Motivation

The intent of this book is to give some insights on modeling and formal reasoning. These activities are supposed to be performed before undertaking the effective coding of a computer system, so that the system in question will be correct by construction.

In this book, we will thus learn how to build models of programs and, more generally, discrete systems. But this will be done with practice in mind. For this we shall study a large number of examples coming from various sources of computer system development: sequential programs, concurrent programs, distributed programs, electronic circuits, reactive systems, etc.

We will understand that the model of a program is quite different from the program itself. And we will learn that it is far easier to reason about the model than about the program. We will be made aware of the very important notions of abstraction and refinement; the idea being that an executable program is only obtained at the final stage of a sometimes long sequence consisting of gradually building more and more accurate models of the future program (think of the various blueprints made by an architect).

We shall make it very clear what we mean by reasoning about a model. This will be done by using some simple mathematical methods, which will be presented first by means of some examples then by reviewing classical logic (propositional and predicate calculus) and set theory. We will understand the necessity of performing proofs in a very rigorous fashion.