Pipe-calculus: Difference between revisions

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Revision as of 20:23, 9 May 2023

851 bytes removed , 9 May 2023

→‎Syntax

KalmanKeri

283

edits

@@ Line 105: / Line 105: @@
 \def\rule{ ::= ~}
-\begin{alignat}{2}
+\begin{alignat}{3}
-& \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 \mathsf{'+} \mid \mathsf{'*} \mid ... \\
 & \mbox{Variables}~    & x, y \rule & \mathsf{a} \mid \mathsf{b} \mid ... \\
-& \mbox{Prefixes}~     & p, q \rule & a^+ \mid a^- \mid ~?x \mid ~!s \\
+& \mbox{Prefixes}~     & p, q \rule
+         & ~ a^+             & & \text{Positive literal (signal)} \\
+& & \mid & ~ a^-             & & \text{Negative literal (match)} \\
+& & \mid & ~ ?x              & & \text{Abstraction (input)} \\
+& & \mid & ~ !s              & & \text{Argument (output)} \\
-& \mbox{Terms}~        & s, t \rule & ~
+& \mbox{Terms}~        & s, t \rule
-p . s
+         & ~ p . s            & & \text{Prefix operator} \\
-\mid s \seq t \mid \succeed
+& & \mid & ~ s \seq t         & & \text{Sequential composition} \\
-\mid s \mathsf{|} t \mid \fail
+& & \mid & ~ s \mathsf{|} t   & & \text{Alternative composition} \\
-\mid s \pipe t \mid \pass
+& & \mid & ~ s \pipe t        & & \text{Pipe (interpretation)} \\
-\mid x
+& & \mid & ~ \succeed         & & \text{Successful termination} \\
-\mid (s)
+& & \mid & ~ \fail            & & \text{Failure} \\
+& & \mid & ~ \pass            & & \text{Passive process} \\
+& & \mid & ~ x                & & \text{Variable} \\
+& & \mid & ~ (s)              & & \text{Grouping} \\
 \end{alignat}
 </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).
-There are two kinds of '''prefixes''', positive and negative literals. They can only occur on the left hand side of a prefix operator.
-'''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.
-<math>\pass</math> denotes a passive pipeline that transfers its input unchanged to the output.
-For better readability, let's define some syntax sugar that will be used throughout this article. Extend the syntax of terms as follows.
-<math>\mbox{Terms}~ s, t ::= ... \mid a \pto s \mid a \nto s \mbox{, where}</math>
-<math>
-\begin{alignat}{1}
-~~~~ & a \pto s & = & ~\pos a \seq s \\
-~~~~ & a \nto s & = & ~\neg a \seq s \\
-\end{alignat}
-</math>
-We name the new operators '''positive arrow''' and '''negative arrow''' respectively.
-When it is clear from context, we can call a negative arrow simply an arrow.
-The precedence and associativity of operators is summarized in the following table.
 {| class="wikitable"
-|+ Summary of operators
+|+ Operator summary
 |-
 ! style="text-align:left;"| Symbol
@@ Line 156: / Line 141: @@
 ! style="text-align:left;"| Precedence
 |-
-| <math>\seq~\pto~\nto</math> || right || highest
+| <math>\seq</math> || right || highest
 |-
-| <math>\mid</math>           || right ||
+| <math>\mid</math> || right ||
 |-
-| <math>\rhd</math>           || right || lowest
+| <math>\rhd</math> || right || lowest
 |}