By C. Ausnit, et al

ISBN-10: 3540961828

ISBN-13: 9783540961826

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**Example text**

Indeed, there is a long history of erroneous definitions of substitution in the literature of logic and programming semantics. See Stoy 1977 for a careful discussion of substitution. 16 In chapter 3 we will introduce stream processing, which is a way of handling apparently ``infinite'' data structures by incorporating a limited form of normal-order evaluation. 2 we will modify the Scheme interpreter to produce a normal-order variant of Scheme. 17 ``Interpreted as either true or false'' means this: In Scheme, there are two distinguished values that are denoted by the constants #t and #f.

What behavior will he observe with an interpreter that uses normal-order evaluation? Explain your answer. 7 Example: Square Roots by Newton's Method Procedures, as introduced above, are much like ordinary mathematical functions. They specify a value that is determined by one or more parameters. But there is an important difference between mathematical functions and computer procedures. Procedures must be effective. As a case in point, consider the problem of computing square roots. We can define the square-root function as This describes a perfectly legitimate mathematical function.

The contraction occurs as the operations are actually performed. This type of process, characterized by a chain of deferred operations, is called a recursive process. Carrying out this process requires that the interpreter keep track of the operations to be performed later on. , the length of the chain of deferred multiplications, and hence the amount of information needed to keep track of it, grows linearly with n (is proportional to n), just like the number of steps. Such a process is called a linear recursive process.

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