An Universal Termination Condition for Solving Goals in Equational Languages

A decomposition procedure, called DP, operating on a ”sorted” set of equations is here used as the operational semantics of CTRS. Then, a class of CTRS called conic-flat, is defined for which DP is shown to be universally terminating when solving the equation t1=Rt2, with t1 or t2 ground.

[1]  Bharat Jayaraman.  Semantics of EqL , 1988, IEEE Trans. Software Eng..

[2]  G. Huet,et al.  Equations and rewrite rules: a survey , 1980 .

[3]  Marianne Baudinet.  Proving Termination Properties of Prolog Programs: A Semantic Approach , 1988, LICS.

[4]  Stéphane Kaplan,et al.  Simplifying Conditional Term Rewriting Systems: Unification, Termination and Confluence , 1987, J. Symb. Comput..

[5]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[6]  Pascal Van Hentenryck,et al.  Extended Unification Algorithms for the Integration of Functional Programming into Logic Programming , 1987, J. Log. Program..

[7]  M. C. Verri,et al.  On the termination of an algorithm for unification in equational theories , 1989, Fourth IEEE Region 10 International Conference TENCON.

[8]  Nachum Dershowitz,et al.  Orderings for term-rewriting systems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[9]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[10]  Corrado Moiso,et al.  An Algorithm for Unification in Equational Theories , 1986, SLP.

[11]  Ronald V. Book,et al.  Formal language theory : perspectives and open problems , 1980 .

[12]  Uday S. Reddy,et al.  Narrowing as the Operational Semantics of Functional Languages , 1985, SLP.

[13]  Wayne Snyder,et al.  A General Complete E-Unification Procedure , 1987, RTA.

[14]  Jean-Marie Hullot,et al.  Canonical Forms and Unification , 1980, CADE.

[15]  Alberto Martelli,et al.  An Efficient Unification Algorithm , 1982, TOPL.

[16]  Nachum Dershowitz,et al.  Solving Goals in Equational Languages , 1988, CTRS.

[17]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[18]  Mitsuhiro Okada,et al.  A Logical Analysis on Theory of Conditional Rewriting , 1988, CTRS.