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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 155
Setname	ir_computersa
ID	103400
OCR Text	Show 145 (much of) List, Prolog, and Act 1," Proc. of the Workshop on Logtc Programming for I nte/1 i gent Systems, 1981 . 61. K.M. Kahn, "Uniform -- a language based upon unification wh1ch unifies (much of) List, Prolog, and Act 1," in Logic programmtng: relations, func tions, and equations, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 62. S. Kaplan, "Fai r conditional term rewriting systems: unification, termination and confluence," Tech. report 194 LRI, Orsay, 1984. 63. S. Kaplan, Conditional rewrite rules, accepted in Theoretical Computer Science, 1984. 64. R.M. Ke ller, "Semantics and applications of function graphs," Tech. report UUCS-8-112, University of Utah, Dept. of Computer Science, October 1980. 65. R.M. Keller, "FEL (Function Equation Language) Programmer's Guide," Tech. report AMPS Technical Memorandum No. 7, Computer Science Dept., University of Utah, 1982. 66. D.O. Knudson, "Elimination of the functional reflexive axioms in unit refutation proofs," Ph.D. dissertation, Northwestern University, 1973. 67. D. Knuth and P. Bendix, "Simple word problems in universal algebras," in Computational problems in abstract algebra, J . Leech, ed., Pergamon Press, New York, 1970, pp. 163-279. 68. W.A. Kornfeld, "Equality for Pro log," Proc. 8th International Joint Conference on Artificial Intel I igence, Karlsruhe, West Germany, August 1983. 69. W.A. Kornfeld, "Equality for Pro log," in Logic programming: rei ations, functions, and equations, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 70. R.A. Kowalski, Logic for problem solving, North-Holland, New York, 1979. 71. R. A. Kowalski, "Predicate logic as a programming language," Proceeding of IF I P, Amsterdam: North Holland, 74, pp. 556-574. 72. R.A. Kowalski and D. Kuehner, Linear resolution with selection functions , Mathematics Unit, Edinburgh University, 1970. 73. D.S. Lankford, "Canonical inference," Tech. report ATP-32, Department of Mathematics and Computer Science, University of Texas at Austin, December 1975. 74. D.S. Lankford and A.M. Ballantyne, "Decision procedures for simple equational theories with commutative-associative axioms: Complete sets of commutative-associative reductions," Tech. report ATP-39, Dept. of Math. and Computer Science, U. of Texas at Austin, August 1977.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6059h53/103400