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Presheaf Semantics for Guarded Dependent Type Theory 23rd International Conference on Types for Proofs and Programs TYPES 2017 Budapest, Hungary, 29 May - 1 June 2017 Abstracts Department of Programming Languages and Compilers, Faculty of Informatics, E¨otv¨osLor´andUniversity Budapest, 2017 23rd International Conference on Types for Proofs and Programs, TYPES 2017 Budapest, Hungary, 29 May - 1 June 2017 Abstracts http://types2017.elte.hu Edited by Ambrus Kaposi Department of Programming Languages and Compilers Faculty of Informatics E¨otv¨osLor´andUniversity P´azm´any P´eters´et´any 1/C, 1117 Budapest, Hungary http://www.inf.elte.hu Cover design by Andr´asF´orizs ISBN 978-963-284-883-9 (print) ISBN 978-963-284-884-6 (pdf) c 2017 the editor and authors Preface This volume contains the abstracts of the talks presented at the 23rd International Conference on Types for Proofs and Programs, TYPES 2017, to take place in Budapest, Hungary, 29 May - 1 June 2017. The TYPES meetings are a forum to present new and on-going work in all aspects of type theory and its applications, especially in formalised and computer assisted reasoning and computer programming. The meetings from 1990 to 2008 were annual workshops of a sequence of five EU funded networking projects. Since 2009, TYPES has been run as an independent conference series. Previous TYPES meetings were held in Antibes (1990), Edinburgh (1991), B˚astad(1992), Nijmegen (1993), B˚astad (1994), Torino (1995), Aussois (1996), Kloster Irsee (1998), L¨okeberg (1999), Durham (2000), Berg en Dal near Nijmegen (2002), Torino (2003), Jouy-en-Josas near Paris (2004), Nottingham (2006), Cividale del Friuli (2007), Torino (2008), Aussois (2009), Warsaw (2010), Bergen (2011), Toulouse (2013), Paris (2014), Tallinn (2015), Novi Sad (2016). The TYPES areas of interest include, but are not limited to: foundations of type theory and constructive mathematics; applications of type theory; dependently typed programming; indus- trial uses of type theory technology; meta-theoretic studies of type systems; proof assistants and proof technology; automation in computer-assisted reasoning; links between type theory and functional programming; formalizing mathematics using type theory. The TYPES conferences are of open and informal character. Selection of contributed talks is based on short abstracts; reporting work in progress and work presented or published elsewhere is welcome. A formal post-proceedings volume is prepared after the conference; papers submitted to that must represent unpublished work and are subjected to a full review process. The programme of TYPES 2017 includes three invited talks by Edwin Brady (University of St Andrews), Sara Negri (Unviersity of Helsinki) and Jakob Rehof (TU Dortmund). The contributed part of the programme consists of 50 talks. Similarly to the 2011 and the 2013-2016 editions of the conference, the post-proceedings of TYPES 2015 will appear in Dagstuhl's Leibniz International Proceedings in Informatics (LIPIcs) series. We are grateful for the support of COST Action CA15123 EUTypes. May 17, 2017 Ambrus Kaposi and Tam´asKozsik Budapest iii Organisation Program Committee Andreas Abel Gothenburg University Thorsten Altenkirch University of Nottingham Jos´eCarlos Esp´ıritoSanto University of Minho Fredrik Forsberg University of Strathclyde Silvia Ghilezan University of Novi Sad Hugo Herbelin INRIA,France Martin Hofmann LMU Munich Ambrus Kaposi E¨otv¨osLor´andUniversity (co-chair) Tam´asKozsik E¨otv¨osLor´andUniversity (co-chair) Assia Mahboubi INRIA, France Alexandre Miquel University of the Republic, Uruguay Keiko Nakata SAP Potsdam Andrew Polonsky University of Bergen Simona Ronchi Della Rocca University of Torino Aleksy Schubert University of Warsaw Wouter Swierstra Utrecht University Tarmo Uustalu Tallinn University of Technology Organising committee Ambrus Kaposi, Tam´asKozsik, Andr´asKov´acsand the Department of Programming Languages and Compilers Host Faculty of Informatics at E¨otv¨osLor´andUniversity Sponsor COST Action CA15123 EUTypes iv Table of Contents Invited talks An Architecture for Dependently Typed Applications in Idris ::::::::::::::::::::::::: 1 Edwin Brady Proof systems based on neighbourhood semantics ::::::::::::::::::::::::::::::::::: 2 Sara Negri Bounding Principles for Decision Problems with Intersection Types:::::::::::::::::::: 3 Jakob Rehof Contributed talks Normalization by Evaluation for Sized Dependent Types ::::::::::::::::::::::::::::: 4 Andreas Abel, Andrea Vezzosi and Th´eoWinterhalter A Type Theory with Native Homotopy Universes ::::::::::::::::::::::::::::::::::: 6 Robin Adams and Andrew Polonsky Monads from multi-sorted binding signatures ::::::::::::::::::::::::::::::::::::::: 8 Benedikt Ahrens, Ralph Matthes and Anders M¨ortberg Typing with Leftovers: a Mechanisation of ILL ::::::::::::::::::::::::::::::::::::: 10 Guillaume Allais From setoid hell to homotopy heaven? ::::::::::::::::::::::::::::::::::::::::::::: 12 Thorsten Altenkirch Type Theory with Weak J ::::::::::::::::::::::::::::::::::::::::::::::::::::::: 14 Thorsten Altenkirch, Paolo Capriotti, Thierry Coquand, Nils Anders Danielsson, Si- mon Huber and Nicolai Kraus Domain Theory in Type Theory via QIITs ::::::::::::::::::::::::::::::::::::::::: 16 Thorsten Altenkirch, Paolo Capriotti and Bernhard Reus Normalisation by Evaluation for a Type Theory with Large Elimination ::::::::::::::: 18 Thorsten Altenkirch, Ambrus Kaposi and Andr´asKov´acs Monadic containers and universes ::::::::::::::::::::::::::::::::::::::::::::::::: 20 Thorsten Altenkirch and Gun Pinyo A Probabilistic Approach of Behavioural Types ::::::::::::::::::::::::::::::::::::: 22 Bogdan Aman and Gabriel Ciobanu Bouncing threads for infinitary proof theory :::::::::::::::::::::::::::::::::::::::: 24 David Baelde, Amina Doumane, Guilhem Jaber and Alexis Saurin The Clocks Are Ticking: No More Delays! Reduction Semantics for Type Theory with Guarded Recursion :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 26 Patrick Bahr, Hans Bugge Grathwohl and Rasmus Ejlers Møgelberg v Regularity for Free :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 28 Thibaut Balabonski, Marco Gaboardi, Chantal Kelller and Beno^ıtValiron A modular formalization of type theory in Coq ::::::::::::::::::::::::::::::::::::: 31 Andrej Bauer, Philipp G. Haselwarter and Th´eoWinterhalter Presheaf semantics for guarded dependent type theory ::::::::::::::::::::::::::::::: 33 AleˇsBizjak and Rasmus Ejlers Møgelberg An interpretation of system F through bar recursion ::::::::::::::::::::::::::::::::: 35 Valentin Blot The Steenrod squares in homotopy type theory ::::::::::::::::::::::::::::::::::::: 37 Guillaume Brunerie Verifying Functional Reactive Programs with Side Effects :::::::::::::::::::::::::::: 39 Manuel B¨arenz and Sebastian Seufert Notions of type formers :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 41 Paolo Capriotti Automatically Constructing a Type System from the Small-Steps Semantics :::::::::::: 43 Stefan Ciobaca and Vlad Andrei Tudose A Model of Type Theory in Stacks :::::::::::::::::::::::::::::::::::::::::::::::: 45 Thierry Coquand, Bassel Mannaa and Fabian Ruch The Boolean Pythagorean Triples Problem in Coq :::::::::::::::::::::::::::::::::: 47 Lu´ısCruz-Filipe, Joao Marques-Silva and Peter Schneider-Kamp Towards practical out-of-order unification :::::::::::::::::::::::::::::::::::::::::: 49 Nils Anders Danielsson and V´ıctorL´opez Juan Models and termination of proof reduction in the lambda Pi-calculus modulo theory ::::: 51 Gilles Dowek Untyped Confluence In Dependent Type Theories ::::::::::::::::::::::::::::::::::: 53 Gilles Dowek, Jean-Pierre Jouannaud, Assaf Ali and Jiaxiang Liu Lower End of the Linial-Post Spectrum :::::::::::::::::::::::::::::::::::::::::::: 55 Andrej Dudenhefner and Jakob Rehof Characterization of strong normalizability for a lambda-calculus with co-control :::::::: 57 Jose Espirito Santo and Silvia Ghilezan Inhabitation in Simply-Typed Lambda-Calculus through a Lambda-Calculus for Proof Search ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 59 Jos´eEsp´ırito Santo, Ralph Matthes and Lu´ısPinto Dependent Type Theory with Contextual Types :::::::::::::::::::::::::::::::::::: 61 Francisco Ferreira, David Thibodeau and Brigitte Pientka Inductive-Recursive Definitions and Composition :::::::::::::::::::::::::::::::::::: 63 Neil Ghani, Conor McBride, Fredrik Nordvall Forsberg and Stephan Spahn vi Verifiable certificates for predicate subtyping ::::::::::::::::::::::::::::::::::::::: 65 Frederic Gilbert Strong Bisimilarity Implies Trace Semantics in CSP-Agda :::::::::::::::::::::::::::: 67 Bashar Igried and Anton Setzer Derivation of elimination principles from a context :::::::::::::::::::::::::::::::::: 69 Ambrus Kaposi, Andr´asKov´acs,P´eterDivi´anszkyand Bal´azsK}om}uves A Type-Theoretic Alternative to LISP ::::::::::::::::::::::::::::::::::::::::::::: 71 G. A. Kavvos Quantitative Types for the Lambda-Mu Calculus with Explicit and Implicit Replacement 73 Delia Kesner and Pierre Vial Theory and Demo of PML2: Proving Programs in ML ::::::::::::::::::::::::::::::: 75 Rodolphe Lepigre Intersection and Union Types from a Proof-functional Point of View::::::::::::::::::: 77 Luigi Liquori and Claude Stolze Extensions by Definition in Type Theory::::::::::::::::::::::::::::::::::::::::::: 79 Georgiana Elena Lungu and Zhaohui Luo Adjective Clustering in the Mizar Type System ::::::::::::::::::::::::::::::::::::: 81 Adam Naumowicz Parametric Quantifiers for Dependent Types :::::::::::::::::::::::::::::::::::::::
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