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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 156
Setname	ir_computersa
ID	103401
OCR Text	Show 146 75. D.S. Lankford and A.M. Ballantyne, "Decision procedures for s1mple equational theories with permutative axioms: Complete sets of permutative reductions," Tech. report ATP-37, Dept. of Math. and Computer Sc1ence, U. of Texas at Austin, April 1977. 76. D.S. Lankford and A.M. Ballantyne, "Decision procedures for s1mple equational theories with commutative axioms: Complete sets of commutative reductions," Tech. report ATP-37, Dept. of Math. and Computer Science, U. of Texas at Austin, March 1977. 77. P. Lescanne, "Computer experiments with the REVE term rewnting system generator," Proc. 1Oth POPL, January 1983, pp. 99-108. 78. G. Lindstrom and P. Panangaden, "Stream-based execution of logic programs," Proc. of the International Symposium on Logic Programmt ng, Atlantic City, New Jersey, February, 1984, pp. 168-176. 79. G. Lindstrom, "Functional programming and the logical variables," Proc. 12th POPL, New Orleans, January 1985. 80. D.W. Loveland, Automated theorem proving: a logical basis, NorthHolland, New York, 1978. 81. Y. Malachi, Z. Manna and R. Waldinger, "TABLOG: the deductive tableau programming language," Proceedings of the ACM Symposium on Lisp and Functional Programming, Austin, Texas, 1984, pp. 323-330. 82. Y. Malachi, Z. Manna and R. Waldinger, "TABLOG: the deductive tableau programming language," in Logic programming: rei at ions, functions, and equations, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 83. A. Martelli and U. Montanari, "An efficient unification algorithm," ACM Transaction on Programming Languages and Systems, Vol. 4, No. 2, April 1982, pp. 258-282. 84. B. Meltzer, "A new look at mathematics and its mechanization," in Machine intelligence 3, D. Michie, ed., American Elsevier, New York, 1968, pp. 63-70. 85. P Mishra, "Static inference in applicative languages," Ph.D. dissertation, University of Utah, March 1985. 86. M. O'Donnell, "Computing in systems described by equations," in Lecture notes in computer science, Volume 58, Springer-Verlag, New York, 1977. 87. M.S. Paterson and M.N. Wegman, "Linear unifications," Journal of Computer System Science, Vol. 16, No. 2, April 1978, pp. 158-167. 88. L.M. Pereira, F.C.N. Pereira and D.H.D. Warren, User's guide to DECsystem-10 Prolog, University of Edinburgh, 1978. 89. G.E. Peterson and M.E. Stickel, "Complete sets of reductions for some
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6059h53/103401