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Pipe-calculus: Difference between revisions
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* ''top'' <math>\top</math> is a process that successfully terminated. | * ''top'' <math>\top</math> is a process that successfully terminated. | ||
* ''bottom'' <math>\bot</math> is also a terminated process. In certain contexts it denotes failure. | * ''bottom'' <math>\bot</math> is also a terminated process. In certain contexts it denotes failure. | ||
=== Prefixes === | |||
''Prefixes'' are basic units of behavior (called ''actions'' in process algebra). In pipe-calculus they can only occur together with a continuation. | |||
=== Sequence === | === Sequence === | ||
Sequences bring the concept of temporal order to pipe-calculus. In <math>s \mathrel{;} t</math>, <math>s</math> is executed before <math>t</math> (more precisely, the behavior of <math>s</math> is observed before the behavior of <math>t</math>). | |||
If <math>s</math> fails (it reduces to <math>\bot</math>), <math>t</math> is not executed at all and the sequence fails. | If <math>s</math> fails (it reduces to <math>\bot</math>), <math>t</math> is not executed at all and the sequence fails. | ||
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<math>\top \mathrel{;} t = t</math> | <math>\top \mathrel{;} t = t</math> | ||
In <math>s ; s</math>, <math>s</math> is executed twice. | In <math>s ; s</math>, <math>s</math> is executed twice. In other words, sequence is not idempotent. | ||
Logically <math>;</math> has | Logically <math>;</math> has common properties with non-commutative (shortcut) conjunction. | ||
Prefixed forms also obey this temporal ordering: the behavior of the prefix is observed before the behavior of the continuation<ref>Wikipedia implies that prefixed forms are specialized forms of sequential composition: "In process calculi, the sequentialisation operator is usually integrated with input or output, or both." ([[Wikipedia:Process_calculus#Sequential_composition|Process calculus]] on Wikipedia) | |||
</ref>. | |||
=== Choice === | === Choice === | ||