Editing Process calculus (section)

=== Reduction semantics ===
The key operational reduction rule, containing the computational essence of process calculi, can be given solely in terms of parallel composition, sequentialization, input, and output. The details of this reduction vary among the calculi, but the essence remains roughly the same. The reduction rule is:

:<math>
x\langle y\rangle \cdot P \; \vert \; x(v)\cdot Q  \longrightarrow P \; \vert \; Q[^y\!/\!_v]
</math>

The interpretation to this reduction rule is:
# The process <math>x\langle y\rangle \cdot P</math> sends a message, here <math>\mathit{y}</math>, along the channel <math>\mathit{x}</math>. Dually, the process <math>x(v)\cdot Q</math> receives that message on channel <math>\mathit{x}</math>.
# Once the message has been sent, <math>x\langle y\rangle \cdot P</math> becomes the process <math>\mathit{P}</math>, while <math>x(v)\cdot Q</math> becomes the process <math>Q[^y\!/\!_v]</math>, which is <math>\mathit{Q}</math> with the place-holder <math>\mathit{v}</math> substituted by <math>\mathit{y}</math>, the data received on <math>\mathit{x}</math>.
The class of processes that <math>\mathit{P}</math> is allowed to range over as the continuation of the output operation substantially influences the properties of the calculus.