DROPS

Volume

LIPIcs, Volume 26

19th International Conference on Types for Proofs and Programs (TYPES 2013)

TYPES 2013, April 22-26, 2013, Toulouse, France

Editors: Ralph Matthes and Aleksy Schubert

Document

DOI: 10.4230/LIPIcs.TYPES.2016.8

Coq Support in HAHA

Authors: Jacek Chrzaszcz, Aleksy Schubert, and Jakub Zakrzewski

Published in: LIPIcs, Volume 97, 22nd International Conference on Types for Proofs and Programs (TYPES 2016)

Abstract

HAHA is a tool that helps in teaching and learning Hoare logic. It is targeted at an introductory course on software verification. We present a set of new features of the HAHA verification environment that exploit Coq. These features are (1) generation of verification conditions in Coq so that they can be explored and proved interactively and (2) compilation of HAHA programs into CompCert certified compilation tool-chain. With the interactive Coq proving support we obtain an interesting functionality that makes it possible to carefully examine step-by-step verification conditions and systematically discover flaws in their formulation. As a result Coq back-end serves as a kind of specification debugger.

Cite as

Jacek Chrzaszcz, Aleksy Schubert, and Jakub Zakrzewski. Coq Support in HAHA. In 22nd International Conference on Types for Proofs and Programs (TYPES 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 97, pp. 8:1-8:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chrzaszcz_et_al:LIPIcs.TYPES.2016.8,
  author =	{Chrzaszcz, Jacek and Schubert, Aleksy and Zakrzewski, Jakub},
  title =	{{Coq Support in HAHA}},
  booktitle =	{22nd International Conference on Types for Proofs and Programs (TYPES 2016)},
  pages =	{8:1--8:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-065-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{97},
  editor =	{Ghilezan, Silvia and Geuvers, Herman and Ivetic, Jelena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2016.8},
  URN =		{urn:nbn:de:0030-drops-98562},
  doi =		{10.4230/LIPIcs.TYPES.2016.8},
  annote =	{Keywords: Hoare logic, program verification, Coq theorem prover, teaching}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2016.12

Synthesis of Functional Programs with Help of First-Order Intuitionistic Logic

Authors: Marcin Benke, Aleksy Schubert, and Daria Walukiewicz-Chrzaszcz

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract

Curry-Howard isomorphism makes it possible to obtain functional programs from proofs in logic. We analyse the problem of program synthesis for ML programs with algebraic types and relate it to the proof search problems in appropriate logics. The problem of synthesis for closed programs is easily equivalent to the proof construction in intuitionistic propositional logic and thus fits in the class of PSPACE-complete problems. We focus further attention on the synthesis problem relative to a given external library of functions. It turns out that the problem is undecidable for unbounded instantiation in ML. However its restriction to instantiations with atomic types only results in a case equivalent to proof search in a restricted fragment of intuitionistic first-order logic, being the core of Sigma_1 level of the logic in the Mints hierarchy. This results in EXPSPACE-completeness for this special case of the ML program synthesis problem.

Cite as

Marcin Benke, Aleksy Schubert, and Daria Walukiewicz-Chrzaszcz. Synthesis of Functional Programs with Help of First-Order Intuitionistic Logic. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{benke_et_al:LIPIcs.FSCD.2016.12,
  author =	{Benke, Marcin and Schubert, Aleksy and Walukiewicz-Chrzaszcz, Daria},
  title =	{{Synthesis of Functional Programs with Help of First-Order Intuitionistic Logic}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.12},
  URN =		{urn:nbn:de:0030-drops-59765},
  doi =		{10.4230/LIPIcs.FSCD.2016.12},
  annote =	{Keywords: ML, program synthesis}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2014.251

Restricted Positive Quantification Is Not Elementary

Authors: Aleksy Schubert, Pawel Urzyczyn, and Daria Walukiewicz-Chrzaszcz

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

Abstract

We show that a restricted variant of constructive predicate logic with positive (covariant) quantification is of super-elementary complexity. The restriction is to limit the number of eigenvariables used in quantifier introductions rules to a reasonably usable level. This construction suggests that the known non-elementary decision algorithms for positive logic may actually be best possible.

Cite as

Aleksy Schubert, Pawel Urzyczyn, and Daria Walukiewicz-Chrzaszcz. Restricted Positive Quantification Is Not Elementary. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 251-273, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{schubert_et_al:LIPIcs.TYPES.2014.251,
  author =	{Schubert, Aleksy and Urzyczyn, Pawel and Walukiewicz-Chrzaszcz, Daria},
  title =	{{Restricted Positive Quantification Is Not Elementary}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{251--273},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.251},
  URN =		{urn:nbn:de:0030-drops-55002},
  doi =		{10.4230/LIPIcs.TYPES.2014.251},
  annote =	{Keywords: constructive logic, complexity, automata theory}
}

Document

DOI: 10.4230/LIPIcs.CSL.2015.128

Automata Theoretic Account of Proof Search

Authors: Aleksy Schubert, Wil Dekkers, and Henk P. Barendregt

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract

Automata theoretical techniques are developed that handle inhabitant search in the simply typed lambda calculus. The automata-theoretic model for inhabitant search, which can be viewed as proof search by the Curry-Howard isomorphism, is proven to be adequate by reduction of the inhabitant existence problem to the emptiness problem for the automata. To strengthen the claim, it is demonstrated that the latter has the same complexity as the former. We also discuss the basic closure properties of the automata.

Cite as

Aleksy Schubert, Wil Dekkers, and Henk P. Barendregt. Automata Theoretic Account of Proof Search. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 128-143, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{schubert_et_al:LIPIcs.CSL.2015.128,
  author =	{Schubert, Aleksy and Dekkers, Wil and Barendregt, Henk P.},
  title =	{{Automata Theoretic Account of Proof Search}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{128--143},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.128},
  URN =		{urn:nbn:de:0030-drops-54113},
  doi =		{10.4230/LIPIcs.CSL.2015.128},
  annote =	{Keywords: simple types, automata, trees, languages of proofs}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.TYPES.2013

LIPIcs, Volume 26, TYPES'13, Complete Volume

Authors: Ralph Matthes and Aleksy Schubert

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

LIPIcs, Volume 26, TYPES'13, Complete Volume

Cite as

19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Proceedings{matthes_et_al:LIPIcs.TYPES.2013,
  title =	{{LIPIcs, Volume 26, TYPES'13, Complete Volume}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013},
  URN =		{urn:nbn:de:0030-drops-46370},
  doi =		{10.4230/LIPIcs.TYPES.2013},
  annote =	{Keywords: Applicative (Functional) Programming, Software/Program Verification, Specifying and Verifying and Reasoning about Programs, Mathematical Logic}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.TYPES.2013.i

Frontmatter, Table of Contents, Preface, Conference Organization

Authors: Ralph Matthes and Aleksy Schubert

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

Frontmatter, Table of Contents, Preface, Conference Organization

Cite as

19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. i-x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{matthes_et_al:LIPIcs.TYPES.2013.i,
  author =	{Matthes, Ralph and Schubert, Aleksy},
  title =	{{Frontmatter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{i--x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.i},
  URN =		{urn:nbn:de:0030-drops-46225},
  doi =		{10.4230/LIPIcs.TYPES.2013.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.1

Update Monads: Cointerpreting Directed Containers

Authors: Danel Ahman and Tarmo Uustalu

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

We introduce update monads as a generalization of state monads. Update monads are the compatible compositions of reader and writer monads given by a set and a monoid. Distributive laws between such monads are given by actions of the monoid on the set. We also discuss a dependently typed generalization of update monads. Unlike simple update monads, they cannot be factored into a reader and writer monad, but rather into similarly looking relative monads. Dependently typed update monads arise from cointerpreting directed containers, by which we mean an extension of an interpretation of the opposite of the category of containers into the category of set functors.

Cite as

Danel Ahman and Tarmo Uustalu. Update Monads: Cointerpreting Directed Containers. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{ahman_et_al:LIPIcs.TYPES.2013.1,
  author =	{Ahman, Danel and Uustalu, Tarmo},
  title =	{{Update Monads: Cointerpreting Directed Containers}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{1--23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.1},
  URN =		{urn:nbn:de:0030-drops-46235},
  doi =		{10.4230/LIPIcs.TYPES.2013.1},
  annote =	{Keywords: monads and distributive laws, reader, writer and state monads, monoids and monoid actions, directed containers}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.24

A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle

Authors: Federico Aschieri and Margherita Zorzi

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

We propose a very simple modification of Kreisel's modified realizability in order to computationally realize Markov's Principle in the context of Heyting Arithmetic. Intuitively, realizers correspond to arbitrary strategies in Hintikka-Tarski games, while in Kreisel's realizability they can only represent winning strategies. Our definition, however, does not employ directly game semantical concepts and remains in the style of functional interpretations. As term calculus, we employ a purely functional language, which is Goedel's System T enriched with some syntactic sugar.

Cite as

Federico Aschieri and Margherita Zorzi. A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 24-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{aschieri_et_al:LIPIcs.TYPES.2013.24,
  author =	{Aschieri, Federico and Zorzi, Margherita},
  title =	{{A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{24--44},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.24},
  URN =		{urn:nbn:de:0030-drops-46245},
  doi =		{10.4230/LIPIcs.TYPES.2013.24},
  annote =	{Keywords: Markov's Principle, Intuitionistic Realizability, Heyting Arithmetic, Game Semantics}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.45

Formally Verified Implementation of an Idealized Model of Virtualization

Authors: Gilles Barthe, Gustavo Betarte, Juan Diego Campo, Jesús Mauricio Chimento, and Carlos Luna

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

VirtualCert is a machine-checked model of virtualization that can be used to reason about isolation between operating systems in presence of cache-based side-channels. In contrast to most prominent projects on operating systems verification, where such guarantees are proved directly on concrete implementations of hypervisors, VirtualCert abstracts away most implementations issues and specifies the effects of hypervisor actions axiomatically, in terms of preconditions and postconditions. Unfortunately, seemingly innocuous implementation issues are often relevant for security. Incorporating the treatment of errors into VirtualCert is therefore an important step towards strengthening the isolation theorems proved in earlier work. In this paper, we extend our earlier model with errors, and prove that isolation theorems still apply. In addition, we provide an executable specification of the hypervisor, and prove that it correctly implements the axiomatic model. The executable specification constitutes a first step towards a more realistic implementation of a hypervisor, and provides a useful tool for validating the axiomatic semantics developed in previous work.

Cite as

Gilles Barthe, Gustavo Betarte, Juan Diego Campo, Jesús Mauricio Chimento, and Carlos Luna. Formally Verified Implementation of an Idealized Model of Virtualization. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 45-63, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{barthe_et_al:LIPIcs.TYPES.2013.45,
  author =	{Barthe, Gilles and Betarte, Gustavo and Campo, Juan Diego and Chimento, Jes\'{u}s Mauricio and Luna, Carlos},
  title =	{{Formally Verified Implementation of an Idealized Model of Virtualization}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{45--63},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.45},
  URN =		{urn:nbn:de:0030-drops-46254},
  doi =		{10.4230/LIPIcs.TYPES.2013.45},
  annote =	{Keywords: virtualization, Cache and TLB, Executable specification, Error management, Isolation}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.64

Ramsey Theorem for Pairs As a Classical Principle in Intuitionistic Arithmetic

Authors: Stefano Berardi and Silvia Steila

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

We produce a first order proof of a famous combinatorial result, Ramsey Theorem for pairs and in two colors. Our goal is to find the minimal classical principle that implies the "miniature" version of Ramsey we may express in Heyting Arithmetic HA. We are going to prove that Ramsey Theorem for pairs with recursive assignments of two colors is equivalent in HA to the sub-classical principle Sigma-0-3-LLPO. One possible application of our result could be to use classical realization to give constructive proofs of some combinatorial corollaries of Ramsey; another, a formalization of Ramsey in HA, using a proof assistant. In order to compare Ramsey Theorem with first order classical principles, we express it as a schema in the first order language of arithmetic, instead of using quantification over sets and functions as it is more usual: all sets we deal with are explicitly defined as arithmetical predicates. In particular, we formally define the homogeneous set which is the witness of Ramsey theorem as a Delta-0-3-arithmetical predicate.

Cite as

Stefano Berardi and Silvia Steila. Ramsey Theorem for Pairs As a Classical Principle in Intuitionistic Arithmetic. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 64-83, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{berardi_et_al:LIPIcs.TYPES.2013.64,
  author =	{Berardi, Stefano and Steila, Silvia},
  title =	{{Ramsey Theorem for Pairs As a Classical Principle in Intuitionistic Arithmetic}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{64--83},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.64},
  URN =		{urn:nbn:de:0030-drops-46269},
  doi =		{10.4230/LIPIcs.TYPES.2013.64},
  annote =	{Keywords: Formalization, Constructivism, Classical logic, Ramsey Theorem}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.84

Extracting Imperative Programs from Proofs: In-place Quicksort

Authors: Ulrich Berger, Monika Seisenberger, and Gregory J. M. Woods

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

The process of program extraction is primarily associated with functional programs with less focus on imperative program extraction. In this paper we consider a standard problem for imperative programming: In-place Quicksort. We formalize a proof that every array of natural numbers can be sorted and apply a realizability interpretation to extract a program from the proof. Using monads we are able to exhibit the inherent imperative nature of the extracted program. We see this as a first step towards an automated extraction of imperative programs. The case study is carried out in the interactive proof assistant Minlog.

Cite as

Ulrich Berger, Monika Seisenberger, and Gregory J. M. Woods. Extracting Imperative Programs from Proofs: In-place Quicksort. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 84-106, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{berger_et_al:LIPIcs.TYPES.2013.84,
  author =	{Berger, Ulrich and Seisenberger, Monika and Woods, Gregory J. M.},
  title =	{{Extracting Imperative Programs from Proofs: In-place Quicksort}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{84--106},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.84},
  URN =		{urn:nbn:de:0030-drops-46274},
  doi =		{10.4230/LIPIcs.TYPES.2013.84},
  annote =	{Keywords: Program Extraction, Verification, Realizability, Imperative Programs, In-Place Quicksort,Computational Monads, Minlog}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.107

A Model of Type Theory in Cubical Sets

Authors: Marc Bezem, Thierry Coquand, and Simon Huber

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

We present a model of type theory with dependent product, sum, and identity, in cubical sets. We describe a universe and explain how to transform an equivalence between two types into an equality. We also explain how to model propositional truncation and the circle. While not expressed internally in type theory, the model is expressed in a constructive metalogic. Thus it is a step towards a computational interpretation of Voevodsky's Univalence Axiom.

Cite as

Marc Bezem, Thierry Coquand, and Simon Huber. A Model of Type Theory in Cubical Sets. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 107-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{bezem_et_al:LIPIcs.TYPES.2013.107,
  author =	{Bezem, Marc and Coquand, Thierry and Huber, Simon},
  title =	{{A Model of Type Theory in Cubical Sets}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{107--128},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.107},
  URN =		{urn:nbn:de:0030-drops-46284},
  doi =		{10.4230/LIPIcs.TYPES.2013.107},
  annote =	{Keywords: Models of dependent type theory, cubical sets, Univalent Foundations}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.129

Isomorphism of "Functional" Intersection Types

Authors: Mario Coppo, Mariangiola Dezani-Ciancaglini, Ines Margaria, and Maddalena Zacchi

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

Type isomorphism for intersection types is quite odd, since it is not a congruence and it does not extend type equality in the standard interpretation of types. The lack of congruence is due to the proof theoretic nature of the intersection introduction rule, which requires the same term to be the subject of both premises. A partial congruence can be recovered by introducing a suitable notion of type similarity. Type equality in standard models becomes included in type isomorphism whenever atomic types have "functional" interpretations, i.e. they are equivalent to arrow types. This paper characterises type isomorphism for a type system in which the equivalence between atomic types and arrow types is induced by the initial projections of the Scott's model via the correspondence between inverse limit models and filter lambda-models.

Cite as

Mario Coppo, Mariangiola Dezani-Ciancaglini, Ines Margaria, and Maddalena Zacchi. Isomorphism of "Functional" Intersection Types. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 129-149, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

Copy BibTex To Clipboard

@InProceedings{coppo_et_al:LIPIcs.TYPES.2013.129,
  author =	{Coppo, Mario and Dezani-Ciancaglini, Mariangiola and Margaria, Ines and Zacchi, Maddalena},
  title =	{{Isomorphism of "Functional" Intersection Types}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{129--149},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.129},
  URN =		{urn:nbn:de:0030-drops-46296},
  doi =		{10.4230/LIPIcs.TYPES.2013.129},
  annote =	{Keywords: Type Isomorphism, Lambda calculus, Intersection Types}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2013.150

A Hybrid Linear Logic for Constrained Transition Systems

Authors: Joëlle Despeyroux and Kaustuv Chaudhuri

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus.

Cite as

Joëlle Despeyroux and Kaustuv Chaudhuri. A Hybrid Linear Logic for Constrained Transition Systems. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 150-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

Copy BibTex To Clipboard

@InProceedings{despeyroux_et_al:LIPIcs.TYPES.2013.150,
  author =	{Despeyroux, Jo\"{e}lle and Chaudhuri, Kaustuv},
  title =	{{A Hybrid Linear Logic for Constrained Transition Systems}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{150--168},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.150},
  URN =		{urn:nbn:de:0030-drops-46302},
  doi =		{10.4230/LIPIcs.TYPES.2013.150},
  annote =	{Keywords: Linear logic, hybrid logic, stochastic pi-calculus, focusing, adequacy}
}

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