Consistency of the theory of contexts

Journal of Functional Programming

Volumn 16, Issue 3, 2006, Pages 327-395

  Bucalo, Anna ^a   Honsell, Furio ^a   Miculan, Marino ^a   Scagnetto, Ivan ^a   Hoffman, Martin ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AXIOMATIZATION; CLASSICAL HIGHER-ORDER LOGIC; FUNCTOR CATEGORY; HIGHER-ORDER ABSTRACT SYNTAX; MODEL-BASED OPC; RECURSIONS; STRUCTURAL INDUCTION; THEORY OF CONTEXTS;

FUNCTIONAL PROGRAMMING;

FORMAL LOGIC;

EID: 33646396504     PISSN: 09567968     EISSN: 14697653     Source Type: Journal    
DOI: 10.1017/S0956796806005892     Document Type: Article

References (43)

1. Ambler, S., Crole, R. and Momigliano, A. (eds). (2001) Mechanized reasoning about languages with variable binding. Electronic Notes in Theoretical Computer Science, vol. 58.1. Elsevier.
2. Barr, M. and Wells, C. F. (1999) Category theory for computing science. Les Publications CMR.
3. Bucalo, A., Hofmann, M., Honsell, F., Miculan, M. and Scagnetto, I. (2005) Appendices of "Consistency of the Theory of Contexts". Available online at the Journal of Functional Programming web site.
4. Cattani, G. L., Stark, I. and Winskel, G. (1997) Presheaf models for the π-calculus. Proc. CTCS.
5. Church, A. (1940) A formulation of the simple theory of types. Journal of Symbolic Logic, 5, 56-68.
6. Crole, R. L. (2003) Basic category theory for models of syntax. Pages 133-177 of: Backhouse, R. C. and Gibbons, J. (eds), Generic Programming. Lecture Notes in Computer Science, vol. 2793. Springer.
7. Despeyroux, J., Felty, A. and Hirschowitz, A. (1995) Higher-order syntax in Coq. Proc. of tlca'95. Lecture Notes in Computer Science, vol. 905. Springer-Verlag.
8. Fiore, M. and Turi, D. (2001) Semantics of name and value passing. Pages 93-104 of: Mairson, H. (ed), Proc. 16th LICS. Boston, USA: IEEE.
9. Fiore, M., Moggi, E. and Sangiorgi, D. (1996) A fully-abstract model for the π-calculus. Proc. 11th LICS. IEEE.
10. Fiore, M. P., Plotkin, G. D. and Turi, D. (1999) Abstract syntax and variable binding. In: Longo, G. (ed.), Proceedings, 14th Annual IEEE Symposium on Logic in Computer Science. IEEE.
11. Gabbay, M. J. and Pitts, A. M. (1999) A new approach to abstract syntax involving binders. In: Longo, G. (ed.), Proceedings, 14th Annual IEEE Symposium on Logic in Computer Science. IEEE.
12. Gabbay, M. J. and Pitts, A. M. (2002) A new approach to abstract syntax with variable binding. Formal Aspects of Computing, 13, 341-363.
13. Harper, R., Honsell, F. and Plotkin, G. (1993) A framework for defining logics. Journal of the ACM, 40(1), 143-184.
14. Hofmann, M. (1999) Semantical analysis of higher-order abstract syntax. In: Longo, G. (ed.), Proceedings, 14th Annual IEEE Symposium on Logic in Computer Science. IEEE.
15. Honsell, F., Miculan, M. and Scagnetto, I. (2001a) An axiomatic approach to metareasoning on systems in higher-order abstract syntax. Pages 963-978 of: Proc. ICALP'01. Lecture Notes in Computer Science, vol. 2076. Springer-Verlag.
16. Honsell, F., Miculan, M. and Scagnetto, I. (2001b) π-calculus in (co)inductive type theory. Theoretical Computer Science, 253(2), 239-285.
17. Hyland, J. M. E., Johnstone, P. T. and Pitts, A. M. (1980) Tripos theory. Math. Proc. Cambridge Philos. Soc., 88, 205-232.
18. INRIA (2003) The Coq proof assistant. http://coq.inria.fr/doc/main.html.
19. Jacobs, B. (1995) Parameters and parametrization in specification using distributive categories. Fund. Informaticae, 24(3).
20. Jacobs, B. (1999) Categorical logic and type theory. Studies in Logic and the Foundations of Mathematics, vol. 141. Elsevier.
21. Johnstone, P. (1977) Topos theory. London Mathematical Society Monographs, no. 10. London: Academic Press.
22. Longo, G (ed.) (1999) Proceedings, 14th Annual IEEE Symposium on Logic in Computer Science. IEEE.
23. Mac Lane, S. (1971) Categories for the Working Mathematician. Springer-Verlag.
24. Mac Lane, S. and Moerdijk, I. (1994) Sheaves in geometry and logic: a first introduction to topos theory. Universitext. Springer-Verlag.
25. McDowell, R. and Miller, D. (2002) Reasoning with higher-order abstract syntax in a logical framework. ACM Trans. Computational Logic, 3(1), 80-136.
26. Miculan, M. (1997) Encoding logical theories of programs. PhD thesis, Dipartimento di Informatica, Università di Pisa, Italy.
27. Miculan, M. (2001) Developing (meta)theory of lambda-calculus in the theory of contexts. In: Ambler, S., Crole, R. & Momigliano, A. (eds.), Mechanized reasoning about languages with variable binding. Electronic Notes in Theoretical Computer Science, vol. 58.1. Elsevier.
28. Milner, R., Parrow, J. and Walker, D. (1992) A calculus of mobile processes. Inform. and Comput. 100(1), 1-77.
29. Moggi, E. (1989) An abstract view of programming languages. Tech. rept. ECS-LFCS-90-113. LFCS, University of Edinburgh.
30. Moggi, E. (1993) Notions of computation and monads. Inform. and Comput., 1.
31. Oles, F. J. (1985) Type categories, functor categories and block structure. In: Nivat, M. and Reynolds, J. C. (eds.). Algebraic Semantics. Cambridge University Press.
32. Pfenning, F. and Elliott, C. (1988) Higher-order abstract syntax. Pages 199-208 of: Proc. of ACM SIGPLAN'88 Symposium on Language Design and Implementation.
33. Pfenning, F. and Schürmann, C. (1999) System description: Twelf - A meta-logical framework for deductive systems. Pages 202-206 of: Ganzinger, H. (ed.), Proceedings of the 16th International Conference on Automated Deduction (CADE-16). LNAI, vol. 1632. Trento, Italy: Springer-Verlag.
34. Pitts, A. M. (1981) The theory of triposes. PhD thesis, Cambridge Univ.
35. Pitts, A. M. (1999) Tripos theory in retrospect. In: Birkedal, L. and Rosolini, G. (eds.), Tutorial workshop on realizability semantics, FLoC'99, Trento, Italy. Electronic Notes in Theoretical Computer Science, vol. 23. Elsevier.
36. Pitts, A. M. (2003) Nominal logic, a first order theory of names and binding. Information and Computation, 186, 165-193.
37. Reynolds, J. C. (1981) The essence of Algol. Pages 345-372 of: de Bakker and van Vliet (eds.), Algorithmic Languages. Proc. ACM Annual Conference. North-Holland.
38. Röckl, C., Hirschkoff, D. and Berghofer, S. (2001) Higher-order abstract syntax with induction in Isabelle/HOL: Formalising the π-calculus and mechanizing the theory of contexts. Pages 359-373 of: Honsell, F. and Miculan, M. (eds.), Proc. fossacs 2001. LNCS, vol. 2030. Springer-Verlag.
39. Scagnetto, I. (2002) Reasoning about names in higher-order abstract syntax. PhD thesis, Dipartimento di Matematica e Informatica, Università di Udine, Italy.
40. Scagnetto, I. and Miculan, M. (2002) Ambient calculus and its logic in the calculus of inductive constructions. In: Pfenning, F. (ed.), Proc. Third International Workshop on Logical Frameworks and Meta-languages (LFM'02). Electronic Notes in Theoretical Computer Science, vol. 70.2. Elsevier.
41. Stark, I. (1994) Names and higher-order functions. PhD thesis. University of Cambridge. Available as Technical Report 363, University of Cambridge Computer Laboratory.
42. Stark, I. (1996) A fully abstract domain model for the π-calculus. Pages 36-42 of: Proc. LICS'96. IEEE.
43. van Oosten, J. (1991) Exercises in realizability. PhD thesis, Department of Mathematics and Computer Science, University of Amsterdam.