Acyclic Solos and Differential Interaction Nets

We present a restriction of the solos calculus which is stable under reduction and expressive enough to contain an encoding of the pi-calculus. As a consequence, it is shown that equalizing names that are already equal is not required by the encoding of the pi-calculus. In particular, the induced solo diagrams bear an acyclicity property that induces a faithful encoding into differential interaction nets. This gives a (new) proof that differential interaction nets are expressive enough to contain an encoding of the pi-calculus. All this is worked out in the case of finitary (replication free) systems without sum, match nor mismatch.

[1]  Emmanuel Beffara,et al.  Concurrent Nets: A Study of Prefixing in Process Calculi , 2005, EXPRESS.

[2]  Björn Victor,et al.  The fusion calculus: expressiveness and symmetry in mobile processes , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[3]  Mario Tokoro,et al.  An Object Calculus for Asynchronous Communication , 1991, ECOOP.

[4]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[5]  Y. Lafont.  From proof-nets to interaction nets , 1995 .

[6]  Nobuko Yoshida,et al.  Combinatory representation of mobile processes , 1994, POPL '94.

[7]  Vladimir Alexiev,et al.  Non-deterministic interaction nets , 1999 .

[8]  Damiano Mazza.  Interaction nets : semantics and concurrent extensions , 2006 .

[9]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[10]  Thomas Ehrhard,et al.  On Köthe sequence spaces and linear logic , 2002, Mathematical Structures in Computer Science.

[11]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[12]  Gérard Boudol,et al.  Asynchrony and the Pi-calculus , 1992 .

[13]  Thomas Ehrhard,et al.  Differential Interaction Nets , 2005, WoLLIC.

[14]  Claudia Faggian,et al.  Ludics nets, a game model of concurrent interaction , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[15]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[16]  Gianluigi Bellin,et al.  On the pi-Calculus and Linear Logic , 1992, Theor. Comput. Sci..

[17]  Lionel Khalil.  Généralisation des réseaux d'interaction avec l'agent amb de Mc Carthy : propriétés et applications , 2003 .

[18]  Laurent Regnier,et al.  Lambda-calcul et reseaux , 1992 .

[19]  Damiano Mazza,et al.  Multiport Interaction Nets and Concurrency , 2005, CONCUR.

[20]  Cosimo Laneve,et al.  Solos in Concert , 1999, ICALP.

[21]  Cosimo Laneve,et al.  Solo Diagrams , 2001, TACS.

[22]  Samson Abramsky,et al.  Computational Interpretations of Linear Logic , 1993, Theor. Comput. Sci..

[23]  Thomas Ehrhard,et al.  Interpreting a finitary pi-calculus in differential interaction nets , 2007, Inf. Comput..

[24]  Vladimir Alexiev.  Non-deterministic Interaction Nets (Thesis Presentation) , 1999 .

[25]  Thomas Ehrhard,et al.  Interpreting a Finitary Pi-calculus in Differential Interaction Nets , 2007, CONCUR.

[26]  Robin Milner,et al.  Bigraphs and mobile processes (revised) , 2004 .

[27]  Olivier Laurent,et al.  An exact correspondence between a typed pi-calculus and polarised proof-nets , 2010, Theor. Comput. Sci..

[28]  Giuseppe Longo.  Mathematical Structures in Computer Science , 2012 .

[29]  Robin Milner.  Pi-Nets: A Graphical Form of pi-Calculus , 1994, ESOP.

[30]  J. Girard.  PROOF-NETS : THE PARALLEL SYNTAX FOR PROOF-THEORY , 1996 .