Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems: Abstract Properties and Applications to Term Rewriting Systems

Journal of the ACM (JACM)

Volumn 27, Issue 4, 1980, Pages 797-821

  Huet, Gérard ^a  

^a INRIA   (France)

Author keywords

Church Rosser property; combinatorial theories; confluence; equality theorem prowng; equattonal theories; operauonal semantics

Indexed keywords

EID: 84976811006     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/322217.322230     Document Type: Article

References (39)

1. Aho, A., Sethi, R., and Ullman, J. Code optimization and finite Church-Rosser systems In Proceedings of Courant Computer Science Symposium 5, R Rustin, Ed., Prentice Hall, Englewood Cliffs, N.J, 1972, pp 89-105.
2. Brown, T A A structured design method for specialized proof procedures PhD Thesis, California Institute of Technology, Pasadena, Calif., 1975.
3. Burstall, R Proving properties of programs by structural induction Comput J. 12(1969), 41-48.
4. Church, A., and Rosser, J.B. Some properties of conversion. Trans. AMS 39(1936), 472-482.
5. Cohn, P M Universal algebra. Harper and Row, New York, 1965.
6. Curry, H B., and Feys, R Combinatory Logic, Vol 1 North Holland, Amsterdam, 1958.
7. Dershowitz, N, and Manna, Z Proving termination with multiset orderings Commun ACM 22, 8 (Aug. 1979), 465-476.
8. Guard, J R, Oglesby, F.C., Bennett, J.H., and Settle, L.G. Semi-automated mathematics J. ACM 16 (1969), 49-62.
9. Hindley, R An abstract Church-Rosser theorem Pt 1, J Symbolic Logic 34 (1969), 545-560.Pt 2, J Symbolic Logic 39(1974), 1-21.
10. Hindley, R An abstract Church-Rosser theorem Pt 2, J Symbolic Logic 39 (1974), 1-21.
11. Hindley, R, Lercher, B., and Seldin, J.P. Introduction to combinatory logic In London Mathematical Society Lecture Notes 7, Cambridge University Press, Cambridge, England, 1972.
12. Huet, G. Experiments with an interactive prover for logic with equality Rep. 1106, Jennings Computing Center, Case Western Reserve Univ, Cleveland, Ohio, 1970.
13. Huet, G Résolution d'équations dans des langages d'ordre 1, 2, …,ω Thèse d'Etat, Univ Pans VII, Pans, Sept 1976.
14. Huet, G, and Lankford, D.S. On the uniform halting problem for term rewriting systems Lab Rep No 283, INR1A, Le Chesnay, France, March 1978.
15. Huet, G., and Levy, J J. Call by need computations in non-ambiguous linear term rewriting systems. Lab. Rep. No. 359, INRIA, Le Chesnay, France, Aug. 1979.
16. KLOP, J W A counter example to the Church-Rosser property for lambda calculus with subjective pairing Preprint No 102, Dep of Mathematics, Univ. of Utrecht, Utrecht, The Netherlands, 1978.
17. Knuth, D., and Bendix, P. Simple word problems in universal algèbras In Computational Problems in Abstract Algebra, J Leech, Ed., Pergamon Press, Elmsford, N.Y, 1970, pp. 263-297.
18. Lankford, D S. Canonical inference Rep ATP-25, Dep. Mathematics and Computer Sciences, Univ. of Texas, Austin, Texas, Dec 1975.
19. Lankford, D S., and Ballantyne, A.M. Decision procedures for simple equational theories with commutative axioms Complete sets of commutative reductions. Rep. ATP-35, Dep. Mathematics and Computer Sciences, Univ of Texas, Austin, Texas, March 1977.
20. Lankford, D.S., and Ballantyne, A M. Decision procedures for simple equational theories with permutative axioms. Complete sets of permutative reductions Rep. ATP-37, Dep. of Mathematics and Computer Sciences, Univ of Texas, Austin, Texas, April 1977.
21. Lankford, D.S., and Ballantyne, A.M. Decision procedures for simple equational theories with commutative-associative axioms: Complete sets of commutative-associative reductions Rep ATP-39, Dep Mathematics and Computer Sciences, Univ. of Texas, Austin, Texas, Aug. 1977.
22. Lipton, R.J., and Snyder, L On the halting of tree replacement systems Proc of Waterloo Conf. on Theoretical Computer Science, Univ of Waterloo, Waterloo, Ontario, Aug 1977, pp 43-46.
23. Manna, Z., and Ness, S. On the termination of Markov algorithms. Proc 3rd Hawaii Int. Conf. on System Sciences, Jan. 1970, pp. 789-792.
24. Newman, M.H. A On theories with a combinatorial definition of “equivalence” Ann Math, 43 (1942), 223-243.
25. Nivat, M. Congruences parfaites et quasi-parfaites Séminaire Dubreuil 7, 1971-72.
26. preliminary version On some families of languages related to the Dyck language. Proc 2nd Ann. ACM Symp on Theory of Computing, Northampton, Mass., May 1970, pp. 221-225.
27. Paterson, M.S., and Wegman, M N Linear unification Proc 8th Ann ACM Symp. on Theory of Computing, Hershey, Pa, May 1976, pp. 181-186.
28. Peterson, G E, and Stickel, M E Complete sets of reductions for equational theories with complete unification algorithms Tech. Rep., Dep. of Computer Science, Univ. of Arizona, Tucson, Anz., Sept 1977.
29. Plaisted, D. Well-founded orderings for proving termination of systems of rewrite rules Tech Rep. 78932, Dep. of Computer Science, Univ. of Illinois, Urbana-Champaign, III, July 1978.
30. Plaisted, D. A recursively defined ordering for proving termination of term rewnting systems Tech. Rep 78-943, Dep of Computer Science, Univ of Illinois, Urbana-Champaign, III, Sept 1978.
31. Plotkin, G Lattice-theoretic properties of subsumption Memo MIP-R77, Univ. of Edinburgh, Edinburgh, Scotland, 1970.
32. Plotkin G. Building-in equational theories In Machine Intelligence 7, B. Meltzer and D. Michie, Eds., American Elsevier, New York, 1972, pp 73-90.
33. Reynolds, J Transformational systems and the algebraic structure of atomic formulas. In Machine Intelligence 5, B Meltzer and D Michie, Eds, American Elsevier, New York, 1970, pp. 135-152.
34. Robinson, J. A. A machine-oriented logic based on the resolution principle J. ACM 12, 1 (Jan. 1965), 23-41.
35. Rosen, B K. Tree-manipulating systems and Church-Rosser theorems J. ACM 20, 1 (Jan. 1973), 160-187.
36. Sethi, R Testing for the Church-Rosser property J ACM 21, 4 (Oct 1974), 671-679. Errata, J. ACM 22, 3 (July 1975), 424.
37. Sethi, R Errata, J ACM 22, 3 (July 1975), 424.
38. Slagle, J R Automated theorem proving for theories with simplifiers, commutativity, and associativity. J ACM 21, 4 (Oct 1974), 622-642.
39. Staples, J Church-Rosser theorems for replacement systems In Algebra and Logic, J. Crossley, Ed., Lecture Notes in Mathematics No 450, Springer-Verlag, 1975.