bnf.doc

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%      <assignment>& -> & <non-macro assignment> | <macro assignment>\\
%      <equals> & ->& <optional spaces> | <optional spaces>"="_{12}\\
%      <def>&->&"\def"|"\gdef"|"\edef"|"\xdef"\\
%      <normal integer>&->&<integer constant>\\
%               &&|<integer constant><one optional space>\\
%               &&|"'"_{12}<octal constant><one optional space>\\
%               &&|`"`_{12}<hexadecimal constant><one optional space>\\
%               &&|"`"_{12}<character token><one optional space>\\
%      <S>&->& "a" <B>\\
%      <S>&->&\Empty\\
%      <B>&->& "b" <B>\\
%      <B>&->&{@ a{@ b{@ c{@ d{@ e<B>}}}}}\\
%      <B>&->& ["c"{@"ab"}"d"] | {@ {@"aba"}["d"]{@"baab"}}
%   \end{eqnarray*}
%\end{bnf}
%\end{verbatim}
%\begin{bnf}
%   \begin{eqnarray*}
%      <assignment>& -> & <non-macro assignment> | <macro assignment>\\
%      <equals> & ->& <optional spaces> | <optional spaces>"="_{12}\\
%      <def>&->&"\def"|"\gdef"|"\edef"|"\xdef"\\
%      <normal integer>&->&<integer constant>\\
%               &&|<integer constant><one optional space>\\
%               &&|"'"_{12}<octal constant><one optional space>\\
%               &&|`"`_{12}<hexadecimal constant><one optional space>\\
%               &&|"`"_{12}<character token><one optional space>\\
%      <S>&->& "a" <B>\\
%      <S>&->&\Empty\\
%      <B>&->& "b" <B>\\
%      <B>&->&{@ a{@ b{@ c{@ d{@ e<B>}}}}}\\
%      <B>&->& ["c"{@"ab"}"d"] | {@ {@"aba"}["d"]{@"baab"}}
%   \end{eqnarray*}
%\end{bnf}
%
%\StopEventually{}
%\section{Implementation of the long forms}
%The "NonTerminal" environment is easy to implement.
%We set nonterminal letters in roman by default, that is, maths family~0,
%and make sure that spaces are respected. The boolean is there to
%make the checking of the short forms easier later. Certain characters
%can be excluded from the text of a nonterminal, and an error message
%issued if they are encountered.
%    \begin{macrocode}
\newif\ifnonterminal
\def\NonTerminal{\left\langle\obeyspaces\ControlSpaces
   \nonterminaltrue\NonTerminalStyle}
\def\endNonTerminal{\right\rangle}
\def\NonTerminalStyle{\fam0 }
{\obeyspaces\gdef\ControlSpaces{\let =\ }}
%    \end{macrocode}
%
%The "Star", "Optional" and "Bracket" environments are all similar.
%A small amount of extra space has been introduced round each,
%to improve their appearance.
%    \begin{macrocode}
\def\Star{\,\left\{}  \def\endStar{\right\}\,}
\def\Optional{\,\left[} \def\endOptional{\right]\,}
\def\Bracket{\,\left(} \def\endBracket{\right)\,}
%    \end{macrocode}
%
%The single symbols have easy definitions.
%    \begin{macrocode}
\def\OR{\mathop{\left|\right.}\nolimits}
\def\Production{\mathrel{\longrightarrow}}
\def\Yields{\mathrel{\Longrightarrow}}
\def\Empty{\varepsilon}
%    \end{macrocode}
%
%By far the most difficult effect to produce is that of a terminal.
%We could make "\Terminal" expand to "\verb*", but that prevents us
%from including extra text before and after the terminal string.
%Thus a definition similar to that of "\verb*" from NFSS is included.
%    \begin{macrocode}
\begingroup
 \catcode`\`=\active
 \gdef\TerminalFont{\tt \catcode96\active
   \def`{\leavevmode\kern\z@\char96 }}
\endgroup
\begingroup
  \catcode`\~=\active
  \lccode`\~=`\^^M
  \lowercase{\endgroup
    \gdef\Terminal{\relax\PreTerminal
      \ifmmode \hbox \else \leavevmode\null \fi
      \bgroup
      \TerminalFont
      \catcode`~\active
      \def~{\egroup\@latexerr{Terminal string ended by
                              end of line.}\@ehc}%
    \let\do\@makeother \dospecials
    \@sTerminal}}
\def\@sTerminal#1{%
  \catcode`#1\active
  \lccode`\~`#1%
  \lowercase{\def~{\egroup\PostTerminal}}}%
%    \end{macrocode}
%The default leading and trailing text is defined to be empty.
%    \begin{macrocode}
\def\PreTerminal{} \def\PostTerminal{}
%    \end{macrocode}
%
%\section{Implementation of the short forms}
%
%Our first task is to make $<$ and $>$ available as mathematical symbols.
%    \begin{macrocode}
\mathchardef\lt="313C \mathchardef\gt="313E
%    \end{macrocode}
%The next task is more subtle, and at first puzzled the author when he
%tried to make a preliminary version of these macros work.
%The problem is that we are making "-" into an active character.
%If we do this we find that it tries to expand in text as well, and so
%we make sure that it only expands in maths mode.
%Our objective is to make "->" expand to $\Production$, but here is
%where things go wrong. In plain \TeX, the control sequence
%"\longrightarrow" is defined to expand to a "\relbar" and a "\rightarrow".
%In turn, a relbar expands to yield a "-" again, and so we are in an
%infinite loop.
%
%The solution seems to be to abandon the definition of "\relbar" in
%plain \TeX\ and produce our own. The same applies to "=" and "\Relbar".
%We also make a hyphen available for use within nonterminals.
%    \begin{macrocode}
\mathchardef\HYPHEN="2D  \mathchardef\MINUS="2200
\mathchardef\Relbar="303D  \def\relbar{\mathrel{\smash{\MINUS}}}
\mathchardef\EQUALS="303D
%    \end{macrocode}
%
%We next define "\bnf" to set the mathcodes of the characters we wish to
%use to the active value \verb|"8000|. Thus in text they will behave as
%normal characters, but in mathematics they will expand as though they were
%active characters.  We also allow "bnf" to be an environment.
%    \begin{macrocode}
\def\mathactive{"8000}
\def\bnf{%
   \mathcode`"=\mathactive
   \mathcode`[=\mathactive \mathcode`\]=\mathactive
   \mathcode`(=\mathactive \mathcode`\)=\mathactive
   \mathcode`|=\mathactive \mathcode`-=\mathactive
   \mathcode`<=\mathactive \mathcode`\>=\mathactive
   \mathcode`@=\mathactive \mathcode`==\mathactive
   \mathcode96 \mathactive
}
\def\endbnf{}
%    \end{macrocode}
%
%Several characters are not allowed to appear in nonterminal names,
%and so we define an error message to warn the user.
%    \begin{macrocode}
\def\NotInNonTerminal{\errmessage{Not allowed in a non-terminal}}
%    \end{macrocode}
%
%Several of our mathactive characters have similar definitions;
%we use this fact to allow some condensation of our file.
%    \begin{macrocode}
\def\NotNTdef#1#2{\gdef#1{\ifnonterminal\NotInNonTerminal\else#2\fi}}
%    \end{macrocode}
%
%The expansion text of all our mathactive characters must be defined
%inside a group in which they are all active.
%    \begin{macrocode}
\begingroup
   \catcode`"\active
   \catcode`[\active \catcode`\]\active
   \catcode`(\active \catcode`\)\active
   \catcode`|\active \catcode`-\active
   \catcode`<\active \catcode`>\active
   \catcode`@\active \catcode`=\active
   \catcode96 \active
%    \end{macrocode}
%First we have the two short forms of "\Terminal".
%    \begin{macrocode}
   \gdef"{\Terminal"}%
   \gdef`{\Terminal`}%
%    \end{macrocode}
%Next a block of definitions of characters which are illegal inside
%nonterminals.
%    \begin{macrocode}
   \NotNTdef[\Optional        \NotNTdef]\endOptional
   \NotNTdef(\Bracket         \NotNTdef)\endBracket
   \NotNTdef|\OR              \NotNTdef<\NonTerminal
%    \end{macrocode}
%The end of a nonterminal has to be defined directly, of course.
%    \begin{macrocode}
   \gdef>{\endNonTerminal}%
%    \end{macrocode}
%A "-" character in a nonterminal is just a hyphen, but otherwise it
%could possibly be a production arrow.
%    \begin{macrocode}
   \gdef-{%
      \ifnonterminal
         \def\Nnext{\HYPHEN}%
      \else
         \def\Nnext{\futurelet\Next\SeeIfProdn}%
      \fi\Nnext}
%    \end{macrocode}
%The "=" character, on the other hand, should not appear in a nonterminal.
%Otherwise, it could be a yields arrow.
%    \begin{macrocode}
   \gdef={%
      \ifnonterminal
         \def\Nnext{\NotInNonTerminal}%
      \else
         \def\Nnext{\futurelet\Next\SeeIfYields}%
      \fi\Nnext}%
%    \end{macrocode}
%The "@" character should examine the next character to see whether it should
%be given a special treatment.
%    \begin{macrocode}
   \gdef@{% either an escape char or a star group
      \ifnonterminal
         \def\Nnext{\NotInNonTerminal}%
      \else
         \def\Nnext{\futurelet\Next\SeeIfSpecial}%
      \fi\Nnext}%
\endgroup
%    \end{macrocode}
%
%All that remains now is to see that the checks used above
%are defined. First we have the check for a production.
%    \begin{macrocode}
\def\SeeIfProdn{%
   \if\noexpand\Next\noexpand>%
      \def\Nnext{\Production\@gobble}%
   \else
      \def\Nnext{\MINUS}%
   \fi
   \Nnext}
%    \end{macrocode}
%Second we have the check for a yields.
%    \begin{macrocode}
\def\SeeIfYields{%
   \if\noexpand\Next\noexpand>%
      \def\Nnext{\Yields\@gobble}%
   \else
      \def\Nnext{\EQUALS}%
   \fi\Nnext}
%    \end{macrocode}
%Finally the "@" character must produce a "Star" environment unless it
%is immediately followed by "<" or~">".
%    \begin{macrocode}
\def\SeeIfSpecial{%
   \if\noexpand\Next\noexpand<%
      \def\Nnext{\lt\@gobble}%
   \else
      \if\noexpand\Next\noexpand>%
         \def\Nnext{\gt\@gobble}%
      \else
         \def\Nnext{\Star\bgroup\aftergroup\endStar\aftergroup\egroup}%
      \fi
   \fi\Nnext}
%    \end{macrocode}
%\Finale

%\endinput
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Dr M J Piff                      %%  e-mail:
%% Department of Pure Mathematics   %%
%% University of Sheffield          %%  [e-mail]
%% Hicks Building                   %%  [e-mail]
%% Hounsfield Road                  %%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% SHEFFIELD S3 7RH                 %%  Telephone: SHEFFIELD [phone]
%% England                          %%             Ext. 4431
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