Types for Proofs and Programs 19 th TYPES Meeting Toulouse , France

The Types Meeting is a forum to present new and ongoing work in all aspects of type theory and its applications, especially in formalized and computer assisted reasoning and computer programming. Since 1992, Types Meetings have been annual workshops of several multilateral scientific EU-financed projects, of which the Types Project was the most recent. Although organized in Europe, the meetings were always open internationally, as evidenced by invited speakers and authors of contributed talks. TYPES 2013 was intended to be a conference in our traditional workshop style, and the selection of contributions was based on abstracts of up to two pages. Abstracts were generally reviewed by three members of the program committee (in some cases helped by external reviewers whose names should not be disclosed here): The present volume provides final versions of the abstracts of three invited speakers (chosen by the program committee) and 34 contributed talks. We have to regret that one accepted talk had to be withdrawn by its author since he could not come to the conference. 3 TYPES 2013 Preface Acknowledgements Thanks go to all the authors of abstract submissions, whether accepted or not. They were the raw material to shape this scientific meeting. A big thank you to the invited speakers for accepting this invitation to come to Toulouse. And, of course, the effort of the program committee members is gratefully acknowledged and also the anonymous external reviewers. I am much obliged to Andrej Voronkov and the support team of EasyChair for this marvellous tool free of charge that is very beneficial for the program committee and in particular for (co-)chairing it and also still quite useful for preparing this volume. A note on the PDF version of this document: all the given links to web pages were verified yesterday. Finally, and very importantly, the following institutions generously helped with funding and/or in providing lecture halls and services that TYPES 2013 could take place (in alphabetic order): Homotopy Type Theory (HoTT) refers to the homotopical interpretation [1] of Martin-Löf's intensional, constructive type theory (MLTT) [5], together with several new principles motivated by that interpretation. Voevodsky's Univalent Foundations program [6] is a conception for a new foundation for mathematics, based on HoTT and implemented in a proof assistant like Coq [2]. Among the new principles to be added to MLTT are the Univalence Axiom [4], and the so-called higher inductive types (HITs), a new idea …