# Duality and i/o-Types in the π-Calculus

2 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
3 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : We study duality between input and output in the π-calculus. In dualisable versions of π, including πI and fusions, duality breaks with the addition of ordinary input/output types. We introduce $\overline\pi$, intuitively the minimal symmetrical conservative extension of π with input/output types. We prove some duality properties for $\overline\pi$ and we study embeddings between $\overline\pi$ and π in both directions. As an example of application of the dualities, we exploit the dualities of $\overline\pi$ and its theory to relate two encodings of call-by-name λ-calculus, by Milner and by van Bakel and Vigliotti, syntactically quite different from each other.
Document type :
Journal articles

Cited literature [10 references]

https://hal.archives-ouvertes.fr/hal-00798028
Submitted on : Thursday, March 7, 2013 - 6:27:02 PM
Last modification on : Wednesday, December 19, 2018 - 1:08:13 PM
Long-term archiving on : Saturday, June 8, 2013 - 9:40:08 AM

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• HAL Id : hal-00798028, version 1

### Citation

Daniel Hirschkoff, Jean-Marie Madiot, Davide Sangiorgi. Duality and i/o-Types in the π-Calculus. Lecture Notes in Computer Science, Springer, 2012, 7454, pp 302-316. ⟨hal-00798028⟩

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