Concurrent Structures in Game Semantics Simon Castellan

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Concurrent Structures in Game Semantics Simon Castellan Concurrent structures in game semantics Simon Castellan To cite this version: Simon Castellan. Concurrent structures in game semantics. Logic in Computer Science [cs.LO]. Université de Lyon, 2017. English. NNT : 2017LYSEN034. tel-01587718 HAL Id: tel-01587718 https://tel.archives-ouvertes.fr/tel-01587718 Submitted on 14 Sep 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Numéro National de Thèse: 2017LYSENO34. THÈSE DE DOCTORAT DE L’UNIVERSTÉ DE LYON opérée par l’École Normale Supérieure de Lyon École doctorale: 512 École doctorale en Informatique et Mathématiques de Lyon Spécialité de doctorat : Informatique Discipline : Informatique fondamentale Soutenue publiquement le 13/07/2017, par: Simon Castellan Structures concurrentes en sémantique des jeux Devant le jury composé de: Hyland, Martin Professor at the University of Cambridge Rapporteur Dal Lago, Ugo Professore Associoto all’Università di Bologna Rapporteur Alglave, Jade Senior Lecturer at University College London Examinatrice Curien, Pierre-Louis Directeur de Rercherche à l’Université Paris VII Examinateur Winskel, Glynn Professor at the University of Cambridge Examinateur Yoshida, Nobuko Professor at Imperial College London Examinatrice Laurent, Olivier Directeur de Recherche à l’ENS de Lyon Directeur de thèse Clairambault, Pierre Chargé de Recherche à l’ENS de Lyon Co-Encadrant 1 2 Remerciements et autres acknowledgements Mais, vous savez, moi je ne crois pas qu’il y ait de bonne ou de mauvaise situation. Moi, si je devais résumer ma vie aujourd’hui avec vous, je di- rais que c’est d’abord des rencontres, Des gens qui m’ont tendu la main, peut-être à un moment où je ne pouvais pas, où j’étais seul chez moi. Et c’est assez curieux de se dire que les hasards, les rencontres forgent une destinée... Otis, sur la situation de thésard (Astérix et Obélix: Mission Cléopâtre) I am immensely grateful to people who accompanied (be it simply for a very short while) my way for the last three years. I have been extremely lucky and honoured to be surrounded by such awesome and bienveillants people, who helped me grow and taught me so much on a scientific level as well as on a personal level, while being patient with my (numerous) mistakes. Merci infiniment à Pierre pour m’avoir encadré et guidé mes premiers pas dans la recherche – il y a près de six ans maintenant. Merci pour tout le temps que tu as pu me consacrer ; des tableaux à craie du Milner alcove jusqu’à la relecture approfondie et minutieuse des premières version de ma thèse pas toujours très matures, en passant par d’innombrables discussions et aventures sur de multiples continents. Merci à Olivier pour les nombreuses discussions scientifiques (en par- ticulier sur les arcanes de la logique linéaire et de la géométrie de l’interaction) toujours enrichissantes et les conseils précieux pour la rédaction ou les candida- tures. Thanks to Glynn for all the wonderful times in Cambridge. You taught me a lot, on a scientific level as well as on a personal level. I am very grateful in par- ticular to Pierre and you for my (social) integration during my first internship in Cambridge where I was not treated as a master student but as a (young) researcher. Many thanks to Martin and Ugo for accepting to review my manuscript and get into the intricate details of concurrent games. Thanks to Martin for many enlightening scientific discussions, and for having accepted to review my man- uscript. To the members of my Jury: Nobuko Yoshida, Pierre-Louis Curien, and Jade Alglave who listened to me exposing my work on weak memory models and gave me insights for interesting problems to solve. Merci à l’équipe Plume, une équipe qu’elle est bien pour y faire sa thèse : merci à Colin pour son support et ses conseils, à Patrick et à Russ pour leur bien- veillance, à Denis et Damien partenaires de badminton du midi. Un grand merci à Daniel sans qui cette aventure n’aurait jamais démarrée, tout ça à cause d’une question sur les inductions transfinies! Merci pour ta bonne humeur constante et contagieuse. Aux plus jeunes de l’équipe Plume : Paul, et sa jovialité toujours renouvelée, Fabio & Jean-Marie, les cobureaux qui ont dit non aux postdocs et oui aux postes permanents, à Aurore pour m’avoir fait découvrir le swing, à Guilhem. Thanks to Anupam: sharing a flat with you was no dogmatic slumber. Au LIP : merci à Laure pour me forcer à parler à des non-sémanticiens, aux thésards : Fabrice, Matthieu, Sébastien M. Merci à Catherine et Marie pour leur aide indispensable pour naviguer les méandres administratifs de la soutenance de thèse. 3 To the Cambridge crowd: thanks to Jean, Kayvan, Hugo, Justus, Ohad (for being annoyingly awesome), Matt, Ian and Philip. Thanks to Raphaël for our scottish adventures and much more. Many thanks to Charlotte, Constantino, and Ed for living at de Freville avenue and sharing a wine-fueled summer. Merci à Thomas pour Bourdieu, à Fred pour la colloc geek de Roseford road. Merci à gasche pour m’avoir fait découvrir OCaml et tout ce qui s’en suit, il y a longtemps, très longtemps. Aux lyonnais d’hier : Lucca, PE, Guillaume et son goût contagieux pour Céline, Vincent et nos déambulations à la pleine lune dans le cinquième. Aux lyonnais d’aujourd’hui : Pierre M., Laura-Mae, Barthélémy et nos discus- sions « philosophie du dimanche ». Aux amis de toujours : Jérôme, Fabien, Erwan & Antoine. Merci à ma famille: à mes parents pour leur support pendant trois ans de péré- grinations internationales; à Sophie, Flo et mes nièces que les dites pérégrinations m’ont forcé à ne pas voir autant je l’aurais voulu. ᾿Επαινῶ τῷ ἀστέρι ἐμῶ ἐν τῷ ἂθέῳ αἰθέρι Table des matières Chapitre 1. Introduction 7 Partie 1. Concurrence 17 Chapitre 2. Jeux concurrents avec évènements essentiels 19 1. Jeux et stratégies sous forme de structures d’évènements 20 2. Interaction close de pré-stratégies 27 3. Une catégorie de stratégies couverrtes 33 4. Stratégies découvertes à bisimulation faible près 37 5. Stratégies essentielles 51 6. Preuve de la structure catégorique 55 Chapitre 3. Jeux concurrents fins 61 1. Arènes dilatées 62 2. Structures d’évènements avec symmétrie 65 3. Jeux avec symmétrie et stratégies uniformes 68 4. Composition de stratégies uniformes 73 5. Isomorphisme faible 79 6. Une catégorie compact close 87 Chapitre 4. Jeux Hyland-Ong concurrents 95 1. Stratégies non linéaires et non déterministes 96 2. Une catégorie cartésienne fermée 102 3. Interprétation adéquate de ndPCF 113 Partie 2. Innocence 121 Chapitre 5. Innocence concurrente et bon parenthésage 123 0. Stratégies négatives et filaire 124 1. Bon parenthésage 126 2. Vers une définition de l’innocence concurrente 133 3. Stratégies innocentes 138 Chapitre 6. Pleine abstraction intensionnelle pour ndPCF 149 1. Forme réduite de stratégies innocentes 150 2. Décomposition de stratégies d’ordre supérieur 158 3. Pleine abstraction intensionnelle pour ndPCF 168 Partie 3. Impureté relâchée 177 Chapitre 7. Mémoire faible dans un cadre premier ordre 181 5 6 TABLE DES MATIÈRES 1. Un langage assembleur et sa sémantique 181 2. Interpréter TSO avec des structures d’évènements 186 3. Déséquentialisation des accès mémoires 197 Chapitre 8. Mémoire faible dans un cadre d’ordre supérieur 203 1. PCFmem: une extension de PCF avec des opérations mémoires 204 2. Sémantique de threads dans un contexte d’ordre supérieur 206 3. Implémentation de la mémoire 212 Conclusion et perspectives 217 Première partie : Concurrence 217 Seconde partie : Innocence 218 Troisième partie : Impureté relâchée 218 Bibliography 221 CHAPTER 1 Introduction Had we but world enough, and time, This coyness, [thesis], were no crime. We would sit down and think which way To walk, and pass our long [writing]’s day; My vegetable [draft] should grow Vaster than empires, and more slow. An hundred years should go to [the debut] An age at least to every part, For, [thesis], you deserve this state, Nor would I write at lower rate. Andrew Marvell, On writing dissertations (To his coy mistress) « Ça vous tente d’aller au restaurant gastronomique mercredi prochain ? » est une invitation terrifiante à entendre un lundi. Est-ce que l’on se retrouve au restaurant dans deux jours, ou dans neuf? Chacun a sa propre interprétation et certaines per- sonnes sont convaincues de l’absence d’ambiguïté de cette formulation. Cocher les deux jours sur son agenda est souvent la seule façon d’éviter le faux-pas em- barrassant de demander des clarifications. Ceci illustre le fossé entre ce l’on veut dire et ce que l’on dit. Afin de faciliter la communication, les langues contiennent souvent des mécanismes d’indirections qui rendent l’interprétation d’une phrase souvent dépendante du contexte, comme c’est le cas pour la formule « mercredi prochain » : la date (objective) du rendez- vous dépend de la date d’aujourd’hui. La fonction primordiale de ces indirections est d’éviter de répéter des choses que son interlocuteur sait déjà. Tous ces malentendus existent bien que nos langues naturelles soient déjà très proches de notre façon de penser. Imaginez maintenant que, au lieu de commu- niquer avec l’un de vos pairs, conscient de ces conventions social, il vous faut communiquer, une recette par exemple, à quelqu’un qui prend le vocabulaire de cuisine (« casserole », « poêle » par exemple) au premier degré, sans le remettre en question.
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