Recursive Path Orderings Can Be Context-Sensitive

Borralleras, Cristina; Lucas, Salvador; Rubio, Albert

doi:10.1007/3-540-45620-1_27

Cited by 24 publications

(28 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such adaptions were done for classical methods like RPO or polynomial orders [7,18,24]. However, much more powerful techniques like the dependency pair (DP) method [5] are implemented in almost all current termination tools for TRSs.…”

Section: Example 1 Consider This Context-sensitive Term Rewrite Systmentioning

confidence: 99%

See 1 more Smart Citation

Improving Context-Sensitive Dependency Pairs

Alarcón

Emmes

Fuhs

et al. 2008

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

View full text Add to dashboard Cite

Abstract. Context-sensitive dependency pairs (CS-DPs) are currently the most powerful method for automated termination analysis of contextsensitive rewriting. However, compared to DPs for ordinary rewriting, CS-DPs suffer from two main drawbacks: (a) CS-DPs can be collapsing. This complicates the handling of CS-DPs and makes them less powerful in practice. (b) There does not exist a "DP framework " for CS-DPs which would allow one to apply them in a flexible and modular way. This paper solves drawback (a) by introducing a new definition of CS-DPs. With our definition, CS-DPs are always non-collapsing and thus, they can be handled like ordinary DPs. This allows us to solve drawback (b) as well, i.e., we extend the existing DP framework for ordinary DPs to contextsensitive rewriting. We implemented our results in the tool AProVE and successfully evaluated them on a large collection of examples.

show abstract

Section: Example 1 Consider This Context-sensitive Term Rewrite Systmentioning

confidence: 99%

“…M ∞,µ contains all minimal non-terminating terms: t ∈ M ∞,µ iff t is non-termi- 7 Alternatively, one could also use different U-symbols for different collapsing DPs. 8 We omitted the DP U(p(y)) → P(y) that is "identical" to (14).…”

Section: Soundnessmentioning

confidence: 99%

Improving Context-Sensitive Dependency Pairs

Alarcón

Emmes

Fuhs

et al. 2008

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, our attempts to prove termination of R µ Z by using CiME failed for every considered combination (including techniques that potentially deal with non-simply terminating TRS's like the use of dependency pairs together with polynomial orderings) of proof criteria. Similarly, termination of R µ GM or R µ C cannot be proved either using kbo or rpo (see [2] for a formal justification of this claim). In fact, we could even prove that they are not simply terminating (see [31]).…”

Section: A Non-transformational Approach To Modularity?mentioning

confidence: 99%

“…Recent interesting developments include in particular the approach of Giesl & Middeldorp for proving innermost termination of CSRS's via transformations to ordinary TRS's along the lines of [12], as well as the rpo-style approach of [2] for directly proving termination of CSRS's without any intermediate transformations and without recurring to ordinary TRS's. A comparison of our results and approach with the latter ones mentioned remains to be done.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Modular termination of context-sensitive rewriting

Gramlich

Lucas

2002

Proceedings of the 4th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming

Self Cite

View full text Add to dashboard Cite

Context-sensitive rewriting (CSR) has recently emerged as an interesting and flexible paradigm that provides a bridge between the abstract world of general rewriting and the (more) applied setting of declarative specification and programming languages such as OBJ*, CafeOBJ, ELAN, and Maude. A natural approach to study properties of programs written in these languages is to model them as contextsensitive rewriting systems. Here we are especially interested in proving termination of such systems, and thereby providing methods to establish termination of e.g. OBJ* programs. For proving termination of context-sensitive rewriting, there exist a few transformation methods, that reduce the problem to termination of a transformed ordinary term rewriting system (TRS). These transformations, however, have some serious drawbacks. In particular, most of them do not seem to support a modular analysis of the termination problem. In this paper we will show that a substantial part of the well-known theory of modular term rewriting can be extended to CSR, via a thorough analysis of the additional complications arising from context-sensitivity. More precisely, we will mainly concentrate on termination (properties). The obtained modularity results correspond nicely to the fact that in the above languages the modular design of programs and specifications is explicitly promoted, since it can now also be complemented by modular analysis techniques.

show abstract

Context-Sensitive Rewriting Strategies

Lucas¹

2002

Information and Computation

View full text Add to dashboard Cite

Recursive Path Orderings Can Be Context-Sensitive

Cited by 24 publications

References 14 publications

Improving Context-Sensitive Dependency Pairs

Improving Context-Sensitive Dependency Pairs

Modular termination of context-sensitive rewriting

Context-Sensitive Rewriting Strategies

Contact Info

Product

Resources

About