44 Search Results for "Miller, Dale"

Volume

LIPIcs, Volume 84

2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

FSCD 2017, September 3-9, 2017, Oxford, UK

Editors: Dale Miller

Document
DOI: 10.4230/LIPIcs.FSCD.2023.10
E-Unification for Second-Order Abstract Syntax

Authors: Nikolai Kudasov

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
Higher-order unification (HOU) concerns unification of (extensions of) λ-calculus and can be seen as an instance of equational unification (E-unification) modulo βη-equivalence of λ-terms. We study equational unification of terms in languages with arbitrary variable binding constructions modulo arbitrary second-order equational theories. Abstract syntax with general variable binding and parametrised metavariables allows us to work with arbitrary binders without committing to λ-calculus or use inconvenient and error-prone term encodings, leading to a more flexible framework. In this paper, we introduce E-unification for second-order abstract syntax and describe a unification procedure for such problems, merging ideas from both full HOU and general E-unification. We prove that the procedure is sound and complete.
Cite as

Nikolai Kudasov. E-Unification for Second-Order Abstract Syntax. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kudasov:LIPIcs.FSCD.2023.10,
  author =	{Kudasov, Nikolai},
  title =	{{E-Unification for Second-Order Abstract Syntax}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.10},
  URN =		{urn:nbn:de:0030-drops-179944},
  doi =		{10.4230/LIPIcs.FSCD.2023.10},
  annote =	{Keywords: E-unification, higher-order unification, second-order abstract syntax}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2023.3
A Positive Perspective on Term Representation (Invited Talk)

Authors: Dale Miller and Jui-Hsuan Wu

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
We use the focused proof system LJF as a framework for describing term structures and substitution. Since the proof theory of LJF does not pick a canonical polarization for primitive types, two different approaches to term representation arise. When primitive types are given the negative polarity, LJF proofs encode terms as tree-like structures in a familiar fashion. In this situation, cut elimination also yields the familiar notion of substitution. On the other hand, when primitive types are given the positive polarity, LJF proofs yield a structure in which explicit sharing of term structures is possible. Such a representation of terms provides an explicit method for sharing term structures. In this setting, cut elimination yields a different notion of substitution. We illustrate these two approaches to term representation by applying them to the encoding of untyped λ-terms. We also exploit concurrency theory techniques - namely traces and simulation - to compare untyped λ-terms using such different structuring disciplines.
Cite as

Dale Miller and Jui-Hsuan Wu. A Positive Perspective on Term Representation (Invited Talk). In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{miller_et_al:LIPIcs.CSL.2023.3,
  author =	{Miller, Dale and Wu, Jui-Hsuan},
  title =	{{A Positive Perspective on Term Representation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{3:1--3:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.3},
  URN =		{urn:nbn:de:0030-drops-174648},
  doi =		{10.4230/LIPIcs.CSL.2023.3},
  annote =	{Keywords: term representation, sharing, focused proof systems}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.21
Linear Lambda-Calculus is Linear

Authors: Alejandro Díaz-Caro and Gilles Dowek

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
We prove a linearity theorem for an extension of linear logic with addition and multiplication by a scalar: the proofs of some propositions in this logic are linear in the algebraic sense. This work is part of a wider research program that aims at defining a logic whose proof language is a quantum programming language.
Cite as

Alejandro Díaz-Caro and Gilles Dowek. Linear Lambda-Calculus is Linear. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{diazcaro_et_al:LIPIcs.FSCD.2022.21,
  author =	{D{\'\i}az-Caro, Alejandro and Dowek, Gilles},
  title =	{{Linear Lambda-Calculus is Linear}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.21},
  URN =		{urn:nbn:de:0030-drops-163024},
  doi =		{10.4230/LIPIcs.FSCD.2022.21},
  annote =	{Keywords: Proof theory, Lambda calculus, Linear logic, Quantum computing}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.10
Two Applications of Logic Programming to Coq

Authors: Matteo Manighetti, Dale Miller, and Alberto Momigliano

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

Abstract
The logic programming paradigm provides a flexible setting for representing, manipulating, checking, and elaborating proof structures. This is particularly true when the logic programming language allows for bindings in terms and proofs. In this paper, we make use of two recent innovations at the intersection of logic programming and proof checking. One of these is the foundational proof certificate (FPC) framework which provides a flexible means of defining the semantics of a range of proof structures for classical and intuitionistic logic. A second innovation is the recently released Coq-Elpi plugin for Coq in which the Elpi implementation of λProlog can send and retrieve information to and from the Coq kernel. We illustrate the use of both this Coq plugin and FPCs with two example applications. First, we implement an FPC-driven sequent calculus for a fragment of the Calculus of Inductive Constructions and we package it into a tactic to perform property-based testing of inductive types corresponding to Horn clauses. Second, we implement in Elpi a proof checker for first-order intuitionistic logic and demonstrate how proof certificates can be supplied by external (to Coq) provers and then elaborated into the fully detailed proof terms that can be checked by the Coq kernel.
Cite as

Matteo Manighetti, Dale Miller, and Alberto Momigliano. Two Applications of Logic Programming to Coq. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{manighetti_et_al:LIPIcs.TYPES.2020.10,
  author =	{Manighetti, Matteo and Miller, Dale and Momigliano, Alberto},
  title =	{{Two Applications of Logic Programming to Coq}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{10:1--10:19},
  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.2020.10},
  URN =		{urn:nbn:de:0030-drops-138896},
  doi =		{10.4230/LIPIcs.TYPES.2020.10},
  annote =	{Keywords: Proof assistants, logic programming, Coq, \lambdaProlog, property-based testing}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.TYPES.2016.1
Mechanized Metatheory Revisited: An Extended Abstract (Invited Paper)

Authors: Dale Miller

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

Abstract
Proof assistants and the programming languages that implement them need to deal with a range of linguistic expressions that involve bindings. Since most mature proof assistants do not have built-in methods to treat this aspect of syntax, many of them have been extended with various packages and libraries that allow them to encode bindings using, for example, de Bruijn numerals and nominal logic features. I put forward the argument that bindings are such an intimate aspect of the structure of expressions that they should be accounted for directly in the underlying programming language support for proof assistants and not added later using packages and libraries. One possible approach to designing programming languages and proof assistants that directly supports such an approach to bindings in syntax is presented. The roots of such an approach can be found in the mobility of binders between term-level bindings, formula-level bindings (quantifiers), and proof-level bindings (eigenvariables). In particular, by combining Church's approach to terms and formulas (found in his Simple Theory of Types) and Gentzen's approach to sequent calculus proofs, we can learn how bindings can declaratively interact with the full range of logical connectives and quantifiers. I will also illustrate how that framework provides an intimate and semantically clean treatment of computation and reasoning with syntax containing bindings. Some implemented systems, which support this intimate and built-in treatment of bindings, will be briefly described.
Cite as

Dale Miller. Mechanized Metatheory Revisited: An Extended Abstract (Invited Paper). In 22nd International Conference on Types for Proofs and Programs (TYPES 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 97, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{miller:LIPIcs.TYPES.2016.1,
  author =	{Miller, Dale},
  title =	{{Mechanized Metatheory Revisited: An Extended Abstract}},
  booktitle =	{22nd International Conference on Types for Proofs and Programs (TYPES 2016)},
  pages =	{1:1--1:16},
  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.2016.1},
  URN =		{urn:nbn:de:0030-drops-98603},
  doi =		{10.4230/LIPIcs.TYPES.2016.1},
  annote =	{Keywords: mechanized metatheory, mobility of binders, lambda-tree syntax, higher-order abstract syntax}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSCD.2017
LIPIcs, Volume 84, FSCD'17, Complete Volume

Authors: Dale Miller

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
LIPIcs, Volume 84, FSCD'17, Complete Volume
Cite as

2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{miller:LIPIcs.FSCD.2017,
  title =	{{LIPIcs, Volume 84, FSCD'17, Complete Volume}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017},
  URN =		{urn:nbn:de:0030-drops-79063},
  doi =		{10.4230/LIPIcs.FSCD.2017},
  annote =	{Keywords: Theory of Computation, Computation by Abstract Devices, Analysis of Algorithms and Problem Complexity, Logics and Meanings of Programs, Mathematical Logic and Formal Languages, Programming Techniques, Software/Program Verification, Programming Languages, Deduction and Theorem Proving}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSCD.2017.0
Front Matter, Table of Contents, Preface, Steering Committee, Program Committee, External Reviewers

Authors: Dale Miller

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Front Matter, Table of Contents, Preface, Steering Committee, Program Committee, External Reviewers
Cite as

2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{miller:LIPIcs.FSCD.2017.0,
  author =	{Miller, Dale},
  title =	{{Front Matter, Table of Contents, Preface, Steering Committee, Program Committee, External Reviewers}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{0:i--0:xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.0},
  URN =		{urn:nbn:de:0030-drops-77126},
  doi =		{10.4230/LIPIcs.FSCD.2017.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Steering Committee, Program Committee, External Reviewers}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2017.1
Type Systems for the Relational Verification of Higher Order Programs (Invited Talk)

Authors: Marco Gaboardi

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Relational program verification is a variant of program verification where one focuses on guaranteeing properties about the executions of two programs, and as a special case about two executions of a single program on different inputs. Relational verification becomes particularly interesting when non-functional aspects of a computation, like probabilities or resource cost, are considered. Several approached to relational program verification have been developed, from relational program logics to relational abstract interpretation. In this talk, I will introduce two approaches to relational program verification for higher-order computations based on the use of type systems. The first approach consists in developing powerful type system where a rich language of assertions can be used to express complex relations between two programs. The second approach consists in developing more restrictive type systems enriched with effects expressing in a lightweight way relations between different runs of the same program. I will discuss the pros and cons of these two approaches on a concrete example: relational cost analysis, which aims at giving a bound on the difference in cost of running two programs, and as a special case the difference in cost of two executions of a single program on different inputs.
Cite as

Marco Gaboardi. Type Systems for the Relational Verification of Higher Order Programs (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gaboardi:LIPIcs.FSCD.2017.1,
  author =	{Gaboardi, Marco},
  title =	{{Type Systems for the Relational Verification of Higher Order Programs}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.1},
  URN =		{urn:nbn:de:0030-drops-77429},
  doi =		{10.4230/LIPIcs.FSCD.2017.1},
  annote =	{Keywords: Relational verification, refinement types, type and effect systems, complexity analysis}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2017.2
Uniform Resource Analysis by Rewriting: Strenghts and Weaknesses (Invited Talk)

Authors: Georg Moser

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
In this talk, I'll describe how rewriting techniques can be successfully employed to built state-of-the-art automated resource analysis tools which favourably compare to other approaches. Furthermore I'll sketch the genesis of a uniform framework for resource analysis, emphasising success stories, without hiding intricate weaknesses. The talk ends with the discussion of open problems.
Cite as

Georg Moser. Uniform Resource Analysis by Rewriting: Strenghts and Weaknesses (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{moser:LIPIcs.FSCD.2017.2,
  author =	{Moser, Georg},
  title =	{{Uniform Resource Analysis by Rewriting: Strenghts and Weaknesses}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.2},
  URN =		{urn:nbn:de:0030-drops-77438},
  doi =		{10.4230/LIPIcs.FSCD.2017.2},
  annote =	{Keywords: resource analysis, term rewriting, automation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2017.3
Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this talk will overview why the problem is so difficult. We will then pave the way towards a solution, by presenting a new automaton model and a Kleene-like theorem for CKA. More precisely, we connect a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours. We also survey how the present work can be used to to extend the network specification language NetKAT with primitives for concurrency so as to model and reason about concurrency within networks. This is joint work with Tobias Kappe, Paul Brunet, Bas Luttik, and Fabio Zanasi.
Cite as

Alexandra Silva. Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{silva:LIPIcs.FSCD.2017.3,
  author =	{Silva, Alexandra},
  title =	{{Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.3},
  URN =		{urn:nbn:de:0030-drops-77445},
  doi =		{10.4230/LIPIcs.FSCD.2017.3},
  annote =	{Keywords: Kleene algebras, Pomset languages, concurrency, NetKAT}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2017.4
Quantitative Semantics for Probabilistic Programming (Invited Talk)

Authors: Christine Tasson

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Probabilistic programming has many applications in statistics, physics, ... so that all programming languages have been equipped with probabilistic library. However, there is a need in developing semantical tools in order to formalize higher order and recursive probabilistic languages. Indeed, it is well known that categories of measurable spaces are not Cartesian closed. We have been studying quantitative semantics of probabilistic spaces to fill this gap. A first step has been to focus on probabilistic programming languages with discrete types such as integers and booleans. In this setting, probabilistic programs can be seen as linear combinations of deterministic programs. Probabilistic Coherent Spaces constitute a Cartesian closed category that is fully abstract with respect to probabilistic Call-By-Push-Value. Moreover, this toy language is endowed with a memorization operator that allow to encode most discrete probabilistic programs. The second step is to move on probabilistic programming with continuous types representing for instance reals endowed with Lebesgue measurable sets. We introduce the category of cones and stable functions which is Cartesian closed. The trick is to enlarge the category of measurable spaces to gain closeness and to embrace measurable spaces. Besides, the category of cones is a sound and adequate model of a higher order and recursive probabilistic language in which most classical distributions and probabilistic tools can be encoded. This is joint work with Thomas Ehrhard and Michele Pagani.
Cite as

Christine Tasson. Quantitative Semantics for Probabilistic Programming (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{tasson:LIPIcs.FSCD.2017.4,
  author =	{Tasson, Christine},
  title =	{{Quantitative Semantics for Probabilistic Programming}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.4},
  URN =		{urn:nbn:de:0030-drops-77456},
  doi =		{10.4230/LIPIcs.FSCD.2017.4},
  annote =	{Keywords: denotational semantics, probabilistic programming, programming language, probability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.5
Displayed Categories

Authors: Benedikt Ahrens and Peter LeFanu Lumsdaine

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
We introduce and develop the notion of displayed categories. A displayed category over a category C is equivalent to "a category D and functor F : D -> C", but instead of having a single collection of "objects of D" with a map to the objects of C, the objects are given as a family indexed by objects of C, and similarly for the morphisms. This encapsulates a common way of building categories in practice, by starting with an existing category and adding extra data/properties to the objects and morphisms. The interest of this seemingly trivial reformulation is that various properties of functors are more naturally defined as properties of the corresponding displayed categories. Grothendieck fibrations, for example, when defined as certain functors, use equality on objects in their definition. When defined instead as certain displayed categories, no reference to equality on objects is required. Moreover, almost all examples of fibrations in nature are, in fact, categories whose standard construction can be seen as going via displayed categories. We therefore propose displayed categories as a basis for the development of fibrations in the type-theoretic setting, and similarly for various other notions whose classical definitions involve equality on objects. Besides giving a conceptual clarification of such issues, displayed categories also provide a powerful tool in computer formalisation, unifying and abstracting common constructions and proof techniques of category theory, and enabling modular reasoning about categories of multi-component structures. As such, most of the material of this article has been formalised in Coq over the UniMath library, with the aim of providing a practical library for use in further developments.
Cite as

Benedikt Ahrens and Peter LeFanu Lumsdaine. Displayed Categories. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ahrens_et_al:LIPIcs.FSCD.2017.5,
  author =	{Ahrens, Benedikt and Lumsdaine, Peter LeFanu},
  title =	{{Displayed Categories}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.5},
  URN =		{urn:nbn:de:0030-drops-77220},
  doi =		{10.4230/LIPIcs.FSCD.2017.5},
  annote =	{Keywords: Category theory, Dependent type theory, Computer proof assistants, Coq, Univalent mathematics}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.6
The Confluent Terminating Context-Free Substitutive Rewriting System for the lambda-Calculus with Surjective Pairing and Terminal Type

Authors: Yohji Akama

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo, inspired by Knuth-Bendix completion, introduced a confluent rewriting system of the naive rewriting system. Their system is a confluent (CR) rewriting system stable under contexts. They left the strong normalization (SN) of their rewriting system open. By Girard's reducibility method with restricting reducibility theorem, we prove SN of their rewriting, and SN of the extensions by polymorphism and (terminal types caused by parametric polymorphism). We extend their system by sum types and eta-like reductions, and prove the SN. We compare their system to type-directed expansions.
Cite as

Yohji Akama. The Confluent Terminating Context-Free Substitutive Rewriting System for the lambda-Calculus with Surjective Pairing and Terminal Type. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{akama:LIPIcs.FSCD.2017.6,
  author =	{Akama, Yohji},
  title =	{{The Confluent Terminating Context-Free Substitutive Rewriting System for the lambda-Calculus with Surjective Pairing and Terminal Type}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.6},
  URN =		{urn:nbn:de:0030-drops-77346},
  doi =		{10.4230/LIPIcs.FSCD.2017.6},
  annote =	{Keywords: reducibility method, restricted reducibility theorem, sum type, typedirected expansion, strong normalization}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.7
Improving Rewriting Induction Approach for Proving Ground Confluence

Authors: Takahito Aoto, Yoshihito Toyama, and Yuta Kimura

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
In (Aoto&Toyama, FSCD 2016), a method to prove ground confluence of many-sorted term rewriting systems based on rewriting induction is given. In this paper, we give several methods that add wider flexibility to the rewriting induction approach for proving ground confluence. Firstly, we give a method to deal with the case in which suitable rules are not presented in the input system. Our idea is to construct additional rewrite rules that supplement or replace existing rules in order to obtain a set of rules that is adequate for applying rewriting induction. Secondly, we give a method to deal with non-orientable constructor rules. This is accomplished by extending the inference system of rewriting induction and giving a sufficient criterion for the correctness of the system. Thirdly, we give a method to deal with disproving ground confluence. The presented methods are implemented in our ground confluence prover AGCP and experiments are reported. Our experiments reveal the presented methods are effective to deal with problems for which state-of-the-art ground confluence provers can not handle.
Cite as

Takahito Aoto, Yoshihito Toyama, and Yuta Kimura. Improving Rewriting Induction Approach for Proving Ground Confluence. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{aoto_et_al:LIPIcs.FSCD.2017.7,
  author =	{Aoto, Takahito and Toyama, Yoshihito and Kimura, Yuta},
  title =	{{Improving Rewriting Induction Approach for Proving Ground Confluence}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.7},
  URN =		{urn:nbn:de:0030-drops-77310},
  doi =		{10.4230/LIPIcs.FSCD.2017.7},
  annote =	{Keywords: Ground Confluence, Rewriting Induction, Non-Orientable Equations, Term Rewriting Systems}
}
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