23 Search Results for "Matthes, Ralph"


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
Univalent Monoidal Categories

Authors: Kobe Wullaert, Ralph Matthes, and Benedikt Ahrens

Published in: LIPIcs, Volume 269, 28th International Conference on Types for Proofs and Programs (TYPES 2022)


Abstract
Univalent categories constitute a well-behaved and useful notion of category in univalent foundations. The notion of univalence has subsequently been generalized to bicategories and other structures in (higher) category theory. Here, we zoom in on monoidal categories and study them in a univalent setting. Specifically, we show that the bicategory of univalent monoidal categories is univalent. Furthermore, we construct a Rezk completion for monoidal categories: we show how any monoidal category is weakly equivalent to a univalent monoidal category, universally. We have fully formalized these results in UniMath, a library of univalent mathematics in the Coq proof assistant.

Cite as

Kobe Wullaert, Ralph Matthes, and Benedikt Ahrens. Univalent Monoidal Categories. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 15:1-15:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{wullaert_et_al:LIPIcs.TYPES.2022.15,
  author =	{Wullaert, Kobe and Matthes, Ralph and Ahrens, Benedikt},
  title =	{{Univalent Monoidal Categories}},
  booktitle =	{28th International Conference on Types for Proofs and Programs (TYPES 2022)},
  pages =	{15:1--15:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-285-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{269},
  editor =	{Kesner, Delia and P\'{e}drot, Pierre-Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2022.15},
  URN =		{urn:nbn:de:0030-drops-184580},
  doi =		{10.4230/LIPIcs.TYPES.2022.15},
  annote =	{Keywords: Univalence, Monoidal categories, Rezk completion, Displayed (bi)categories, Proof assistant Coq, UniMath library}
}
Document
Size-Based Termination for Non-Positive Types in Simply Typed Lambda-Calculus

Authors: Yuta Takahashi

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)


Abstract
So far, several typed lambda-calculus systems were combined with algebraic rewrite rules, and the termination (in other words, strong normalisation) problem of the combined systems was discussed. By the size-based approach, Blanqui formulated a termination criterion for simply typed lambda-calculus with algebraic rewrite rules which guarantees, in some specific cases, the termination of the rewrite relation induced by beta-reduction and algebraic rewrite rules on strictly or non-strictly positive inductive types. Using the inflationary fixed-point construction, we extend this termination criterion so that it is possible to show the termination of the rewrite relation induced by some rewrite rules on types which are called non-positive types. In addition, we note that a condition in Blanqui’s proof can be dropped, and this improves the criterion also for non-strictly positive inductive types.

Cite as

Yuta Takahashi. Size-Based Termination for Non-Positive Types in Simply Typed Lambda-Calculus. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{takahashi:LIPIcs.TYPES.2021.12,
  author =	{Takahashi, Yuta},
  title =	{{Size-Based Termination for Non-Positive Types in Simply Typed Lambda-Calculus}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.12},
  URN =		{urn:nbn:de:0030-drops-167811},
  doi =		{10.4230/LIPIcs.TYPES.2021.12},
  annote =	{Keywords: termination, higher-order rewriting, non-positive types, inductive types}
}
Document
On Model-Theoretic Strong Normalization for Truth-Table Natural Deduction

Authors: Andreas Abel

Published in: LIPIcs, Volume 188, 26th International Conference on Types for Proofs and Programs (TYPES 2020)


Abstract
Intuitionistic truth table natural deduction (ITTND) by Geuvers and Hurkens (2017), which is inherently non-confluent, has been shown strongly normalizing (SN) using continuation-passing-style translations to parallel lambda calculus by Geuvers, van der Giessen, and Hurkens (2019). We investigate the applicability of standard model-theoretic proof techniques and show (1) SN of detour reduction (β) using Girard’s reducibility candidates, and (2) SN of detour and permutation reduction (βπ) using biorthogonals. In the appendix, we adapt Tait’s method of saturated sets to β, clarifying the original proof of 2017, and extend it to βπ.

Cite as

Andreas Abel. On Model-Theoretic Strong Normalization for Truth-Table Natural Deduction. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{abel:LIPIcs.TYPES.2020.1,
  author =	{Abel, Andreas},
  title =	{{On Model-Theoretic Strong Normalization for Truth-Table Natural Deduction}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{1:1--1:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-182-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{188},
  editor =	{de'Liguoro, Ugo and Berardi, Stefano and 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.TYPES.2020.1},
  URN =		{urn:nbn:de:0030-drops-138805},
  doi =		{10.4230/LIPIcs.TYPES.2020.1},
  annote =	{Keywords: Natural deduction, Permutative conversion, Reducibility, Strong normalization, Truth table}
}
Document
Coinductive Proof Search for Polarized Logic with Applications to Full Intuitionistic Propositional Logic

Authors: José Espírito Santo, Ralph Matthes, and Luís Pinto

Published in: LIPIcs, Volume 188, 26th International Conference on Types for Proofs and Programs (TYPES 2020)


Abstract
The approach to proof search dubbed "coinductive proof search", and previously developed by the authors for implicational intuitionistic logic, is in this paper extended to LJP, a focused sequent-calculus presentation of polarized intuitionistic logic, including an array of positive and negative connectives. As before, this includes developing a coinductive description of the search space generated by a sequent, an equivalent inductive syntax describing the same space, and decision procedures for inhabitation problems in the form of predicates defined by recursion on the inductive syntax. We prove the decidability of existence of focused inhabitants, and of finiteness of the number of focused inhabitants for polarized intuitionistic logic, by means of such recursive procedures. Moreover, the polarized logic can be used as a platform from which proof search for other logics is understood. We illustrate the technique with LJT, a focused sequent calculus for full intuitionistic propositional logic (including disjunction). For that, we have to work out the "negative translation" of LJT into LJP (that sees all intuitionistic types as negative types), and verify that the translation gives a faithful representation of proof search in LJT as proof search in the polarized logic. We therefore inherit decidability of both problems studied for LJP and thus get new proofs of these results for LJT.

Cite as

José Espírito Santo, Ralph Matthes, and Luís Pinto. Coinductive Proof Search for Polarized Logic with Applications to Full Intuitionistic Propositional Logic. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{espiritosanto_et_al:LIPIcs.TYPES.2020.4,
  author =	{Esp{\'\i}rito Santo, Jos\'{e} and Matthes, Ralph and Pinto, Lu{\'\i}s},
  title =	{{Coinductive Proof Search for Polarized Logic with Applications to Full Intuitionistic Propositional Logic}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-182-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{188},
  editor =	{de'Liguoro, Ugo and Berardi, Stefano and 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.TYPES.2020.4},
  URN =		{urn:nbn:de:0030-drops-138837},
  doi =		{10.4230/LIPIcs.TYPES.2020.4},
  annote =	{Keywords: Inhabitation problems, Coinduction, Lambda-calculus, Polarized logic}
}
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)


Copy BibTex To Clipboard

@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
Heterogeneous Substitution Systems Revisited

Authors: Benedikt Ahrens and Ralph Matthes

Published in: LIPIcs, Volume 69, 21st International Conference on Types for Proofs and Programs (TYPES 2015) (2018)


Abstract
Matthes and Uustalu (TCS 327(1--2):155--174, 2004) presented a categorical description of substitution systems capable of capturing syntax involving binding which is independent of whether the syntax is made up from least or greatest fixed points. We extend this work in two directions: we continue the analysis by creating more categorical structure, in particular by organizing substitution systems into a category and studying its properties, and we develop the proofs of the results of the cited paper and our new ones in UniMath, a recent library of univalent mathematics formalized in the Coq theorem prover.

Cite as

Benedikt Ahrens and Ralph Matthes. Heterogeneous Substitution Systems Revisited. In 21st International Conference on Types for Proofs and Programs (TYPES 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 69, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{ahrens_et_al:LIPIcs.TYPES.2015.2,
  author =	{Ahrens, Benedikt and Matthes, Ralph},
  title =	{{Heterogeneous Substitution Systems Revisited}},
  booktitle =	{21st International Conference on Types for Proofs and Programs (TYPES 2015)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-030-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{69},
  editor =	{Uustalu, Tarmo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2015.2},
  URN =		{urn:nbn:de:0030-drops-84724},
  doi =		{10.4230/LIPIcs.TYPES.2015.2},
  annote =	{Keywords: formalization of category theory, nested datatypes, Mendler-style recursion schemes, representation of substitution in languages with variable binding}
}
Document
Complete Volume
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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
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)


Copy BibTex To Clipboard

@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}
}
  • Refine by Author
  • 7 Matthes, Ralph
  • 2 Ahrens, Benedikt
  • 2 Berger, Ulrich
  • 2 Schubert, Aleksy
  • 1 Abel, Andreas
  • Show More...

  • Refine by Classification
  • 4 Theory of computation → Type theory
  • 2 Theory of computation → Logic and verification
  • 2 Theory of computation → Proof theory
  • 1 Software and its engineering → Abstract data types
  • 1 Software and its engineering → Coroutines
  • Show More...

  • Refine by Keyword
  • 3 Coq
  • 2 Markov's Principle
  • 2 theorem proving
  • 1 Abstract Machines
  • 1 Agda
  • Show More...

  • Refine by Type
  • 22 document
  • 1 volume

  • Refine by Publication Year
  • 16 2014
  • 2 2021
  • 1 2013
  • 1 2018
  • 1 2019
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail