, let's try the first few examples from the reading. Type each in the pane, hit return, and see if you get the same value.

> (sqrt 144)
> (+ 3 4)
> (+ 3 (* 4 5))
> (* (+ 3 4) 5)
> (string-append "Hello" " " "Sam")
"Hello Sam"

Exercise 2: Reflection: How Do You Know It's Correct?

Short Version

  • Try typing (sqrt 137641).
  • Reflect on how you know whether or not the answer is correct.

Detailed Version

Of course, the computer is using some algorithm to compute values for the expressions you enter. How do you know that the algorithm is correct? One reason that you might expect it to be correct is that DrScheme and GIMP are is widely-used programs (and ones that we've asked you to use). However, there are bugs even in widely-used programs. You may recall a controversy a few years back in which it was discovered that a common computer chip computed a few specific values incorrectly, and no one had noticed. More recently, it was found that the output routine in Microsoft Excel produced the wrong output for a few values. In addition, you know that some Grinnell students have hacked together DrFu, our bridge between DrScheme and the GIMP, so you might be a bit suspicious.

Each time you do a computation, particularly a computation for which you have designed the algorithm, you should consider how you might verify the result. (You need not verify every result, but you should have an idea of how you might do so.) When writing an algorithm, you can then also use the verification process to see if your algorithm is right.

Let's start with a relatively simple example. Suppose we ask you to ask DrScheme to compute the square root of 137641. You should be able to do so by entering an appropriate Scheme expression:

> (sqrt 137641)

Scheme will give you an answer. How can you test the correctness of this answer? What if you don't trust DrScheme's multiplication procedure? (Be prepared to answer this question for the class as a whole.)

Exercise 3: DrScheme's Definitions Pane

Short Version

  • The interactions pane is temporary. The top pane, called the definitions pane is more permanent.
  • When you click Run, the interactions pane is erased and the instructions in the definitions pane are executed.
  • Enter the definitions from the reading.
  • Ask DrScheme to compute the average and maximum grade.

Detailed Version

As you may recall from the reading, the upper text area in the DrScheme window, which is called the definitions pane, is used when you want to prepare a program “off-line”, that is, without immediately executing each step. Instead of processing what you type line by line, DrScheme waits for you to click on the button labelled Run (the second button from the right, in the row just below the menu bar) before starting to execute the program in the definitions pane. If you never click on that button, fine -- your program is never executed.

Warning: When you click on the Run button, the contents of the interactions pane are erased. The idea is that executing the program in the definitions pane may invalidate the results of previous interactions. Erasing the results that may now be inconsistent with the new definitions ensures that all visible interactions use the same vocabulary. This is actually a helpful feature of DrScheme, but it can take you by surprise the first time you see it happen. Just make sure that you have everything you need from the interactions pane before clicking on Run.

Let's try using the definitions pane. First, enter the following in that pane.

(define grade1 90)
(define grade2 67)
(define grade3 80)
(define grade4 85)
(define grade5 100)
(define grade6 91)

Next, try computing the average in the interactions pane.

  > (/ (+ grade1 grade2 grade3 grade4 grade5 grade6) 6)
  Error: eval: unbound variable: grade1

It is likely that you will get an error message, just as the example suggests. Why? (Please make sure you have an answer before going on.)

Next, click Run and try entering the expression again. (Remember, Esc+P will bring back the previous expression.)

:Note: we've formatted the code for the definitions pane differently than we've formatted the code for the interactions pane. We'll try to be consistent, so that you can better tell where instructions are to go.

Exercise 4: Definitions, Revisited

Let's try another definition. Define name as your name in quotation marks. For example,

(define name "Sam")

Click Run and then find the value of the following expression.

> (string-append "Hello " name)

Exercise 5: Saving to Files

Let's make sure that you can save and restore the work you do in the definitions pane.

  • Save your definitions as /home/username/Desktop/grades.scm. (Substitute your own username for username.)
  • Quit DrScheme and GIMP.
  • Restart DrFu.
  • In DrScheme, open /home/username/Desktop/grades.scm.
  • Click Run
  • In the interactions pane, enter the expressions from above
    • (/ (+ grade1 grade2 grade3 grade4 grade5 grade6) 6)
    • (string-append "Hello " name)

Exercise 6: Loading Definitions

Let's try using the definitions you created without having them open in the definitions pane.

  • Add a new grade, grade7, to grades.scm and save the file, but do not run it.
  • Quit DrScheme and GIMP.
  • Restart DrFu.
  • In the interactions pane of the new window, type grade7. You should get an error message, which tells you that grade7 is not yet defined.
  • In the interactions pane of the new window, type (load "/home/username/Desktop/grades.scm")
  • In the interactions pane, type grade7. You should now see a value.

In the future, we will be creating some .scm files that we change infrequently. Those files we will typically load, rather than open.

Exercise 7: A Library

Throughout the semester, you will find yourself defining a number of values (including algorithms, which Scheme considers values). So that you don't have to go back to lots of places to look for things you've done before, we suggest that you create a file, library.scm in which you enter values and other stuff that you'll need again and again.

Create that file, and give it two values, first-name, which should have the value of your first name, and last-name, which, should have the value of your last name.

For example,

(define first-name "Sam")
(define last-name "Rebelsky")

Exercise 8. Other Notations

As you've learned, Scheme expects you to use parentheses and prefix notation when writing expressions. What happens if you use more traditional mathematical notation? Let's explore that question.

Type each of the following expressions at the Scheme prompt and see what reaction you get.

  • (2 + 3)
  • 7 * 9
  • sqrt(49)

You may wish to read the notes on this problem for an explanation of the results that you get.

Exercise 9: Showing Images

So far, it's been hard to tell that DrScheme is associated at all with GIMP. However, you can use DrFu to control GIMP in a variety of ways. We'll start with a simple one. We will load an image and then show that image. The procedure (image-load file-name) loads an image from a file and returns an integer that your programs can use to identify the image. The procedure (image-show image-id) shows that image.

a. In the interactions pane, write a Scheme expression to load the image "/home/rebelsky/glimmer/samples/rebelsky-stalkernet.jpg". When you run that expression, you should see a number. Make a note of that number.

b. In the interactions pane, write a Scheme expression to show the image.

c. Save your StalkerNet picture (or a friend's StalkerNet picture) to your desktop. If you need help doing so, ask your instructor or class mentor.

d. In the interactions pane, write a Scheme expression to load that image. The full name of the image will be something like "/home/yourusername/Desktop/nameoffile.jpg".

e. Write a Scheme expression that tells DrFu to show the image.

f. As you may have observed, it can be a bit of a pain to have to type in the full path of a file. Typically, we write definitions to avoid retyping.

In your library.scm, use define to give the name prof-picture to the file containing my StalkerNet photo and the name my-photo to your StalkerNet photo.

For Those with Extra Time

Extra 1: Definitions, Revisited

As you observed in the primary exercises for this laboratory, you can use the definitions pane to name values that you expect to use again (or that you simply find it more convenient to refer to with a mnemonic). So far, all we've named is simple values. However, you can also name the results of expressions.

a. In the definitions pane, write a definition that assigns the name seconds-per-minute to the value 60.

b. In the definitions pane, write a definition that assigns the name minutes-per-hour to the value 60.

c. In the definitions pane, write a definition that assigns the name hours-per-day to the value 24.

d. In the definitions pane, write a definition that assigns the name seconds-per-day to the product of those three values. Note that you should use the following expression to express that product.

(* seconds-per-minute minutes-per-hour hours-per-day)

e. Run your definitions and confirm in the interactions pane that seconds-per-day is defined correctly.

f. Add these four definitions to the library.scm file you created earlier.

Extra 2: Grading

Let's play for a bit with how one might use DrScheme to compute grades. (We teach you this, in part, so that you can figure out your estimated grade in this class and others.) Let's define five names, grade1 through grade5 that potentially represent grades on five homework assignments.

(define grade1 95)
(define grade2 93)
(define grade3 105)
(define grade4 30)
(define grade5 80)

Looking at those grades, you might observe that the student seems to have spent a bit of extra work on the third assignment, but that the extra work so disrupted the student's life that the next assignment was a disaster. (You may certainly analyze the grades differently.)

a. Write a definition that assigns the name average-grade to the average of the grades.

Many faculty members discard these “outliers”, with a grading policy of “I take the average of your grades after dropping the highest grade and the lowest grade”.

b. Write a definition that assigns the name highest-grade to a computed highest grade. (That is, highest-grade should remain correct, even if I change the values associated with grade1 through grade5.) In writing this definition, you may find the max procedure useful.

c. Write a definition that assigns the name lowest-grade to a computed lowest grade. You may find the min procedure useful.

d. Write a definition that assigns the name modified-average to the modified average grade (that is, the grade that results from dropping the lowest and highest grades and then averaging the result).

Notes on the Problems

Notes on Exercise 8: Other Notations

> (2 + 3)
Error: illegal function 

When the Scheme interpreter sees the left parenthesis at the beginning of the expression (2 + 3), it expects the expression to be a procedure call, and it expects the procedure to be identified right after the left parenthesis. But 2 does not identify a procedure; it stands for a number. (A “procedure application” is the same thing as a procedure call.)

> 7 * 9

In the absence of parentheses, the Scheme interpreter sees 7 * 9 as three separate and unrelated expressions -- the numeral 7; *, a name for the primitive multiplication procedure; and 9, another numeral. It interprets each of these as a command to evaluate an expression: “Compute the value of the numeral 7! Find out what the name * stands for! Compute the value of the numeral 9!” So it performs the first of these commands and displays 7; then it carries out the second command, reporting that * is the name of the primitive procedure *; and finally it carries out the third command and displays the result, 9. This behavior is confusing, but it's strictly logical if you look at it from the computer's point of view (remembering, of course, that the computer has absolutely no common sense).

> sqrt(49)
Error: illegal function 

As in the preceding case, DrScheme sees sqrt(49) as two separate commands: sqrt means “Find out what sqrt is!” and (49) means “Call the procedure 49, with no arguments!” DrScheme responds to the first command by reporting that sqrt is the primitive procedure for computing square roots and to the second by pointing out that the number 49 is not a procedure.

Return to the problem.

Creative Commons License

Samuel A. Rebelsky,

Copyright (c) 2007-8 Janet Davis, Matthew Kluber, and Samuel A. Rebelsky. (Selected materials copyright by John David Stone and Henry Walker and used by permission.)

This material is based upon work partially supported by the National Science Foundation under Grant No. CCLI-0633090. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. To view a copy of this license, visit or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.