Introduction

Summary

This book is a very long discourse explaining how, in my opinion, the task of programming (in the small as well as in the large) can be accomplished by returning to mathematics.

By this, I first mean that the precise mathematical definition of what a program does must be present at the origin of its construction. If such a definition is lacking, or if it is too complicated, we might wonder whether our future program will mean anything at all. My belief is that a program, in the absolute, means absolutely nothing. A program only means something relative to a certain intention, that must predate it, in one form or another. At this point, I have no objection with people feeling more comfortable with the word “English” replacing the word “mathematics”. I just wonder whether such people are not assigning themselves a more difficult task.

I also think that this “return to mathematics” should be present in the very process of program construction. Here the task is to assign a program to a well-defined meaning. The idea is to accompany the technical process of program construction by a similar process of proof construction, which guarantees that the proposed program agrees with its intended meaning.

Simultaneous concerns about the architecture of a program and that of its proof are surprisingly efficient. For instance, when the proof is cumbersome, there are serious chances that the program will be too; and ingredients for structuring proofs (abstraction, instantiation, decomposition) are very similar to those for structuring programs.