20 Search Results for "Hofmann, Martin"


Document
Invited Talk
Quotients in Dependent Type Theory (Invited Talk)

Authors: Andrew M. Pitts

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)


Abstract
Constructs that involve taking a quotient are commonplace in mathematics. Here I will consider how they are treated within dependent type theory. The notion of quotient type has its origins in the Nuprl theorem-proving system [R. L. Constable et al., 1986] for extensional type theory. Later Hofmann formulated a version for intensional type theory in his thesis [M. Hofmann, 1995]. This depends on having a pre-existing notion of intensional identity type. Hofmann used Martin-Löf’s notion, the indexed family inductively generated from proofs of reflexivity [B. Nordström et al., 1990]. The recent homotopical view of identity in terms of path types [The Univalent Foundations Program, 2013] gives a more liberal perspective and has brought with it the notion of higher inductive type (HIT) [P. L. Lumsdaine and M. Shulman, 2019], subsuming both inductive and quotient types. Inductively defined indexed families of types (in all their various forms) are perhaps the most useful concept that dependent type theory has contributed to the practice of computer assistance for formalizing mathematical proofs. However, it is often the case that a particular application of such types needs not only to inductively generate a collection of objects, but also to make identifications between the objects. In classical mathematics one can first generate and then identify, using the Axiom of Choice to lift infinitary constructions to the quotient. HITs can allow one to avoid such non-constructive uses of choice by inter-twining generation and identification. Perhaps more important than the constructive/non-constructive issue is that simultaneously declaring how to generate and how to identify can be a very natural way of defining some construct from the user’s point of view. This is why HITs promise to be so useful, once we have robust and convenient mechanisms in theorem-proving systems for defining HITs and defining functions out of HITs. Although some HITs have been axiomatized in various systems, at the moment the only system I know of with built in support for defining quite general forms of HIT and using them is the implementation of cubical type theory [C. Cohen et al., 2018] within recent versions of the Agda system [A. Vezzosi et al., 2019]. The higher dimensional aspect of identity in cubical type theory is fascinating; nevertheless, the simpler one-dimensional version of identity, in which one has uniqueness of identity proofs (UIP), is adequate for many applications. Although some regard UIP as a bug of early versions of Agda with it’s original form of dependent pattern matching [T. Coquand, 1992], it is by choice a feature of the Lean prover [J. Avigad et al., 2020]. Altenkirch and Kaposi [T. Altenkirch and A. Kaposi, 2016] have termed the one-dimensional version of HITs quotient inductive types (QITs) and they promise to be very useful even in the setting of type theory with UIP. In this talk I survey some of these developments, including a recent reduction of QITs to quotients [M. P. Fiore et al., 2020], and the prospects for better support in theorem-provers for quotient constructions.

Cite as

Andrew M. Pitts. Quotients in Dependent Type Theory (Invited Talk). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{pitts:LIPIcs.FSCD.2020.3,
  author =	{Pitts, Andrew M.},
  title =	{{Quotients in Dependent Type Theory}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.3},
  URN =		{urn:nbn:de:0030-drops-123256},
  doi =		{10.4230/LIPIcs.FSCD.2020.3},
  annote =	{Keywords: dependent type theory, quotient, quotient inductive type, theorem-proving systems}
}
Document
Martin Hofmann’s Case for Non-Strictly Positive Data Types

Authors: Ulrich Berger, Ralph Matthes, and Anton Setzer

Published in: LIPIcs, Volume 130, 24th International Conference on Types for Proofs and Programs (TYPES 2018)


Abstract
We describe the breadth-first traversal algorithm by Martin Hofmann that uses a non-strictly positive data type and carry out a simple verification in an extensional setting. Termination is shown by implementing the algorithm in the strongly normalising extension of system F by Mendler-style recursion. We then analyze the same algorithm by alternative verifications first in an intensional setting using a non-strictly positive inductive definition (not just a non-strictly positive data type), and subsequently by two different algebraic reductions. The verification approaches are compared in terms of notions of simulation and should elucidate the somewhat mysterious algorithm and thus make a case for other uses of non-strictly positive data types. Except for the termination proof, which cannot be formalised in Coq, all proofs were formalised in Coq and some of the algorithms were implemented in Agda and Haskell.

Cite as

Ulrich Berger, Ralph Matthes, and Anton Setzer. Martin Hofmann’s Case for Non-Strictly Positive Data Types. In 24th International Conference on Types for Proofs and Programs (TYPES 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 130, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{berger_et_al:LIPIcs.TYPES.2018.1,
  author =	{Berger, Ulrich and Matthes, Ralph and Setzer, Anton},
  title =	{{Martin Hofmann’s Case for Non-Strictly Positive Data Types}},
  booktitle =	{24th International Conference on Types for Proofs and Programs (TYPES 2018)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-106-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{130},
  editor =	{Dybjer, Peter and Esp{\'\i}rito Santo, Jos\'{e} and Pinto, Lu{\'\i}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2018.1},
  URN =		{urn:nbn:de:0030-drops-114052},
  doi =		{10.4230/LIPIcs.TYPES.2018.1},
  annote =	{Keywords: non strictly-positive data types, breadth-first traversal, program verification, Mendler-style recursion, System F, theorem proving, Coq, Agda, Haskell}
}
Document
From Theory to Practice of Algebraic Effects and Handlers (Dagstuhl Seminar 16112)

Authors: Andrej Bauer, Martin Hofmann, Matija Pretnar, and Jeremy Yallop

Published in: Dagstuhl Reports, Volume 6, Issue 3 (2016)


Abstract
Dagstuhl Seminar 16112 was devoted to research in algebraic effects and handlers, a chapter in the principles of programming languages which addresses computational effects (such as I/O, state, exceptions, nondeterminism, and many others). The speakers and the working groups covered a range of topics, including comparisons between various control mechanisms (handlers vs. delimited control), implementation of an effect system for OCaml, compilation techniques for algebraic effects and handlers, and implementations of effects in Haskell.

Cite as

Andrej Bauer, Martin Hofmann, Matija Pretnar, and Jeremy Yallop. From Theory to Practice of Algebraic Effects and Handlers (Dagstuhl Seminar 16112). In Dagstuhl Reports, Volume 6, Issue 3, pp. 44-58, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@Article{bauer_et_al:DagRep.6.3.44,
  author =	{Bauer, Andrej and Hofmann, Martin and Pretnar, Matija and Yallop, Jeremy},
  title =	{{From Theory to Practice of Algebraic Effects and Handlers (Dagstuhl Seminar 16112)}},
  pages =	{44--58},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{3},
  editor =	{Bauer, Andrej and Hofmann, Martin and Pretnar, Matija and Yallop, Jeremy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.6.3.44},
  URN =		{urn:nbn:de:0030-drops-61489},
  doi =		{10.4230/DagRep.6.3.44},
  annote =	{Keywords: algebraic effects, computational effects, handlers, implementation techniques, programming languages}
}
Document
Multivariate Amortised Resource Analysis for Term Rewrite Systems

Authors: Martin Hofmann and Georg Moser

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)


Abstract
We study amortised resource analysis in the context of term rewrite systems. We introduce a novel amortised analysis based on the potential method. The method is represented in an inference system akin to a type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed rewrite system. The crucial feature of the inference system is the admittance of multivariate bounds in the context of arbitrary data structures in a completely uniform way. This extends our earlier univariate resource analysis of typed term rewrite systems and continues our program of applying automated amortised resource analysis to rewriting.

Cite as

Martin Hofmann and Georg Moser. Multivariate Amortised Resource Analysis for Term Rewrite Systems. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 241-256, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{hofmann_et_al:LIPIcs.TLCA.2015.241,
  author =	{Hofmann, Martin and Moser, Georg},
  title =	{{Multivariate Amortised Resource Analysis for Term Rewrite Systems}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{241--256},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.241},
  URN =		{urn:nbn:de:0030-drops-51675},
  doi =		{10.4230/LIPIcs.TLCA.2015.241},
  annote =	{Keywords: program analysis,amortised analysis, term rewriting,multivariate bounds}
}
Document
Invited Talk
Computing With a Fixed Number of Pointers (Invited Talk)

Authors: Martin Hofmann and Ramyaa Ramyaa

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)


Abstract
Consider the P-complete problem Horn which asks whether a given set of Horn clauses is (un)satisfiable. To solve it one keeps a dynamic set of atoms that are forced to be true. Using the clauses one then adds atoms to this set until saturation is reached. It is easy to see that this dynamic set will in general more than constant size even if we allow to discard already proved atoms. Given that we need logarithmic space to store a single atom on a Turing machine tape this seems like a strong intuitive argument for the hypothesis that logarithmic space is different from polynomial time. We thus tried to find formal models of computation in which this intuitive argument can be made rigorous. Thus, we study computational models that can be simulated in logarithmic space and encompass logspace algorithms which manipulate a constant size of objects that require logarithmic space individually such as pointers or graph nodes. The hope is then to be able to show that such models are provably unable to solve P-complete problems. We report in this survey article on our partial results towards this goal as well as the state-of-the-art in general.

Cite as

Martin Hofmann and Ramyaa Ramyaa. Computing With a Fixed Number of Pointers (Invited Talk). In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 3-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{hofmann_et_al:LIPIcs.FSTTCS.2013.3,
  author =	{Hofmann, Martin and Ramyaa, Ramyaa},
  title =	{{Computing With a Fixed Number of Pointers}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{3--18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.3},
  URN =		{urn:nbn:de:0030-drops-44009},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.3},
  annote =	{Keywords: Logarithmic space, Jumping graph automata, st-connectivity, co-st-connectivity, Cayley graphs}
}
Document
10351 Abstracts Collection – Modelling, Controlling and Reasoning About State

Authors: Amal Ahmed, Nick Benton, Lars Birkedal, and Martin Hofmann

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
From 29 August 2010 to 3 September 2010, the Dagstuhl Seminar 10351 ``Modelling, Controlling and Reasoning About State '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. Links to extended abstracts or full papers are provided, if available.

Cite as

Amal Ahmed, Nick Benton, Lars Birkedal, and Martin Hofmann. 10351 Abstracts Collection – Modelling, Controlling and Reasoning About State. In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{ahmed_et_al:DagSemProc.10351.1,
  author =	{Ahmed, Amal and Benton, Nick and Birkedal, Lars and Hofmann, Martin},
  title =	{{10351 Abstracts Collection – Modelling, Controlling and Reasoning About State}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.1},
  URN =		{urn:nbn:de:0030-drops-28116},
  doi =		{10.4230/DagSemProc.10351.1},
  annote =	{Keywords: Mutable State, Program Logics, Semantics, Type Systems, Verification}
}
Document
10351 Executive Summary – Modelling, Controlling and Reasoning About State

Authors: Amal Ahmed, Nick Benton, Lars Birkedal, and Martin Hofmann

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
From 29 August 2010 to 3 September 2010, the Dagstuhl Seminar 10351 ``Modelling, Controlling and Reasoning About State '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. 44 researchers, with interests and expertise in many different aspects of modelling and reasoning about mutable state, met to present their current work and discuss ongoing projects and open problems. This executive summary provides a general overview of the goals of the seminar and of the topics discussed.

Cite as

Amal Ahmed, Nick Benton, Lars Birkedal, and Martin Hofmann. 10351 Executive Summary – Modelling, Controlling and Reasoning About State. In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{ahmed_et_al:DagSemProc.10351.2,
  author =	{Ahmed, Amal and Benton, Nick and Birkedal, Lars and Hofmann, Martin},
  title =	{{10351 Executive Summary – Modelling, Controlling and Reasoning About State}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.2},
  URN =		{urn:nbn:de:0030-drops-28108},
  doi =		{10.4230/DagSemProc.10351.2},
  annote =	{Keywords: Mutable State, Program Logics, Semantics, Type Systems, Verification}
}
Document
A Theory of Termination via Indirection

Authors: Robert Dockins and Aquinas Hobor

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
Step-indexed models provide approximations to a class of domain equations and can prove type safety, partial correctness, and program equivalence; however, a common misconception is that they are inapplicable to liveness problems. We disprove this by applying step-indexing to develop the first Hoare logic of total correctness for a language with function pointers and semantic assertions. In fact, from a liveness perspective, our logic is stronger: we verify explicit time resource bounds. We apply our logic to examples containing nontrivial "higher-order" uses of function pointers and we prove soundness with respect to a standard operational semantics. Our core technique is very compact and may be applicable to other liveness problems. Our results are machine checked in Coq.

Cite as

Robert Dockins and Aquinas Hobor. A Theory of Termination via Indirection. In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{dockins_et_al:DagSemProc.10351.3,
  author =	{Dockins, Robert and Hobor, Aquinas},
  title =	{{A Theory of Termination via Indirection}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.3},
  URN =		{urn:nbn:de:0030-drops-28050},
  doi =		{10.4230/DagSemProc.10351.3},
  annote =	{Keywords: Step-indexed Models, Termination}
}
Document
Limitations of Applicative Bisimulation (Preliminary Report)

Authors: Vasileios Koutavas, Paul Blain Levy, and Eijiro Sumii

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
We present a series of examples that illuminate an important aspect of the semantics of higher-order functions with local state. Namely that certain behaviour of such functions can only be observed by pro- viding them with arguments that contain the functions themselves. This provides evidence for the necessity of complex conditions for functions in modern semantics for state, such as logical relations and Kripke-like bisimulations, where related functions are applied to related arguments (that may contain the functions). It also suggests that simpler semantics, such as those based on applicative bisimulations where functions are ap- plied to identical arguments, would not scale to higher-order languages with local state.

Cite as

Vasileios Koutavas, Paul Blain Levy, and Eijiro Sumii. Limitations of Applicative Bisimulation (Preliminary Report). In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{koutavas_et_al:DagSemProc.10351.4,
  author =	{Koutavas, Vasileios and Levy, Paul Blain and Sumii, Eijiro},
  title =	{{Limitations of Applicative Bisimulation (Preliminary Report)}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.4},
  URN =		{urn:nbn:de:0030-drops-28074},
  doi =		{10.4230/DagSemProc.10351.4},
  annote =	{Keywords: Imperative languages, higher-order functions, local state}
}
Document
Program Equivalence with Names

Authors: Nikos Tzevelekos

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
The nu-calculus of Pitts and Stark was introduced as a paradigmatic functional language with a very basic local-state effect: references of unit type. These were called names, and the motto of the new language went as follows: "Names are created with local scope, can be tested for equality, and are passed around via function application, but that is all." Because of this limited framework, the hope was that fully abstract models and complete proof techniques could be obtained. However, it was soon realised that the behaviour of nu-calculus programs is quite intricate, and program equivalence in particular is surprisingly difficult to capture. Here we shall focus on the following "hard" equivalence. new x,y in f. (fx=fy) == f. true We shall examine attempts and proofs of the above, explain the advantages and disadvantages of the proof methods and discuss why program equivalence in this simple language remains to date a mystery.

Cite as

Nikos Tzevelekos. Program Equivalence with Names. In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{tzevelekos:DagSemProc.10351.5,
  author =	{Tzevelekos, Nikos},
  title =	{{Program Equivalence with Names}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.5},
  URN =		{urn:nbn:de:0030-drops-28092},
  doi =		{10.4230/DagSemProc.10351.5},
  annote =	{Keywords: Nu-calculus, Local State, Logical Relations, Game Semantics, Environmental Bisimulations}
}
Document
Step-Indexed Biorthogonality: a Tutorial Example

Authors: Andrew M. Pitts

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
The purpose of this note is to illustrate the use of step-indexing combined with biorthogonality to construct syntactical logical relations. It walks through the details of a syntactically simple, yet non-trivial example: a proof of the "CIU Theorem'' for contextual equivalence in the untyped call-by-value $lambda$-calculus with recursively defined functions.

Cite as

Andrew M. Pitts. Step-Indexed Biorthogonality: a Tutorial Example. In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{pitts:DagSemProc.10351.6,
  author =	{Pitts, Andrew M.},
  title =	{{Step-Indexed Biorthogonality: a Tutorial Example}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.6},
  URN =		{urn:nbn:de:0030-drops-28067},
  doi =		{10.4230/DagSemProc.10351.6},
  annote =	{Keywords: Biorthogonality, logical relations, operational semantics, step-indexing}
}
Document
Step-Indexing: The Good, the Bad and the Ugly

Authors: Nick Benton and Chung-Kil Hur

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)


Abstract
Over the last decade, step-indices have been widely used for the construction of operationally-based logical relations in the presence of various kinds of recursion. We first give an argument that step-indices, or something like them, seem to be required for defining realizability relations between high-level source languages and low-level targets, in the case that the low-level allows egregiously intensional operations such as reflection or comparison of code pointers. We then show how, much to our annoyance, step-indices also seem to prevent us from exploiting such operations as aggressively as we would like in proving program transformations.

Cite as

Nick Benton and Chung-Kil Hur. Step-Indexing: The Good, the Bad and the Ugly. In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{benton_et_al:DagSemProc.10351.7,
  author =	{Benton, Nick and Hur, Chung-Kil},
  title =	{{Step-Indexing: The Good, the Bad and the Ugly}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.7},
  URN =		{urn:nbn:de:0030-drops-28085},
  doi =		{10.4230/DagSemProc.10351.7},
  annote =	{Keywords: Step-Indexing, Logical Relations, Low-Level Languages, Compiler Correctness}
}
Document
08061 Abstracts Collection – Types, Logics and Semantics for State

Authors: Amal Ahmed, Nick Benton, Martin Hofmann, and Greg Morrisett

Published in: Dagstuhl Seminar Proceedings, Volume 8061, Types, Logics and Semantics for State (2008)


Abstract
From 3 February to 8 February 2008, the Dagstuhl Seminar 08061 ``Types, Logics and Semantics for State'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Amal Ahmed, Nick Benton, Martin Hofmann, and Greg Morrisett. 08061 Abstracts Collection – Types, Logics and Semantics for State. In Types, Logics and Semantics for State. Dagstuhl Seminar Proceedings, Volume 8061, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{ahmed_et_al:DagSemProc.08061.1,
  author =	{Ahmed, Amal and Benton, Nick and Hofmann, Martin and Morrisett, Greg},
  title =	{{08061 Abstracts Collection – Types, Logics and Semantics for State}},
  booktitle =	{Types, Logics and Semantics for State},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8061},
  editor =	{Amal Ahmed and Nick Benton and Martin Hofmann and Greg Morrisett},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08061.1},
  URN =		{urn:nbn:de:0030-drops-14281},
  doi =		{10.4230/DagSemProc.08061.1},
  annote =	{Keywords: Mutable State, Program Logics, Semantics, Type Systems, Program Analysis}
}
Document
08061 Executive Summary – Types, Logics and Semantics for State

Authors: Amal Ahmed, Nick Benton, Martin Hofmann, and Greg Morrisett

Published in: Dagstuhl Seminar Proceedings, Volume 8061, Types, Logics and Semantics for State (2008)


Abstract
From 3 February to 8 February 2008, the Dagstuhl Seminar 08061 State" Conference and Research Center (IBFI), Schloss Dagstuhl. 45 researchers, with interests and expertise in many different aspects of modelling and reasoning about mutable state, met to present their current work and discuss ongoing projects and open problems.

Cite as

Amal Ahmed, Nick Benton, Martin Hofmann, and Greg Morrisett. 08061 Executive Summary – Types, Logics and Semantics for State. In Types, Logics and Semantics for State. Dagstuhl Seminar Proceedings, Volume 8061, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{ahmed_et_al:DagSemProc.08061.2,
  author =	{Ahmed, Amal and Benton, Nick and Hofmann, Martin and Morrisett, Greg},
  title =	{{08061 Executive Summary – Types, Logics and Semantics for State}},
  booktitle =	{Types, Logics and Semantics for State},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8061},
  editor =	{Amal Ahmed and Nick Benton and Martin Hofmann and Greg Morrisett},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08061.2},
  URN =		{urn:nbn:de:0030-drops-14269},
  doi =		{10.4230/DagSemProc.08061.2},
  annote =	{Keywords: Mutable State, Program Logics, Semantics, Type Systems, Program Analysis}
}
Document
A Unified Framework for Verification Techniques for Object Invariants

Authors: Sophia Drossopoulou, Adrian Francalanza, P. Müller, and Alexander J. Summers

Published in: Dagstuhl Seminar Proceedings, Volume 8061, Types, Logics and Semantics for State (2008)


Abstract
Object invariants define the consistency of objects. They have subtle semantics, mainly because of call-backs, multi-object invariants, and subclassing. Several verification techniques for object invariants have been proposed. It is difficult to compare these techniques, and to ascertain their soundness, because of their differences in restrictions on programs and invariants, in the use of advanced type systems (e.g., ownership types), in the meaning of invariants, and in proof obligations. We develop a unified framework for such techniques. We distil seven parameters that characterise a verification technique, and identify sufficient conditions on these parameters which guarantee soundness. We instantiate our framework with three verification techniques from the literature, and use it to assess soundness and compare expressiveness.

Cite as

Sophia Drossopoulou, Adrian Francalanza, P. Müller, and Alexander J. Summers. A Unified Framework for Verification Techniques for Object Invariants. In Types, Logics and Semantics for State. Dagstuhl Seminar Proceedings, Volume 8061, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{drossopoulou_et_al:DagSemProc.08061.3,
  author =	{Drossopoulou, Sophia and Francalanza, Adrian and M\"{u}ller, P. and Summers, Alexander J.},
  title =	{{A Unified Framework for  Verification Techniques for Object Invariants}},
  booktitle =	{Types, Logics and Semantics for State},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8061},
  editor =	{Amal Ahmed and Nick Benton and Martin Hofmann and Greg Morrisett},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08061.3},
  URN =		{urn:nbn:de:0030-drops-14278},
  doi =		{10.4230/DagSemProc.08061.3},
  annote =	{Keywords: Object invariants, visible states semantics, verification, sound}
}
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