This lab is also available in PDF.
Summary: In this laboratory, you will continue to explore
the syntax and capabilities of the Scheme programming language.
Note:
You may want to keep the
corresponding reading at hand.
Start DrScheme and make sure that you're in Pretty Big Scheme mode.
You may want to review the DrScheme
lab to make sure you understand DrScheme.
a. Ask DrScheme to subtract 68343 from 81722.
b. Verify that the answer is correct.
a. Ask DrScheme to multiply 162 by 1383.
b. How would you verify that the answer is correct?
a. Ask DrScheme to add 3 and 4.
b. Ask DrScheme to add 3 and 4 and then add 5 to the result. You'll
need two calls to +.
c. Ask DrScheme to add 3, 4, and 5 using only one call to +.
d. What happens if you call the procedure + with no arguments?
With only one? Why do you think it gives these results?
In the previous exercise, you explored what happens when you call the
procedure + with zero and one arguments. Let us explore
the same questions for other procedures.
a. What do you expect to happen if you call the procedure * with
one argument?
b. Verify your answer experimentally. If the results differ, try to
explain the result Scheme gives.
c. What do you expect to happen if you call the procedure * with
no arguments?
d. Verify your answer experimentally. If the results differ, try to
explain the result Scheme gives.
e. What do you expect to happen if you call the procedure - with
one argument?
f. Verify your answer experimentally. If the results differ, try to
explain the result Scheme gives.
g. What do you expect to happen if you call the procedure - with
no arguments?
h. Verify your answer experimentally. If the results differ, try to
explain the result Scheme gives.
Have DrScheme compute the absolute value of -197. You can use the
abs procedure.
a. Ask DrScheme to compute the cube of 19 (that is, the result of
raising 19 to the power 3). You can use expt to compute
exponents.
b. Ask DrScheme to computer the nineteenth power of 3.
c. What do these results indicate about the relationship between
procedures and arguments in Scheme?
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.
a. Write a definition that will cause Scheme to recognize dozen
as a name for the number 12.
b. Write a definition that will cause Scheme to recognize
raise-to-power as a synonym for expt.
c. Use both names in expressions to verify that Scheme has understood
them.
a. What do you expect to happen when you ask DrScheme to compute the square root of -4?
b. Verify your answer experimentally.
c. What do your results suggest?
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 in the DrScheme lab.
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.) 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).
Quit DrScheme and log out of the workstation.
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.
;
