\(
% cbs-katex.sty
%
\newcommand{\STYLE}[2]{\htmlClass{cbs-#1}{#2}}
\newcommand{\DECL}[3]{\htmlId{#1:#2}{#3}}
\newcommand{\REF}[3]{\href{###1:#2}{#3}}
\newcommand{\HYPER}[5]{\href{#1/#2/index.html###3:#4}{#5}}
% \SHADE{MATH} can be defined to produce a shaded background to highlight
% inline MATH in running text:
\newcommand{\SHADE}[1]{#1}
% \KEY{TEXT}, \STRING{TEXT}, \ATOM{TEXT}, \LEX{TEXT} can be used in math mode:
\newcommand{\KEY}[1]{\textsf{\textit{\STYLE{Key}{#1}}}}
\newcommand{\STRING}[1]{\textsf{``\texttt{#1}''}}
\newcommand{\ATOM}[1]{\textsf{`\texttt{#1}'}}
\newcommand{\LEX}[1]{\textsf{\STYLE{Key}{`}\texttt{#1}\STYLE{Key}{'}}}
% The following commands produce ASCII characters that are treated specially by LaTeX:
\newcommand{\HASH}{\char`\#}
\newcommand{\DOLLAR}{\char`\$}
\newcommand{\PERCENT}{\char`\%}
\newcommand{\AMPERSAND}{\char`\&}
\newcommand{\APOSTROPHE}{\char`\'}
\newcommand{\BACKSLASH}{\char`\\}
\newcommand{\CARET}{\char`\^}
\newcommand{\UNDERSCORE}{\char`\_}
\newcommand{\GRAVE}{\char`\`}
\newcommand{\LEFTBRACE}{\char`\{}
\newcommand{\RIGHTBRACE}{\char`\}}
\newcommand{\TILDE}{\textasciitilde} % {\char`\~}
% \NAME{name} highlights the name;
% \NAMEDECL{name} declares Name.name as the target of links to name;
% \NAMEREF{name} links name to the target Name.name in the current file;
% \NAMEHYPER{url}{file}{name} links name to Name.name at url/file/file.pdf.
% Similarly for \VAR{partvariable}, \SYN{syntaxname}, \SEM{semanticsName},
% and \SECT{sectionnumber}
% The kerns in \SUB and \VAR avoid overlaps with primes:
\newcommand{\SUB}[1]{_{\kern-2mu\STYLE{PartVariable}{\textsf{#1}}}}
% PLAIN
\newcommand{\VAR}[1]{\STYLE{PartVariable}{\textsf{\textit{#1}\kern2mu}}}
\newcommand{\NAME}[1]{\STYLE{Name}{\textsf{#1}}}
\newcommand{\SYN}[1]{\STYLE{SyntaxName}{\textsf{#1}}}
\newcommand{\SEM}[1]{\STYLE{SemanticsName}{\textsf{#1}}}
\newcommand{\SECT}[1]{\STYLE{SectionNumber}{\textsf{#1}}}
% DECL
\newcommand{\VARDECL}[1]{\DECL{PartVariable}{#1}{\VAR{#1}}}
\newcommand{\NAMEDECL}[1]{\DECL{Name}{#1}{\NAME{#1}}}
\newcommand{\SYNDECL}[1]{\DECL{SyntaxName}{#1}{\SYN{#1}}}
\newcommand{\SEMDECL}[1]{\DECL{SemanticsName}{#1}{\SEM{#1}}}
\newcommand{\SECTDECL}[1]{\DECL{SectionNumber}{#1}{\textsf{#1}}}
% REF
\newcommand{\VARREF}[1]{\REF{PartVariable}{#1}{\VAR{#1}}}
\newcommand{\NAMEREF}[1]{\REF{Name}{#1}{\NAME{#1}}}
\newcommand{\SYNREF}[1]{\REF{SyntaxName}{#1}{\SYN{#1}}}
\newcommand{\SEMREF}[1]{\REF{SemanticsName}{#1}{\SEM{#1}}}
\newcommand{\SECTREF}[1]{\REF{SectionNumber}{#1}{\SECT{#1}}}
% HYPER
\newcommand{\VARHYPER}[3]{\HYPER{#1}{#2}{PartVariable}{#3}{\VAR{#3}}}
\newcommand{\NAMEHYPER}[3]{\HYPER{#1}{#2}{Name}{#3}{\NAME{#3}}}
\newcommand{\SYNHYPER}[3]{\HYPER{#1}{#2}{SyntaxName}{#3}{\SYN{#3}}}
\newcommand{\SEMHYPER}[3]{\HYPER{#1}{#2}{SemanticsName}{#3}{\SEM{#3}}}
\newcommand{\SECTHYPER}[3]{\HYPER{#1}{#2}{SectionNumber}{#3}{\SECT{#3}}}
% \LEFTPHRASE MATH \RIGHTPHRASE produces [[ MATH ]] with proper brackets:
\newcommand{\LEFTPHRASE}{\llbracket}
\newcommand{\RIGHTPHRASE}{\rrbracket}
% \LEFTGROUP MATH \RIGHTGROUP produces ( MATH ) where the parentheses are
% highlighted the same as keywords:
\newcommand{\LEFTGROUP}{\STYLE{Key}{(}}
\newcommand{\RIGHTGROUP}{\STYLE{Key}{)}}
% MATH\PLUS produces a superscript +
% MATH\STAR produces a superscript *
% MATH\QUERY produces a superscript ?
\newcommand{\PLUS}{{}^{\texttt{+}}}
\newcommand{\STAR}{{}^{\texttt{*}}}
\newcommand{\QUERY}{{}^{\texttt{?}}}
% \RULE{& PREMISE \\ & ...}{& FORMULA ... \\ & ...} produces an inference rule
% with separately aligned premises and conclusion
% PREMISE
% ...
% -----------
% FORMULA ...
% ...
\newcommand{\RULE}[2]
{\frac{\begin{aligned}#1\end{aligned}}{\begin{aligned}#2\end{aligned}}}
% \AXIOM{& FORMULA ... \\ & ...} produces an aligned formula
%
% FORMULA ...
% ...
\newcommand{\AXIOM}[1]{\begin{aligned}#1\end{aligned}}
% \TO TYPE produces => TYPE
\newcommand{\TO}{\mathop{\Rightarrow}}
% TERM \TRANS TERM produces TERM ---> TERM
\newcommand{\TRANS}{\longrightarrow}
% TERM \xrightarrow{LABEL} TERM puts the label above the long arrow
%
\)
Note that \(\SHADE{\NAMEREF{multiset}
( \cdots )}\) is not a constructor operation. The order of
argument values is ignored, but duplicates are significant, e.g.,
\(\SHADE{\NAMEREF{multiset}
( 1,
2,
2 )}\) is equivalent to \(\SHADE{\NAMEREF{multiset}
( 2,
1,
2 )}\), but not to
\(\SHADE{\NAMEREF{multiset}
( 1,
2 )}\) or \(\SHADE{\NAMEREF{multiset}
( 2,
1 )}\).
For each multiset \(\SHADE{\VAR{MS}}\), the sequence of values \(\SHADE{\VAR{V}\STAR}\) returned by
\(\SHADE{\NAMEREF{multiset-elements}
( \VAR{MS} )}\) contains each element of \(\SHADE{\VAR{MS}}\) the same number of times
as \(\SHADE{\VAR{MS}}\) does.
The order of the values in \(\SHADE{\VAR{V}\STAR}\) is unspecified, and may vary between multisets.
\(\SHADE{\NAMEREF{multiset-insert}
( \VAR{GV},
\VAR{N},
\VAR{MS} )}\) returns the multiset that differs from \(\SHADE{\VAR{MS}}\)
by containing \(\SHADE{\VAR{N}}\) more copies of \(\SHADE{\VAR{GV}}\).
\(\SHADE{\NAMEREF{multiset-delete}
( \VAR{MS},
\VAR{GV},
\VAR{N} )}\) removes \(\SHADE{\VAR{N}}\) copies of \(\SHADE{\VAR{V}}\) from the multiset \(\SHADE{\VAR{MS}}\),
or all copies of \(\SHADE{\VAR{GV}}\) if there are fewer than \(\SHADE{\VAR{N}}\) in \(\SHADE{\VAR{MS}}\).
\(\SHADE{\NAMEREF{is-submultiset}
( \VAR{MS}\SUB{1},
\VAR{MS}\SUB{2} )}\) tests whether every element of \(\SHADE{\VAR{MS}\SUB{1}}\) has equal or
fewer occurrences in \(\SHADE{\VAR{MS}\SUB{1}}\) than in \(\SHADE{\VAR{MS}\SUB{2}}\).