Chapter

Computing with New Resources

Volume 8808 of the series Lecture Notes in Computer Science pp 307-322

Date:

Symmetries and Dualities in Name-Passing Process Calculi

  • Daniel HirschkoffAffiliated withENS Lyon, Université de Lyon CNRS, INRIA Email author 
  • , Jean-Marie MadiotAffiliated withENS Lyon, Université de Lyon CNRS, INRIA
  • , Davide SangiorgiAffiliated withINRIA/Università di Bologna

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Abstract

We study symmetries and duality between input and output in the \(\pi \)-calculus. We show that in dualisable versions of \(\pi \), including \(\pi \) and fusions, duality breaks with the addition of ordinary input/output types. We illustrate two proposals of calculi that overcome these problems. One approach is based on a modification of fusion calculi in which the name equivalences produced by fusions are replaced by name preorders, and with a distinction between positive and negative occurrences of names. The resulting calculus allows us to import subtype systems, and related results, from the pi-calculus. The second approach consists in taking the minimal symmetrical conservative extension of \(\pi \) with input/output types.