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Pipe-calculus: Difference between revisions
→Equational theory
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| <math>\rhd</math> || Pipe || right || lowest | | <math>\rhd</math> || Pipe || right || lowest | ||
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== Equational theory == | |||
Sequential composition is associative. | |||
<math> | |||
\begin{align} | |||
s \seq (t \seq u) = & (s \seq t) \seq u \\ | |||
\end{align} | |||
</math> | |||
Alternative composition is commutative, associative and idempotent. | |||
<math> | |||
\begin{align} | |||
t \; | \; u = & u \; | \; t \\ | |||
s \; | \; (t \; | \; u) = & (s \; | \; t) \; | \; u \\ | |||
t \; | \; t = & t \\ | |||
\end{align} | |||
</math> | |||
Alternative composition is right distributive over sequential composition. | |||
<math> | |||
\begin{align} | |||
(s \; | \; t) ; u = & s ; u \; | \; t ; u | |||
\end{align} | |||
</math> | |||
== Connection with process calculus == | == Connection with process calculus == | ||