Foundations

In this chapter, we will not be concerned with programming languages but with the limits of the programs that we can write, asking whether there exist problems that no program can solve. A motivation for this research is the question that we asked at the end of Sect. 2.3 : that is, is it possible to construct a static semantic analyser which can verify constraints imposed by the programming language’s definition? We will soon discover, however, that the answer to the question is rather more general. It is a kind of absolute limit to what can (and cannot) be done with a computer. Although the material in this chapter can appear abstract, our treatment is wholly elementary.