Context-Sensitive Rewriting Strategies

Lucas, Salvador

doi:10.1006/inco.2002.3176

Cited by 23 publications

(48 citation statements)

References 56 publications

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“…Formally, we have t µ → →r,p t iff t → →r,p t and p ∈ Pos µ (t) and we say a TRS R is µ-terminating iff no infinite µ → R -chain exists. The replacement map µ S is canonical [8] for the left-linear TRS R s , guaranteeing through the second condition of the above Definition 11 that non-variable positions of left-hand sides are allowed. In that definition, the replacement map µ S is extended to the possibly non-left-linear TRS R d ∪ R s by allowing all arguments of symbols from Σ d .…”

Section: Be a Maximal Outermost-fair Reduction And Letmentioning

confidence: 99%

Productivity of Non-Orthogonal Term Rewrite Systems

Raffelsieper

2012

Electron. Proc. Theor. Comput. Sci.

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Productivity is the property that finite prefixes of an infinite constructor term can be computed using a given term rewrite system. Hitherto, productivity has only been considered for orthogonal systems, where non-determinism is not allowed. This paper presents techniques to also prove productivity of non-orthogonal term rewrite systems. For such systems, it is desired that one does not have to guess the reduction steps to perform, instead any outermost-fair reduction should compute an infinite constructor term in the limit. As a main result, it is shown that for possibly non-orthogonal term rewrite systems this kind of productivity can be concluded from context-sensitive termination. This result can be applied to prove stabilization of digital circuits, as will be illustrated by means of an example.

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Section: Be a Maximal Outermost-fair Reduction And Letmentioning

confidence: 99%

Productivity of Non-Orthogonal Term Rewrite Systems

Raffelsieper

2012

Electron. Proc. Theor. Comput. Sci.

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“…Rewriting with equations as rules can furthermore be made contextsensitive by providing a replacement map μ that indicates which argument positions of a function symbol f must be reduced before equations for f are applied [18,19]. In this way we arrive at the notion of a Context-Sensitive Membership Rewrite Theory (CS-MRT), which is the operational form of a membership equational program [8].…”

Section: Introductionmentioning

confidence: 99%

“…However, it is in some ways more intuitive to keep the order-sorted notation whenever possible, only using explicit memberships when a given axiom does not have an equivalent order-sorted formulation. For instance, in Example 1. in [7,8] allow us to prove (operational) termination of the original module as termination of a Context-Sensitive Term Rewriting System (CS-TRS), i.e., a TRS together with some replacement restrictions associated to the symbols in the signature, see [18,19]. The obtained CS-TRS can be proved terminating by using existing termination tools like AProVE [12] or mu-term [1,20] which are able to deal with such kind of termination problems.…”

Section: Introductionmentioning

confidence: 99%

Operational Termination of Membership Equational Programs: the Order-Sorted Way

Lucas

Meseguer

2009

Electronic Notes in Theoretical Computer Science

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Our main goal is automating termination proofs for programs in rewriting-based languages with features such as: (i) expressive type structures, (ii) conditional rules, (iii) matching modulo axioms, and (iv) contextsensitive rewriting. Specifically, we present a new operational termination method for membership equational programs with features (i)-(iv) that can be applied to programs in membership equational logic (MEL). The method first transforms a MEL program into a simpler, yet semantically equivalent, conditional order-sorted (OS) program. Subsequent trasformations make the OS-program unconditional, and, finally, unsorted. In particular, we extend and generalize to this richer setting an order-sorted termination technique for unconditional OS programs proposed byÖlveczky and Lysne. An important advantage of our method is that it minimizes the use of conditional rules and produces simpler transformed programs whose termination is often easier to prove automatically.

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“…Then, for a given TRS, we obtain a restriction of rewriting which we call context-sensitive rewriting. Proving termination of CSR is an interesting problem with several applications in the fields of term rewriting and programming languages (see [5,6,8,11,13] for further motivation).…”

Section: Introductionmentioning

confidence: 99%

“…With context-sensitive rewriting (CSR [10,11]) we can achieve a terminating behavior with non-terminating Term Rewriting Systems (TRSs [14,15]), by pruning (all) infinite rewrite sequences. In CSR we only rewrite μ-replacing subterms.…”

Section: Introductionmentioning

confidence: 99%

Improving the Context-sensitive Dependency Graph

Alarcón

Gutiérrez

Lucas

2007

Electronic Notes in Theoretical Computer Science

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The dependency pairs method is one of the most powerful technique for proving termination of rewriting and it is currently central in most automatic termination provers. Recently, it has been adapted to be used in proofs of termination of context-sensitive rewriting. The use of collapsing dependency pairs i.e., having a single variable in the right-hand side is a novel and essential feature to obtain a correct framework in this setting. Unfortunately, dependency pairs behave as a kind of glue in the context-sensitive dependency graph which makes the cycles bigger, thus making some proofs of termination harder. In this paper we show that this effect can be safely mitigated by removing some arcs from the graph, thus leading to faster and easier proofs. Narrowing dependency pairs is also introduced and used here to eventually simplify the treatment of the context-sensitive dependency graph. We show the practicality of the new techniques with some benchmarks.

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Context-Sensitive Rewriting Strategies

Cited by 23 publications

References 56 publications

Productivity of Non-Orthogonal Term Rewrite Systems

Productivity of Non-Orthogonal Term Rewrite Systems

Operational Termination of Membership Equational Programs: the Order-Sorted Way

Improving the Context-sensitive Dependency Graph

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