283
edits
Pipe-calculus: Difference between revisions
→Syntax
KalmanKeri (talk | contribs) (→Syntax) |
KalmanKeri (talk | contribs) (→Syntax) |
||
| Line 66: | Line 66: | ||
=== Syntax === | === Syntax === | ||
<math> | <math> | ||
\def\ | \def\pos{\mathsf{pos}~} | ||
\def\ | \def\neg{\mathsf{neg}~} | ||
\def\seq{\mathrel{;}} | \def\seq{\mathrel{;}} | ||
\def\succeed{\textbf{ | \def\succeed{\textbf{succeed}} | ||
\def\alt{\mid} | \def\alt{\mid} | ||
\def\fail{\textbf{fail}} | \def\fail{\textbf{fail}} | ||
| Line 82: | Line 82: | ||
& \mbox{Atoms}~ & a, b \rule & \mathsf{A} \mid \mathsf{B} \mid \mathsf{'foo} \mid \mathsf{'bar} \mid ... \\ | & \mbox{Atoms}~ & a, b \rule & \mathsf{A} \mid \mathsf{B} \mid \mathsf{'foo} \mid \mathsf{'bar} \mid ... \\ | ||
& \mbox{ | & \mbox{Primary}~ & p, q \rule & \pos a \mid \neg a \\ | ||
& \mbox{Terms}~ & s, t \rule & ~ | & \mbox{Terms}~ & s, t \rule & ~ | ||
p | |||
\mid s \seq t \mid \succeed | \mid s \seq t \mid \succeed | ||
\mid s \mathsf{|} t \mid \fail | \mid s \mathsf{|} t \mid \fail | ||
\mid s \pipe t \mid \pass \ | \mid s \pipe t \mid \pass | ||
\mid (s) | |||
\end{alignat} | \end{alignat} | ||
</math> | </math> | ||
'''Atoms''' are unscoped symbols. We assume a countably infinite set of atoms that is disjunct from the set of constants (operators, keywords and punctuation). | '''Atoms''' are unscoped symbols. We assume a countably infinite set of atoms that is disjunct from the set of constants (operators, keywords and punctuation). | ||
There are two kinds of '''primary terms''', positive and negative literals. | |||
There are two ''' | '''Sequential composition''' <math>\seq</math> constructs ordered pairs. The symbol <math>\succeed</math> denotes an empty sequence which can be interpreted as successful termination. | ||
'''Alternative composition''' <math>\alt</math> connects a pair of alternatives. <math>\fail</math> denotes an empty set of alternatives, or intuitively failure to find any viable alternative. | |||
The <math>\pipe</math> '''pipe''' operator constructs '''pipelines'''. Intuitively a pipeline is a transformer with unidirectional data flow. | |||
''' | |||
The '''pipe''' operator | |||
<math>\pass</math> denotes a passive pipeline that transfers its input unchanged to the output. | <math>\pass</math> denotes a passive pipeline that transfers its input unchanged to the output. | ||
| Line 112: | Line 106: | ||
<math> | <math> | ||
\begin{alignat}{1} | \begin{alignat}{1} | ||
~~~~ & a \pto s & = & ~\ | ~~~~ & a \pto s & = & ~\pos a \seq s \\ | ||
~~~~ & a \nto s & = & ~\ | ~~~~ & a \nto s & = & ~\neg a \seq s \\ | ||
\end{alignat} | \end{alignat} | ||
</math> | </math> | ||