This book is much more than a new programming manual. It introduces a method in which the program design is included in the global process that goes from understanding the problem to the validation of its solution.

The mathematical basis of the method provides the exactness while the proposed notation eliminates the ambiguities of the vernacular language. At the same time, the process is simple enough for an industrial use “Industrial” is in fact the key word.

The general aim of formal methods is to provide correctness of the problem specification. Here we can see how the solution can be found, step by step, by a continuously monitored process. The mathematical verification of each step is so closely bound to the refinement activity that it is no longer possible to separate the design choices from the checking process. Imagination is helped by exactness!

But how about the efficiency? Isn't the design too long? Are the design people able to do this work? Are the machines powerful enough to implement the method? The answers are easy to give. Let me tell you.

My company has been involved, since the sixties, in the realisation of train control systems, which must meet stringent safety requirements. As soon as we began to use programmed logic (end of the seventies) we had to solve the problem of software correctness. Together with other methods, we chose to use the program proving method proposed by C.A.R. Hoare. In 1986, J.-R. Abrial introduced us to the B method. We decided to learn it and to use it. The tools did not exist at the time.