Note: We call our processes / threads$P$or$Q$in these examples.

name

Stands for communication channels, variables.

restriction

Name creation

concurrency

Processes are executed concurrently: $P ~|~ Q$

communication - input prefixing

Process is waiting for a message on channel $c$ - it can be binded to the name $x$ in $c(x)$ .

communication - output prefixing

Process is sending a message on channel $c$ - it can be binded to the name $x$ in $\overline{c}\lang x\rang$ .

replication

$!P$ is a process that can always create a new copy of $P$ .

creation of a new name

$(\nu x)P$ is a process that allcoates the name $x$ within the process $P$ .

nil process

written $0$ . Execution is complete / has stopped.

Formal definition

In the Backus-Naur-From BNF grammar.

$\begin{aligned}P, Q::=& ~~~x(y) . P \\& \mid \bar{x}\langle y\rangle . P \\&\mid P \mid Q \\& \mid(\nu x) P \\& \mid ~! P \\& \mid 0\end{aligned}$

$x(y) . P$ Receive on channel $x$ , bind result to $y$ , run $P$

$\bar{x}\langle y\rangle . P$ Send value of $y$ to channel $x$ , run $P$

$P \mid Q$ Run $P$ and $Q$ simultaniously

$(\nu x) P$ Create new channel $x$ and run $P$

$!P$ Repeatedly generate copies of $P$

$0$ Terminate Process