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Publication Type	technical report
School or College	College of Engineering
Department	Computing, School of
Creator	You, Jia-Huai
Title	First-Order Unification in Equational Theories and its Application to Logic Programming
Date	1985
Description	This thesis studies first-order unification in equational theories, called E-unification, paying particular attention to complete unification algorithms for classes of equational theories. It also investigates how results and notions of E-unification can be applied to logic programming systems that support equality handling and functional notation. First-order unification in equational theories is proved to be complete. An E-unification algorithm using the narrowing process is then shown to be complete for the class of theories that can be described by a closed linear term rewriting system with the non-repetition property. This result sets the stage for investigation of applications to logic programming. An extended equational programming paradigm, referred to as equational logic programming, is proposed, which uses "narrowing" and "deletion upon successful unification" as the inference rules, and enjoys the semantic simplicity of the classical theory of equality. It is shown that the kind of programming features that were initially possessed solely by Prolog can also be provided in this extended equational programming paradigm. Finally, a computational model integrating functional programming and logic programming is described.
Type	Text
Subject	first-order unification; equational theory; logic programming; e-unification; semantic unification; dec-20; prolog
Subject LCSH	Computer programming
Language	eng
Bibliographic Citation	You, J. (1985). First-Order Unification in Equational Theories and its Application to Logic Programming.
Series	University of Utah Computer Science Technical Report
Relation is Part of	ARPANET
Format Medium	application/pdf
Format Extent	57,396,893 bytes
File Name	You-First_Order_Unification.pdf
Conversion Specifications	Original scanned with Kirtas 2400 and saved as 400 ppi uncompressed TIFF. PDF generated by Adobe Acrobat Pro X for CONTENTdm display
ARK	ark:/87278/s6059h53
Setname	ir_computersa
ID	103405
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6059h53

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Title	Page 152
Setname	ir_computersa
ID	103397
OCR Text	Show 142 language," Tech. report Doc 83/5, Dept. of Computing, Imperial College of Science and Technology, University of London, March 1983. 15. W.F. Clocks in and C.S. Mellish, Programming in Prolog, Springer-Verlag, New York, 1981 . 16. S. Cohen, "The APPLOG language," in Logic programming: relations, functions, and equations, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 17. A. Colmerauer, "Prolog and infinite trees," in Logic programming, K. L. Clark and S.-A. Tarn lund, eds., Academic Press, New York, · 1982, pp. 231-252. 18. J. Darlington, A.J. Field and H. Pull, "The unification of functional and logic languages," in Logic programming: relations, functions, and equations, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 19. A.L. Davis and R.M. Keller, "Data flow graphs," Computer, Vol. 15, No. 2, February 1982, pp. 26-41. 20. J.B. Dennis, "First version of a data flow procedure language," in Lecture notes in computer science, Volume 19, G. Goos and J. Hartman is, eds., Springer-Verlag, New York, 1974, pp. 362-376. 21. N. Dershowitz, "Orderings for term rewriting systems," Journal of Theoretical Computer Science, Vol. 17, No. 3, March 1982, pp. 279-301 . 22. N. Dershowitz, J. Hsiang and D. Plaisted, "Associative-commutative rewriting," Proc. 10th Int. Joint Conference on Artificial Intelligence, 1983. 23. N. Dershowitz, "Equations as programming languages," Proc. 4th Jerusalem Conference on Information Technology, May 1984, pp. 114-123. 24. N. Dershowitz and D. Plaisted, "Logic programming cum applicative programming," Proc. of 1985 International symposium on Logic Programming, Boston, Mass., July 1985. 25. N. Dershowitz, "Computing with term rewriting systems," Proc. An NSF Workshop on the Rewrite Rule Laboratory, April 1984. 26. M.H. van Emden, "Programming with resolution logic," in Machine intel- 1 igence 8, E. W. Elcock and D. Michie, eds., Ellis Horwood, London, 1978, pp. 266-299. 27. M.H. Van Emden and J.W. Lloyd, "A logical reconstruction of Prolog II," Journal of Logic Programming, Vol. 2, 1984, pp. 143-149. 28. F. Fages and G. Huet, "Complete sets of unifiers and matchers in equational theories," Proceedings, 5th Conference on Trees, Algebra and Programming, 1983, pp. 205-220.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6059h53/103397