Clearly, we wish to use familiar notions of mathematics, such as numbers, sets, sequences, and so on, rather than computer-dependent entities such as bitstrings. In this book these deliberations determine the choice of notation for the description of algorithms and their data. The nature and frequency of these operations will, however, not be known to the designer of a general-purpose language and its compiler, and any choice the designer makes may be inappropriate for some potential applications. For example, it would not make sense to include geometric objects as basic data items in a general-purpose language, since their proper repesentation will, because of its inherent complexity, be largely dependent on the operations to be applied to these objects.
This fact sets definite limits on the degree of abstraction from a given real computer.
The closer the abstractions are to a given computer, the easier it is to make a representation choice for the engineer or implementor of the language, and the higher is the probability that a single choice will be suitable for all (or almost all) conceivable applications.
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