Lazy narrowing: Strong completeness and eager variable elimination

Theoretical Computer Science

Volumn 167, Issue 1-2, 1996, Pages 95-130

  Middeldorp, Aart ^a   Okui, Satoshi ^a   Ida, Tetsuo ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; COMPUTATION THEORY; COMPUTER PROGRAMMING LANGUAGES; FORMAL LOGIC;

LAZY NARROWING; STRONG COMPLETENESS;

COMPUTER SCIENCE;

EID: 0030264105     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(96)00071-0     Document Type: Article

References (23)

1. L. Bachmair, H. Ganzinger, C. Lynch and W. Snyder, Basic paramodulation, Inform. and Comput. 121 (1995) 172-192.
2. N. Dershowitz and J.-P. Jouannaud, Rewrite systems, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B (North-Holland, Amsterdam, 1990) 243-320.
3. N. Dershowitz and Z. Manna, Proving termination with multiset orderings, Comm. ACM 22 (1979) 465-476.
4. M. Fay, First-order unification in equational theories, in: Proc. 4th Conf. on Automated Deduction (1979) 161-167.
5. J. Gallier and W. Snyder, Complete sets of transformations for general E-unification, Theoret. Comput. Sci. 67 (1989) 203-260.
6. M. Hanus, Efficient implementation of narrowing and rewriting, in: Proc. Internat. Workshop on Processing Declarative Knowledge, Lecture Notes in Artificial Intelligence, Vol. 567 (Springer, Berlin, 1991) 344-365.
7. M. Hanus, The integration of functions into logic programming: from theory to practice, J. Logic Programming 19/20 (1994) 583-628.
8. S. Hölldobler, A unification algorithm for confluent theories, in: Proc. 14th Internat. Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 267 (Springer, Berlin, 1987) 31-41.
9. S. Hölldobler, Foundations of Equational Logic Programming, Lecture Notes in Artificial Intelligence, Vol. 353 (Springer, Berlin, 1989).
10. G. Huet and J.-J. Lévy, Computations in orthogonal rewriting systems, I and II, in: J.-L. Lassez and G. Plotkin, eds., Computational Logic, Essays in Honor of Alan Robinson, (MIT Press, Cambridge, MA, 1991) 396-443.
11. J.-M. Hullot, Canonical forms and unification, in: Proc. 5th Conf. on Automated Deduction, Lecture Notes in Computer Science, Vol. 87 (Springer, Berlin, 1980) 318-334.
12. J.W. Klop, Term rewriting systems, in: S. Abramsky, D. Gabbay and T. Maibaum, eds., Handbook of Logic in Computer Science, Vol. II (Oxford University Press, Oxford, 1992) 1-112.
13. J.W. Lloyd, Foundations of Logic Programming, (Springer, Berlin, 2nd ed. 1987).
14. A. Martelli, C. Moiso and G.F. Rossi, Lazy unification algorithms for canonical rewrite systems, in: H. Aït-Kaci and M. Nivat, eds., Resolution of Equations in Algebraic Structures, Vol. II, Rewriting Techniques (Academic Press, New York, 1989) 245-274.
15. A. Martelli and U. Montanari, An efficient unification algorithm, ACM Trans. on Programming Languages Systems 4 (1982) 258-282.
16. A. Martelli, G.F. Rossi and C. Moiso, An algorithm for unification in equational theories, in: Proc. 1986 Symp. on Logic Programming (1986) 180-186.
17. A. Middeldorp and E. Hamoen, Completeness results for basic narrowing, Appl. Algebra Engrg. Comm. Comput. 5 (1994) 213-253.
18. A. Middeldorp and S. Okui, A deterministic lazy narrowing calculus, in: Proc. Fuji Internat. Workshop on Functional and Logic Programming (World Scientific, Singapore, 1995) 104-118.
19. M. Moser, Improving transformation systems for general E-unification, in: Proc. 5th Internat. Conf. on Rewriting Techniques and Applications, Lecture Notes in Computer Science, Vol. 690 (Springer, Berlin, 1993) 92-105.
20. J.A. Robinson, A machine-oriented logic based on the resolution principle, J. ACM 12 (1965) 23-41.
21. J.R. Slagle, Automatic theorem proving in theories with simplifiers, commutativity and associativity, J. ACM 21 (1974) 622-642.
22. W. Snyder, A Proof Theory for General Unification (Birkhäuser, Basel, 1991).
23. Y.H. You, Enumerating outer narrowing derivations for constructor based term rewriting systems, J. Symbolic Comput. 7 (1989) 319-343.