Introduction to ''Interactive models of computation and program behaviour"

Since the mid-eighties of the last century, a fruitful interplay between computer scientists and mathematicians has led to much progress in the understanding of programming languages, and has given new impulse to areas of mathematics such as proof theory or category theory. The volume of which this text is an introduction contains three contributions: Categorical semantics of linear logic, by P.-A. Melliès, Realizability in classical logic, by J.-L. Krivien, Abstract machines for dialogue games, by P.-L. Curien and H. Herbelin, which we place here in perspective