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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 153
Setname	ir_computersa
ID	103398
OCR Text	Show 143 29. F. Fages, "Associa t ive-commut ative unif icat ion," Proc. of 7th Inter national Conference on Automated Deduction, May 1984. 30. M.J. Fay, "First-order unification in an equational th eory," Master's thesis, Department of Information Sci en ce , University of Ca lif. at Santa Cruz, June 1978. 31. M.J. Fay, "First-order un if ication in an equational theory," 4th Workshop on Automated Deduction, Austin, Texas, February 1979, pp. 161-167. 32. L. Fribourg, "A superposition oriented theorem prover," Tech. report 11, L.I.T.P., 1983, To appear in Theoretical Computer Science, short version in Proc. IJCAI-83, 923-925. 33. L. Fribourg, "Oriented equational clauses as a programming language," Journal of Logic Programming, Vol. 2, 1984, pp. 165-177. 34. D.P. Friedman and D.S. Wise, "CONS should not evaluate its arguments," in Automata, languages and programming, S. Michaelson and R. Milner, eds., Edinburgh University Press, Edinburgh, 1976. 35. J. Goguen and J. Meseguer, "Equality, types, modules and generics for logic programming," Proc. Second International Logic Programming Conference, Uppsala, July 1984. 36. J. Goguen and J. Meseguer, "Equality, types, modules and generics for logic programming," Journal of Logic Programming, Vol. 2, 1984, pp. 179-210. 37. J. Goguen and J. Meseguer, "EOLOG: equality, types, modules and generics for logic programming," in Logic programming: relations, func tions, and equations, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 38. J.F. Guard, J. Oglesby, J. Bennett and L. Settle, "Semi-automated mathematics," JACM, Vol. 18, March 1969, pp. 42-62. 39. A. Hansson, S. Haridi and S.-A. Tarnlund, "Properties of a logic programming language," in Logic programming, K.L. Clark and S.-A Tarnlund, eds., Academic Press, New York, 1982, pp. 267-280. 40. P. Henderson, Functional programming: application and implementation, Prentice-Hall, New York, 1980. 41. L. Henschen, Private communication, April 1985. 42. C.M. Hoffmann and M.J. O'Donnell, "Programming with equations," ACM Transaction on Programming Languages and Systems , Vol. 4, No. 1, January 1982, pp. 83-112. 43. C.M. Hoffmann and M. O'Donnell, "Implementation of an interpreter for abstract equations," Proc. 11th POPL, January 1984, pp. 111-121.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6059h53/103398