Computational semantics of term rewriting systems
Algebraic methods in semantics
Rewrite, rewrite, rewrite, rewrite, rewrite, …
Selected papers of the 16th international colloquium on Automata, languages, and programming
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Context-sensitive rewriting strategies
Information and Computation
Membership algebra as a logical framework for equational specification
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Termination of Context-Sensitive Rewriting
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Transformation techniques for context-sensitive rewrite systems
Journal of Functional Programming
Proving termination of membership equational programs
Proceedings of the 2004 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Proving termination of context-sensitive rewriting by transformation
Information and Computation
Two-way equational tree automata for AC-like theories: decidability and closure properties
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
A sufficient completeness checker for linear order-sorted specifications modulo axioms
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Tree automata with equality constraints modulo equational theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Combining Equational Tree Automata over AC and ACI Theories
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Journal of Symbolic Computation
Order-sorted parameterization and induction
Semantics and algebraic specification
Constructors, sufficient completeness, and deadlock freedom of rewrite theories
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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We propose three different notions of completeness for ordersorted equational specifications supporting context-sensitive rewriting modulo axioms relative to a replacement map µ. Our three notions are: (1) a definition of µ-canonical completeness under which µ-canonical forms coincide with canonical forms; (2) a definition of semantic completeness that guarantees that the µ-operational semantics and standard initial algebra semantics are isomorphic; and (3) an appropriate definition of µ-sufficient completeness with respect to a set of constructor symbols. Based on these notions, we use equational tree automata techniques to obtain decision procedures for checking these three kinds of completeness for equational specifications satisfying appropriate requirements such as weak normalization, ground confluence and sort-decreasingness, and left-linearity. The decision procedures are implemented as an extension of the Maude sufficient completeness checker.