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Summary: Many programs need to make choices. In this reading, we consider Scheme's conditional expressions, expressions that allow programs to behave differently in different situations.
When Scheme encounters a procedure call, it looks at all of the subexpressions within the parentheses and evaluates each one. Sometimes, however, the programmer wants Scheme to exercise more discretion. Specifically, the programmer wants to select just one subexpression for evaluation from two or more alternatives. In such cases, one uses a conditional expression, an expression that tests whether some condition is met and selects the subexpression to evaluate on the basis of the outcome of that test.
For instance, let's write a procedure to compute the disparity
between two given real numbers, the amount by which one of them exceeds
the other. We can compute this result by subtraction, but before we can do the
subtraction we need to know which of the two given numbers (let's call them
aft) is greater, so that we can make it
the minuend and the other the subtrahend.
That is, if
fore is greater, we compute the disparity by
evaluating the expression
(- fore aft); otherwise, the
expression we need is
(- aft fore).
To write a disparity procedure, we need a mechanism to choose which expression to evaluate. Such mechanisms are the key subject of this reading.
A conditional expression, specifically, an
expression, selects one or the other of these expressions, depending
on the outcome of a test. The general form is
(if test consequent alternative)
We'll return to the particular details in a moment. For now, let's consider the conditional we might write for the disparity procedure.
(if (> fore aft) ; If fore is greater than aft ... (- fore aft) ; ... subtract aft from fore (- aft fore)) ; ... otherwise subtract fore from aft.
To turn this expression into a procedure, we need to add the
keyword, a name (
disparity), a lambda expression, and such.
We also want to give appropriate documentation.
Here is the complete definition of the
;;; Procedure: ;;; disparity ;;; Parameters: ;;; fore, an exact number ;;; aft, an exact number ;;; Purpose: ;;; Compute the amount by which one number ;;; exceeds another. ;;; Produces: ;;; excess, an exact number. ;;; Preconditions: ;;; Both fore and aft are exact numbers (unverified). ;;; Postconditions: ;;; The greater of fore and aft is equal to the sum of excess ;;; and the lesser of fore and aft. If fore and aft are equal, ;;; excess is equal to 0. ;;; Citation: ;;; Based on a similar procedure created by John David Stone of ;;; Grinnell College which is dated January 27, 2000. (define disparity (lambda (fore aft) (if (> fore aft) (- fore aft) (- aft fore))))
if expression of the form
(if test consequent alternative),
the test is always
evaluated first. If its value is
#t (which you may
true), then the consequent
s evaluated, and the alternate (the expression following the
consequent) is ignored. On the other hand, if the value of the test
#f, then the consequent is ignored and the alternate
if expressions in which the value of the test
is non-Boolean. However, all non-Boolean values are classified as
truish and cause the evaluation of the consequent.
Some particularly astute readers may have noted that it is possible to
disparity without an
if. For the time
being, accept that this is a simple motivating example. (Those of you
who aren't sure how to do without
if in this example can
refer to an appendix.)
It is possible to write an if expression without the alternative. Such an
expression has the form
(if test consequent).
In this case, the test is still evaluated first. If the test holds
(that is, has a value of
#t or anything other than
#f), the consequent is evaluated and its value is returned.
If the test fails to hold (that is, has value
if expression has no value.
We mention this issue here for completeness. At this stage of your career, you are unlikely to need or want the alternative-free if, and you should avoid using it.
When there are more than two alternatives, it is often more convenient
to set them out using a
cond expression. Like
cond is a keyword. (Recall that keywords
differ from procedures in that the order of evaluation of the parameters
cond keyword is followed by zero
or more lists-like expressions called
(cond (test-0 consequent-0) ... (test-n consequent-1) (else alternate))
The first expression within a
cond clause is a test,
similar to the test in an
if expression. When the value of
such a test is found to be
#f, the subexpression that
follows the test is ignored and Scheme proceeds to the test at the
beginning of the next
cond clause. But when a test is
evaluated and the value turns out to be true, or even
is, anything other than
#f), the consequent for that test
is evaluated and its value is the value of the whole cond expression..
cond clauses are completely ignored.
In other words, when Scheme encounters a
cond expression, it
works its way through the
cond clauses, evaluating the test at
the beginning of each one, until it reaches a test that succeeds
(one that does not have
#f as its value). It then makes a
ninety-degree turn and evaluates the consequent in the selected
cond clause, retaining the value of the consequent.
If all of the tests in a
cond expression are found to be
false, the value of the
cond expression is unspecified (that
is, it might be anything!). To prevent the surprising results that can
ensue when one computes with unspecified values, good programmers
customarily end every
cond expression with a
cond clause in which the keyword
else appears in
place of a test. Scheme treats such a
cond clause as if it
had a test that always succeeded. If it is reached, the subexpressions
else are evaluated, and the value of the last one
is the value of the whole
For example, here is a
cond expression that inspects a list
(cond ((null? ls) 'empty) ((symbol? (car ls)) 'list-that-starts-with-a-symbol) (else 'something-else))
The expression has three
cond clauses. In the first, the test
(null? ls). If
ls happens to be the empty
list, the value of this first test is
#t, so we evaluate
whatever comes after the test to find the value of the entire expression,
in this case, the symbol
ls is not the empty list, then we proceed instead to the
cond clause. Its test is
ls)) -- in other words,
look at the first element of
. If it is, then
again we evaluate whatever comes after the test and obtain the symbol
ls and determine whether it is a symbol
However, if the first element of
ls is not a symbol,
then we proceed instead to the third
Since the keyword
else appears in this
clause in place of a test, we take that as an automatic success
'something-else, so that that value of
cond expression in this case is the symbol
Although we have written our conditionals with one consequent per test (and we encourage you to do the same), it is, in fact, possible to have multiple consequents per test.
(cond (test-0 consequent-0-0 consequent-0-1 ... consequent-0-m) ... (else alternate-0 alternate-1 ... alternate-a))
In this case, when a test succeeds, each of the remaining subexpressions
(that is, consequents) in the same
cond clause is evaluated
in turn, and the value of the last one becomes the value of the entire
Note that both
or provide a type of
conditional behavior. As you may recall from
the reading on Boolean values,
and evaluates each argument in turn until it hits a value that
#f and then returns
#f (or returns the last
value if none return
each argument in turn until it finds one that is not
which case it returns that value, or until it runs out of values, in which
case it returns
(or exp0 exp1 ... expn)
behaves much like the following
except that the
or version evaluates each expression once,
rather than twice.
(cond (exp0 exp0) (exp1 exp1) ... (expn expn) (else #f))
(and exp0 exp1 ... expn)
behaves much like the following
(cond ((not exp0) #f) ((not exp1) #f) ... ((not expn) #f) (else expn))
Most beginning programmers find the
cond versions much more
understandable, but some advanced Scheme programmers use the
or forms because they find them clearer.
and is quite repetitious.
It is possible to write
using the absolute value procedure,
(define disparity (lambda (fore aft) (abs (- fore aft))))
I usually create these pages
on the fly, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
It also means that I tend to update them regularly (see the history for
more details). Feel free to contact me with any suggestions for changes.
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