# Concurrency theory

## Idea

Concurrency (or maybe rather parallelism (Harper)) is a joint property of several (maybe interacting) processes proceeding simultaneously. Here the word “simultaneously” indicates that the evolution of the participating processes is indexed along an irreversible directed object.

## Calculi

### Pi Calculus

The processes can either be the nil process $0$, parallel execution $P \mid Q$, sending on channel $c$ and then continuing $\overline{c}\langle x \rangle.P$, receiving on channel $c$ and then continuing $c(x).P$, replicating a process $!P$ or introduction of a new name $(\nu x)P$.