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Ludics is a Model for the Finitary Linear Pi-Calculus [chapter]

Claudia Faggian, Mauro Piccolo
2007 Lecture Notes in Computer Science  
Ludics is a Game model, developed as an abstraction of Linear Logic. The strategies are a linear version of Hyland-Ong innocent strategies.  ...  We prove that the model is fully complete and fully abstract w.r.t. the calculus. The linear π-calculus: The linear π-calculus has been introduced by N. Yoshida and K.  ...  The linear π-calculus is a typed version of asynchronous π-calculus introduced by Yoshida, Honda and Berger. We interpret π-processes of the finitary fragment of the calculus into linear strategies.  ... 
doi:10.1007/978-3-540-73228-0_12 fatcat:ms5aqiitofaq5diksfzqwystci

Partial Orders, Event Structures and Linear Strategies [chapter]

Claudia Faggian, Mauro Piccolo
2009 Lecture Notes in Computer Science  
We mention that, as established in [7], Ludics has a close relation with the Linear Pi-calculus [26], i.e. a process calculus which is asynchronous and internal (see [20] ).  ...  The former are a true concurrency model introduced by Nielsen, Plotkin, Winskel, the latter a family of linear innocent strategies developed starting from Girard's work in the setting of Ludics.  ...  In ongoing work [8] we extend [7] , to show that Ludics is in fact able to model a variant of the Linear π-calculus extended with recursion. Even with recursion, the game model is linear.  ... 
doi:10.1007/978-3-642-02273-9_9 fatcat:s7a7slzvljhufjaq3d2psrg5vu

Semantically linear programming languages

Luca Paolini, Mauro Piccolo
2008 Proceedings of the 10th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '08  
We give an interpretation of SℓPCF into a model of linear coherence spaces and we show that such semantics is fully abstract with respect to our language.  ...  We propose a paradigmatic programming language (called SℓPCF) which is linear in a semantic sense.  ...  Acknowledgments We wish to express our gratitude to Antonio Bucciarelli and Marco Gaboardi for some useful discussions about topics considered in this paper.  ... 
doi:10.1145/1389449.1389462 dblp:conf/ppdp/PaoliniP08 fatcat:xq7u66ai75gv3fneegxuhujcke

An approach to innocent strategies as graphs

Pierre-Louis Curien, Claudia Faggian
2012 Information and Computation  
We work in the setting of L-nets, introduced by Faggian and Maurel as a game model of concurrent interaction.  ...  An interface Ξ Λ induces the definition of a polarity for each address of the form σ such that there is σ σ for σ ∈ Ξ ∪ Λ: the polarity of σ is the same as the polarity of σ if the length of τ (where σ  ...  Acknowledgments We wish to thank Dominic Hughes and Rob van Glabbeek for fruitful exchanges on the technique of domination, and Olivier Laurent for numerous discussions on MALL proof nets.  ... 
doi:10.1016/j.ic.2011.12.006 fatcat:3biucnw5ajhjpkfefry6rss6de

A Logic of Sequentiality [chapter]

Martin Churchill, James Laird
2010 Lecture Notes in Computer Science  
Using further categorical properties of this model, we prove a full completeness result: each total strategy is the semantics of a unique cut-free core proof in the system.  ...  We describe the semantics of our logic formally by giving a notion of categorical model and an instance based on a simple category of games.  ...  The authors would like to thank Guy McCusker for useful discussion and comments on earlier drafts; and Makoto Takeyama for the insights provided by jointly formalising this work in the theorem prover Agda  ... 
doi:10.1007/978-3-642-15205-4_19 fatcat:6q55s6nrtvdorjei5tfb6fyqgm

Order algebras: a quantitative model of interaction

2017 Mathematical Structures in Computer Science  
This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational  ...  as linear combinations is the same.  ...  Things get more subtle when modelling a calculus with name passing like the πcalculus [27] .  ... 
doi:10.1017/s0960129516000360 fatcat:sjkv2oxoxbafhirrn6miwnbub4