Merge pull request #3013 from henrikt-ma/cleanup/unit-syntax

Clean up chapter 'Unit Expressions'

chapters/unitexpressions.tex

@@ -1,105 +1,86 @@
 \chapter{Unit Expressions}\label{unit-expressions}
 
-Unless otherwise stated, the syntax and semantics of unit expressions in
-Modelica conform with the international standards
-\emph{International System of Units (SI)} by BIPM superseding parts of
-ISO 31/0-1992
-\emph{General principles concerning quantities, units and symbols} and ISO
-1000-1992 \emph{SI units and recommendations for the use of their multiples
-and of certain other units}.
-Unfortunately, these standards do not define a formal syntax for
-unit expressions. There are recommendations and Modelica exploits them.
-
-Note that this document uses the American spelling meter, whereas the SI specification from BIPM uses the British spelling metre.
-
-Examples for the syntax of unit expressions used in Modelica: \lstinline!"N.m"!,
-\lstinline!"kg.m/s2"!, \lstinline!"kg.m.s-2"! \lstinline!"1/rad"!,
-\lstinline!"mm/s"!.
+Unless otherwise stated, the syntax and semantics of unit expressions in Modelica conform with the international standards \emph{International System of Units (SI)} by BIPM superseding parts of ISO 31/0-1992 \emph{General principles concerning quantities, units and symbols} and ISO 1000-1992 \emph{SI units and recommendations for the use of their multiples and of certain other units}.
+Unfortunately, these standards do not define a formal syntax for unit expressions.
+There are recommendations and Modelica exploits them.
+
+Note that this document uses the American spelling \emph{meter}, whereas the SI specification from BIPM uses the British spelling \emph{metre}.
+
+Examples for the syntax of unit expressions used in Modelica: \lstinline!"N.m"!, \lstinline!"kg.m/s2"!, \lstinline!"kg.m.s-2"!, \lstinline!"1/rad"!, \lstinline!"mm/s"!.
 
 \section{The Syntax of Unit Expressions}\label{the-syntax-of-unit-expressions}
 
+The Modelica unit string syntax allows neither comments nor white-space, and a unit string shall match the \lstinline[language=grammar]!unit-expression! rule:
 \begin{lstlisting}[language=grammar]
-unit_expression:
-   unit_numerator [ "/" unit_denominator ]
+unit-expression :
+   unit-numerator [ "/" unit-denominator ]
 
-unit_numerator:
-   "1" | unit_factors | "(" unit_expression ")"
+unit-numerator :
+   "1" | unit-factors | "(" unit-expression ")"
 
-unit_denominator:
-   unit_factor | "(" unit_expression ")"
+unit-denominator:
+   unit-factor | "(" unit-expression ")"
 \end{lstlisting}
 
-The unit of measure of a dimension free quantity is denoted by \lstinline!"1"!. The
-SI standard does not define any precedence between multiplications and
-divisions. The SI standard does not allow multiple units to the right of the
-division-symbol (\lstinline!/!) since the result is ambiguous; either the divisor shall be enclosed in parentheses,
-or negative exponents used instead of division, for example, \lstinline!"J/(kg.K)"! may be written as \lstinline!"J.kg-1.K-1"!.
+The unit of measure of a dimension free quantity is denoted by \lstinline!"1"!.
+The SI standard does not define any precedence between multiplications and divisions.
+The SI standard does not allow multiple units to the right of the division-symbol (\lstinline!/!) since the result is ambiguous; either the divisor shall be enclosed in parentheses, or negative exponents used instead of division, for example, \lstinline!"J/(kg.K)"! may be written as \lstinline!"J.kg-1.K-1"!.
 
 \begin{lstlisting}[language=grammar]
-unit_factors:
-   unit_factor [ unit_mulop unit_factors ]
-
-unit_mulop:
-   "."
+unit-factors :
+   unit-factor [ "." unit-factors ]
 \end{lstlisting}
 
-The SI standard specifies that a multiplication operator symbol is written as space
-or as a dot. The SI standard requires that this \emph{dot} is a bit above the base line: `·', which is not part of ASCII.
+The SI standard specifies that a multiplication operator symbol is written as space or as a dot.
+The SI standard requires that this \emph{dot} is a bit above the base line: `·', which is not part of ASCII.
 The ISO standard also prefers `·', but Modelica supports the ISO alternative `.', which is an ordinary \emph{dot} on the base line.
 
-For example, Modelica does not support \lstinline!"Nm"! for newton-meter,
-but requires it to be written as \lstinline!"N.m"!.
+For example, Modelica does not support \lstinline!"Nm"! for newton-meter, but requires it to be written as \lstinline!"N.m"!.
 
 \begin{lstlisting}[language=grammar]
-unit_factor:
-  unit_operand [ unit_exponent ]
+unit-factor :
+  unit-operand [ unit-exponent ]
 
-unit_exponent:
-   [ "+" | "-" ] integer
+unit-exponent :
+   [ "+" | "-" ] UNSIGNED-INTEGER
 \end{lstlisting}
 
 The SI standard uses super-script for the exponentation, and does thus not define any operator symbol for exponentiation.
-A \lstinline!unit_factor! consists of a \lstinline!unit_operand! possibly suffixed by a
-possibly signed integer number, which is interpreted as an exponent.
-There must be no spacing between the \lstinline!unit_operand! and a possible
-\lstinline!unit_exponent!.
+A \lstinline[language=grammar]!unit-factor! consists of a \lstinline[language=grammar]!unit-operand! possibly suffixed by a possibly signed integer number, which is interpreted as an exponent.
+There must be no spacing between the \lstinline[language=grammar]!unit-operand! and a possible \lstinline[language=grammar]!unit-exponent!.
 
 \begin{lstlisting}[language=grammar]
-unit_operand:
-   unit_symbol | unit_prefix unit_symbol
+unit-operand :
+   unit-symbol | unit-prefix unit-symbol
+
+unit-prefix :
+   "Y" | "Z" | "E" | "P" | "T" | "G" | "M" | "k" | "h" | "da"
+   | "d" | "c" | "m" | "u" | "n" | "p" | "f" | "a" | "z" | "y"
 
-unit_prefix:
-   Y | Z | E | P | T | G | M | k | h | da | d | c | m | u | n | p | f | a | z | y
+unit-symbol :
+   unit-char { unit-char }
 \end{lstlisting}
 
-A \lstinline!unit_symbol! is a string of letters. A basic support of units in
-Modelica should know the basic and derived units of the SI system. It is
-possible to support user defined unit symbols. In the base version Greek
-letters is not supported, but full names must then be written, for
-example \lstinline!"Ohm"!.
+A \lstinline[language=grammar]!unit-symbol! is a non-empty string of \lstinline[language=grammar]!unit-char! characters.
+The set of allowed characters is currently not defined.
+It is required that basic and derived units of the SI system are recognized, but tools are allowed to additionally support user-defined unit symbols.
+The required unit symbols do not make use of Greek letters, but a unit such as $\Omega$ is spelled out as \lstinline!"Ohm"!.
 
-A \lstinline!unit_operand! should first be interpreted as a \lstinline!unit_symbol! and only
-if not successful the second alternative assuming a prefixed operand
-should be exploited. There must be no spacing between the \lstinline!unit_symbol!
-and a possible \lstinline!unit_prefix!. The values of the prefixes are according to
-the ISO standard. The letter \lstinline!u! is used as a symbol for the prefix
-micro.
+A \lstinline[language=grammar]!unit-operand! should first be interpreted as a \lstinline[language=grammar]!unit-symbol! and only if not successful the second alternative assuming a prefixed operand should be exploited.
+There must be no spacing between the \lstinline[language=grammar]!unit-symbol! and a possible \lstinline[language=grammar]!unit-prefix!.
+The values of the prefixes are according to the ISO standard.
+The letter \lstinline!u! is used as a symbol for the prefix \emph{micro}.
 
 \begin{nonnormative}
-A tool may present \lstinline!Ohm! as $\Omega$ and the prefix \lstinline!u! as $\mu$, and similarly \lstinline!m2! as $m^2$.
+A tool may present \lstinline!Ohm! as $\Omega$ and the prefix \lstinline!u! as $\mu$, and similarly \lstinline!m2! as m\textsuperscript{2}.
 \end{nonnormative}
 
 \section{Examples}\label{examples2}
 
-The unit expression \lstinline!"m"! means meter and not milli
-(10\textsuperscript{-3}), since prefixes cannot be used in isolation.
-For millimeter use \lstinline!"mm"! and for square meter, m\textsuperscript{2}, write
-\lstinline!"m2"!.
+The unit expression \lstinline!"m"! means meter and not milli (10\textsuperscript{-3}), since prefixes cannot be used in isolation.
+For millimeter use \lstinline!"mm"! and for square meter, m\textsuperscript{2}, write \lstinline!"m2"!.
 
-The expression \lstinline!"mm2"! means (10\textsuperscript{-3}m)2 =
-10\textsuperscript{-6}m\textsuperscript{2}. Note that exponentiation
-includes the prefix.
+The expression \lstinline!"mm2"! means (10\textsuperscript{-3}m)\textsuperscript{2} = 10\textsuperscript{-6}m\textsuperscript{2}.
+Note that exponentiation includes the prefix.
 
-The unit expression \lstinline!"T"! means tesla, but note that the letter \lstinline!T! is
-also the symbol for the prefix tera which has a multiplier value of
-10\textsuperscript{12}.
+The unit expression \lstinline!"T"! means tesla, but note that the letter \lstinline!T! is also the symbol for the prefix tera which has a multiplier value of 10\textsuperscript{12}.