# Ian Stark

## Presheaf Models for the Pi-Calculus

Gian Luca Cattani, Ian Stark and Glynn Winskel

In Category Theory and Computer Science: Proceedings of the 7th International Conference CTCS '97, Santa Margherita Ligure, Italy, September 4-6, 1997, Lecture Notes in Computer Science 1290, pages 106-126. Springer-Verlag, 1997.

A version of this paper also appeared as BRICS Report RS-97-34.

### Abstract

Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also handle systems where the language of actions may change dynamically as a process evolves. The example is the pi-calculus, a calculus for mobile processes' whose communication topology varies as channels are created and discarded. A denotational semantics is described for the pi-calculus within an indexed category of profunctors; the model is fully abstract for bisimilarity, in the sense that bisimulation in the model, obtained from open maps, coincides with the usual bisimulation obtained from the operational semantics of the pi-calculus. While attention is concentrated on the late' semantics of the pi-calculus, it is indicated how the early' and other variants can also be captured.

@InProceedings{cattani/stark/winskel:prempc,
author =       {Gian Luca Cattani and Ian Stark and Glynn Winskel},
title =        {Presheaf Models for the $\pi$-Calculus},
booktitle =    {Category Theory and Computer Science: Proceedings
of the 7th International Conference CTCS~'97},
year =         1997,
series =       {Lecture Notes in Computer Science},
number =       1290,
pages =        {106--126},
publisher =    {Springer-Verlag},
url =          {http://www.inf.ed.ac.uk/~stark/prempc.html}
}
`