Extending Context-Sensitivity in Term Rewriting

Gramlich, Bernhard; Schernhammer, Felix

doi:10.4204/eptcs.15.5

Cited by 4 publications

(16 citation statements)

References 20 publications

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“…Finally, in Section 5 we extended our approach to strategies defined by forbidden patterns [6]. Forbidden patterns are very expressive and in particular, they can also be used to describe strategies such as innermost, outermost, or context-sensitive rewriting.…”

Section: Resultsmentioning

confidence: 99%

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Loops under Strategies ... Continued

Thiemann

Sternagel

Giesl

et al. 2010

Electron. Proc. Theor. Comput. Sci.

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While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where the existence of a loop implies non-termination of the rewrite system. However, most programming languages use specific evaluation strategies, whereas loop detection techniques usually do not take strategies into account. So even if a rewrite system has a loop, it may still be terminating under certain strategies. Therefore, our goal is to develop decision procedures which can determine whether a given loop is also a loop under the respective evaluation strategy. In earlier work, such procedures were presented for the strategies of innermost, outermost, and context-sensitive evaluation. In the current paper, we build upon this work and develop such decision procedures for important strategies like leftmost-innermost, leftmost-outermost, (max-)parallel-innermost, (max-)parallel-outermost, and forbidden patterns (which generalize innermost, outermost, and context-sensitive strategies). In this way, we obtain the first approach to disprove termination under these strategies automatically

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Section: Resultsmentioning

confidence: 99%

“…Finally, recently a generalization of innermost / outermost / context-sensitive rewriting has been introduced: rewriting with forbidden patterns [6]. In this paper we also develop a decision procedure for loops under forbidden patterns.…”

Section: Introductionmentioning

confidence: 99%

Loops under Strategies ... Continued

Thiemann

Sternagel

Giesl

et al. 2010

Electron. Proc. Theor. Comput. Sci.

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“…To support a broad variety of strategies we consider forbidden pattern rewriting, which covers for instance innermost, outermost, and context-sensitive rewriting [9,15]. Hence the formalization of techniques for forbidden pattern strategies has the significant advantage that a wide range of strategies can be treated by the same formalism, so CeTA internally converts all outermost and context-sensitive strategies into forbidden patterns before the certifier for nontermination proofs is invoked, cf.…”

Section: Forbidden Patternsmentioning

confidence: 99%

“…It now covers techniques for nonlooping nonterminating TRSs. Moreover, as strategy specification we now support an extended version of forbidden patterns [9], which generalizes many common strategies like (leftmost)innermost, (leftmost)-outermost, and context-sensitive rewriting [15]. Finally, we also integrated a mechanism to support partial nontermination proofs, which further increases the applicability of our certifier and led to the detection of a severe soundness bug of AProVE, which has now been fixed.…”

Section: Introductionmentioning

confidence: 99%

Certification of Nontermination Proofs Using Strategies and Nonlooping Derivations

Nagele

Thiemann

Winkler

2014

Verified Software: Theories, Tools and Experiments

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The development of sophisticated termination criteria for term rewrite systems has led to powerful and complex tools that produce (non)termination proofs automatically. While many techniques to establish termination have already been formalized-thereby allowing to certify such proofs-this is not the case for nontermination. In particular, the proof checker CeTA was so far limited to (innermost) loops. In this paper we present an Isabelle/HOL formalization of an extended repertoire of nontermination techniques. First, we formalized techniques for nonlooping nontermination. Second, the available strategies include (an extended version of) forbidden patterns, which cover in particular outermost and context-sensitive rewriting. Finally, a mechanism to support partial nontermination proofs further extends the applicability of our proof checker.

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“…• For the termination analysis one is not restricted to the CDP framework. One can for instance use the transformation of [11].…”

Section: For All Cdp Sequencesmentioning

confidence: 99%

Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

Gramlich

Schernhammer

2010

Electron. Proc. Theor. Comput. Sci.

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We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the calling contexts of the corresponding recursive function calls, it is possible to incorporate the forbidden pattern restrictions in the (adapted) notion of dependency pair chains, thus yielding a sound and complete approach to termination analysis. Building upon this contextual dependency pair framework we introduce a dependency pair processor that simplifies problems by analyzing the contextual information of the dependency pairs. Moreover, we show how this processor can be used to synthesize forbidden patterns suitable for a given term rewriting system on-the-fly during the termination analysis.

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Extending Context-Sensitivity in Term Rewriting

Cited by 4 publications

References 20 publications

Loops under Strategies ... Continued

Loops under Strategies ... Continued

Certification of Nontermination Proofs Using Strategies and Nonlooping Derivations

Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

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