Engineering formal metatheory

Conference Record of the Annual ACM Symposium on Principles of Programming Languages

Volumn , Issue , 2008, Pages 3-15

  Aydemir, Brian ^a   Charguéraud, Arthur ^b   Pierce, Benjamin C ^a   Pollack, Randy ^c   Weirich, Stephanie ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b INRIA   (France)

^c UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

binding; coq; locally nameless

Indexed keywords

BINDING; CALCULUS OF CONSTRUCTION; COQ; COQ PROOF ASSISTANT; DATATYPES; EQUIVARIANCE; FIRST-ORDER REPRESENTATION; FORMAL DEVELOPMENT; FREE VARIABLE; INDUCTION PRINCIPLES; LOCALLY NAMELESS; MACHINE-CHECKED PROOFS; META-THEORY; PROOF ASSISTANT; PROOF-CARRYING CODE; RECURSIONS; STRONG INVERSION; STRUCTURAL INDUCTION PRINCIPLE; SUBJECT REDUCTION; SYSTEM F; TOOL SUPPORT; VARIABLE BINDING;

COMPUTER PROGRAMMING LANGUAGES;

EID: 84865652525     PISSN: 07308566     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1328438.1328443     Document Type: Conference Paper

References (57)

1. Thorsten Altenkirch. A formalization of the strong normalization proof for System F in LEGO. In Bezem and Groote (1993), pages 13-28.
2. Andrew W. Appel. Foundational proof-carrying code. In IEEE Symposium on Logic in Computer Science (LICS), Boston, Massachusetts, pages 247-258, June 2001.
3. Michael Ashley-Rollman, Karl Crary, and Robert Harper. Submission to the POPLMARK challenge. Available from http://www.cis.upenn.edu/~plclub/mmm/, 2005.
4. Brian E. Aydemir, Aaron Bohannon, Matthew Fairbairn, J. Nathan Foster, Benjamin C. Pierce, Peter Sewell, Dimitrios Vytiniotis, Geoffrey Washburn, Stephanie Weirich, and Steve Zdancewic. Mechanized metatheory for the masses: The POPLMARK challenge. In Joe Hurd and Tom Melham, editors, Theorem Proving in Higher Order Logics: 18th International Conference, TPHOLs 2005, volume 3603 of Lecture Notes in Computer Science, pages 50-65. Springer, 2005.
5. Henk P. Barendregt. The Lambda Calculus. North Holland, revised edition, 1984.
6. Bruno Barras and Benjamin Werner. Coq in coq. Available from http://pauillac.inria.fr/~barras/coq-work-eng.html, 1997.
7. M. Bezem and J. F. Groote, editors. Typed Lambda Calculi and Applications: International Conference on Typed Lambda Calculi and Applications, TLCA '93, volume 664 of Lecture Notes in Computer Science, 1993. Springer.
8. Anna Bucalo, Furio Honsell, Marino Miculan, Ivan Scagnetto, and Martin Hoffman. Consistency of the theory of contexts. J. Funct. Program, 16 (3), 2006.
9. Adam Chlipala. Submission to the POPLMARK challenge, part 1a. Available from http://www.cs.berkeley.edu/~adamc/poplmark/, 2006.
10. The Coq Development Team. The Coq proof assistant reference manual, version 8.1. Available from http://coq.inria.fr/, 2007.
11. Thierry Coquand. An algorithm for testing conversion in type theory. In Gérard Huet and Gordon Plotkin, editors, Logical Frameworks, pages 255-279. Cambridge University Press, 1991.
12. Karl Crary. Toward a foundational typed assembly language. In POPL '03: Proceedings of the 30th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 198-212. ACM Press, 2003.
13. N. G. de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indagationes Mathematicae, 34(5):381-392, 1972.
14. Joëlle Despeyroux, Amy Felty, and André Hirschowitz. Higher-order abstract syntax in Coq. In Typed Lambda Calculi and Applications, Second International Conference on Typed Lambda Calculi and Applications, TLCA '95, volume 902 of Lecture Notes in Computer Science, pages 124-138. Springer, 1995.
15. Also available as INRIA Research Report 2556.
16. Peter Dybjer. Inductive families. Formal Aspects of Computing, 6:1-26, 1994.
17. Jonathan M. Ford and Ian A. Mason. Operational techniques in PVS - A preliminary evaluation. Electronic Notes in Theoretical Computer Science, 42, 2001.
18. Gerhard Gentzen. The Collected Papers of Gerhard Gentzen. North- Holland, 1969. Edited by Mandred Szabo.
19. Andrew D. Gordon. A mechanisation of name-carrying syntax up to alpha-conversion. In J. J. Joyce and C.-J. H. Seger, editors, Higher-order Logic Theorem Proving And Its Applications, Proceedings, 1993, volume 780 of Lecture Notes in Computer Science, pages 414-426. Springer, 1994.
20. Andrew D. Gordon and Tom Melham. Five axioms of alpha-conversion. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics: 9th International Conference, TPHOLs '96, volume 1125 of Lecture Notes in Computer Science, pages 173-190. Springer, 1996.
21. Robert Harper and Daniel R. Licata. Mechanizing metatheory in a logical framework. Journal of Functional Programming, 17(4-5):613-673, 2007.
22. Robert Harper, Furio Honsell, and Gordon Plotkin. A framework for defining logics. Journal of the ACM, 40(1):143-184, 1993.
23. Dimitri Hendriks and Vincent van Oostrom. Adbmal. In F. Baader, editor, Automated Deduction - CADE-19, volume 2741 of Lecture Notes in Artificial Intelligence, pages 136-150. Springer-Verlag, 2003.
24. Peter Homeier. A proof of the Church-Rosser theorem for the lambda calculus in higher order logic. In Richard J. Boulton and Paul B. Jackson, editors, TPHOLs 2001: Supplemental Proceedings, pages 207-222. Division of Informatics, University of Edinburgh, September 2001. Available as Informatics Research Report EDI-INF-RR-0046.
25. Furio Honsell, Marino Miculan, and Ivan Scagnetto. The theory of contexts for first order and higher order abstract syntax. Electronic Notes in Theoretical Computer Science, 62, 2002.
26. Gérard Huet. The constructive engine. In Raghavan Narasimhan, editor, A Perspective in Theoretical Computer Science: Commerative Volume for Gift Siromoney. World Scientific Publishing, 1989.
27. Also available as INRIA Technical Report 110.
28. Gérard Huet. Residual theory in λ-calculus: A formal development. Journal of Functional Programming, 4(3):371-394, July 1994.
29. Also available as INRIA Research Report 2009 (August 1993).
30. Gerwin Klein and Tobias Nipkow. A machine-checked model for a Javalike language, virtual machine, and compiler. ACM Transactions on Programming Languages and Systems, 28(4):619-695, 2006.
31. J. L. Krivine. Lambda-Calculus, Types and Models. Ellis Horwood, 1990.
32. Daniel K. Lee, Karl Crary, and Robert Harper. Towards a mechanized metatheory of Standard ML. In POPL '07: Proceedings of the 34th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 173-184. ACM Press, 2007.
33. Xavier Leroy. Formal certification of a compiler back-end, or: programming a compiler with a proof assistant. In Proc. of the 33rd Symposium on Principles of Programming Languages, pages 42-54. ACM Press, 2006.
34. Xavier Leroy. A locally nameless solution to the POPLmark challenge. Research report 6098, INRIA, January 2007.
35. Zhaohui Luo and Robert Pollack. The LEGO proof development system: A user's manual. Technical Report ECS-LFCS-92-211, University of Edinburgh, May 1992.
36. Conor McBride and James McKinna. Functional pearl: I am not a number - I am a free variable. In Haskell '04: Proceedings of the 2004 ACM SIGPLAN Workshop on Haskell, pages 1-9. ACM Press, 2004.
37. James McKinna and Robert Pollack. Pure Type Systems formalized. In Bezem and Groote (1993), pages 289-305.
38. James McKinna and Robert Pollack. Some lambda calculus and type theory formalized. Journal of Automated Reasoning, 23(3-4):373-409, 1999.
39. Tobias Nipkow. More Church-Rosser proofs (in Isabelle/HOL). Journal of Automated Reasoning, 26(1):51-66, January 2001.
40. Michael Norrish and Konrad Slind. HOL 4. Available from http://hol.sourceforge.net/, 2007.
41. Frank Pfenning and Conal Elliot. Higher-order abstract syntax. In PLDI '88: Proceedings of the ACM SIGPLAN 1988 Conference on Programming Language Design and Implementation, pages 199-208. ACM Press, 1988.
42. Frank Pfenning and Carsten Schürmann. System description: Twelf - A meta-logical framework for deductive systems. In Harald Ganzinger, editor, Automated Deduction, CADE 16: 16th International Conference on Automated Deduction, volume 1632 of Lecture Notes in Artificial Intelligence, pages 202-206. Springer, 1999.
43. Andrew M. Pitts. Nominal logic, a first order theory of names and binding. Information and Computation, 186:165-193, 2003.
44. Randy Pollack. Reasoning about languages with binding: Can we do it yet?, February 2006. Presentation, slides available from http://homepages.inf.ed.ac. uk/rpollack/.
45. Robert Pollack. Closure under alpha-conversion. In H. Barendregt and T. Nipkow, editors, TYPES'93: Workshop on Types for Proofs and Programs, Nijmegen, May 1993, Selected Papers, volume 806 of Lecture Notes in Computer Science, pages 313-332. Springer, 1994a.
46. Robert Pollack. The Theory of LEGO: A Proof Checker for the Extended Calculus of Constructions. PhD thesis, Univ. of Edinburgh, 1994b.
47. Dag Prawitz. Natural Deduction: Proof Theoretical Study. Almquist and Wiksell, Stockholm, 1965.
48. Ole Rasmussen. The Church-Rosser theorem in Isabelle: A proof porting experiment. Technical Report 364, University of Cambridge, Computer Laboratory, March 1995.
49. Wilmer Ricciotti. Submission to the POPLMARK challenge, part 1a. Available from http://ricciott.web.cs.unibo.it/, 2007.
50. Peter Sewell, Francesco Zappa Nardelli, Scott Owens, Gilles Peskine, Thomas Ridge, Susmit Sarkar, and Rok Strniša. Ott: Effective tool support for the working semanticist. In ICFP '07: Proceedings of the 2007 ACM SIGPLAN International Conference on Functional Programming, pages 1-12. ACM, 2007.
51. Natarajan Shankar. A mechanical proof of the Church-Rosser theorem. Journal of the Association for Computing Machinery, 35(3):475-522, 1988.
52. Allen Stoughton. Substitution revisited. Theoretical Computer Science, 59 (3):317-325, 1988.
53. Christian Urban. Nominal techniques in Isabelle/HOL. Journal of Automatic Reasoning, 2007. To appear; available from http://www4.in.tum.de/~urbanc/ publications.html.
54. Christian Urban and Randy Pollack. Locally nameless representation in Nominal Isabelle. Talk at Workshop on Mechanizing Metatheory. Available from www4.in.tum.de/~urbanc/Publications/ln.pdf, 2007.
55. Christian Urban, Stefan Berghofer, and Julien Narboux. Nominal datatype package for Isabelle/HOL. Available from http://isabelle.in.tum.de/nominal/, 2007a.
56. Christian Urban, Stefan Berghofer, and Michael Norrish. Barendregt's variable convention in rule inductions. In Proceedings of the 21th Conference on Automated Deduction (CADE 2007), volume 4603 of Lecture Notes in Computer Science, pages 35-50. Springer, 2007b.
57. René Vestergaard and James Brotherston. A formalised first-order confluence proof for the λ-calculus using one-sorted variable names. Information and Computation, 183(2):212-244, 2003.