In recent years, extensions of rewriting techniques that go beyond the traditional untyped algebraic rewriting framework have been investigated and developed. Among these extensions, conditional and typed systems are particularly important, as are higher-order systems, graph rewriting systems, etc. The international CTRS (Conditional and Typed Rewriting Systems) workshops are intended to offer a forum for researchers on such extensions of rewriting techniques. This volume presents the proceedings of the second CTRS workshop, which contributed to discussion and evaluation of new directions of research. (The proceedings of the first CTRS workshop are in Lecture Notes in Computer Science, Vol. 308.) Several important directions for extensions of rewriting techniques were stressed, which are reflected in the organization of the chapters in this volume: - Theory of conditional and Horn clause systems, - Infinite terms, non-terminating systems, and termination, - Extension of Knuth-Bendix completion, - Combined systems, combined languages and modularity, - Architecture, compilers and parallel computation, - Basic frameworks for typed and order-sorted systems, - Extension of unification and narrowing techniques.

The 1st International Workshop on Conditional Term Rewriting Systems took place in Orsay (University of Paris-Sud) in July 1987, and brought together most of the researchers involved in the field. Conditional rewriting has actually known important breakthroughs during the last two years; it was the purpose of the workshop to put the results together, to present new, original contributions to the domain, and to discuss still unsolved issues. These contributions are reported in the proceedings. The main questions that have been addressed are the different semantics for conditional rewriting and their classification, possible extensions to the basic formalism, and the relationship between conditional rewriting and logic programming. Also, more practical issues such as applications and implementations of conditional term rewriting systems have been addressed. Descriptions of seven actual systems allowing conditional rewriting are included.