Published: 30th December 2021
DOI: 10.4204/EPTCS.353
ISSN: 2075-2180

EPTCS 353

Proceedings Second Joint International Workshop on
Linearity & Trends in Linear Logic and Applications
Online, 29-30 June 2020

Edited by: Ugo Dal Lago and Valeria de Paiva
Preface
Ugo Dal Lago and Valeria de Paiva
Exponentially Handsome Proof Nets and Their Normalization
Matteo Acclavio		1
A Deep Inference System for Differential Linear Logic
Matteo Acclavio and Giulio Guerrieri		26
Super Exponentials in Linear Logic
Esaïe Bauer and Olivier Laurent		50
Linear Additives
Gianluca Curzi		74
A Braided Lambda Calculus
Masahito Hasegawa		94
Deriving Distributive Laws for Graded Linear Types
Jack Hughes, Michael Vollmer and Dominic Orchard		109
Harmony in the Light of Computational Ludics
Alberto Naibo and Yuta Takahashi		132
Flag: a Self-Dual Modality for Non-Commutative Contraction and Duplication in the Category of Coherence Spaces
Christian Retoré 		157
*-Autonomous Envelopes and Conservativity
Michael Shulman		175
A Linear Algebra Approach to Linear Metatheory
James Wood and Robert Atkey		195

Preface

This volume contains a selection of the papers presented at the Second Joint Linearity and Trends in Linear Logic and Applications workshop (Linearity&TLLA 2020), held online on 29-30 June 2020, due to the corona virus pandemic. The workshop was affiliated with FSCD (Formal Structures for Computation and Deduction) at IJCAR-FSCD 2020 and part of the Paris Nord Summer of LoVe (Logic and Verification). The workshop Linearity&TLLA 2020 was the merging of the 6th edition of the International Workshop on Linearity and of the 4th edition of the International Workshop on Trends in Linear Logic and its Applications.

The original workshops have much in common, both in terms of the contents of the articles presented as in terms of the researchers likely to attend them, so a merging seemed sensible and it was decided that we would have a joint workshop, with one organiser from the Linearity Workshop (Valeria de Paiva) and one from the Trends in Linear Logic and Applications workshop (Ugo dal Lago). Both workshops aim at bringing together researchers who are currently developing theory and applications of linear calculi or use linear logic as a technical tool or as a methodological discipline. The joint Linearity&TLLA workshop goal is to foster the interaction of Linear Logic researchers and provide a forum for presenting new ideas and work in progress on those new ideas. The workshop also enables newcomers to Linear Logic to learn about current activities in this active area.

Since the time of Girard's introduction of linear logic (LL) there has been a stream of research where linearity is a key issue, covering both theoretical topics and applications in several areas of Mathematical Logic and Computer Science. Work on proof representation and interpretations (proof nets, denotational semantics, geometry of interaction, etc), complexity classes (including implicit complexity), programming languages, especially linear operational constructs and type systems based on linear logic, and more recently probabilistic and quantum computation, program analysis, expressive operational semantics, and techniques for program transformation, update analysis and efficient implementation have been discussed using LL ideas. Linearity and the foundational concepts of LL also serve as bridges to other topics in mathematics (functional analysis, categories) as well as in linguistics and philosophy.

Trying to cover all this breadth of research is not easy. The programme of the workshop consisted of eighteen contributed papers and four invited talks, by Kaustuv Chaudhuri, Olivier Laurent, Shin-ya Katsumata and Simona Ronchi Della Rocca. After a second round of reviewing, ten papers were selected for publication in the Linearity&TLLA 2020 post-proceedings you are reading. EasyChair was used to manage the reviewing process and the generation of the preproceedings.

The Programme Committee of Linearity&TLLA 2020 consisted of Raphaëlle Crubillé, Ugo dal Lago (co-chair), Harley Eades III, Koko Muroya, Michele Pagani, Valeria de Paiva (co-chair), Elaine Pimentel, Giselle Reis, Thomas Seiller, Daniel Ventura, and Lionel Vaux. We would like to thank all those who contributed to Linearity&TLLA 2020, particularly the invited speakers, programme committee members, reviewers and local organisers of the workshop. We also would like to thank EPTCS for their help in publishing these proceedings.

Ugo Dal Lago and Valeria de Paiva.