Summary:
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:
- Type predicates:
boolean?,
integer?,
list?,
null?,
number?,
pair?,
procedure?,
symbol?
- Equality comparators:
=,
eq?,
eqv?,
equal?,
- Numeric comparators:
< (strictly less than),
<= (less than or equal to),
= (equal to),
>= (greater than or equal to),
> (strictly greater than)
- Boolean operations:
and,
or,
not
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? |
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symbol? |
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string? |
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procedure? |
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boolean? |
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list? |
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Note: You can fill in a column very quickly if you define a
procedure that, given a value, makes a list of the results of
applying each predicate to that value. Here's a start.
(define col
(lambda (val)
(list 'number? (number? val)
'symbol? (symbol? val))))
Which of the following does Scheme consider an empty list?
-
null
-
'null
-
()
-
(list 'a)
-
(list)
-
'nothing
-
(cdr (list 'a))
a. What type is not? That is, is it a number, a symbol,
a string, ...?
b. What predicate would you use to verify your answer? That is, what
value would you use for the blank in the following?
c. What type is 'not? That is, is it a number, a symobl,
a string, ....?
d. What predicate would you use to verify your answer? That is, what
value would you use for the blank in the following?
Fill in the following tables for each of the operations and
and or. In the first table, the result column should be
the value of (and arg1 arg2), where arg1 is
the first argument and arg2 is the second argument. In
the second table, the result column should be the value of
(or arg1 arg2).
and
| First argument |
Second argument |
Result |
#f |
#f |
|
#f |
#t |
|
#t |
#f |
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#t |
#t |
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or
| First argument |
Second argument |
Result |
#f |
#f |
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#f |
#t |
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#t |
#f |
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#t |
#t |
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Define a predicate, (bigger? num1 num2), that takes two
real numbers as arguments and returns #t if the absolute
value of the first is greater than the absolute value of the second,
#f if it is not.
Call your procedure twice -- once with arguments that ensure that the
value of the procedure call is #t, once with arguments that make the
value #f.
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.
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? side1 side2 side3), 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.
You may recall the following alternate addition procedure from
the reading.
;;; Procedure:
;;; safe-add
;;; 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 safe-add
(lambda (x y)
(and (number? x) (number? y) (+ x y))))
Define similar procedures, safe-subtract and
safe-multiply, 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, safe-divide, 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, (first-odd i1 i2 i3), that
takes as parameters three integers and returns the first odd value.
If none of the integers is odd, first-odd should return
#f.
(and) has value true (#t) because
and has a value of true if none of the parameters have
value false
. Since this calls has no parameters, none are false.
Alternately, you can think of #t as the and-itive identity
.
That is, (and #t x) is x.
(or) has value false (#f) because
or has value false if none of the parameters is
non-false
. Since this call has no parameters, none are non-false.
Alternately, you can think of #f as the or-itive identity
.
That is, (or #f x) is x.
Return to the problem.
;
