Fundamentals of Computer Science I (CS151.01 2006F)
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Related Courses:
[CSC151.02 2006F (Davis)]
[CSCS151 2005S (Stone)]
[CSC151 2003F (Rebelsky)]
[CSC153 2004S (Rebelsky)]
In this lab, you will have the opportunity to explore a number of issues relating to predicates, Boolean values, and conditional operations.
Procedures covered in this lab include:
boolean?
,
integer?
,
list?
,
null?
,
number?
,
pair?
,
procedure?
,
symbol?
=
,
eq?
,
eqv?
,
equal?
,
<
(strictly less than),
<=
(less than or equal to),
=
(equal to),
>=
(greater than or equal to),
>
(strictly greater than)
and
,
or
,
not
not
?
and
and or
Although this laboratory focuses on Boolean operations, it also uses some numeric predicates. You may therefore want to rescan the reading on numbers.
After making sure that you're prepared, start DrScheme.
Fill in a few interesting
entries in following table.
You need not fill int the whole table; simply do as much as you
think gives you a good sense of the various predicates.
5  5.0  'five  "five"  list  #t  #f  (cons 'a null)  null  'null  ()  
number? 

symbol? 

string? 

procedure? 

boolean? 

list? 
Which of the following does Scheme consider an empty list?
null
'null
()
(list 'a)
(list)
'nothing
Consider the following definitions
(define alpha (list 'a 'b 'c)) (define beta (list 'a 'b 'c)) (define gamma alpha) (define delta (cons (car alpha) (cdr alpha)))
Determine which of the lists are
eq?
,
eqv?
,
or
equal?
.
What, if anything, did you find surprising in the results of the previous exercises?
By looking at
the Scheme report, see if you can find a pair of values
that are equal in the sense of =
but not in the sense of eqv
.
not
?
a. What type is not
?
b. What predicate would you use to verify your answer?
Fill in the following tables for each of the operations and
and or
.
and
First argument  Second argument  Result 
#f 
#f 

#f 
#t 

#t 
#f 

#t 
#t 
or
First argument  Second argument  Result 
#f 
#f 

#f 
#t 

#t 
#f 

#t 
#t 
a. Write a Boolean expression that determines if the value named by
grade
is between 0 and 100, inclusive.
b. Test that expression using different values of grade
.
and
and or
a. Determine the value and
returns when called with no parameters.
b. Explain why you think the designers of Scheme had and
return that value.
c. Determine the value and
returns when called with integers as parameters.
d. Explain why you think the designers of Scheme had and
return that value.
e. Determine the value or
returns when called with no parameters.
f. Explain why you think the designers of Scheme had or
return that value.
g. Determine the value or
returns when called with only integers as parameters.
h. Explain why you think the designers of Scheme had or
return that value.
If you are puzzled by some of the answers, you may want to look at the notes on this problem, available at the end of the lab.
Define and test a Scheme predicate, (primitive? val)
,
that returns #t
if val is a symbol, number, character,
or Booelan value, and #f
otherwise.
Define and test a Scheme predicate between?
that takes three
arguments, all real numbers, and determines whether the second one lies
strictly between the first and third (returning #t
if it is,
#f
if it is not). For example, 6 lies strictly between 5 and
13, so both (between? 5 6 13)
and
(between? 13 6 5)
should have the value
#t
.
Three line segments can be assembled into a triangle if, and only
if, the length of each of them is less than the sum of the lengths of the
other two. Define a Scheme predicate triangle?
that takes
three arguments, all positive real numbers, and determines whether line
segments of those three lengths (assumed to be measured in the same units)
could be assembled into a triangle.
Note that you will have to use a combination of and
s
and or
s to solve this problem.
You may recall the following alternate addition procedure from the reading.
;;; Procedure: ;;; safeadd ;;; Parameters: ;;; x, a number [verified] ;;; y, a number [verified] ;;; Purpose: ;;; Add x and y. ;;; Produces: ;;; sum, a number. ;;; Preconditions: ;;; (No additional preconditions) ;;; Postconditions: ;;; sum = x + y ;;; Problems: ;;; If either x or y is not a number, sum is #f. (define safeadd (lambda (x y) (and (number? x) (number? y) (+ x y))))
Define similar procedures, safesubtract
and
safemultiply
, that confirm that their parameters are
numbers before subtracting and multiplying, respectively.
What is the advantage of defining such procedures?
You may note that the divide procedure, /
, produces an
error if the divisor is 0. We might, therefore, hope for a safer
version that returns #f
rather than giving up, when the
divisor is 0 (or when either dividend or divisor is not a number).
Define a procedure, safedivide
, that does just that.
a. Consider the expression (and (integer? x) (odd? x) x)
.
What value does it return if x
is not an integer?
If x
is even? If x
is odd?
b. Using what you've determined about the previous expression, write
a procedure, (firstodd i1 i2 i3)
, that
takes as parameters three integers and returns the first odd value.
If none of the integers is odd, firstodd
should return
#f
.
(and)
has value true (#t
) because
. Since this
calls has no parameters, none are false.
and
has a
value of true if none of the parameters have value false
(or)
has value false (#f
) because
. Since this call has no parameters, none are nonfalse.
or
has value false if none of the parameters is
nonfalse
Tuesday, 5 September 2006 [Samuel A. Rebelsky]
http://www.cs.grinnell.edu/~rebelsky/Courses/CS151//2003F/Labs/conditionals.html
.
Friday, 8 September 2006 [Samuel A. Rebelsky]
Saturday, 9 Septemer 2006 [Samuel A. Rebelsky]
symbolorlist?
question to the new
primitive?
question.
http://www.cs.grinnell.edu/~rebelsky/Courses/CS151//2006F/Labs/boolean.html
.
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[Academic Honesty]
[Instructions]
Current:
[Outline]
[EBoard]
[Reading]
[Lab]
[Homework]
Groupings:
[EBoards]
[Examples]
[Exams]
[Handouts]
[Homework]
[Labs]
[Outlines]
[Projects]
[Readings]
Reference:
[Scheme Report (R5RS)]
[Scheme Reference]
[DrScheme Manual]
Related Courses:
[CSC151.02 2006F (Davis)]
[CSCS151 2005S (Stone)]
[CSC151 2003F (Rebelsky)]
[CSC153 2004S (Rebelsky)]
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I usually create these pages on the fly
, which means that I rarely
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