On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Commutation, transformation, and termination
Proc. of the 8th international conference on Automated deduction
Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
On termination of the direct sum of term-rewriting systems
Information Processing Letters
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
A sufficient condition for the termination of the direct sum of term rewriting systems
Proceedings of the Fourth Annual Symposium on Logic in computer science
Modular term rewriting systems and the termination
Information Processing Letters
Modularity of confluence: a simplified proof
Information Processing Letters
Modular properties of conditional term rewriting systems
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
Confluence by decreasing diagrams
Theoretical Computer Science
Completeness of combinations of conditional constructor systems
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Termination is not modular for confluent variable-preserving term rewriting systems
Information Processing Letters
On the modularity of termination of term rewriting systems
Theoretical Computer Science
Modular proofs for completeness of hierarchical term rewriting systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Modularity in noncopying term rewriting
Theoretical Computer Science
Modular termination of r-consistent and left-linear term rewriting systems
Theoretical Computer Science
Modular properties of composable term rewriting systems
Journal of Symbolic Computation
Termination for direct sums of left-linear complete term rewriting systems
Journal of the ACM (JACM)
On the modularity of normal forms in rewriting
Journal of Symbolic Computation
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Simple termination of rewrite systems
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Term rewriting and all that
Operational and Semantic Equivalence Between Recursive Programs
Journal of the ACM (JACM)
Lazy rewriting on eager machinery
ACM Transactions on Programming Languages and Systems (TOPLAS)
Advanced topics in term rewriting
Advanced topics in term rewriting
Simple termination of context-sensitive rewriting
Proceedings of the 2002 ACM SIGPLAN workshop on Rule-based programming
Modular termination of context-sensitive rewriting
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Hierarchical termination revisited
Information Processing Letters
Context-sensitive rewriting strategies
Information and Computation
Simple Termination of Hierarchical Combinations of Term Rewriting Systems
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Modular aspects of rewrite-based specifications
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Semi-Completeness of Hierarchical and Super-Hierarchical Combinations of Term Rewriting Systems
TAPSOFT '95 Proceedings of the 6th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
On the Modularity of Deciding Call-by-Need
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
Completeness of Hierarchical Combinations of term Rewriting Systems
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Modular Aspects of Properties of Term Rewriting Systems Related to Normal Forms
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Modularity of Completeness Revisited
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Modularity of Termination in Term Graph Rewriting
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Compositional Term Rewriting: An Algebraic Proof of Toyama's Theorem
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
On Proving Termination by Innermost Termination
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Innocuous Constructor-Sharing Combinations
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
On the Modularity of Confluence of Constructor-Sharing Term Rewriting Systems
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Implementing Term Rewriting by Graph Reduction: Termination of Combined Systems
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Collapsed Tree Rewriting: Completeness, Confluence, and Modularity
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Sufficient Conditions for Modular Termination of Conditional Term Rewriting Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Combinations of Simplifying Conditional Term Rewriting Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Modular Properties of Constructor-Sharing Conditional Term Rewriting Systems
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
Termination of Lazy Rewriting Revisited
Electronic Notes in Theoretical Computer Science (ENTCS)
Confluence by Decreasing Diagrams
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
On modularity in infinitary term rewriting
Information and Computation
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Signature extensions preserve termination: an alternative proof via dependency pairs
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Confluent term rewriting systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Abstract Relations Between Restricted Termination And Confluence Properties Of Rewrite Systems
Fundamenta Informaticae
| Hi-index | 5.23 |
We revisit modularity in term rewriting which for the last 25 years has been a very active and fruitful research field. Starting with the pioneering works of Yoshihito Toyama on the modularity of confluence and the non-modularity of termination he thus initiated an extremely productive line of research, with many non-trivial and deep results, striking counterexamples and a substantial amount of systematic theoretical foundations, methodological principles and novel proof techniques. In this focused summary we will revisit the modularity analysis for ordinary term rewriting systems, considering various confluence and termination properties and restricting ourselves mainly to the case of disjoint unions. We will summarize known results on the (non-)modularity of various confluence and termination properties, and exhibit crucial ideas, constructions and phenomena. Later on we will also briefly consider various extensions, applications, related questions and open problems, as well as recent developments.