Mechanizing coinduction and corecursion in higher-order logic

Journal of Logic and Computation

Volumn 7, Issue 2, 1997, Pages 175-204

  Paulson, Lawrence C ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Coinduction; Corecursion; Higher order logic; Isabelle

Indexed keywords

EID: 0346801207     PISSN: 0955792X     EISSN: None     Source Type: Journal    
DOI: 10.1093/logcom/7.2.175     Document Type: Article

References (33)

1. S. Abramsky. The lazy lambda calculus. In Research Topics in Functional Programming, D. A. Turner, ed. pp. 65-116. Addison-Wesley, 1977.
2. P. Aczel. An introduction to inductive definitions. In Handbook of Mathematical Logic, J. Barwise, ed. pp. 739-782. North-Holland, 1977.
3. P. Aczel. Non-Well-Founcled Sets. CSLI, 1988.
4. P. B. Andrews, M. Bishop, S. Issar, D. Nesmith, F. Pfenning and H. Xi. TPS: A theorem proving system for classical type theory. Journal of Automated Reasoning, 16, 1996 (in press).
5. R. Bird and P. Wadler. Introduction to Functional Programming. Prentice-Hall, 1988.
6. A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5, 56-68, 1940.
7. L. J. M. Claesen and M. J. C. Gordon, eds. Higher Order Logic Theorem Proving and Its Applications. NorthHolland, 1993.
8. T. Coquand and C. Paulin. Inductively defined types. In COLOG-88: International Conference on Computer Logic, Estonian Academy of Sciences, Tallinn, P. Martin-Löf and G. Mints, eds. pp. 50-66. Vol. 417 of Lecture Notes in Computer Science, Springer, 1990.
9. B. A. Davey and H. A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 1990.
10. W. M. Farmer, J. D. Guttman and F. J. Thayer. IMPS: An interactive mathematical proof system. Journal of Automated Reasoning, 11, 213-248, 1993.
11. J. Frost. A case study of co-induction in Isabelle. Technical Report 359, Computer Laboratory, University of Cambridge, February 1995.
12. H. Geuvers. Inductive and coinductive types with iteration and recursion. In Types for Proofs and Programs, Båstad, June 1992, B. Nordström, K. Petersson and G. Plotkin, eds. pp. 193-217. Informal proceedings.
13. J.-Y. Girard. Proofs and Types. Cambridge University Press, 1989. Translated by Y. Lafont and P. Taylor.
14. M. J. C. Gordon and T. F. Melham. Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, 1993.
15. M. J. C. Gordon, R. Milner and C. P. Wadsworth. Edinburgh LCF: A Mechanised Logic of Computation. Vol. 78 of Lecture Notes in Computer Science, Springer, 1979.
16. E. L. Gunter. A broader class of trees for recursive type definitions for HOL. In Higher Order Logic Theorem Proving and Its Applications: HUG '93, J. Joyce and C. Seger, eds. pp. 141-154. Vol. 780 of Lecture Notes in Computer Science, Springer, 1994.
17. F. Leclerc and C. Paulin-Mohring. Programming with streams in Coq. A case study: the sieve of Eratosthenes. In Types for Proofs and Programs: International Workshop TYPES '93, H. Barendregt and T. Nipkow, eds. pp. 191-212. Vol. 806 of Lecture Notes in Computer Science, Springer, 1993.
18. T.F.Melham. Automating recursive type definitions in higher order logic. In Current Trends in Hardware Verification and Automated Theorem Proving, G. Birtwistle and P. A. Subrahmanyam, eds. pp. 341-386. Springer, 1989.
19. N. P. Mendier. Recursive types and type constraints in second-order lambda calculus. In Second Annual Symposium on Logic in Computer Science, pp. 30-36. IEEE Computer Society Press, 1987.
20. R. Milner. Communication and Concurrency. Prentice-Hall, 1989.
21. R. Milner and M. Tofte. Co-induction in relational semantics. Theoretical Computer Science, 87, 209-220, 1991.
22. L. C. Paulson. Logic and Computation: Interactive proof with Cambridge LCF. Cambridge University Press, 1987.
23. L. C. Paulson. The foundation of a generic theorem prover. Journal of Automated Reasoning, 5, 363-397, 1989.
24. L. C. Paulson. Set theory for verification: I. From foundations to functions. Journal of Automated Reasoning, 11, 353-389, 1993.
25. L. C. Paulson. Isabelle: A Generic Theorem Prover. Vol. 828 of Lecture Notes in Computer Science, Springer, 1994.
26. L. C. Paulson. Set theory for verification: II. Induction and recursion. Journal of Automated Reasoning, 15, 167-215, 1995.
27. L. C. Paulson. A concrete final coalgebra theorem for ZF set theory. In Types for Proofs and Programs: International Workshop TYPES '94, P. Dybjer, B. Nordström and J. Smith, eds. pp. 120-139. Vol. 996 of Lecture Notes in Computer Science, Springer, 1995.
28. A. M. Pitts. A co-induction principle for recursively defined domains. Theoretical Computer Science, 124, 195-219, 1994.
29. J. J. M. M. Rutten and D. Tun. On the foundations of final semantics: Non-standard sets, metric spaces, partial orders. In Semantics: Foundations and Applications, J. de Bakker, W.-P. de Roever and G. Rozenberg, eds. pp. 477-530. Vol. 666 of Lecture Notes in Computer Science, Springer, 1993.
30. D. S. Scott. A type-theoretical alternative to ISWIM, CUCH, OWHY. Theoretical Computer Science, 121, 411-440, 1993. Annotated version of the 1969 manuscript.
31. A. Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5, 285-309, 1955.
32. M. Tofte. Type inference for polymorphic references. Information and Computation, 89, 1-34, 1990.
33. A. N. Whitehead and B. Russell. Principia Mathematica. Cambridge University Press, 1962. Paperback edition to *56, abridged from the 2nd edition (1927).