Course Information

This is a course about the foundations of programming languages. A programming language is defined by its syntax, static semantics, and dynamic semantics. Each of these components of the language is based on familiar mathematical and logical foundations.

Syntax: formal languages, grammars, inductive datatypes.
Static Semantics: type theory, abstract interpretation, data-flow analysis, etc.
Dynamic semantics: abstract machines, lambda-calculus, pi-calculus, etc.

Studying the foundations of programming languages has at least the following benefits:

Despite their apparent diversity, programming languages (including not just general purpose programming languages, but also domain-specific languages, scripting languages, and other little languages) have a lot more in common than may first seem. Understanding the foundations allows a programmer to seamlessly learn and work with a variety of languages.
Mapping the features of a given programming language to their mathematical and logical foundations gives a programmer a detailed and rigorous understanding of all the subtleties of the language.
To make any interesting guarantees about the behavior of programs written in a particular programming language, one must define a mathematical model for the language and formally prove some properties about it.

We will study everything in the context of Java. The mathematical foundations of Java are not that different from those of other modern languages, but Java is interesting for three reasons. First it is widely accessible and popular. Second it has several subtle points that programmers can easily misunderstand or overlook. And third it became popular by making claims about the safety of applets. Because software practice is moving away from monolothic applications to dynamically-loaded distributed components, this safety claim was particularly interesting. For our purposes, it is even more interesting that the initial claim that Java applets are safe is wrong and the entire class-loading architecture had to be redesigned from scratch!

In summary, the Java language, with its important safety properties, provides a good context for the study of the foundations of programming languages.

In more detail, the course will proceed as follows:

Develop a formal mathematical model that describes the static and dynamic semantics of Java.
Use the model to prove type safety which is one the fundamental component of any security guarantee.
Because Java is a large language, both the semantics and the proof are large, and we need some automated support. We will use AsmGofer (which is a formalism for specifying abstract state machines built on an old implementation of Haskell).
We will then repeat the previous development with the JVM.

This development closely follows the Jbook but skips most of Part II which is related to the compiler and its correctness. This material is also interesting but I don't think we have time to cover it. See the schedule for more details.