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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, to select just one subexpression for evaluation from two or
more alternatives. In such cases, one uses a *conditional
expression* -- that is, 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 by subtraction, but before we can do the
subtraction we need to know which of the two given numbers (let's call them
`fore`

and `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)`

.

A conditional expression
-- specifically, an * if-expression* -- selects one or
the other of these expressions, depending on the outcome of a test, thus:

(if (> fore aft) ; If FORE is greater than AFT ... (- fore aft) ; ... subtract AFT from FORE ... (- aft fore)) ; ... and otherwise subtract FORE from AFT.

Here is the complete definition of the `disparity`

procedure:

;;; disparity: compute the amount by which one real number ;;; exceeds another ;;; John David Stone ;;; Department of Mathematics and Computer Science ;;; Grinnell College ;;; stone@cs.grinnell.edu ;;; created January 27, 2000 ;;; last revised September 6, 2000 by Sam Rebelsky ;;; Givens: ;;; FORE and AFT, both real numbers. ;;; Result: ;;; EXCESS, a real number. ;;; Preconditions: ;;; None. ;;; Postcondition: ;;; The greater of FORE and AFT is equal to the sum of EXCESS ;;; and the lesser of FORE and AFT. (define disparity (lambda (fore aft) (if (> fore aft) (- fore aft) (- aft fore) ) ) )

In an `if`

-expression, the *test* (the expression
following the keyword `if`

) is always evaluated first. If its
value is `#t`

, then the *consequent* (the expression
following the test) is evaluated, and the *alternate* (the
expression following the consequent) is ignored. On the other hand, if the
value of the test is `#f`

, then the consequent is ignored and
the alternate is evaluated.

Scheme accepts `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.

When there are more than two alternatives, it is often more convenient to
set them out using a * cond-expression*. Like

`if`

, `cond`

is a keyword. It is followed by zero or
more lists of expressions called `cond`

-clauses`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 subexpressions that follow the test are
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 ``truish'' -- anything other than `#f`

-- each of the remaining expressions in the same `cond`

-clause
is evaluated in turn, and the value of the last one becomes the value of
the entire `cond`

-expression. Subsequent
`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 other expressions in the selected
`cond`

-clause, retaining the value of the last expression.

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
following `else`

are evaluated, and the value of the last one
is the value of the whole `cond`

-expression.

For example, here is a `cond`

-expression that inspects a list
called `ls`

:

(cond ((null? ls) 'none) ((symbol? (car ls)) 'first) (else 'other))

The expression has three `cond`

-clauses. In the first, the test
is `(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 `none`

If `ls`

is not the empty list, then we proceed instead to the
second `cond`

-clause. Its test is ```
(symbol? (car
ls))
```

-- in other words, ``look at the first element of
`ls`

and determine whether it is a symbol.'' If it is, then
again we evaluate whatever comes after the test and obtain the symbol
`first`

.

However, if the first element of `ls`

is not a symbol, then we
proceed instead to the third `cond`

-clause. Since the keyword
`else`

appears in this `cond`

-clause in place of a
test, we take that as an automatic success and evaluate
`'other`

, so that that value of the whole
`cond`

-expression in this case is the symbol `other`

.

Wednesday, 6 September 2000

- Created.
- Based on part of the narrative in a lab from CSC151 2000S.

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**Disclaimer** Often, these pages were created "on the fly" with little, if any, proofreading. Any or all of the information on the pages may be incorrect. Please contact me if you notice errors.

This page may be found at http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2000F/Readings/conditionals.html

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