Fundamentals of Computer Science I (CSC-151.02 2000F)

Conditional Evaluation

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).

If Expressions

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

;;; 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.

Multiple Alternatives

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. 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 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

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