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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 154
Setname	ir_computersa
ID	103399
OCR Text	Show 144 44. G. Huet, "Conf luent reduction," Proc. 18th IEEE Symposium on Faun dat ions of Computer Science, 1977. 45. G. Huet, "The undecidability of unification in third order log1c," I nfor mat ion and Control, Vol. 22, 1973, pp. 257-267. 46. G. Huet, "A unification algorithm for typed lambda calculus," T heoret1cal Computer Science, Vol. 1, No. 1, 1975, pp. 27-57. 47. G. Huet, "Resol ution d'equations dans des langages d'order 1 ,2, ... omega," Ph.D. dissertation, Univ. de Pairs VII, 1976. 48. G. Huet, "Confl uent reduction: abstract properties and application to term rewriting systems," JACM, Vol. 27, No. 4, October 1980, pp. 797-821 . 49. G. Huet, "A complete proof of correctness of the Knuth-Bendix completion procedure," Journal of Computer and System Science, Vol. 23, 1981, pp. 11-21. 50. G. Huet and D.C. Oppen, "Equations and rewrite rules: a survey," in For mal language theory: per spectives and open problems, R.V. Book, ed., Academic Press, New York, 1980, pp. 349-405. 51. J.M. Hullot, "Canonical forms and unification," Proc. 5th Conference on Automated Deducti on, 1980, pp. 318-334. 52. H. Hussmann, "Unification in conditional-equational t heories," Tech. report MIP 8502, Universitat Passau, January 1985. 53. H. Hussmann, "Rapid prototyping for algebraic specification - RAP system user's manual," Tech. report MIP 8504, Universitat Passau, 1985. 54. J. Jaffar, J-L. Lassez and M.J. Maher, "A logic programming language scheme," in Logic prog ramming: re i at ions, functions, and equati ons, D. DeGroot and G. Lindstrom, eds., Prentice-Hall, New York, 1985. 55. J.P. Jouannaud, C. Kirchner and H. Kirchner, "Incremental construction of unification algorithms in equational theories," 10th Colloquium on Automata, Languages and Programmi ng, 1983. 56. J.P. Jouannaud, "Church-Rosser computations with equational term rewriting systems," Proc. 5th CAAP, Nancy, France, January 1983. 57. J.P. Jouannaud and H. Kirchner, "Completion of a set of rules modulo a set of equations," Proc. 11th POPL, Salt Lake City, Utah, January 1984. 58. J.P. Jouannaud, M. Munoz, "Termination of a set of rules modulo a set of equations," 7th International Confer ence on Automated Deduction, Napa, California, May 1984. 59. G. Kahn and D.B. MacQueen, "Coroutines and networks of parallel processes," Information Processi ng 77, North-Holland, 1977, pp. 993-998. 60. K.M. Kahn, "Uniform -- a language based upon unif ication which unifies
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6059h53/103399