2 Search Results for "Rydeheard, David"

Document
DOI: 10.4230/LIPIcs.TYPES.2023.4
A Sound and Complete Substitution Algorithm for Multimode Type Theory

Authors: Joris Ceulemans, Andreas Nuyts, and Dominique Devriese

Published in: LIPIcs, Volume 303, 29th International Conference on Types for Proofs and Programs (TYPES 2023)

Abstract
Multimode Type Theory (MTT) is a generic type theory that can be instantiated with an arbitrary mode theory to model features like parametricity, cohesion and guarded recursion. However, the presence of modalities in MTT significantly complicates the substitution calculus of this system. Moreover, MTT’s syntax has explicit substitutions with an axiomatic system - not an algorithm - governing the connection between an explicitly substituted term and the resulting term in which variables have actually been replaced. So far, the only results on eliminating explicit substitutions in MTT rely on normalisation by evaluation and hence also immediately normalise a term. In this paper, we present a substitution algorithm for MTT that is completely separated from normalisation. To this end, we introduce Substitution-Free Multimode Type Theory (SFMTT): a formulation of MTT without explicit substitutions, but for which we are able to give a structurally recursive substitution algorithm, suitable for implementation in a total programming language or proof assistant. On the usual formulation of MTT, we consider σ-equality, the congruence generated solely by equality rules for explicit substitutions. There is a trivial embedding from SFMTT to MTT, and a converse translation that eliminates the explicit substitutions. We prove soundness and completeness of our algorithm with respect to σ-equivalence and thus establish that MTT with σ-equality has computable σ-normal forms, given by the terms of SFMTT.
Cite as

Joris Ceulemans, Andreas Nuyts, and Dominique Devriese. A Sound and Complete Substitution Algorithm for Multimode Type Theory. In 29th International Conference on Types for Proofs and Programs (TYPES 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 303, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ceulemans_et_al:LIPIcs.TYPES.2023.4,
  author =	{Ceulemans, Joris and Nuyts, Andreas and Devriese, Dominique},
  title =	{{A Sound and Complete Substitution Algorithm for Multimode Type Theory}},
  booktitle =	{29th International Conference on Types for Proofs and Programs (TYPES 2023)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-332-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{303},
  editor =	{Kesner, Delia and Reyes, Eduardo Hermo and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2023.4},
  URN =		{urn:nbn:de:0030-drops-204826},
  doi =		{10.4230/LIPIcs.TYPES.2023.4},
  annote =	{Keywords: dependent type theory, modalities, multimode type theory, explicit substitutions, substitution algorithm}
}
Document
DOI: 10.4230/OASIcs.FSFMA.2013.80
Modelling and Reasoning about Dynamic Networks as Concurrent Systems

Authors: Yanti Rusmawati and David Rydeheard

Published in: OASIcs, Volume 31, 1st French Singaporean Workshop on Formal Methods and Applications (FSFMA 2013)

Abstract
We propose a new approach to modelling and reasoning about dynamic networks. Dynamic networks consist of nodes and edges whose operating status may change over time (for example, the edges may be unreliable and operate intermittently). Message-passing in such networks is inherently difficult and reasoning about the behaviour of message-passing algorithms is also difficult. We develop a series of abstract models which allow us to focus on the correctness of routing methods. We model the dynamic network as a ``demonic'' process which runs concurrently with routing updates and message-passing. This allows us to use temporal logic and fairness constraints to reason about dynamic networks. The models are implemented as multi-threaded programs and, to validate them, we use an experimental run-time verification tool called RuleR.
Cite as

Yanti Rusmawati and David Rydeheard. Modelling and Reasoning about Dynamic Networks as Concurrent Systems. In 1st French Singaporean Workshop on Formal Methods and Applications (FSFMA 2013). Open Access Series in Informatics (OASIcs), Volume 31, pp. 80-85, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{rusmawati_et_al:OASIcs.FSFMA.2013.80,
  author =	{Rusmawati, Yanti and Rydeheard, David},
  title =	{{Modelling and Reasoning about Dynamic Networks as Concurrent Systems}},
  booktitle =	{1st French Singaporean Workshop on Formal Methods and Applications (FSFMA 2013)},
  pages =	{80--85},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-56-9},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{31},
  editor =	{Choppy, Christine and Sun, Jun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FSFMA.2013.80},
  URN =		{urn:nbn:de:0030-drops-40921},
  doi =		{10.4230/OASIcs.FSFMA.2013.80},
  annote =	{Keywords: dynamic networks, temporal logic, concurrent systems}
}
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