Why, how and what should be taught about Formal Methods?

I started to teach formal methods (FM) in an undergraduate, mandatory course of a Computer Science degree at Universidad Nacional de Rosario (Argentina) in 1998. After all these years I still have more questions than answers. In particular, I still can’t find satisfactory answers to questions I asked to myself back in 1998. However, at the same time, I still believe that I am doing the right thing. I would like to share and discuss with all of you my doubts and what I have learned during all these years regarding what should or should not be taught about FM to undergraduate students. This talk will be more a collection of questions and doubts rather than (firm) statements. So let’s begin with some of them. Should we teach FM to undergraduate students? I dislike absolute answers to sociological questions (teaching is, after all, a sociological activity). For instance, should we teach FM regardless of the length of the plan of study? The answer would be yes provided FM are considered so fundamental to the profession that none of them can graduate without passing a course on FM. So, are FM that fundamental to the profession of programmers? Here, the discussion can be forked again: a) Fundamental to do what? What is the profession under the umbrella of informatics? Does the professional working on the avionic system of an aircraft need the same education as a system administrator?; and b) Do we really mean programmers? Why don’t we say software engineers? Is the same a programmer as a software engineer? Should both of them know FM? But, let’s go back to the previous question, the one referring to ‘fundamentals’. Are FM fundamental to Computer Science or to Software Engineering? I think that if they are fundamental to something it’s (just) to Software Engineering. David Parnas has already stated the difference between Computer Science and Software Engineering [2]. He has been quite critical about how FM were designed and used. He says that they don’t reflect the way mathematics is used in other engineering disciplines. And this makes software engineers to seldom use FM. So, should we teach FM to undergraduate students of Software Engineering degrees? Let’s assume for a moment that we should teach FM to future software engineers. What FM should we teach? As you know, there are dozens of mathematical approaches to software development that fall within the realm of FM. It simply makes no sense to teach all of them as it make no sense to teach all the programming languages. Choosing what programming languages to teach might seem easier: just pick the top 3 used in industry. Why 3? Why not just 1? Why the top used in industry? Are the top programming languages used in industry fundamental to the software professional? I think that most of us will agree