Abstract
Computationally we are concerned here with any segment of code which carries out a calculation and is executed between successive state changes (often in the guise of input or output instructions). Performing a calculation is synonymous with evaluating a function. Mathematically, a function is something which generates a unique result from each acceptable data value. Regarded as a complete program, it should be possible in principle to read all the required input into some ‘variable’ called x, evaluate f(x) — spoken “f of x” — and then ‘write’ the answer. Throughout Chapters 1 to 7 we shall only be concerned with the second of these three phases. In particular, within the specifications, we will not be interested in any changes of value. Most of our reasoning will involve values which are constant but unknown.
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