Abstract
Unification in equational theories, i.e. solving equations in varieties, is a basic operation in many applications of Computer Science, particularly in Automated Deduction [Si 84]. A combination of unification algorithms for regular finitary collapse free equational theories with disjoint function symbols is presented. The idea is first to replace certain subterms by constants and to unify this constant abstraction and then to handle the replaced subterms in a recursive step. Total correctness is shown, i.e. the algorithm terminates and yields a correct and complete set of unifiers provided the special algorithms do.
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Birkhoff, G., ‘On the Structure of Abstract Algebra', Proc. Cambridge Phil. Soc., Vol. 31, 433–454, (1935)
Burris, S. and Sankappanavar, H.P., ‘A Course in Universal Algebra', Springer-Verlag, (1981)
Fages, F., ‘Associative-Commutative Unification', in Proc. of 7th CADE (ed. R.E.Shostak). Springer-Verlag, LNCS 170, 194–208, (1984)
Fages, F. and Huet, G., ‘Unification and Matching in Equational Theories', Proc. of CAAP'83 (ed. G. Ausiello and M. Protasi), Springer-Verlag, LNCS 159, 205–220, (1983)
Goguen, J. A., Thatcher, J.W. and Wagner, E. G., ‘An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types', in ‘Current Trends in Programming Methodology, Vol.4, Data Structuring’ (ed. R. T. Yeh), Prentice Hall, (1978)
Grätzer, G., ‘Universal Algebra', Springer-Verlag, (1979)
Herold, A., ‘A Combination of Unification Algorithms', MEMO SEKI-85-VIII-KL, Universität Kaiserslautern, (1985)
Huet, G. and Oppen, D. C., ‘Equations and Rewrite Rules: A Survey', in ‘Formal Languages: Perspectives and Open Problems (ed R. Book), Academic Press, (1980)
Herold, A. and Siekmann, J., ‘Unification in Abelian Semigroups', MEMO SEKI-85-III-KL, Universität Kaiserslautern, (1985)
Huet, G., ‘Résolution d'équations dans des langages d'ordre 1, 2... ω'. Thèse de doctorat d'état. Université Paris VII, (1976)
Kirchner, C., ‘Methodes et outils de conception systematique d'algorithmes d'unification dans les théories équationelles', Thèse de doctorat d'état, Université de Nancy 1, (1985)
Loveland, D., ‘Automated Theorem Proving', North-Holland, (1978)
Livesey, M. and Siekmann, J., ‘Unification of Sets and Multisets', Universität Karisruhe, Techn. Report, (1976)
McNulty, G., ‘The Decision Problem for Equational Bases of Algebras', Annals of Mathematical Logic 10, 193–259, (1976)
Robinson, J. A., ‘A Machine-Oriented Logic Based on the Resolution Principle', JACM, 12, No. 1, 23–41, (1965)
Schmidt-Schauß, M., ‘Unification under Associativity and Idempotence is of Type Nullary', MEMO SEKI, Universität Kaiserslautern, (1986), (submitted to JAR)
Siekmann, J., ‘Universal Unification', in Proc. of 7th CADE (ed R.E. Shostak), Springer-Verlag, LNCS 170, 1–42, (1984)
Stickel, M.E., ‘A Unification Algorithm for Associative-Commutative Functions', JACM 28, No. 3, 423–434, (1981)
Taylor, W., ‘Equational Logic', Houston Journal of Mathematics 5, (1979)
Tidén, E., ‘Unification in Combinations of Theories with Disjoint Sets of Function Symbols', Royal Institute of Technology, Department of Computing Science, S-100 44 Stockholm, Sweden, (1985)
Yelick, K., ‘Combining Unification Algorithms for Confined Regular Equational Theories', in Proc. of ‘Rewriting Techniques and Applications’ (ed J.-P. Jouannaud), Springer-Verlag, LNCS 202, 365–380, (1985)
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Herold, A. (1986). Combination of unification algorithms. In: Siekmann, J.H. (eds) 8th International Conference on Automated Deduction. CADE 1986. Lecture Notes in Computer Science, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16780-3_111
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DOI: https://doi.org/10.1007/3-540-16780-3_111
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