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Pipe-calculus: Difference between revisions
→Equational theory
KalmanKeri (talk | contribs) |
KalmanKeri (talk | contribs) |
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== Equational theory == | == Equational theory == | ||
Sequential composition is associative. | Sequential composition is associative. <math>\null</math> is a neutral element. | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
s \seq (t \seq u) = & (s \seq t) \seq u \\ | s \seq (t \seq u) = & (s \seq t) \seq u \\ | ||
t \seq \null = \null \seq t = t \\ | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Alternative composition is commutative, associative and idempotent. | Alternative composition is commutative, associative and idempotent. <math>\fail</math> is its neutral element. | ||
<math> | <math> | ||
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s \mid (t \mid u) = & (s \mid t) \mid u \\ | s \mid (t \mid u) = & (s \mid t) \mid u \\ | ||
t \mid t = & t \\ | t \mid t = & t \\ | ||
t \mid \fail = t \\ | |||
\end{align} | \end{align} | ||
</math> | </math> | ||