33 Search Results for "Lynch, Christopher"


Volume

LIPIcs, Volume 6

Proceedings of the 21st International Conference on Rewriting Techniques and Applications

RTA 2010, July 11-13, 2010, Edinburgh, Scotland, UK

Editors: Christopher Lynch

Document
An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems

Authors: Dohan Kim and Christopher Lynch

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)


Abstract
Rewriting modulo equations has been researched for several decades but due to the lack of suitable orderings, there are some limitations to rewriting modulo permutation equations. Given a finite set of permutation equations E, we present a new RPO-based ordering modulo E using (permutation) group actions and their associated orbits. It is an E-compatible reduction ordering on terms with the subterm property and is E-total on ground terms. We also present a completion and ground completion method for rewriting modulo a finite set of permutation equations E using our ordering modulo E. We show that our ground completion modulo E always admits a finite ground convergent (modulo E) rewrite system, which allows us to obtain the decidability of the word problem of ground theories modulo E.

Cite as

Dohan Kim and Christopher Lynch. An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{kim_et_al:LIPIcs.FSCD.2021.19,
  author =	{Kim, Dohan and Lynch, Christopher},
  title =	{{An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.19},
  URN =		{urn:nbn:de:0030-drops-142572},
  doi =		{10.4230/LIPIcs.FSCD.2021.19},
  annote =	{Keywords: Recursive Path Ordering, Permutation Equation, Permutation Group, Rewrite System, Completion, Ground Completion}
}
Document
Complete Volume
LIPIcs, Volume 6, RTA'10, Complete Volume

Authors: Christopher Lynch

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
LIPIcs, Volume 6, RTA'10, Complete Volume

Cite as

Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@Proceedings{lynch:LIPIcs.RTA.2010,
  title =	{{LIPIcs, Volume 6, RTA'10, Complete Volume}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010},
  URN =		{urn:nbn:de:0030-drops-41003},
  doi =		{10.4230/LIPIcs.RTA.2010},
  annote =	{Keywords: Programming Techniques, Software Engineering, Programming Languages, Computation by Abstract Devices, Analysis of Algorithms and Problem Complexity Logics and Meanings of Programs, Mathematical Logic and Formal Languages, Symbolic and Algebraic Manipulation, Artificial Intelligence.}
}
Document
Front Matter
Frontmatter (Titlepage, Table of Contents, Author List, PC List, Reviewer List)

Authors: Christopher Lynch

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
Front matter including table of contents, author list, PC list, and reviewer list.

Cite as

Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. i-xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{lynch:LIPIcs.RTA.2010.i,
  author =	{Lynch, Christopher},
  title =	{{Frontmatter (Titlepage, Table of Contents, Author List, PC List, Reviewer List)}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{i--xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.i},
  URN =		{urn:nbn:de:0030-drops-26684},
  doi =		{10.4230/LIPIcs.RTA.2010.i},
  annote =	{Keywords: Table of Contents, Author List, PC List, Reviewer List}
}
Document
Preface

Authors: Christopher Lynch

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
Preface

Cite as

Christopher Lynch. Preface. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 13-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{lynch:LIPIcs.RTA.2010.XIII,
  author =	{Lynch, Christopher},
  title =	{{Preface}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{13--14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.XIII},
  URN =		{urn:nbn:de:0030-drops-26675},
  doi =		{10.4230/LIPIcs.RTA.2010.XIII},
  annote =	{Keywords: Preface}
}
Document
Automata for Data Words and Data Trees

Authors: Mikolaj Bojanczyk

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
Data words and data trees appear in verification and XML processing. The term ``data'' means that positions of the word, or tree, are decorated with elements of an infinite set of data values, such as natural numbers or ASCII strings. This talk is a survey of the various automaton models that have been developed for data words and data trees.

Cite as

Mikolaj Bojanczyk. Automata for Data Words and Data Trees. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{bojanczyk:LIPIcs.RTA.2010.1,
  author =	{Bojanczyk, Mikolaj},
  title =	{{Automata for Data Words and Data Trees}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{1--4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.1},
  URN =		{urn:nbn:de:0030-drops-26397},
  doi =		{10.4230/LIPIcs.RTA.2010.1},
  annote =	{Keywords: Automata, Data Word, Data Tree}
}
Document
Realising Optimal Sharing

Authors: Vincent van Oostrom

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
Realising Optimal Sharing

Cite as

Vincent van Oostrom. Realising Optimal Sharing. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 5-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{vanoostrom:LIPIcs.RTA.2010.5,
  author =	{van Oostrom, Vincent},
  title =	{{Realising Optimal Sharing}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{5--6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.5},
  URN =		{urn:nbn:de:0030-drops-26403},
  doi =		{10.4230/LIPIcs.RTA.2010.5},
  annote =	{Keywords: Optimal Sharing}
}
Document
Automated Confluence Proof by Decreasing Diagrams based on Rule-Labelling

Authors: Takahito Aoto

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
Decreasing diagrams technique (van Oostrom, 1994) is a technique that can be widely applied to prove confluence of rewrite systems. To directly apply the decreasing diagrams technique to prove confluence of rewrite systems, rule-labelling heuristic has been proposed by van Oostrom (2008). We show how constraints for ensuring confluence of term rewriting systems constructed based on the rule-labelling heuristic are encoded as linear arithmetic constraints suitable for solving the satisfiability of them by external SMT solvers. We point out an additional constraint omitted in (van Oostrom, 2008) that is needed to guarantee the soundness of confluence proofs based on the rule-labelling heuristic extended to deal with non-right-linear rules. We also present several extensions of the rule-labelling heuristic by which the applicability of the technique is enlarged.

Cite as

Takahito Aoto. Automated Confluence Proof by Decreasing Diagrams based on Rule-Labelling. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 7-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{aoto:LIPIcs.RTA.2010.7,
  author =	{Aoto, Takahito},
  title =	{{Automated Confluence Proof by Decreasing Diagrams based on Rule-Labelling}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{7--16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.7},
  URN =		{urn:nbn:de:0030-drops-26418},
  doi =		{10.4230/LIPIcs.RTA.2010.7},
  annote =	{Keywords: Confluence, Decreasing Diagrams, Automation, Term Rewriting Systems}
}
Document
Higher-Order (Non-)Modularity

Authors: Claus Appel, Vincent van Oostrom, and Jakob Grue Simonsen

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints.

Cite as

Claus Appel, Vincent van Oostrom, and Jakob Grue Simonsen. Higher-Order (Non-)Modularity. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 17-32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{appel_et_al:LIPIcs.RTA.2010.17,
  author =	{Appel, Claus and van Oostrom, Vincent and Simonsen, Jakob Grue},
  title =	{{Higher-Order (Non-)Modularity}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{17--32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.17},
  URN =		{urn:nbn:de:0030-drops-26427},
  doi =		{10.4230/LIPIcs.RTA.2010.17},
  annote =	{Keywords: Higher-order rewriting, modularity, termination, normalization}
}
Document
Closing the Gap Between Runtime Complexity and Polytime Computability

Authors: Martin Avanzini and Georg Moser

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
In earlier work, we have shown that for confluent TRSs, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise this result to full rewriting, for that we exploit graph rewriting. We give a new proof of the adequacy of graph rewriting for full rewriting that allows for a precise control of the resources copied. In sum we completely describe an implementation of rewriting on a Turing machine (TM for short). We show that the runtime complexity of the TRS and the runtime complexity of the TM is polynomially related. Our result strengthens the evidence that the complexity of a rewrite system is truthfully represented through the length of derivations. Moreover our result allows the classification of nondeterministic polytime-computation based on runtime complexity analysis of rewrite systems.

Cite as

Martin Avanzini and Georg Moser. Closing the Gap Between Runtime Complexity and Polytime Computability. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 33-48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{avanzini_et_al:LIPIcs.RTA.2010.33,
  author =	{Avanzini, Martin and Moser, Georg},
  title =	{{Closing the Gap Between Runtime Complexity and Polytime Computability}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{33--48},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.33},
  URN =		{urn:nbn:de:0030-drops-26436},
  doi =		{10.4230/LIPIcs.RTA.2010.33},
  annote =	{Keywords: Term rewriting, graph rewriting, complexity analysis, polytime computability}
}
Document
Abstract Models of Transfinite Reductions

Authors: Patrick Bahr

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a weak and a strong variant of convergence as known from infinitary term rewriting. Furthermore, we introduce an axiomatic model of reductions that is general enough to cover all of these models of transfinite reductions as well as the ordinary model of finite reductions. It is shown that, in this unifying axiomatic model, many basic relations between termination and confluence properties known from finite reductions still hold. The introduced models are applied to term rewriting but also to term graph rewriting. We can show that for both term rewriting as well as for term graph rewriting the partial order model forms a conservative extension to the metric model.

Cite as

Patrick Bahr. Abstract Models of Transfinite Reductions. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 49-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{bahr:LIPIcs.RTA.2010.49,
  author =	{Bahr, Patrick},
  title =	{{Abstract Models of Transfinite Reductions}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{49--66},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.49},
  URN =		{urn:nbn:de:0030-drops-26445},
  doi =		{10.4230/LIPIcs.RTA.2010.49},
  annote =	{Keywords: Infinitary rewriting, metric, partial order, abstract reduction system, axiomatic, term rewriting, graph rewriting}
}
Document
Partial Order Infinitary Term Rewriting and Böhm Trees

Authors: Patrick Bahr

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
We investigate an alternative model of infinitary term rewriting. Instead of a metric, a partial order on terms is employed to formalise (strong) convergence. We compare this partial order convergence of orthogonal term rewriting systems to the usual metric convergence of the corresponding B{"o}hm extensions. The B{"o}hm extension of a term rewriting system contains additional rules to equate so-called root-active terms. The core result we present is that reachability w.r.t. partial order convergence coincides with reachability w.r.t. metric convergence in the B{"o}hm extension. This result is used to show that, unlike in the metric model, orthogonal systems are infinitarily confluent and infinitarily normalising in the partial order model. Moreover, we obtain, as in the metric model, a compression lemma. A corollary of this lemma is that reachability w.r.t. partial order convergence is a conservative extension of reachability w.r.t. metric convergence.

Cite as

Patrick Bahr. Partial Order Infinitary Term Rewriting and Böhm Trees. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 67-84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{bahr:LIPIcs.RTA.2010.67,
  author =	{Bahr, Patrick},
  title =	{{Partial Order Infinitary Term Rewriting and B\"{o}hm Trees}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{67--84},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.67},
  URN =		{urn:nbn:de:0030-drops-26455},
  doi =		{10.4230/LIPIcs.RTA.2010.67},
  annote =	{Keywords: Infinitary term rewriting, B\"{o}hm trees, partial order, confluence, normalisation}
}
Document
Unique Normal Forms in Infinitary Weakly Orthogonal Rewriting

Authors: Joerg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Jan Willem Klop, and Vincent van Oostrom

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property (UNinf) fails by a simple example of a weakly orthogonal TRS with two collapsing rules. By translating this example, we show that UNinf also fails for the infinitary lambda-beta-eta-calculus. As positive results we obtain the following: Infinitary confluence, and hence UNinf, holds for weakly orthogonal TRSs that do not contain collapsing rules. To this end we refine the compression lemma. Furthermore, we consider the triangle and diamond properties for infinitary developments in weakly orthogonal TRSs, by refining an earlier cluster-analysis for the finite case.

Cite as

Joerg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Jan Willem Klop, and Vincent van Oostrom. Unique Normal Forms in Infinitary Weakly Orthogonal Rewriting. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 85-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{endrullis_et_al:LIPIcs.RTA.2010.85,
  author =	{Endrullis, Joerg and Grabmayer, Clemens and Hendriks, Dimitri and Klop, Jan Willem and van Oostrom, Vincent},
  title =	{{Unique Normal Forms in Infinitary Weakly Orthogonal Rewriting}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{85--102},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.85},
  URN =		{urn:nbn:de:0030-drops-26469},
  doi =		{10.4230/LIPIcs.RTA.2010.85},
  annote =	{Keywords: Weakly orthogonal term rewrite systems, unique normal form property, infinitary rewriting, infinitary lambda-beta-eta-calculus,}
}
Document
The Undecidability of Type Related Problems in Type-free Style System F

Authors: Ken-Etsu Fujita and Aleksy Schubert

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
We consider here a number of variations on the System F, that are predicative second-order systems whose terms are intermediate between the Curry style and Church style. The terms here contain the information on where the universal quantifier elimination and introduction in the type inference process must take place, which is similar to Church forms. However, they omit the information on which types are involved in the rules, which is similar to Curry forms. In this paper we prove the undecidability of the type-checking, type inference and typability problems for the system. Moreover, the proof works for the predicative version of the system with finitely stratified polymorphic types. The result includes the bounds on the Leivant’s level numbers for types used in the instances leading to the undecidability.

Cite as

Ken-Etsu Fujita and Aleksy Schubert. The Undecidability of Type Related Problems in Type-free Style System F. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 103-118, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{fujita_et_al:LIPIcs.RTA.2010.103,
  author =	{Fujita, Ken-Etsu and Schubert, Aleksy},
  title =	{{The Undecidability of Type Related Problems in Type-free Style System F}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{103--118},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.103},
  URN =		{urn:nbn:de:0030-drops-26475},
  doi =		{10.4230/LIPIcs.RTA.2010.103},
  annote =	{Keywords: Lambda calculus and related systems, type checking, typability, partial type inference, 2nd order unification, undecidability, Curry style type system}
}
Document
On (Un)Soundness of Unravelings

Authors: Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)


Abstract
We revisit (un)soundness of transformations of conditional into unconditional rewrite systems. The focus here is on so-called unravelings, the most simple and natural kind of such transformations, for the class of normal conditional systems without extra variables. By a systematic and thorough study of existing counterexamples and of the potential sources of unsoundness we obtain several new positive and negative results. In particular, we prove the following new results: Confluence, non-erasingness and weak left-linearity (of a given conditional system) each guarantee soundness of the unraveled version w.r.t. the original one. The latter result substantially extends the only known sufficient criterion for soundness, namely left-linearity. Furthermore, by means of counterexamples we refute various other tempting conjectures about sufficient conditions for soundness.

Cite as

Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer. On (Un)Soundness of Unravelings. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 119-134, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


Copy BibTex To Clipboard

@InProceedings{gmeiner_et_al:LIPIcs.RTA.2010.119,
  author =	{Gmeiner, Karl and Gramlich, Bernhard and Schernhammer, Felix},
  title =	{{On (Un)Soundness of Unravelings}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{119--134},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.119},
  URN =		{urn:nbn:de:0030-drops-26485},
  doi =		{10.4230/LIPIcs.RTA.2010.119},
  annote =	{Keywords: Conditional rewriting, transformation into unconditional systems, unsoundness, unraveling}
}
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