TY  - BOOK
AU  - Barendregt,H.P.
TI  - The lambda calculus: its syntax and semantics 
SN  - 0444875085
U1  - 511.3 
PY  - 1984///
CY  - Amsterdam
PB  - Elsevier Science B.V.
KW  - Lambda calculus
N1  - Preface. - Hints For The Reader. - Pt. I. Towards The Theory. 1. Introduction. 2. Conversion. 3. Reduction. 4. Theories. 5. Models. - Pt. II. Conversion. 6. Classical Lambda Calculus. 7. Thed Theory of Combinators. 8. Classical Lambda Calculus(Continued). 9. The I-Calculus. 10. Bohm Trees. - Pt. III. Reduction. 11. Fundamental Theorems. 12. Strongly Equivalent Reductions. 13. Reduction Strategies. 14. Labelled Reduction. 15. Other Notions of Reduction. - Pt. IV Theories. 16. Sensible Theories. 17. Other Lambda Theories. - Pt. V. Models. 18. Construction of Models. 19. Local Structure of Models. 20. Global Structure of Models. 21. Combinatory Groups. - Appendices. - Appendix A. Typed Lanbda Calculus. - Appendix B. Illative Combinatory Logic. - Appendix C. Variable. - Final Exercises. - Addenda. - References. - Index of Names. - Index of Definitions. - Index of Symbols
N2  - Around 1930 the type free lambda calculus was introduced as a foundation for logic and mathematics.  Due to the appearence of paradoxes, this aim was not fulfilled, however.  Nevertheless a consistent part of the theory turned out to be quite successful as a theory of computations.  It gave an important momentum to early recursion theory and more recently to computer science.  Moreover, in spite of the paradoxes, the possibility of using the lambda calculus as an alternative foundation is still open.  This question recently received a good deal of renewed attention. As a results of these developments, the lambda calculus has grown into a thoery worth studying for its own sake. This pure lambda calculus is the subject matter of this book. Readers interested in applications may also find the book useful, since these applications are usually heuristic rather than direct. Constructions in the lambda calculus give the right intuition for constructions in, for example, the semantics of programming languages. Thus the book is written for logicians, mathematicians, computer scientists and philosophers. - Preface
ER  -