Rewrite, Rewrite, Rewrite, Rewrite, Rewrite, . .

Abstract We study properties of rewrite systems that are not necessarily terminating, but allow instead for transfinite derivations that have a limit. In particular, we give conditions for the existence of a limit and for its uniqueness and relate the operational and algebraic semantics of infinitary theories. We also consider sufficient completeness of hierarchical systems.

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

[2]  Gerard Huet,et al.  Conflunt reductions: Abstract properties and applications to term rewriting systems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

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

[4]  Yasuyoshi Inagaki,et al.  Algebraic Semantics and Complexity of Term Rewriting Systems , 1989, RTA.

[5]  Nachum Dershowitz,et al.  Infinite Normal Forms (Preliminary Version) , 1989, ICALP.

[6]  Joseph A. Goguen,et al.  Initial Algebra Semantics and Continuous Algebras , 1977, J. ACM.

[7]  Hartmut Ehrig,et al.  Algebraic Data Type and Process Specifications based on Projection Spaces , 1988, ADT.

[8]  Yiyun Chen,et al.  Infinite Terms and Infinite Rewritings , 1990, CTRS.

[9]  Nachum Dershowitz,et al.  Termination of Rewriting , 1987, J. Symb. Comput..

[10]  Jan Willem Klop,et al.  Term rewriting systems: a tutorial , 1987 .

[11]  Michael J. O'Donnell,et al.  Equational Logic as a Programming Language , 1985, Logic of Programs.

[12]  Gérard P. Huet,et al.  Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems , 1980, J. ACM.

[13]  Dana S. Scott,et al.  Data Types as Lattices , 1976, SIAM J. Comput..

[14]  William M. Farmer,et al.  Redex Capturing in Term Graph Rewriting , 1990, Int. J. Found. Comput. Sci..

[15]  Stéphane Kaplan,et al.  Conditional Rewrite Rules , 1984, Theor. Comput. Sci..

[16]  Jan Willem Klop,et al.  Transfinite Reductions in Orthogonal Term Rewriting Systems (Extended Abstract) , 1991, RTA.

[17]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[18]  Sanjai Narain,et al.  LOG(F): An Optimal Combination of Logic Programming, Rewriting and Lazy Evaluation , 1988 .

[19]  Martin Wirsing,et al.  Algebraic Specification , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[20]  Bruno Courcelle,et al.  Arbes infinis et systèmes d'équations , 1979, RAIRO Theor. Informatics Appl..

[21]  Nachum Dershowitz,et al.  Rewrite, rewrite, rewrite, rewrite, rewrite... , 1989, POPL '89.

[22]  Joseph E. Stoy,et al.  Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory , 1981 .

[23]  Jean-Claude Raoult,et al.  Operational and Semantic Equivalence Between Recursive Programs , 1980, JACM.