9,708 research outputs found
Termination of rewriting strategies: a generic approach
We propose a generic termination proof method for rewriting under strategies,
based on an explicit induction on the termination property. Rewriting trees on
ground terms are modeled by proof trees, generated by alternatively applying
narrowing and abstracting steps. The induction principle is applied through the
abstraction mechanism, where terms are replaced by variables representing any
of their normal forms. The induction ordering is not given a priori, but
defined with ordering constraints, incrementally set during the proof.
Abstraction constraints can be used to control the narrowing mechanism, well
known to easily diverge. The generic method is then instantiated for the
innermost, outermost and local strategies.Comment: 49 page
Stream Productivity by Outermost Termination
Streams are infinite sequences over a given data type. A stream specification
is a set of equations intended to define a stream. A core property is
productivity: unfolding the equations produces the intended stream in the
limit. In this paper we show that productivity is equivalent to termination
with respect to the balanced outermost strategy of a TRS obtained by adding an
additional rule. For specifications not involving branching symbols
balancedness is obtained for free, by which tools for proving outermost
termination can be used to prove productivity fully automatically
Extending Context-Sensitivity in Term Rewriting
We propose a generalized version of context-sensitivity in term rewriting
based on the notion of "forbidden patterns". The basic idea is that a rewrite
step should be forbidden if the redex to be contracted has a certain shape and
appears in a certain context. This shape and context is expressed through
forbidden patterns. In particular we analyze the relationships among this novel
approach and the commonly used notion of context-sensitivity in term rewriting,
as well as the feasibility of rewriting with forbidden patterns from a
computational point of view. The latter feasibility is characterized by
demanding that restricting a rewrite relation yields an improved termination
behaviour while still being powerful enough to compute meaningful results.
Sufficient criteria for both kinds of properties in certain classes of rewrite
systems with forbidden patterns are presented
Well-definedness of Streams by Transformation and Termination
Streams are infinite sequences over a given data type. A stream specification
is a set of equations intended to define a stream. We propose a transformation
from such a stream specification to a term rewriting system (TRS) in such a way
that termination of the resulting TRS implies that the stream specification is
well-defined, that is, admits a unique solution. As a consequence, proving
well-definedness of several interesting stream specifications can be done fully
automatically using present powerful tools for proving TRS termination. In
order to increase the power of this approach, we investigate transformations
that preserve semantics and well-definedness. We give examples for which the
above mentioned technique applies for the ransformed specification while it
fails for the original one
Automated Termination Proofs for Logic Programs by Term Rewriting
There are two kinds of approaches for termination analysis of logic programs:
"transformational" and "direct" ones. Direct approaches prove termination
directly on the basis of the logic program. Transformational approaches
transform a logic program into a term rewrite system (TRS) and then analyze
termination of the resulting TRS instead. Thus, transformational approaches
make all methods previously developed for TRSs available for logic programs as
well. However, the applicability of most existing transformations is quite
restricted, as they can only be used for certain subclasses of logic programs.
(Most of them are restricted to well-moded programs.) In this paper we improve
these transformations such that they become applicable for any definite logic
program. To simulate the behavior of logic programs by TRSs, we slightly modify
the notion of rewriting by permitting infinite terms. We show that our
transformation results in TRSs which are indeed suitable for automated
termination analysis. In contrast to most other methods for termination of
logic programs, our technique is also sound for logic programming without occur
check, which is typically used in practice. We implemented our approach in the
termination prover AProVE and successfully evaluated it on a large collection
of examples.Comment: 49 page
The local structure of OH species on the V2O3(0 0 0 1) surface: a scanned-energy mode photoelectron diffraction study
Scanned-energy mode photoelectron diffraction (PhD), using O 1s photoemission, together with multiple-scattering simulations, have been used to investigate the structure of the hydroxyl species, OH, adsorbed on a V2O3(0 0 0 1) surface. Surface OH species were obtained by two alternative methods; reaction with molecular water and exposure to atomic H resulted in closely similar PhD spectra. Both qualitative assessment and the results of multiple-scattering calculations are consistent with a model in which only the O atoms of outermost layer of the oxide surface are hydroxylated. These results specifically exclude significant coverage of OH species atop the outermost V atoms, i.e. in vanadyl O atom sites. Ab initio density-functional theory cluster calculations provide partial rationalisation of this result, which is discussed the context of the general understanding of this system
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Extensional and Intensional Strategies
This paper is a contribution to the theoretical foundations of strategies. We
first present a general definition of abstract strategies which is extensional
in the sense that a strategy is defined explicitly as a set of derivations of
an abstract reduction system. We then move to a more intensional definition
supporting the abstract view but more operational in the sense that it
describes a means for determining such a set. We characterize the class of
extensional strategies that can be defined intensionally. We also give some
hints towards a logical characterization of intensional strategies and propose
a few challenging perspectives
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