Abstract abstract reduction

Journal of Logic and Algebraic Programming

Volumn 66, Issue 2, 2006, Pages 239-270

  Struth, Georg ^a  

^a BUNDESWEHR UNIVERSITY MUNICH   (Germany)

Author keywords

Calculus; Algebra; Abstract reduction; Church Rosser theorems; Formal mathematics; Kleene algebra; Rewriting; Semirings; Termination analysis

Indexed keywords

ABSTRACTING; AUTOMATA THEORY; COMPUTER SIMULATION; DATA REDUCTION; MATHEMATICAL TRANSFORMATIONS; MECHANIZATION; SEMANTICS; THEOREM PROVING;

Λ-CALCULUS; Ω-ALGEBRA; ABSTRACT REDUCTION; CHURCH-ROSSER THEOREMS; FORMAL MATHEMATICS; KLEENE ALGEBRA; REWRITING; SEMIRINGS; TERMINATION ANALYSIS;

ALGEBRA;

EID: 30744444213     PISSN: 15678326     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jlap.2005.04.001     Document Type: Article

References (38)

1. L. Bachmair, and N. Dershowitz Commutation, transformation, and termination J.H. Siekmann 8th International Conference on Automated Deduction LNCS vol. 230 1986 Springer-Verlag 5 20
2. R.C. Backhouse, Closure algorithms and the star-hight problem of regular languages, Ph.D. thesis, Imperial College, 1975.
3. R.C. Backhouse, and B.A. Carré Regular algebra applied to path-finding problems J. Inst. Math. Appl. 15 1975 161 186
4. H.P. Barendregt The Lambda Calculus Studies in Logic and the Foundations of Mathematics revised edition 1984 North-Holland
5. F. Bellegarde, P. Lescanne, Termination proofs based on transformation techniques, Technical Report 86-R-034, Centre de Recherche en Informatique de Nancy, 1986.
6. F. Bellegarde, and P. Lescanne Transformation ordering H. Ehrig R.A. Kowalski G. Levi U. Montanari TAPSOFT'87: Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming (CAAP'87) LNCS vol. 249 1987 Springer-Verlag 69 80
7. F. Bellegarde, and P. Lescanne Termination by completion Appl. Algebra Eng. Commun. Comput. 1 1990 79 96
8. M. Bezem, and T. Coquand Newman's lemma-a case study in proof automation and geometric logic Bull. EATCS 79 2003 86 100
9. E. Cohen Separation and reduction R. Backhouse J.N. Oliveira Proc. of Mathematics of Program Construction, 5th International Conference, MPC LNCS vol. 1837 2000 Springer-Verlag 45 59
10. J.H. Conway Regular Algebra and Finite Machines 1971 Chapman and Hall
11. S. Crvenkovič, I. Dolinka, and Z. Ésik The variety of Kleene algebras with conversion is not finitely based Theor. Comput. Sci. 230 2000 235 245
12. M. Davis Computability and Unsolvability 1958 McGraw-Hill
13. J. Desharnais, B. Möller, and G. Struth Termination in modal Kleene algebra J.-J. Levy E.W. Mayr J.C. Mitchell Exploring New Frontiers of Theoretical Informatics IFIP International Federation for Information Processing Series vol. 155 2004 Kluwer 647 660
14. J. Desharnais, B. Möller, G. Struth. Kleene algebra with domain, ACM Trans. Comput. Logic, in press.
15. V. Diekert G. Rozenberg The Book of Traces 1995 World Scientific
16. H. Doornbos, R.C. Backhouse, and J. van der Woude A calculation approach to mathematical induction Theor. Comput. Sci. 179 1997 103 135
17. H. Doornbos, and B. von Karger On the union of well-founded relations L. J. IGPL 6 2 1998 195 201
18. M. Ebert, and G. Struth Diagram chase in relational system development ENTCS 127 2005 87 105
19. S. Eilenberg Automata, Languages and Machines, vol. A 1974 Academic Press
20. P. Freyd, and A. Scedrov Categories Allegories 1990 North-Holland
21. A. Geser, Relative termination, Ph.D. thesis, Fakultät für Mathematik und Informatik, Universität Passau, 1990.
22. J.-P. Jouannaud, and H. Kirchner Completion of a set of rules modulo a set of equations SIAM J. Comput. 15 1986 1155 1194
23. W. Kahl Calculational relation-algebraic proofs in Isabelle/Isar R. Berghammer B. Möller G. Struth Proc. of 7th International Seminar on Relational Methods in Computer Science/Second International Workshop on Applications of Kleene Algebra LNCS vol. 3051 2004 Springer-Verlag 179 190
24. D. Kozen A completeness theorem for Kleene algebras and the algebra of regular events Inform. Comput. 110 2 1994 366 390
25. D. Kozen Kleene algebra with tests and commutativity conditions T. Margaria B. Steffen Proc. of TACAS'96 LNCS vol. 1055 1996 Springer-Verlag 14 33
26. D. Kozen, and M.-C. Patron Certification of compiler optimizations using Kleene algebra with tests J. Lloyd V. Dahl U. Furbach M. Kerber K.-K. Lau C. Palamadessi L.-M. Pereira V. Sagiv P.-J. Stuckey 1st International Conference on Computational Logic (CL2000) LNAI vol. 1861 2001 Springer-Verlag 568 582
27. J. Levy, and J. AgustIÍ Bi-rewriting systems J. Symbol. Comput. 22 1996 279 314
28. J. McKinna, and R. Pollack Some lambda calculus and type theory formalized J. Automat. Reason. 23 3-4 1999 373 409
29. T. Nipkow More Church-Rosser proofs (in Isabelle/HOL) J. Automat. Reason. 26 1 2001 51 66
30. Otter: An automated deduction system, 2004. Available from: .
31. V.N. Redko On defining relations for the algebra of regular events Ukrainian Mathematical Journal 16 1964 120 126
32. G.W. Schmidt, and T. Ströhlein Relations and Graphs: Discrete Mathematics for Computer Scientists EATCS Monographs on Theoretical Computer Science 1993 Springer-Verlag
33. N. Shankar A mechanical proof of the Church-Rosser theorem J. ACM 35 3 1988 475 522
34. G. Struth, Non-symmetric rewriting, Technical Report MPI-I-96-2-004, Max-Planck-Institut für Informatik, 1996.
35. G. Struth, Canonical transformations in algebra, universal algebra and logic, Ph.D. thesis, Institut für Informatik, Universität des Saarlandes, 1998.
36. G. Struth, Isabelle-specification and proofs of Church-Rosser theorems, 2001. Available from: .
37. M. Takahashi Parellel reductions in λ-calculi Inform. Comput. 118 1 1995 120 127
38. Terese Term Rewriting Systems 2003 Cambridge University Press