Editing Communicating sequential processes (section)

==== Traces model ====
The ''traces model'' defines the meaning of a process expression as the set of sequences of events (traces) that the process can be observed to perform. For example,

* <math>\mathrm{traces}\left(\mathrm{STOP}\right) = \left\{ \langle\rangle \right\}</math> since <math>\mathrm{STOP}</math> performs no events
* <math>\mathrm{traces}\left(a\rightarrow b \rightarrow \mathrm{STOP}\right) = \left\{\langle\rangle ,\langle a \rangle, \langle a, b \rangle \right\}</math> since the process <math>(a\rightarrow b \rightarrow \mathrm{STOP})</math> can be observed to have performed no events, the event {{mvar|a}}, or the sequence of events {{mvar|a}} followed by {{mvar|b}}

More formally, the traces model <math>\mathcal T</math> is defined as the set of non-empty prefix-closed subsets of <math>\Sigma^{\ast}</math>. The meaning of a process {{mvar|P}} in the traces model is defined as <math>\mathrm{traces}\left(P\right) \subseteq \Sigma^{\ast}</math> such that:
# <math>\langle\rangle \in \mathrm{traces}\left(P\right)</math> (i.e. <math>\mathrm{traces}\left(P\right)</math> contains the empty sequence)
# <math>s_1 \smallfrown s_2 \in \mathrm{traces}\left(P\right) \implies s_1 \in \mathrm{traces}\left(P\right)</math> (i.e. <math>\mathrm{traces}\left(P\right)</math> is prefix-closed)
where <math>\Sigma^{\ast}</math> is the set of all possible finite sequences of events.