Fundamentals of CS I (CS151 2002F)

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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)) ; ... otherwise subtract fore from aft.

Here is the complete definition of the `disparity`

procedure:

;;; 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))))

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(that is, 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

. If it is, then
again we evaluate whatever comes after the test and obtain the symbol
`ls`

and determine whether it is a 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.

Wednesday, 31 January 2001

- Reformatted.
- Updated comments for
`disparity`

to use Six Ps.

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**Disclaimer**:
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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The source to the document was last modified on Thu Aug 29 15:08:04 2002.

This document may be found at `http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2002F/Readings/conditionals.html`

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Samuel A. Rebelsky, rebelsky@grinnell.edu