Terms and Conditions:

J V Tucker wrote:This is an almost complete first draft of a text-book. It is the text for a second year undergraduate course on the Theory of Programming Languages at Swansea. Criticisms and suggestions are most welcome.

Book Summary:

Data, syntax and semantics are among the Big Ideas of Computer Science. The concepts are extremely general and can be found throughout Computer Science and its applications. Wherever there are languages for specifying, designing, programming or reasoning, one finds data, syntax and semantics.

A programming language is simply a notation for expressing algorithms and performing computations with the help of machines. There are many different designs for programming languages, tailored to the computational needs of many different types of users. Programming languages are a primary object of study in Computer Science, influencing most of the subject and its applications.

This book is an introduction to the mathematical theory of programming languages. It is intended to provide a first course, one that is suitable for all university students of Computer Science to take early in their education; for example, at the beginning of their second year, or, possibly, in the second half of their first year. The background knowledge needed is a first course in elementary set theory and logic, and in imperative programming. The theory will help develop their scientific maturity by asking simple and sometimes deep questions, and by weaning them off examples and giving them a taste for general ideas, principles and techniques, precisely expressed. This book has picked a small number of topics, and attempted to be self-contained and relevant.

The book contains much basic mathematical material on data, syntax and semantics. There are some seemingly advanced features and contemporary topics that may not be common in the elementary text-book literature: data types and their algebraic theory, real numbers, interface definition languages, algebraic models of syntax, computability theory, virtual machines and compiler correctness. Where this book's material is standard (e.g., grammars), it tries to include new and interesting examples and case studies (e.g., internet addressing).

The book is also intended to provide a strong foundation for the further study of the theory of programming languages, and related subjects in algebra and logic, such as: algebraic specification; initial algebra semantics; term rewriting; process algebra; computability and definability theory; program correctness logic; A-calculus and type theory; domains and fixed point theory etc. There are a number of books available for these later stages, and the literature is discussed in a final chapter on further reading.