5 Search Results for "Klop, Jan Willem"

Document
DOI: 10.4230/LIPIcs.FSCD.2024.8
Mechanized Subject Expansion in Uniform Intersection Types for Perpetual Reductions

Authors: Andrej Dudenhefner and Daniele Pautasso

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
We provide a new, purely syntactical proof of strong normalization for the simply typed λ-calculus. The result relies on a novel proof of the equivalence between typability in the simple type system and typability in the uniform intersection type system (a restriction of the non-idempotent intersection type system). For formal verification, the equivalence is mechanized using the Coq proof assistant. In the present work, strong normalization of a given simply typed term M is shown in four steps. First, M is reduced to a normal form N via a suitable reduction strategy with a decreasing measure. Second, a uniform intersection type for the normal form N is inferred. Third, a uniform intersection type for M is constructed iteratively via subject expansion. Fourth, strong normalization of M is shown by induction on the size of the type derivation. A supplementary contribution is a family of perpetual reduction strategies, i.e. strategies which preserve infinite reduction paths. This family allows for subject expansion in the intersection type systems of interest, and contains a reduction strategy with a decreasing measure in the simple type system. A notable member of this family is Barendregt’s F_∞ reduction strategy.
Cite as

Andrej Dudenhefner and Daniele Pautasso. Mechanized Subject Expansion in Uniform Intersection Types for Perpetual Reductions. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dudenhefner_et_al:LIPIcs.FSCD.2024.8,
  author =	{Dudenhefner, Andrej and Pautasso, Daniele},
  title =	{{Mechanized Subject Expansion in Uniform Intersection Types for Perpetual Reductions}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.8},
  URN =		{urn:nbn:de:0030-drops-203371},
  doi =		{10.4230/LIPIcs.FSCD.2024.8},
  annote =	{Keywords: lambda-calculus, simple types, intersection types, strong normalization, mechanization, perpetual reductions}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.21
Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti

Authors: Thiago Felicissimo and Théo Winterhalter

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Proof assistants such as Coq implement a type theory featuring three important features: impredicativity, cumulativity and product covariance. This combination has proven difficult to be expressed in the logical framework Dedukti, and previous attempts have failed in providing an encoding that is proven confluent, sound and conservative. In this work we solve this longstanding open problem by providing an encoding of these three features that we prove to be confluent, sound and to satisfy a restricted (but, we argue, strong enough) form of conservativity. Our proof of confluence is a contribution by itself, and combines various criteria and proof techniques from rewriting theory. Our proof of soundness also contributes a new strategy in which the result is shown in terms of an inverse translation function, fixing a common flaw made in some previous encoding attempts.
Cite as

Thiago Felicissimo and Théo Winterhalter. Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{felicissimo_et_al:LIPIcs.FSCD.2024.21,
  author =	{Felicissimo, Thiago and Winterhalter, Th\'{e}o},
  title =	{{Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.21},
  URN =		{urn:nbn:de:0030-drops-203503},
  doi =		{10.4230/LIPIcs.FSCD.2024.21},
  annote =	{Keywords: Dedukti, Rewriting, Confluence, Dependent types, Cumulativity, Universes}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.149
A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions

Authors: Wojciech Różowski

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Deterministic automata have been traditionally studied through the point of view of language equivalence, but another perspective is given by the canonical notion of shortest-distinguishing-word distance quantifying the of states. Intuitively, the longer the word needed to observe a difference between two states, then the closer their behaviour is. In this paper, we give a sound and complete axiomatisation of shortest-distinguishing-word distance between regular languages. Our axiomatisation relies on a recently developed quantitative analogue of equational logic, allowing to manipulate rational-indexed judgements of the form e ≡_ε f meaning term e is approximately equivalent to term f within the error margin of ε. The technical core of the paper is dedicated to the completeness argument that draws techniques from order theory and Banach spaces to simplify the calculation of the behavioural distance to the point it can be then mimicked by axiomatic reasoning.
Cite as

Wojciech Różowski. A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 149:1-149:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rozowski:LIPIcs.ICALP.2024.149,
  author =	{R\'{o}\.{z}owski, Wojciech},
  title =	{{A Complete Quantitative Axiomatisation of Behavioural Distance of Regular Expressions}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{149:1--149:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.149},
  URN =		{urn:nbn:de:0030-drops-202920},
  doi =		{10.4230/LIPIcs.ICALP.2024.149},
  annote =	{Keywords: Regular Expressions, Behavioural Distances, Quantitative Equational Theories}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.14
Decreasing Diagrams with Two Labels Are Complete for Confluence of Countable Systems

Authors: Jörg Endrullis, Jan Willem Klop, and Roy Overbeek

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be used to obtain such a hierarchy. The decreasing diagrams technique is one of the strongest and most versatile methods for proving confluence of abstract reduction systems, it is complete for countable systems, and it has many well-known confluence criteria as corollaries. So what makes decreasing diagrams so powerful? In contrast to other confluence techniques, decreasing diagrams employ a labelling of the steps -> with labels from a well-founded order in order to conclude confluence of the underlying unlabelled relation. Hence it is natural to ask how the size of the label set influences the strength of the technique. In particular, what class of abstract reduction systems can be proven confluent using decreasing diagrams restricted to 1 label, 2 labels, 3 labels, and so on? Surprisingly, we find that two labels suffice for proving confluence for every abstract rewrite system having the cofinality property, thus in particular for every confluent, countable system. We also show that this result stands in sharp contrast to the situation for commutation of rewrite relations, where the hierarchy does not collapse. Finally, as a background theme, we discuss the logical issue of first-order definability of the notion of confluence.
Cite as

Jörg Endrullis, Jan Willem Klop, and Roy Overbeek. Decreasing Diagrams with Two Labels Are Complete for Confluence of Countable Systems. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{endrullis_et_al:LIPIcs.FSCD.2018.14,
  author =	{Endrullis, J\"{o}rg and Klop, Jan Willem and Overbeek, Roy},
  title =	{{Decreasing Diagrams with Two Labels Are Complete for Confluence of Countable Systems}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.14},
  URN =		{urn:nbn:de:0030-drops-91848},
  doi =		{10.4230/LIPIcs.FSCD.2018.14},
  annote =	{Keywords: confluence, decreasing diagrams, weak diamond property}
}
Document
DOI: 10.4230/LIPIcs.RTA.2010.85
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)

Copy BibTex To Clipboard

@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,}
}
  • Refine by Author
  • 2 Klop, Jan Willem
  • 1 Dudenhefner, Andrej
  • 1 Endrullis, Joerg
  • 1 Endrullis, Jörg
  • 1 Felicissimo, Thiago
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Equational logic and rewriting
  • 2 Theory of computation → Type theory
  • 1 Theory of computation → Regular languages

  • Refine by Keyword
  • 1 Behavioural Distances
  • 1 Confluence
  • 1 Cumulativity
  • 1 Dedukti
  • 1 Dependent types
  • Show More...

  • Refine by Type
  • 5 document

  • Refine by Publication Year
  • 3 2024
  • 1 2010
  • 1 2018

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact