Fundamentals of Computer Science I: Media Computing (CS151.01 2008S)
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.
(+ 3 4)
(+ 3 (* 4 5))
(* (+ 3 4) 5)
(string-append "Hello" " " "Sam")
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.
(+ 3 4)
(+ 3 (* 4 5))
(* (+ 3 4) 5)
(string-append "Hello" " " "Sam")
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:
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.)
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 (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 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 button, the contents of the interactions pane are erased. .
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 Esc+P will bring back the previous expression.)and try entering the expression again. (Remember,
: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.
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)
Let's make sure that you can save and restore the work you do in the definitions pane.
/home/username/Desktop/grades.scm. (Substitute your own username for
(/ (+ grade1 grade2 grade3 grade4 grade5 grade6) 6)
(string-append "Hello " name)
Let's try using the definitions you created without having them open in the definitions pane.
grades.scmand save the file, but do not run it.
grade7. You should get an error message, which tells you that
grade7is not yet defined.
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.
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,
should have the value of your first name, and
which, should have the value of your last name.
(define first-name "Sam") (define last-name "Rebelsky")
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
You may wish to read the notes on this problem for an explanation of the results that you get.
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
( loads an image from a file
and returns an integer that your programs can use to identify
the image. The procedure
( shows that image.
a. In the interactions pane, write a Scheme expression to load the image
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
The full name of the image will be something like
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.
to give the name
prof-picture to the file containing my
StalkerNet photo and the name
my-photo to your StalkerNet
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
you created earlier.
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,
grade5 that potentially represent grades on five
(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
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
to a computed highest grade. (That is,
highest-grade should remain correct, even if I change the
values associated with
In writing this definition, you may find the
c. Write a definition that assigns the name
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).
(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
9 as three separate and unrelated expressions -- the numeral
*, a name for the primitive multiplication
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
So it performs the first of these commands and displays
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,
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).
<procedure>Error: illegal function
As in the preceding case, DrScheme sees
two separate commands:
sqrt means “Find out what
sqrt is!” and
(49) means “Call
49, with no arguments!” DrScheme
responds to the first command by reporting that
the primitive procedure for computing square roots and to the second
by pointing out that the number
49 is not a procedure.
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.
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