Theories of Programming and Formal Methods

The purpose of this paper is to present some set-theoreticmodels of computation. This topic and its usefulness are clearly related to those presented in the book by Hoare and He: “Unifying Theories of Programming” [12]. However, we prefer to use here the term “computation” to that of “programming” as our purpose is not so much to unify various ways of programming (using different programming languages) but rather to see how various mechanical computation paradigms (be they sequential, distributed, parallel, and so on) can be given a unified mathematical theory. Our purpose is also to study how these computations can be specified and then developed by means of refinements and proofs.

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