The programming language SETL is a relatively new member of the so-called "very-high-level" class of languages, some of whose other well-known mem bers are LISP, APL, SNOBOL, and PROLOG. These languages all aim to reduce the cost of programming, recognized today as a main obstacle to future progress in the computer field, by allowing direct manipulation of large composite objects, considerably more complex than the integers, strings, etc., available in such well-known mainstream languages as PASCAL, PL/I, ALGOL, and Ada. For this purpose, LISP introduces structured lists as data objects, APL introduces vectors and matrices, and SETL introduces the objects characteristic for it, namely general finite sets and maps. The direct availability of these abstract, composite objects, and of powerful mathematical operations upon them, improves programmer speed and pro ductivity significantly, and also enhances program clarity and readability. The classroom consequence is that students, freed of some of the burden of petty programming detail, can advance their knowledge of significant algorithms and of broader strategic issues in program development more rapidly than with more conventional programming languages."

An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.

"Set Theory for Computing" provides a comprehensive account of set-oriented symbolic manipulation methods suitable for automated reasoning. Its main objective is twofold: 1) to provide a flexible formalization for a variety of set languages, and 2) to clarify the semantics of set constructs firmly established in modern specification languages and in the programming practice. Topics include: semantic unification, decision algorithms, modal logics, declarative programming, tableau-based proof techniques, and theory-based theorem proving. The style of presentation is self-contained, rigorous and accurate. Some familiarity with symbolic logic is helpful but not a requirement. This book is a useful resource for all advanced students, professionals, and researchers in computing sciences, artificial intelligence, automated reasoning, logic, and computational mathematics. It will serve to complement their intuitive understanding of set concepts with the ability to master them by symbolic and logically based algorithmic methods and deductive techniques.