The Syntax and Semantics of while-Programs

In Chapter 1 we presented a version of the unsolvability of the Halting Program for pascal. The generality of that result rests on the crucial assumption—embodied in our formulation of Church’s Thesis—that the notion of “algorithmic” coincides with the notion of “programmable”. In this chapter we examine the relationship between algorithms and programs more carefully. We define a particularly simple language, a pascal subset called while-programs, with the intent of isolating a set of primitive operations and combination rules which form a convenient and tractable basis for our formulation of computability theory.