Alpha-structural recursion and induction

Journal of the ACM

Volumn 53, Issue 3, 2006, Pages 459-506

  Pitts, Andrew M ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Abstract syntax; Binders; Induction; Names; Recursion

Indexed keywords

ABSTRACTING; BINDERS; EQUIVALENCE CLASSES; FORMAL LOGIC; MATHEMATICAL MODELS; TREES (MATHEMATICS);

ABSTRACT SYNTAX; INDUCTION; NAMES; RECURSION;

SYNTACTICS;

EID: 33746899076     PISSN: 00045411     EISSN: 00045411     Source Type: Journal    
DOI: 10.1145/1147954.1147961     Document Type: Article

References (35)

1. AYDEMIR, B. E., BOHANNON, A., FAIRBAIRN, M., FOSTER, J. N., PIERCE, B. C., SEWELL, P., VYTINIOTIS, D., WASHBURN, G., WEIRICH, S., AND ZDANCEWIC, S. 2005. Mechanised metatheory for the masses: The POPLmark challenge. In Proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005), J. Hurd and T. Melham, Eds. Lecture Notes in Computer Science, vol. 3603. Springer-Verlag, New York, 50-65. www.cis.upenn.edu/group/proj/plclub/mmm/.
2. BARENDREGT, H. P. 1984. The Lambda Calculus: Its Syntax and Semantics, revised ed. North-Holland.
3. BARENDREGT, H. P. 1992. Lambda calculi with types. In Handbook of Logic in Computer Science, S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, Eds. Vol. 2. Oxford University Press, 117-309.
4. BERGER, U., EBERL, M., AND SCHWICHTENBERG, H. 2003. Term rewriting for normalization by evaluation. Inf. Comput. 183, 19-42.
5. BERGER, U., AND SCHWICHTENBERG, H. 1991. An inverse of the evaluation functional for typed X-calculus. In Proceedings of the 6th Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 203-211.
6. CHENEY, J. 2004. Nominal logic programming. Ph.D. dissertation, Cornell University.
7. CHURCH, A. 1940. A formulation of the simple theory of types. J. Symb. Logic 5, 56-68.
8. DE BRUIJN, N. G. 1972. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indag. Math. 34, 381-392.
9. DYBJER, P. 2000. A general formulation of simultaneous inductive-recursive definitions in type theory. J. Symb. Logic 65, 2.
10. DYBJER, P., AND FILINSKI, A. 2002. Normalization and partial evaluation. In Applied Semantics, Advanced Lectures, G. Barthe, P. Dybjer, and J. Saraiva, Eds. Lecture Notes in Computer Science, Tutorial, vol. 2395. Springer-Verlag, New York, 137-192. (International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000).
11. FIORE, M. P. 2002. Semantic analysis of normalisation by evaluation for typed lambda calculus. In Proceedings of the 4th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP 2002), (Pittsburgh, PA), ACM, New York, 26-37.
12. FIORE, M. P., PLOTKIN, G. D., AND TURI, D. 1999. Abstract syntax and variable binding. In Proceedings of the 14th Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 193-202.
13. GABBAY, M. J. 2000. A theory of inductive definitions with α-equivalence: Semantics, implementation, programming language. Ph.D. dissertation, University of Cambridge.
14. GABBAY, M. J. 2002. FM-HOL, a higher-order theory of names. In Workshop on Thirty Five years of Automath, Informal Proceedings, F. Kamareddine, ed. Heriot-Watt University, Edinburgh, Scotland.
15. GABBAY, M. J. 2006. A general mathematics of names in syntax. Math. Struct. Comput. Sci. to appear.
16. GABBAY, M. J., AND PITTS, A. M. 2002. A new approach to abstract syntax with variable binding. Form. Asp. Comput. 13, 341-363.
17. GORDON, A. D., AND MELHAM, T. 1996. Five axioms of alpha-conversion. In Theorem Proving in Higher Order Logics, 9th International Conference. Lecture Notes in Computer Science, vol. 1125. Springer-Verlag, New York, 173-191.
18. GRIFFIN, T. G. 1988. Notational definition -A formal account. In Proceedings of the 3rd Annual Symposium on Logic in Computer Science. IEEE Computer Society Press, 372-383.
19. GUNTER, C. A. 1992. Semantics of programming languages: Structures and techniques, Los Alamitos, CA. Foundations of Computing. MIT Press, Cambridge, MA.
20. HONSELL, F., MICULAN, M., AND SCAGNETTO, I. 2001. An axiomatic approach to metareasoning on nominal algebras in HOAS. In Proceedings of the 28th International Colloquium on Automata, Languages and Programming (ICALP 2001), Crete, Greece, July. F. Orejas, P. G. Spirakis, and J. Leeuwen, Eds. Lecture Notes in Computer Science, vol. 2076. Springer-Verlag, New York, 963-978.
21. JECH, T. J. 1977. About the axiom of choice. In Hand book of Mathematical Logic. J. Barwise, ed. North-Holland, Amsterdam, The Netherlands, 345-370
22. NORRISH, M. 2004. Recursive function definition for types with binders. In Theorem Proving in Higher Order Logics, 17th International Conference. Lecture Notes in Computer Science, vol. 3223. Springer-Verlag, New York, 241-256.
23. PFENNING, F., AND ELLIOTT, C. 1988. Higher-order abstract syntax. In Proceedings of the ACM-SIGPLAN Conference on Programming Language Design and Implementation. ACM, New York, 199-208.
24. PITTS, A.M. 2003. Nominal logic, a first order theory of names and binding. Inf. Comput. 186, 165-193.
25. PITTS, A. M. 2005. Alpha-structural recursion and induction (extended abstract). In Theorem Proving in Higher Order Logics, 18th International Conference (TPHOLs 2005), Oxford UK, Aug. J. Hurd and T. Melham, Eds. Lecture Notes in Computer Science, vol. 3603. Springer-Verlag, New York, 17-34.
26. PLOTKIN, G. D. 1990. An illative theory of relations. In Situation Theory and its Applications, Volume 1, R. Cooper, Mukai, and J. Perry, Eds. CSLI Lecture Notes, vol. 22. Stanford Univ., Stanford, CA, 133-146.
27. PLOTKIN, G. D. 2004. A structural approach to operational semantics. J. Logic Algeb. Prog. 60-61, 17-139.
28. POTHER, F. 2005. An overview of Cαml. In Proeeedings of the ACM SIGPLAN Workshop on ML (Tallinn, Estonia). ACM, New York.
29. SANGIORGI, D., AND WALKER, D. 2001. The π-calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge, UK.
30. SCHÖPP, U. 2006. Names and binding in type theory. Ph.D. dissertation, University of Edinburgh.
31. SCHÖPF, U., AND STARK, I. D.B. 2004. A dependent type theory with names and binding. In Proceedings of the Symposium on Computer Science Logic (CSL04), (Karpacz, Poland). Lecture Notes in Computer Science, vol. 3210. Springer-Verlag, New York, 235-249.
32. SHINWELL, M. R., AND PITTS, A. M. 2005. On a monadic semantics for freshness. Theoret. Comput. Sci. 342, 28-55.
33. STOUGHTON, A. 1988. Substitution revisited. Theoret. Comput. Sci. 59, 317-325.
34. URBAN, C., PITTS, A. M., AND GABBAY, M. J. 2004. Nominal unification. Theoret. Comput. Sci. 323, 473-497.
35. URBAN, C., AND TASSON, C. 2005. Nominal techniques in Isabelle/HOL. In Proceedings of the 20th International Conference on Automated Deduction (CADE-20), (Tallinn, Estonia, July). Lecture Notes in Computer Science, vol. 3632. Springer-Verlag, New York, 38-53.