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Pipe-calculus: Difference between revisions
→Zero-order calculus
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== Informal description == | == Informal description == | ||
=== | === Terms === | ||
<math> | <math> | ||
\def\dot | \def\dot{.} | ||
\def\seq{\mathrel{;}} | \def\seq{\mathrel{;}} | ||
\def\succeed{\textbf{succeed}} | \def\succeed{\textbf{succeed}} | ||
| Line 78: | Line 78: | ||
\def\pass{\textbf{pass}} | \def\pass{\textbf{pass}} | ||
\def\eq{ = ~} | \def\eq{ = ~} | ||
</math> | </math>Pipe-calculus terms are also called '''processes''' to emphasize their interactive, behavioral aspect. Each process has a conceptual '''input''' and '''output''' which are implicit in the rules. Output of one process can be connected to the input of another one. | ||
Some terms contain '''atoms''' which are unscoped and uninterpreted symbols. In grammatical context one can think of atoms as ''tokens''. | |||
The following terms are available in pipe-calculus. | |||
* ''synchronisation'', where | * ''synchronisation'', where | ||
** ''negative literal prefixing'' <math>a^- \dot s</math> is a process that expects an atom <math>a</math> to be signalled on its input. If the expectation is fulfilled, the process proceeds as <math>s</math>, otherwise it fails. | ** ''negative literal prefixing'' <math>a^- \dot s</math> is a process that expects an atom <math>a</math> to be signalled on its input. If the expectation is fulfilled, the process proceeds as <math>s</math>, otherwise it fails. | ||
** ''positive literal prefixing'' <math>a^+ \dot s</math> is a process that signals an atom <math>a</math> on its output before proceeding as <math>s</math>. | ** ''positive literal prefixing'' <math>a^+ \dot s</math> is a process that signals an atom <math>a</math> on its output before proceeding as <math>s</math>. | ||
* ''communication'', where | |||
** ''input prefixing'' <math>?n \dot s</math> is a process that receives a term on its input. On success, it proceeds as <math>s</math> binding the name <math>n</math> to the received term. | |||
** ''output prefixing'' <math>!s \dot t</math> is a process that sends a term <math>s</math> to its output before proceeding as <math>t</math>. | |||
* ''sequence'' <math>s \seq t</math> is a composite process that executes <math>s</math> before proceeding as <math>t</math> unless <math>s</math> fails. In that case the composite process also fails. | * ''sequence'' <math>s \seq t</math> is a composite process that executes <math>s</math> before proceeding as <math>t</math> unless <math>s</math> fails. In that case the composite process also fails. | ||
* ''choice'' <math>s \alt t</math> is a forking process where one fork executes <math>s</math> while the other fork concurrently executes <math>t</math>. If one of the forks fail, the composite process is replaced by the other fork. | * ''choice'' <math>s \alt t</math> is a forking process where one fork executes <math>s</math> while the other fork concurrently executes <math>t</math>. If one of the forks fail, the composite process is replaced by the other fork. | ||