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Journal Articles Lecture Notes in Computer Science Year : 2012

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

Daniel Hirschkoff
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Davide Sangiorgi
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#### 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.

### Dates and versions

hal-00798028 , version 1 (07-03-2013)

### Identifiers

• HAL Id : hal-00798028 , version 1

### Cite

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

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