SICP in Python by wizardforcel

Author:wizardforcel [Unknown]
Language: eng
Format: epub
Publisher: GitBook

2.7.2 Multiple Representations

Data abstraction, using objects or functions, is a powerful tool for managing complexity. Abstract data types allow us to construct an abstraction barrier between the underlying representation of data and the functions or messages used to manipulate it. However, in large programs, it may not always make sense to speak of "the underlying representation" for a data type in a program. For one thing, there might be more than one useful representation for a data object, and we might like to design systems that can deal with multiple representations.

To take a simple example, complex numbers may be represented in two almost equivalent ways: in rectangular form (real and imaginary parts) and in polar form (magnitude and angle). Sometimes the rectangular form is more appropriate and sometimes the polar form is more appropriate. Indeed, it is perfectly plausible to imagine a system in which complex numbers are represented in both ways, and in which the functions for manipulating complex numbers work with either representation.

More importantly, large software systems are often designed by many people working over extended periods of time, subject to requirements that change over time. In such an environment, it is simply not possible for everyone to agree in advance on choices of data representation. In addition to the data-abstraction barriers that isolate representation from use, we need abstraction barriers that isolate different design choices from each other and permit different choices to coexist in a single program. Furthermore, since large programs are often created by combining pre-existing modules that were designed in isolation, we need conventions that permit programmers to incorporate modules into larger systems additively, that is, without having to redesign or re-implement these modules.

We begin with the simple complex-number example. We will see how message passing enables us to design separate rectangular and polar representations for complex numbers while maintaining the notion of an abstract "complex-number" object. We will accomplish this by defining arithmetic functions for complex numbers (add_complex, mul_complex) in terms of generic selectors that access parts of a complex number independent of how the number is represented. The resulting complex-number system contains two different kinds of abstraction barriers. They isolate higher-level operations from lower-level representations. In addition, there is a vertical barrier that gives us the ability to separately design alternative representations.

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