There are many theories of programming; this one seek to describe programs, programming languages and programming in a simple mathematical framework, based on a small set of high-school-level concepts of elementary set theory (sets and binary relations). It uses only three starting operations (union, restriction and composition) and covers the core concepts of programming as well as concurrency, non-determinism, control structures, correctness. From the theory’s definitions it is possible to deduce, as theorems, the axioms of classic theories such as those of Hoare and Kahn.

Bertrand Meyer is an author, consultant and academic specializing in software engineering.