This lab is also available in PDF.
Summary: In this laboratory, you will begin to type
Scheme expressions in DrFu. Scheme is the language in which we will
express many of our algorithms this semester, and DrFu is the environment
in which we will write those expressions.
Contents:
Introduction:
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 DrFu. As you may recall from the
introductory Linux laboratory, DrFu is a locally-developed environment
that applies the interface of DrScheme
to programming for The GIMP.
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 few minutes, you should see a DrScheme
editing window appear. You will do your primary work in this window.
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")
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As you may remember from the
reading on DrFu, 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)
12
> (+ 3 4)
7
> (+ 3 (* 4 5))
23
> (* (+ 3 4) 5)
35
> (string-append "Hello" "Sam")
HelloSam
Short Version
- Try typing
(sqrt 137641).
- Reflect on how you know whether or not the answer is correct.
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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 the GIMP are is widely-used programs (and ones that I'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. 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.)
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 DrFu to compute the average and maximum grade.
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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)
reference to undefined identifier: grade
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.)
Let's try another definition. Define name as your name in
quotation marks. For example,
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.
- Save your definitions as /home/username/Desktop/grades.sct.
- Quit DrScheme and The Gimp.
- Restart DrFu.
- Open /home/username/Desktop/grades.sct.
- Click <Run>
- In the interactions pane, enter the expressions from above
-
(/ (+ 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.
- Add a new grade,
grade7, to grades.sct and
save the file, but do not run it.
- Open a new DrScheme window by selecting
from the menu.
- 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.sct")
- In the interactions pane, type
grade7. You should now see a value.
In the future, we will be creating some .sct 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, I suggest that you create a file, library.sct
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")
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 * 9sqrt(49)
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 DrFu is associated at all with
the GIMP. However, you can use DrFu to control the 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 loads an
image and returns an integer that DrFu can use to reference the image.
The procedure image.show shows that image.
a. Tell DrFu to load the image "/home/rebelsky/glimmer/samples/rebelsky-stalkernet.jpg". When you do so, you should see a number. Make a note of that number.
b. Tell DrFu to show that image.
c. Save your StalkerNet picture (or a friend's StalkerNet picture) to your
desktop.
d. Tell DrFu to load that image. The full name of the image will be something like "/home/yourusername/Desktop/nameoffile.jpg".
e. Tell DrFu to show that image.
f. As you may have observed, it's a pain to have to type in the full path of a file. Typically, we write definitions to avoid retyping.
Use define to give the name sams-picture to my StalkerNet photo and the name my-photo to your StalkerNet photo.
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 without dropping the highest and lowest
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 weighted-average
to the weighed average grade (that is, the grade that results from dropping
the lowest and highest grades and then averaging the result).
As you observed in the DrScheme lab, 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.ss file
you created earlier.
When DrScheme 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.)
In the absence of parentheses, DrScheme 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).
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.
In the past, it has been possible to run DrScheme at home. It has
also been possible to run the GIMP at home. However, the GIMP is
currently undergoing revisions, and DrFu relies on some of those revisions.
Hence, for the first part of this semester, we ask that students come to
the CS wing to do the work for this class. We'll try to provide a
friendly environment for you to work.
Later in the semester, we may be able to provide you with a way to work
at home, but that project is still in development.
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