This volume provides an account of the current state of the theory of combinatory spaces and discusses various applications. Here the term `combinatory space' can be regarded as a system for functional programming, and bears no close connection with combinatory logic. The main text is divided into three chapters. Chapter 1 deals with computational structures and computability; Chapter 2 considers combinatory spaces; and Chapter 3 embraces computability in iterative combinatory spaces. A number of appendices treat a survey of examples of combinatory spaces. All sections of the various chapters contain exercices togethers with hints for solution where appropriate. For the reading of some parts of the book a knowledge of mathematical logic and recursive function theory would be desirable. For researchers and specialists in mathematical logic and its applications and theoretical computer scientists.

Preface. I. Computational Structures and Computability on Them. II. Combinatory Spaces. III. Computability in Iterative Combinatory Spaces. Appendix: A Survey of Examples of Combinatory Spaces. References. Additional Bibliography. Index of Names. Index of Definitions.