This chapter gives a short introduction to the general principles of denotational semantics. We do this by giving a denotational semantics of Bims. It turns out that the semantics of while-loops poses a problem, as the obvious semantics is not compositional. However, at the end of the chapter we find a way to circumvent this problem of non-compositionality.

Background

Denotational semantics is a child of the 1960s and is based on the ground-breaking insights of Christopher Strachey and Dana Scott (Strachey, 1966, 1967; Scott and Strachey, 1971). Since then, a lot of work has gone into providing denotational semantics for existing programming languages such as Algol 60, Pascal, Smalltalk and Lisp.

Denotational semantics has also turned out to be a particularly useful tool in the design and implementation of languages such as Ada, CHILL and Lucid (Schmidt, 1986).

Denotational semantics can also be useful in static program analysis, which is the study of the correctness properties on the basis of analyses of the program text (as opposed to analyses of the behaviour of the program).

Simple examples of static analysis involve methods for code optimization. Here are two examples.

Consider the so-called constant-folding problem: when is it possible to replace an expression involving variables by a constant?