% Master File: blkarray.sty
% Document Previewer: xdvi
% Document Type: laTeX
%%% ====================================================================
%%%  @LaTeX-style-file{
%%%     author          = "David Carlisle",
%%%     version         = "0.04",
%%%     date            = "03 December 1992",
%%%     time            = "11:34:52 GMT",
%%%     filename        = "blkarray.sty",
%%%     address         = "Mathematics Department
%%%                        Manchester University
%%%                        Oxford Road
%%%                        Manchester
%%%                        England
%%%                        M13 9PL",
%%%     email           = "carlisle@ma.man.ac.uk (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "LaTeX, tabular, array, delimiters, ",
%%%     supported       = "yes",
%%%     docstring       = "
%%%
%%%     blkarray.sty
%%%
%%%     A LaTeX style option extending array and tabular
%%%     HIGHLY VOLATILE, use at your own risk!!!!!!!!
%%%
%%%     Documentation requires Mittelbach's doc.sty.
%%%
%%%     The checksum field above was produced by
%%%     Robert Solovay's checksum utility.",
%%%  }
%%% ====================================================================
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%<*x>
% This file may be used without modification as a style (.sty) file.
%
% If you have Mittelbach's doc.sty, this file may be formatted with a
% command like:
%                latex blkarray.sty
%
% If you have the Mittelbach/Duchier/Braams docstrip utility, you may
% produce a faster loading .sty file. Rename this file to: blkarray.doc
% Then run this file through *plain* TeX:
%                tex blkarray.doc
% This should produce the file blkarray.sty.
% If you do not have plain TeX on your system, you can trick LaTeX into
% doing the work as follows:
%                latex \def\fmtname{plain} \input blkarray.doc
% Note that you may need to quote the arguments here to stop your
% operating system treating the \ characters incorrectly.
%
%                latex blkarray.doc
% Will produce a typeset version of the documentation, as above.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\plain{plain}\ifx\fmtname\plain\csname fi\endcsname
     \def\batchfile{blkarray.doc}
     \input docstrip
     \preamble

     Do not distribute the stripped version of this file.
     The checksum in the header refers to the documented version.

     \endpreamble
     \generateFile{blkarray.sty}{t}{\from{blkarray.doc}{}}
     \endinput
\fi
%
\ifcat a\noexpand @\let\next\relax\else\def\next{%
    \documentstyle[blkarray,doc]{article}\MakePercentIgnore}\fi\next
%
%\def\eatmodule<#1>{}\eatmodule
%</x>
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \let\osmall\small\def\small{\osmall\tt}
% \textwidth=355pt   ^^A Allow macrocode text with 72 columns.
% \CodelineIndex     ^^A Code lines numbered.
% \DisableCrossrefs  ^^A No Cross references.
% \MakeShortVerb{\"} ^^A "\foo" works like \verb+\foo+
%
% \title{blkarray.sty}
% \author{D. P. Carlisle}
% \begin{document}
% \maketitle
%
% \begin{center}
% \huge\bf Warning\,!
% \end{center}
% \begin{quote}
% This style option is in the early stages of development. If you want
% to use an extended {\tt array} or {\tt tabular} in a document,
% consider using one of the options in the ARRAY package, available from
% most \TeX-servers.
%
% The commands defined in this style are quite likely to have both their
% user-interface, and their internal definitions changed in later
% versions.
% \end{quote}
%
%\BAextrarowheight=1pt
%\BAextraheightafterhline=2pt
%
% \section{Introduction}
% This style option implements an environment, {\tt blockarray}, that
% may be used in the same way as the {\tt array} or {\tt tabular}
% environments of standard \LaTeX, or their extended versions defined in
% {\tt array.sty}. If used in math-mode, {\tt blockarray} acts like
% {\tt array}, otherwise it acts like {\tt tabular}.
%
% The main feature of this style is that it uses a new method of
% defining column types. In the simplest form, this has been given a
% syntax matching the "\newcolumntype" command of {\tt array.sty}.\\
% "\BAnewcolumntype{C}{>{\large}c}"\\
% defines a column of large centred text.
%
% In {\tt array.sty} column specifiers defined via "\newcolumntype" are
% re-written in a preliminary stage to the primitive types, which are
% then treated by a completely different mechanism (basically a nested
% "\if" testing each token against one of the predefined column types,
% "c", "l", ">", \ldots
%
% In {\tt blockarray.sty}, {\em all\/} column specifiers have equal
% standing, most of the specifiers of Lamport's original are defined
% using "\BAnewcolumntype", e.g.\\
% "\BAnewcolumntype{c}   {>{\hfil}<{\hfil}}"
%
% There are one or two other features built into {\tt blockarray}, these
% will be introduced in no particular order.
%
% \subsection{Explicit Column Separators in the Preamble}
%
% As described in the \LaTeX\ book, originally specifiers like "|" and
% "@"-expressions were always considered to be part of the {\em
% preceding\/} column (except for expressions before the first column).
% This can be inconvenient if that column type is going to be over
% ridden by a "\multicolumn" specification, consider:
%
% \begin{minipage}{3in}
% \begin{verbatim}
% \begin{tabular}{c|c|c}
%  11 & 22                    & 33 \\
%  1  &\multicolumn{1}{l|}{2} &  3 \\
%  11 & 22                    & 33
% \end{tabular}
% \end{verbatim}
% \end{minipage}
% \begin{tabular}{c|c|c}
%  11 & 22                    & 33 \\
%  1  &\multicolumn{1}{l|}{2} &  3 \\
%  11 & 22                    & 33
% \end{tabular}
%
% The rule needs to be specified again in the "\multicolumn" argument as
% "{l|}", {\tt blockarray} lets you move the rule into the third column,
% by specifying "&" in the preamble like so:
%
% \begin{minipage}{3in}
% \begin{verbatim}
% \begin{blockarray}{c|c&|c}
%  11 & 22                     & 33 \\
%  1  &\BAmulticolumn{1}{l}{2} &  3 \\
%  11 & 22                     & 33
% \end{blockarray}
% \end{verbatim}
% \end{minipage}
% \begin{blockarray}{c|c&|c}
%  11 & 22                     & 33 \\
%  1  &\BAmulticolumn{1}{l}{2} &  3 \\
%  11 & 22                     & 33
% \end{blockarray}
%
% I first came across the idea of having such a feature in an array
% preamble when  Rainer Sch\"opf gave a brief introduction to various
% enhanced array styles. An implementation by Denys Duchier had a
% feature like this, however I have not seen that style so I do not know
% the details.
%
% \subsection{Blocks}
% Sometimes you want whole blocks of the table to have a different
% format, this is often the case with headings for instance. This can be
% accomplished using lots of "\multicolumn" commands, but this style
% lets you specify the format for such a block in the usual syntax for
% column specifiers:
%
% \begin{minipage}{3in}
% \begin{verbatim}
% \begin{blockarray}{*{3}{c}}
%  11 & 22 & 33 \\
%  1  & 2  &  3 \\
% \begin{block}{*{3}{>{\bf}l}}
%  11 & 22 & 33 \\
%  1  & 2  & 3  \\
% \end{block}
%  1  & 2  &  3
% \end{blockarray}
% \end{verbatim}
% \end{minipage}
% \begin{blockarray}{*{3}{c}}
%  11 & 22 & 33 \\
%  1  & 2  &  3 \\
% \begin{block}{*{3}{>{\bf}l}}
%  11 & 22 & 33 \\
%  1  & 2  & 3  \\
% \end{block}
%  1  & 2  &  3
% \end{blockarray}
%
% \subsection{Delimiters}
%
% People often want to put delimiters around sub-arrays of a larger
% array, delimiters can now be specified in the preamble argument:
%
% \begin{minipage}{3in}
% \begin{verbatim}
% \begin{blockarray}{[cc]c\}}
%  11 & 22  & 33 \\
%  1  & 2   &  3 \\
% \begin{block}{(ll)l\}}
%  11 & 22 & 33 \\
%  1  & 2  & 3  \\
% \end{block}
%  1  & 2   &  3
% \end{blockarray}
% \end{verbatim}
% \end{minipage}
% \begin{blockarray}{[cc]c\}}
%  11 & 22  & 33 \\
%  1  & 2   &  3 \\
% \begin{block}{(ll)l\}}
%  11 & 22 & 33 \\
%  1  & 2  & 3  \\
% \end{block}
%  1  & 2   &  3
% \end{blockarray}
%
% Note how in the previous example the nested {\tt block} was not
% spanned by the $[\ ]$. each section of the `outer' block was
% separately bracketed. If instead of the {\tt block} environment we use
% {\tt block*}, then the outer brackets will span the inner block,
% however it is not possible to specify any delimiters in the argument
% of {\tt block*}.
%
% \begin{minipage}{3in}
% \begin{verbatim}
% \begin{blockarray}{[cc]c\}}
%  11 & 22  & 33 \\
%  1  & 2   &  3 \\
% \begin{block*}{lll}
%  11 & 22 & 33 \\
%  1  & 2  & 3  \\
% \end{block*}
%  1  & 2   &  3
% \end{blockarray}
% \end{verbatim}
% \end{minipage}
% \begin{blockarray}{[cc]c\}}
%  11 & 22  & 33 \\
%  1  & 2   &  3 \\
% \begin{block*}{lll}
%  11 & 22 & 33 \\
%  1  & 2  & 3  \\
% \end{block*}
%  1  & 2   &  3
% \end{blockarray}
%
% The delimiters, "( ) [ ] \{ \}" have been pre-defined as column
% specifiers,
% however any delimiter, including these ones can be specified using the
% specifiers "\Left" and "\Right"\\
% "\Left{"\meta{text}"}{"\meta{delimiter}"}"\\
% specifies a delimiter together with a `label' which will be vertically
% centred with respect to the block. Note that the delimiter and the
% label take up no horizontal space, and so extra space must be left
% with a "!"- or "@"-expression or the text will over-print adjacent
% columns.
%
% \subsection{Automatic Numbering}
% A column specifier "\BAenum" specifies that the row number is to be
% printed (in a "!"-expression) at that point in each row, this number
% may be accessed with "\label" in the usual way. The number is a
% standard \LaTeX\ counter, "BAenumi", and so the appearence may be
% changed by altering the default definition of "\theBAenumi".
%
% \subsection{Footnotes}
% The "\footnote" command may be used inside {\tt blockarray}.
% Two styles are supported. If the test "BAtablenotes" is true (by
% default, or after "\BAtablenotestrue") then footnotes will appear at
% the end of the table, with lines set to the width of the table. If
% "BAtablenotes" is false, footnotes within the table will be treated as
% standard footnotes, with the text (usually) appearing at the foot of
% the page.
%
% If table notes are being set, the footnote counter is reset at the
% start of the table. Also an extended version of "\footnotetext" can be
% used. As described in the book, "\footnotetext[2]{xxx}" will produce a
% text marked with the footnote symbol for `2'. However for tablenotes,
% the optional argument may also be any non-numeric text, in which case
% it is set directly at the start of the footnote text. So you can  go
% "\footnotetext[\sc source:]{xxx}" or "\footnotetext[\sc note:]{xxx}"
% anywhere in the table body, before the first numbered footnote.
%
% If "BAtablenotes" is false the footnote text will not appear at the
% foot of the page if the whole {\tt blockarray} environment is in an
% environment which treats footnotes in a special way (eg another {\tt
% blockarray}). So if you have a complicated table which requires
% tablenotes, but for \TeX{}nical reasons you wish to enter it in the
% {\tt .tex} file as nested {\tt blockarray} environments, you may set
% "\BAtablenotestrue" for the outer environment, and then locally set it
% to false before each of the nested environments. This will ensure that
% footnotes from all parts of the table will be collected together at
% the end.
%
% This table is set with "\BAtablenotestrue".
%
% \begin{center}
% \begin{blockarray}{||c||c|||}
%   ONE\footnotetext[\sc source:]{Chicago Manual of Style.}
% &
%   TWO\footnote{Note on TWO. This is a reasonably long footnote, to
%   show the line breaking.}
% \\
%   \begin{blockarray}{|ll|}
%     \footnotetext[\sc source:]{Chicago Manual of Style.}^^A
%     \footnotetext[\sc note:]{The above attribution is incorrect.}^^A
%     l-one & l-two \\
%     l-three\footnote{Footnote to l-three.} & l-four \\
%   \end{blockarray}
% &
%   \begin{blockarray}{|ll|}
%     \footnotetext[\sc source:]{Chicago Manual of Style.}^^A
%     \footnotetext[\sc note:]{The above attribution is incorrect.}^^A
%     r-one & r-two \\
%     r-three\footnote{Footnote to r-three} & r-four \\
%   \end{blockarray}
% \\
% THREE\footnote{Note on THREE.} & FOUR \\
% \end{blockarray}
% \end{center}
%
% In this example, the outer table is set with "\BAtablenotestrue", but
% each of the inner tables is set with a local setting
% "\BAtablenotesfalse".
%
% Also the footnotes have been set in a single paragraph. Tablenotes
% will be set `run in' a paragraph, after a "\BAparfootnotes"
% declaration.
% \begin{center}
%
% \BAparfootnotes
% \begin{blockarray}{||c||c|||}%
%   \footnotetext[\sc source:]{Chicago Manual of Style.}^^A
%   \footnotetext[\sc note:]{The above attribution is incorrect.}^^A
%   ONE
% &
%   TWO\footnote{Note on TWO. This is a reasonably long footnote, to
%   show the line breaking.}
% \\\BAtablenotesfalse
%   \begin{blockarray}{|ll|}
%     l-one & l-two \\
%     l-three\footnote{Footnote to l-three.} & l-four \\
%   \end{blockarray}
% &
%   \BAtablenotesfalse
%   \begin{blockarray}{|ll|}
%     r-one & r-two \\
%     r-three\footnote{Footnote to r-three} & r-four \\
%   \end{blockarray}
% \\
% THREE\footnote{Note on THREE.} & FOUR\\
% \end{blockarray}
% \end{center}
%
% \subsection{Non Aligned Material}
%
% The primitive "\noalign" command may be used with standard \LaTeX\
% arrays, but paragraphs inside "\noalign" are broken into lines that
% are the width of the page, (or at least the current value of "\hsize")
% not to the final width of the table. Within a {\tt blockarray}
% "\BAnoalign" specifies material to be packaged into a parbox the same
% width as the table. This makes a `hole' in the current block.
% "\BAnoalign*" is similar, but any delimiters in the current block span
% across the non-aligned paragraphs.
%
% \begingroup
% \catcode`\Z=0
% \begin{verbatim}
% \begin{blockarray}{\BAenum!{.\quad}cc\Right{\}}{\tt block 1}}
% \BAnoalign*{Zldots The paragraphs Zldots}
% \begin{block}{\BAenum!{.\quad}(rr\Right{\}}{{\tt block 2} Zdots}}
% \begin{block*}{\BAenum!{.\quad}(ll)}
% \begin{block}{\BAenum!{.\quad}>{\bf}l\{c\Right{\}}{\tt block 3}}
% \BAmultirow{50pt}{Zldots Spanning Zldots}
% \begin{block}{\BAenum!{.\quad}\{l\}l\Right{\}}{\tt block 4}}
% \BAnoalign{\centering Unlike  Zldots}
% \end{verbatim}
% \endgroup
%
% \begin{blockarray}{\BAenum!{.\quad}cc\Right{\}}{\tt block 1}}
% ccc &cc\\
% c &ccccccccc \\
% \BAnoalign*{\raggedright
% The paragraphs in a {\tt\bslash BAnoalign*} are set to the final width
% of the table.}
% \begin{block}{\BAenum!{.\quad}(rr\Right
%               {\}}{{\tt block 2}, with a nested \tt block*}}
% rrr&rr \\
% rrr&r \\
% \begin{block*}{\BAenum!{.\quad}ll}
% lll&ll \\
% l&lll \\
% \end{block*}
% r&r \\
% \end{block}
% ccc \\
% \begin{block}{\BAenum!{.\quad}>{\bf}l\{c\Right{\}}{\tt block 3}}
% LLL&
% \BAmultirow{50pt}{\centering
% Spanning all the rows in a block.}
%  \\
% LL&  \\
% L&  \\
% \end{block}
% \begin{block}{\BAenum!{.\quad}\{l\}l\Right{\}}{\tt block 4}}
% ll &l\\
% \BAnoalign{\centering
% Unlike {\tt\bslash BAnoalign*}, {\tt\bslash BAnoalign} breaks  any
% delimiters in the current block.}
% l&lll \\
% \end{block}
% c&c
% \end{blockarray}
%
%
% \bigskip
%
% \subsection{Spanning Rows and Columns}
%
% The previous table had an example of the use of a "\BAmultirow"
% command. If an entry contains\\
% "\BAmultirow{"\meta{dimen}"}{"\meta{par-mode material}"}"\\
% then the \meta{par-mode material} will appear in a box at least
% \meta{dimen} wide, spanning all the rows in the current block. If the
% other entries in that column of the current block are not empty, they
% will be over printed by the spanning text.
%
% There is a column specification corresponding to "\BAmultirow". if\\
% "\BAmultirow{"\meta{dimen}"}"\\
% appears in the preamble, then each entry in that column will be
% packaged as a paragraph, in a box at least \meta{dimen} wide, spanning
% all the rows in the current block. If this is the last column in the
% block, you can not use the optional argument to "\\", and no entry in
% the column must be empty, it must at least have "{}" in it. (If you
% need to ask why, you don't want to know!)
%
% Similarly there is a column specification corresponding to
% "\BAmulticolumn".  if\\
% "\BAmulticolumn{"\meta{number}"}{"\meta{column specification}"}"\\
% appears in the preamble to a {\tt block}, then the rows in the block
% should have less entries than the outer block, the  columns
% will line up as expected.
%
% \begin{verbatim}
% \begin{blockarray}{r|lccr|c}
% aaa&bbb&ccc&ddd&eee&fff\\
% \begin{block}{(r|\BAmulticolumn{4}{>{\bf}l}|c)}
% 111&The second entry in each &333\\
% \end{block}
% a&b&c&d&e&f\\
% \begin{block}{[r|lccr\{\BAmultirow{1in}]}
% 111&222&333&444&555&Each entry\\
% 1&2&3&4&5&in this column is packaged as a paragraph.\\
% 1&2&3&4&5&\relax\\
% \end{block}
% a&b&c&d&e&f
% \end{blockarray}
% \end{verbatim}
%
% \begin{blockarray}{r|lccr|c}
% aaa&bbb&ccc&ddd&eee&fff\\
% a&b&c&d&e&f\\
% \begin{block}{(r|\BAmulticolumn{4}{>{\bf}l}|c)}
% 111&The second entry in each &333\\
% 1&row of this block spans 4 &3\\
% 1&columns of the {\tt blockarray}.&3\\
% \end{block}
% a&b&c&d&e&f\\
% a&b&c&d&e&f\\
% \begin{block}{[r|lccr\{\BAmultirow{1in}]}
% 111&222&333&444&555&Each entry\\
% 1&2&3&4&5&\hbadness10000 in this column is packaged as a paragraph.\\
% 1&2&3&4&5&\relax\\
% 1&2&3&4&5&\relax\\
% 1&2&3&4&5&\relax\\
% \end{block}
% a&b&c&d&e&f
% \end{blockarray}
%
% \subsection{Horzontal Lines}
% For  technical reasons (explained in the code section) the
% standard "\hline" does not work with "blockarray". "\BAhline" may be
% used in just the same way, although currently it is implemented
% using\ldots\\
% "\BAhhline". The "\hhline" from "hhline.sty", would work, but this is
% a new implementation, more in the spirit of this style.
%
% \begin{minipage}{3in}
% \begin{verbatim}
% \begin{blockarray}{||c||c&|cc||cc||}
% \BAhhline{|t:=:t:=&|==#==:t|}
% 0&  1  & 2   &  3 &4&5\\
% \BAhline
% 0&  1  & 2   &  3&4&5\\
% \BAhline\BAhline
% 0&  1  & 2   &  3&4&5\\
% \BAhhline{||-||-..||.-}
% 0&  1  & 2   &  3&4&5\\
% \BAhhline{=::=""::"=}
% 0&  1  & 2   &  3&4&5\\
% \BAhhline{|b:=:b:=""::"=:b|}
% \end{blockarray}
% \end{verbatim}
% \end{minipage}
% \begin{blockarray}{||c||c&|cc||cc||}
% \BAhhline{|t:=:t:=&|==#==:t|}
% 0&  1  & 2   &  3 &4&5\\
% \BAhline
% 0&  1  & 2   &  3&4&5\\
% \BAhline\BAhline
% 0&  1  & 2   &  3&4&5\\
% \BAhhline{||-||-..||.-}
% 0&  1  & 2   &  3&4&5\\
% \BAhhline{=::=""::"=}
% 0&  1  & 2   &  3&4&5\\
% \BAhhline{|b:=:b:=""::"=:b|}
% \end{blockarray}
%
% Both "\hline" and "\hhline" increase the (minimum) height of the
% following row by "\BAextraheightafterhline", which defaults to 0pt.
% {\tt array.sty} introduced a parameter, known in this style as
% "\BAextrarowheight", which is a length added to the default height of
% {\em all\/} the rows. One of the stated reasons for introducing this
% was to stop horizontal lines touching large entries like accented
% capitals, however increasing all the row heights has an effect rather
% similar to setting "\arraystretch". This style allows the the extra
% height just to be added after the horizontal rule.
%
% \subsection{Further Thoughts}
% \begin{itemize}
% \item
% The main point of any environment based on "\halign" is to make
% entries line up. Using this style as currently implemented, it is easy
% to spoil this alignment by putting different "@" expressions or rules
% in the same column in different blocks. In practice, if you want
% different "@" expressions, you need to do boxing tricks to make sure
% that they all have the same width. This could be done automatically by
% the "\halign", if the "@"-expressions and rules were put in a separate
% column. (This fact could be hidden from the user, by a method similar
% to the multicolumn column specification).
%
% \item
% The "[tcb]" optional argument does not really work at present, I have
% not done a proper implementation, as I do not know what to do about
% horizontal rules.
%
% Standard \LaTeX\ lines "[t]" and "[b]" up like this:
% xx
% \setbox0=\hbox{\begin{tabular}[t]{|c|}1\\2\\3\end{tabular}}\copy0\
% xx
% \setbox2=\hbox{\begin{tabular}[b]{|c|}1\\2\\3\end{tabular}}\copy2\
% xx
%
% However if there are horizontal lines, it looks like:
% xx
% \setbox4=\hbox{\begin{tabular}[t]{|c|}\hline1\\2\\3\end{tabular}}^^A
% \copy4\
% xx
% \setbox6=\hbox
%  {\begin{tabular}[b]{|c|}1\\2\\3\\\hline\end{tabular}}\copy6\
% xx
%
% I {\em think\/} I want it to look like this:
% xx
% \dimen0\dp4
% \advance\dimen0-\dp0
% \raise\dimen0 \box4\
% xx
% \dimen0\ht6
% \advance\dimen0-\ht2
% \lower\dimen0 \box6\
% xx
%
% This would be reasonably easy to achieve in a `full' {\tt blockarray},
% as each row is taken off and inspected, however I would like an array
% that only uses the features of the original implementation to be
% processed by the `quick' system. Any ideas?
%
% \item
% Many user-level commands and parameters defined in this style are
% named "\BA"\ldots\ This is to avoid clashes with the standard
% environments, especially if these are nested inside {\tt blockarray}.
% If {\tt array} and {\tt tabular} were re-defined in terms of {\tt
% blockarray}, many commands could be renamed, for example,
% "\BAextrarowheight", "\BAmulticolumn", "\BAhline".
%
% \item
% This style uses a lot of macros, and every use of the {\tt blockarray}
% uses a lot more. Does it work at all on a PC?
%
% \end{itemize}
%
%
% \typeout{End of the Introduction and Examples.}
% \typein[\answer]%
%   {Do you want an annotated listing of the macro definitions (y/n) ?}
% \def\next{y}\ifx\answer\next\else\expandafter\stop\fi
%

% \clearpage
% \section{The Macros}
%
% \subsection{Some General Control Macros}
% The macros in this section do not have the "BA" prefix, but rather the
% "GC" prefix, other style files can repeat these definitions without
% using up \TeX's memory.
%
%
% \LaTeX\ provides "\z@", "\@ne", "\tw@", "\thr@@", but I needed some
% more\ldots
%    \begin{macrocode}
\chardef\GC@four=4
\chardef\GC@five=5
\chardef\GC@six=6
%    \end{macrocode}
%
% \subsubsection{Tests}
%
% Tests are like "\ifs" except that instead of the\\
% "\if"\ldots\meta{true-text}"\else"\meta{false-text}"\fi"\\
% notation, they have\\
% "\test"\ldots"{"\meta{true-text}"}{"\meta{false-text}"}"\\
% They are constructed such that they expand directly to either the
% \meta{true-text} or \meta{false-text}, without leaving a trailing
% "\fi".
%
%    \begin{macrocode}
\def\GC@newtest#1{%
  \@namedef{#1true}%
    {\expandafter\let\csname test#1\endcsname\GC@true}%
  \@namedef{#1false}%
    {\expandafter\let\csname test#1\endcsname\GC@false}%
  \@nameuse{#1false}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\GC@def@testfromif#1#2\fi{%
  \def#1##1##{#2##1\expandafter\GC@true\else\expandafter\GC@false\fi}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\GC@true#1#2{#1}
\def\GC@false#1#2{#2}
%    \end{macrocode}
%
% This "\testGC@num" is not very good as it does not delimit the
% \meta{number}s correctly.
%    \begin{macrocode}
\GC@def@testfromif\testGC@x\ifx\fi
\GC@def@testfromif\testGC@num\ifnum\fi
%    \end{macrocode}
%
% \subsubsection{List Macros}
%
% If "\X" is "abc" then "\GC@add@to@front\X{xyz}" is "xyzabc";
%    \begin{macrocode}
\long\def\GC@add@to@front#1#2{%
  \def\@tempa##1{\gdef#1{#2##1}}%
  \expandafter\@tempa\expandafter{#1}}
%    \end{macrocode}
%
% and "\GC@add@to@end\X{xyz}" is "abcxyz".
%    \begin{macrocode}
\long\def\GC@add@to@end#1#2{%
  \expandafter\gdef\expandafter#1\expandafter{#1#2}}
%    \end{macrocode}
%
% \subsection{Allocations}
%
% I have given `meaningful names' to plain-\TeX's scratch registers, I
% am not sure this was a good idea, but it should be OK as long as I
% always access by name, and do not use, say, "\count4" as a scratch
% register. I do not like using numbered registers in the code, and can
% not afford to allocate registers just to get nice names, they are in
% too short supply already!
%
% Only allocate another register if {\tt blockarray} is going to lose
% control at a point where the register value needs to be saved. (eg
% inside a "\BAnoalign" anything can happen.
%
% "\BAtracing" can be set to any integer, the higher the number, the
% more gets printed.
%    \begin{macrocode}
%<*tracing>
\chardef\BAtracing=0
%</tracing>
%    \end{macrocode}
%
%    \begin{macrocode}
\newcounter{BAenumi}\let\BA@row\c@BAenumi
\countdef\BA@row@shadow=6
%    \end{macrocode}
%
%    \begin{macrocode}
\countdef\BA@ftn@shadow=0
%    \end{macrocode}
%
%    \begin{macrocode}
\newcount\BA@col
\countdef\BA@col@shadow=2
%    \end{macrocode}
%
%    \begin{macrocode}
\newcount\BA@block@cnt
\countdef\BA@block@cnt@shadow=4
%    \end{macrocode}
%
%    \begin{macrocode}
\countdef\BA@col@max=8
%    \end{macrocode}
%
%    \begin{macrocode}
\newbox\BA@final@box
\chardef\BA@final@box@shadow=8
%    \end{macrocode}
%
%    \begin{macrocode}
\chardef\BA@first@box=0
%    \end{macrocode}
%
%    \begin{macrocode}
\chardef\BA@tempbox@a=2
%    \end{macrocode}
%
%    \begin{macrocode}
\chardef\BA@tempbox@b=4
%    \end{macrocode}
%
%    \begin{macrocode}
\chardef\BA@block@box=6
%    \end{macrocode}
%
%    \begin{macrocode}
\newdimen\BA@colsep
\BA@colsep=\tabcolsep
%    \end{macrocode}
%
%    \begin{macrocode}
\newtoks\BA@ftn
\toksdef\BA@ftnx@shadow=0
%    \end{macrocode}

% \subsection{`Local' Variables}
%
% Most of {\tt blockarray} happens inside a "\halign" which means that
% the different parts have to make global assignments if they need to
% communicate. However many of these assignments are logically local to
% {\tt blockarray}, or a sub-environment like {\tt block}. This means
% that I have to manage the saving and restoring of local values `by
% hand'.
%
% Three different mechanisms occured to me, I have used all of them in
% this style, mainly just to try them out!
%
% \begin{itemize}
% \item `shadowing' If  "\X" is to be assigned globally, but it is to
% be considered local to a block of code that corresponds to a \TeX\
% group, then it may be shadowed by a local variable "\Y"\\
% "\begingroup\Y=\X"\\
% "\begingroup"\\
% \meta{arbitrary code making global assignments to {\tt X}}\\
% "\endgroup"\\
% "\global\X=\Y\endgroup".\\
% The inner group is needed to protect "\Y" from being changed.
%
% This is effectively the situation in the {\tt blockarray} environment,
% where the outer group is provided by "\begin"\ldots"\end", and the
% inner group is provided by an assignment to a box register.
% \item Generating new command names, according to nesting depth.
% Instead of directly using "\X", the variable can always be indirectly
% accessed by "\csname\nesting X\endcsname". Here "\nesting" should
% expand to a different sequence of tokens for each nested scope in
% which "\X" is  used. "\nesting" might be altered by a local
% assignment, or sometimes  need to be globally incremented at the start
% of the scope, and globally decremented at the end.
% \item Maintaining a stack of previous values. Corresponding to  a
% macro, "\X", is a macro"\Xstack" which consists of a list of the
% values of "\X" in all outer environments. When the local scope ends,
% this stack is popped, and the top value (which was the value of "\X"
% before the environment) is globally assigned to "\X".
% \end{itemize}
%
% The first method has the advantage that the variable is normally
% accessed within the environment, and the code to restore previos
% values is trivial. The main memory usage is in the save-stack, \TeX's
% normal place for saving local vaues.
%
% Shadowing can only be used when the environment corresonds to a \TeX\
% group. The {\tt block} environment does not!, "\end{block}" is not in
% the scope of any local assignments made by "\begin{block}".
%
% The second method, has the advantage that, once the access functions
% are defined, it is easy to declare new local variables, however unless
% you keep track of what has been produced, these variables will
% continue to take up memory space, even after the environment has
% ended. {\tt blockarray} at the moment does not do much clearing up, so
% after a {\tt blockarray} there are typically five macros per column
% per block (u-part, v-part, left right and `mid' delimiters) left
% taking up space. Not to mention macros containing the texts of any
% non-aligned entries.
%
%
% An extra `"."' will locally be added to "\BA@nesting" as each {\tt
% blockarray} is entered, this is used as described above.
%    \begin{macrocode}
\def\BA@nesting{}
%    \end{macrocode}
%
% These two macros help in accessing macros that are `local' to the
% current value of "\BA@nesting".
%    \begin{macrocode}
\def\BA@expafter#1#2{%
  \expandafter#1\csname BA@\BA@nesting#2\endcsname}
\def\BA@use#1{\csname BA@\BA@nesting#1\endcsname}
%    \end{macrocode}
%
% These are similar, but for macros which depend on the column and block
% involved, not just the outer {\tt blockarray} environment.
%    \begin{macrocode}
\def\BA@col@expafter#1#2{%
  \expandafter#1%
    \csname BA@\BA@nesting[\BA@use{blocktype},\the\BA@col]#2\endcsname}
\def\BA@col@use#1{%
  \csname BA@\BA@nesting[\BA@use{blocktype},\the\BA@col]#1\endcsname}
%    \end{macrocode}
%
% The following macros manage a stack as described in the third method
% above.
%    \begin{macrocode}
\def\BA@push@blocktype{%
\edef\@tempa{{{\BA@use{blocktype}}}}%
  \BA@expafter\GC@add@to@front{BTstack\expandafter}\@tempa}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@pop@blocktype{%
\BA@expafter\BA@pop@{BTstack}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@pop@#1{\expandafter\BA@pop@@#1\@@}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@pop@@#1#2\@@{%
  \BA@expafter\gdef{blocktype}{#1}%
  \BA@expafter\gdef{BTstack}{#2}}
%    \end{macrocode}
%
% \subsection{The Block Environment}
%
%    \begin{macrocode}
\def\BA@beginblock#1{%
  \noalign{%
    \BA@push@blocktype
    \global\advance\BA@block@cnt\@ne
    \penalty\the\BA@block@cnt
    \BA@expafter\xdef{blocktype\expandafter}\expandafter
      {\the\BA@block@cnt}%
    \penalty\@ne
    \global\BA@col=1
    \global\BA@expafter\def{blank@row}{\crcr}%
    \BA@clear@entry
    \global\let\BA@l@expr\@empty\global\let\BA@r@expr\@empty
    \BA@colseptrue
    \BA@parse#1\BA@parseend
    \ifnum\BA@col@max=\BA@col\else
       \@latexerr{wrong number of columns in block}\@ehc\fi
    \global\BA@col\z@}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@endblock{%\crcr
  \noalign{%
  \BA@pop@blocktype
  \penalty\BA@use{blocktype}%
  \penalty\tw@}}
%    \end{macrocode}
%
%    \begin{macrocode}
\@namedef{BA@beginblock*}#1{%
  \noalign{%
    \BA@push@blocktype
    \global\advance\BA@block@cnt\@ne
    \BA@expafter\xdef{blocktype\expandafter}\expandafter
      {\the\BA@block@cnt}%
    \global\BA@col=\@ne
    \global\BA@expafter\def{blank@row}{\crcr}%
    \BA@stringafter\let\Left\BA@left@warn
    \BA@stringafter\let\Right\BA@right@warn
    \BA@clear@entry
    \global\let\BA@l@expr\@empty\global\let\BA@r@expr\@empty
    \BA@colseptrue
    \BA@parse#1\BA@parseend
    \ifnum\BA@col@max=\BA@col\else
       \@latexerr{wrong number of columns in block*}\@ehc\fi
    \global\BA@col\z@}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@left@warn#1#2{%
  \@warning{Left delimiter, \string#2, ignored}\BA@parse}
\def\BA@right@warn#1#2{%
  \@warning{Right delimiter, \string#1, ignored}\BA@parse}
%    \end{macrocode}
%
%    \begin{macrocode}
\@namedef{BA@endblock*}{%\crcr
  \noalign{%
  \BA@pop@blocktype}}
%    \end{macrocode}
%
% \subsection{Multicolumn}
%
% First we have the "\multicolumn" command to be used as in original
% \LaTeX.
%
%    \begin{macrocode}
\def\BAmulticolumn#1#2#3{%
  \multispan{#1}%
  \global\advance\BA@col#1\relax
  \edef\BA@nesting{\BA@nesting,}%
  \BA@expafter\def{blocktype}{0}%
  {\BA@defcolumntype{&}##1\BA@parseend{%
     \@latexerr{\string& in multicolumn!}\@ehc\BA@parse\BA@parseend}%
  \global\BA@expafter\def{blank@row}{\crcr}%
  \BA@clear@entry
  \global\let\BA@l@expr\@empty\global\let\BA@r@expr\@empty
  \BA@colseptrue
  \BA@parse#2\BA@parseend}%
  \BA@strut\BA@col@use{u}\ignorespaces#3\BA@vpart}
%    \end{macrocode}
%
% Now something more interesting, a "\BAmulticolumn" column
% specification!
%
%    \begin{macrocode}
\def\BA@make@mc#1{%
  \count@#1\relax
  \BA@make@mcX
  \edef\BA@mc@hash{%
    \noexpand\BA@parse
     >{\BA@mc@spans}\noexpand\BA@MC@restore@hash
     \BA@mc@amps\noexpand\BA@MC@switch@amp}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@make@mcX{%
  \ifnum\count@=\@ne
    \def\BA@mc@spans{\null}%
    \let\BA@mc@amps\@empty
  \else
   \advance\count@\m@ne
    \BA@make@mcX
    \GC@add@to@end\BA@mc@spans{\span}%
    \GC@add@to@end\BA@mc@amps{&@{}}%
  \fi}
%    \end{macrocode}
%
% \subsection{\tt\bslash BAmultirow}
%
% First as a command.
%
%    \begin{macrocode}
\long\def\BAmultirow#1{\kern#1\relax
  \global\BA@quickfalse
  \BA@col@expafter\gdef{mid}}
%    \end{macrocode}
%
% Then as a column specification. (The actual "\BAnewcolumn" comes
% later)
%
%    \begin{macrocode}
\def\BA@mrow@bslash#1{%
  \kern#1\relax
  \global\BA@quickfalse
  \iffalse{\else\let\\\cr\fi\iffalse}\fi
  \BA@mrow}
%    \end{macrocode}
%
%    \begin{macrocode}
\long\def\BA@mrow#1\BA@vpart{%
  \BA@col@expafter\GC@add@to@end{mid}{\endgraf#1}
  \BA@vpart}
%    \end{macrocode}
%
% \subsection{\tt\bslash BAnoalign}
%
%    \begin{macrocode}
\def\BAnoalign{%\crcr
  \noalign{\ifnum0=`}\fi
     \global\BA@quickfalse
     \penalty\the\BA@row
  \@ifstar
      {\penalty\GC@four\BA@noalign}%
      {\penalty\BA@use{blocktype}\penalty\thr@@\BA@noalign}}
%    \end{macrocode}
%
%    \begin{macrocode}
\long\def\BA@noalign#1{%
  \long\BA@expafter\gdef{noalign\the\BA@row}{#1}%
  \ifnum0=`{\fi}}
%    \end{macrocode}
%
% \subsection{\tt\bslash\bslash}
%
% The following code is taken directly from "array.sty", apart from some
% name changes. It is very similar to the version in {\tt latex.tex}.
% Making "\\" into a macro causes problems when you want the entry to be
% taken as a macro argument. One possibility is to "\let" "\\" be
% "\span", and then have the \meta{u-part} of a final column parse the
% optional argument. There is still a problem with "\end{...}". Note
% that at the moment this style assumes that "\\" is used at the end of
% all lines except the last, even before "\begin{block}" or
% "\end{block}", this allows spacing to be specified, and also
% approximates to the truth about what is actually happening. The idea
% of making it easier to allow entries to be taken as arguments may be a
% non-starter if "&" is allowed to become a `short-ref' (ie "\active")
% character.
%
%    \begin{macrocode}
\def\BA@cr{{\ifnum 0=`}\fi
  \@ifstar \BA@xcr \BA@xcr}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@xcr{\@ifnextchar [%
  \BA@argcr {\ifnum 0=`{\fi}\cr}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@argcr[#1]{\ifnum0=`{\fi}\ifdim #1>\z@
  \BA@xargcr{#1}\else \BA@yargcr{#1}\fi}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@xargcr#1{\unskip
  \@tempdima #1\advance\@tempdima \dp\@arstrutbox
  \vrule \@depth\@tempdima \@width\z@ \cr}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@yargcr#1{\cr\noalign{%
     \vskip #1}}
%    \end{macrocode}
%
%    \begin{macrocode}
\newdimen\BAextrarowheight
\newdimen\BAextraheightafterhline
\newdimen\BAarrayrulewidth
   \BAarrayrulewidth\arrayrulewidth
%    \end{macrocode}
%
%    \begin{macrocode}
\newdimen\BAdoublerulesep
   \BAdoublerulesep\doublerulesep
%    \end{macrocode}
%
% The B form of the strut is an extra high strut to use after a
% horizontal rule.
%    \begin{macrocode}
\def\BA@strut{\unhcopy\@arstrutbox}
\let\BA@strutA\BA@strut
\def\BA@strutB{\dimen@\ht\@arstrutbox
  \advance\dimen@\BAextraheightafterhline
  \vrule \@height\dimen@ \@depth \dp\@arstrutbox \@width\z@
  \global\let\BA@strut\BA@strutA}
%    \end{macrocode}
%
% \subsection{Begin and End}
%
% "\begin{block}" is supposed to expand to "\noalign{...", but the code
% for "\begin" would place non-expandable tokens before the "\noalign".
% Within the {\tt blockarray} environment, redefine "\begin" so that if
% its argument corresponds to a command "\BA@begin"\meta{argument}, then
% directly directly expand that command, otherwise do a normal "\begin".
% A matching change is made to "\end".
%    \begin{macrocode}
\let\BA@@begin\begin
\let\BA@@end\end
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@begin#1{%
  \expandafter\testGC@x\csname BA@begin#1\endcsname\relax
    {\BA@@begin{#1}}%
    {\csname BA@begin#1\endcsname}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@end#1{%
  \expandafter\testGC@x\csname BA@end#1\endcsname\relax
    {\BA@@end{#1}}%
    {\csname BA@end#1\endcsname}}
%    \end{macrocode}
%
% \subsection{The {\tt blockarray} Environment}
%
%    \begin{macrocode}
\def\blockarray{\relax
  \@ifnextchar[{\BA@blockarray}{\BA@blockarray[c]}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@blockarray[#1]#2{%
  \expandafter\let\expandafter\BA@finalposition
    \csname BA@position@#1\endcsname
  \let\begin\BA@begin
  \let\end\BA@end
  \ifmmode
    \def\BA@bdollar{$}\let\BA@edollar\BA@bdollar
  \else
    \def\BA@bdollar{\bgroup}\def\BA@edollar{\egroup}%
    \let\BA@bdollar\bgroup\let\BA@edollar\egroup
  \fi
  \let\\\BA@cr
%    \end{macrocode}
% Currently I use "\everycr" this means that every macro that uses
% "\halign" that might be used inside a {\tt blockarray} must locally
% clear "\everycr". The version of {\tt array} in {\tt array.sty} does
% this, but not the one in {\tt latex.tex}.
%    \begin{macrocode}
  \everycr{\noalign{%
     \global\advance\BA@row\@ne
     \global\BA@col\z@}}%
%    \end{macrocode}
% The "\extrarowheight" code from {\tt array.sty}.
%    \begin{macrocode}
  \@tempdima \ht \strutbox
  \advance \@tempdima by\BAextrarowheight
  \setbox\@arstrutbox \hbox{\vrule
             \@height \arraystretch \@tempdima
             \@depth \arraystretch \dp \strutbox
             \@width \z@}%
%    \end{macrocode}
% As explained above various registers which are `local' to {\tt
% blockarray} are always accessed globally, and so must be shadowed by
% local copies, so that the values can be restored at the end.
%    \begin{macrocode}
  \BA@col@shadow=\BA@col
    \global\BA@col=\@ne
  \BA@block@cnt@shadow=\BA@block@cnt
    \global\BA@block@cnt\@M
  \BA@row@shadow\BA@row
    \global\BA@row\z@
  \setbox\BA@final@box@shadow=\box\BA@final@box
    \global\setbox\BA@final@box=\box\voidb@x
  \let\BA@delrow@shadow=\BA@delrow
  \let\testBA@quick@shadow\testBA@quick
    \global\BA@quicktrue
%    \end{macrocode}
% If we are using tablenotes, shadow the footnote counter (or possibly
% mpfootnote), and set up the print style for the table notes.
%    \begin{macrocode}
  \testBAtablenotes
    {\edef\BA@mpftn{\csname c@\@mpfn\endcsname}%
     \@namedef{the\@mpfn}{\BA@fnsymbol{\@nameuse{c@\@mpfn}}}%
     \BA@ftn@shadow=\BA@mpftn\global\BA@mpftn\z@
     \BA@ftnx@shadow=\expandafter{\the\BA@ftn}\global\BA@ftn{}%
      }{}%
%    \end{macrocode}
% Locally increase "\BA@nesting" so that macros accessed by `the second
% method' will be local to this environment.
%    \begin{macrocode}
  \edef\BA@nesting{\BA@nesting.}%
%    \end{macrocode}
% Now start up the code for this block
%    \begin{macrocode}
  \BA@expafter\xdef{blocktype}{10000}%
  \BA@expafter\xdef{BTstack}{\relax}%
  \global\BA@expafter\def{blank@row}{\crcr}%
  \setbox\BA@first@box=\vbox{\ifnum0=`}\fi
    \let\@footnotetext\BA@ftntext\let\@xfootnotenext\BA@xftntext
    \lineskip\z@\baselineskip\z@
    \BA@clear@entry
    \global\let\BA@l@expr\BA@bdollar\global\let\BA@r@expr\BA@edollar
    \global\let\BA@l@expr\@empty\global\let\BA@r@expr\@empty
    \BA@colseptrue
    \BA@parse#2\BA@parseend
    \BA@col@max=\BA@col
%    \end{macrocode}
% There had to be a "\halign" somewhere, and here it is!
%
% Currently I am using a `repeating preamble' because it was easier, but
% I think that I should modify the columntypes for {\tt blockarray} (not
% {\tt block}) so that they construct a preamble with the right number
% of columns. this would give better error checking, and would give the
% possibility of modifying the tabskip glue.
%    \begin{macrocode}
    \tabskip\z@
    \halign\bgroup\BA@strut%\global\BA@col=\z@
       \BA@upart##\BA@vpart&&\BA@upart##\BA@vpart\cr
       \noalign{\penalty\GC@five}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@upart{\global\advance\BA@col\@ne\BA@col@use{u}\ignorespaces}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@vpart{\unskip\BA@col@use{v}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@clear@entry{%
  \global\BA@col@expafter\let{u}\@empty
  \global\BA@col@expafter\let{v}\@empty
  \global\BA@col@expafter\let{left}\relax
  \global\BA@col@expafter\let{mid}\@empty
  \global\BA@col@expafter\let{right}\relax
  \BA@uparttrue}
%    \end{macrocode}
%
%    \begin{macrocode}
\let\BA@fnsymbol=\@fnsymbol
%    \end{macrocode}
%
% The code to place the footnote texts at the foot of the table, each
% footnote starting on a new line. This will only be activated if
% "\BAtablenotestrue".
%    \begin{macrocode}
\def\BA@expft[#1]#2{%
  \noindent\strut\ifodd0#11{%
  \edef\@thefnmark
     {\BA@fnsymbol{#1}}\@makefnmark}\else{#1}\fi\ #2\unskip\strut\par}
%    \end{macrocode}
%
% After a "\BAparfootnotes" declaration, the table notes will be set in
% a single paragraph, with a good chance of line breaks occuring at the
% start of a footnote.
%    \begin{macrocode}
\def\BAparfootnotes{%
  \def\BA@expft[##1]##2{%
   \noindent\strut\ifodd0##11{%
     \edef\@thefnmark{\BA@fnsymbol{##1}}\@makefnmark}\else{##1~}\fi
   ##2\unskip\strut\nobreak
  \hskip \z@ plus 3em \penalty\z@\hskip 2em plus -2.5em minus .5em}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\endblockarray{%
%    \end{macrocode}
% At this point, if no delimiters, "\BAnoalign", or "\BAmultirow" have
% been used, just finish here, this makes {\tt blockarray} was just
% about as efficient as {\tt array} If no fancy tricks have been used.
%    \begin{macrocode}
  \testBA@quick\BA@quick@end\BA@work@back@up
%    \end{macrocode}
% Now we restore the values  that have been `shadowed' by versions that
% are local to this environment.
%    \begin{macrocode}
  \global\BA@block@cnt=\BA@block@cnt@shadow
  \global\BA@col=\BA@col@shadow
  \global\BA@row=\BA@row@shadow
  \global\setbox\BA@final@box=\box\BA@final@box@shadow
  \global\let\BA@delrow=\BA@delrow@shadow
  \global\let\BA@delrow=\BA@delrow@shadow
  \global\let\testBA@quick\testBA@quick@shadow
%    \end{macrocode}
% If tablenotes are being used, reset the shadowed list of footnotes.
% Otherwise execute the list now, to pass the footnotes on to the outer
% environment, or the current page.
%    \begin{macrocode}
  \testBAtablenotes
    {\global\BA@mpftn=\BA@ftn@shadow
     \global\BA@ftn=\expandafter{\the\BA@ftnx@shadow}}
    {\global\BA@ftn\expandafter{\expandafter}\the\BA@ftn}}
%    \end{macrocode}
%
% Here is the `quick ending': just position the box as specified by
% "[tcb]", possibly adding footnotes.
%    \begin{macrocode}
\def\BA@quick@end{%
  \crcr
  \egroup% end of halign
  \ifnum0=`{\fi}% end of \BA@first@box
%<*tracing>
     \ifnum\BAtracing>\z@\typeout{Quick blockarray ends \on@line}\fi
%</tracing>
   \leavevmode\BA@finalposition\BA@first@box}
%    \end{macrocode}
%
% If any delimiters or noaligns have been used, we must take apart the
% table built in "\BA@first@box", and reassemble it. This is done by
% removing the rows one by one, starting with the last row, using
% "\lastbox".
%    \begin{macrocode}
\def\BA@work@back@up{%
  \BA@use{blank@row}%
  \egroup% end of halign
  \setbox\@tempboxa=\lastbox
  \unskip
  \BA@getwidths
%<*tracing>
     \ifnum\BAtracing>\z@\typeout{Full blockarray ends \on@line}\fi
%</tracing>
%<*tracing>
   \ifnum\BAtracing>\thr@@
     \egroup\showbox\BA@first@box
     \setbox\BA@first@box=\vbox\bgroup\unvbox\BA@first@box
   \fi
%</tracing>
  \setbox\BA@block@box=\box\voidb@x
  \BA@check@pen
  \ifnum0=`{\fi}% end of \BA@first@box
%<*check>
  \dimen@=\ht\BA@first@box\advance\dimen@\dp\BA@first@box
  \ifdim\dimen@>\z@\showthe\dimen@\fi
%</check>
     \leavevmode\BA@finalposition\BA@final@box}
%    \end{macrocode}
%
% These macros position the final box, they are just first attempts. In
% particular "[t]" does not work properly because the guard penalty used
% to terminate the main loop means that "\BA@first@box" always has zero
% height. Also if the box has been taken apart, "[t]" and "[b]" will
% cause the position to be based on the {\em centre\/} of the
% corresponding block.
%
% If tablenotes are being used, package the table in a box with the
% notes.
%    \begin{macrocode}
\newdimen\BAfootskip
\BAfootskip=1em
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@position@c#1{\hbox{%
     \testBAtablenotes
      {\let\footnotetext\BA@expft
       \hsize\wd#1\@parboxrestore\footnotesize}%
      {}%
     $\vcenter{%
      \unvbox#1%
      \testBAtablenotes
        {\vskip\BAfootskip
         \the\BA@ftn}{}%
      }$}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@position@t#1{\vtop{%
     \testBAtablenotes
      {\let\footnotetext\BA@expft
       \hsize\wd#1\@parboxrestore\footnotesize}%
      {}%
      \unvbox#1%
      \testBAtablenotes
        {\vskip\BAfootskip
         \the\BA@ftn}{}}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@position@b#1{%
    \testBAtablenotes
      {\vbox{%
        \let\footnotetext\BA@expft
        \hsize\wd#1\@parboxrestore\footnotesize
        \unvbox#1%
        \vskip\BAfootskip
        \the\BA@ftn}}%
      {\box#1}}
%    \end{macrocode}
%
%
% \subsection{Fitting the Parts Together}
%
% Get the widths of each column. It also faithfully copies the tabskip
% glue, even though currently this is always 0pt. The width of the
% column is put into "\BA@delrow" as the argument to the (unexpanded)
% call to "\BA@lr".
%    \begin{macrocode}
\def\BA@getwidths{%
  \setbox\@tempboxa=\hbox{\unhbox\@tempboxa
    \xdef\BA@delrow{\hskip\the\lastskip}\unskip
    \let\BA@lr\relax
    \loop
    \setbox\BA@tempbox@a=\lastbox
    \skip\z@=\lastskip\unskip
    \ifhbox\BA@tempbox@a
    \xdef\BA@delrow{%
      \hskip\the\skip\z@\BA@lr{\the\wd\BA@tempbox@a}\BA@delrow}%
    \repeat}}
%    \end{macrocode}
%
% The main mechanism by which {\tt blkarray} leaves information to be
% used `on the way back' is to leave groups of penalties in the main
% box.
% The last penalty in each group (the first to be seen on the way back)
% is a code penalty, it has the following meanings:\\
% "\penalty 1" --- "\begin{block}"\\
% "\penalty 2" --- "\end{block}"\\
% "\penalty 3" --- "\BAnoalign"\\
% "\penalty 4" --- "\BAnoalign*"\\
% "\penalty 5" --- "\begin{blockarray}"\\
% Note that the {\tt block*} environment does not produce any penalties,
% this environment is just as efficient as "\multicolumn", and does not
% require the second phase, coming back via "\lastbox".
%
% Above the code penalty may be other penalties, depending on the code,
% typically these have the values of the blocktype for the block, or the
% row number.
%    \begin{macrocode}
\def\BA@check@pen{%
  \count@=\lastpenalty\unpenalty
  \ifcase\count@
%    \end{macrocode}
% Grumble Grumble. "\lastpenalty" should be {\tt void} if the previous
% thing was not a penalty, and there should be an "\ifvoid\lastpenalty"
% or something equivalent to test for this. If the user manages to get a
% "\penalty0" into the main box, it will just have to be discarded.
% Actually that is not disastrous, but if a rule, mark, special, insert
% or write gets into that box {\tt blockarray} will go into an infinite
% loop. Every class of \TeX\ object should have a "\last"\ldots\
% so that boxes may be taken apart and reconstructed by special styles
% like this. \TeX\ of course is frozen, so these missing features will
% never be added (while the system is called \TeX).
%
%    \begin{macrocode}
%<*tracing>
     \ifnum\BAtracing>\tw@\typeout{0-???}\fi
%</tracing>
     \BA@get@row
  \or
%<*tracing>
     \ifnum\BAtracing>\tw@\typeout{1-block}\fi
%</tracing>
     \BA@expafter\xdef{blocktype}{\the\lastpenalty}\unpenalty
     \ifnum\lastpenalty=\tw@
%<*tracing>
       \ifnum\BAtracing>\tw@\typeout{discarding 2-endblock}\fi
%</tracing>
       \unpenalty\unpenalty\fi
     \BA@place
  \or
%<*tracing>
     \ifnum\BAtracing>\tw@\typeout{2-endblock}\fi
%</tracing>
     \BA@expafter\xdef{blocktype}{\the\lastpenalty}\unpenalty
     \BA@place
  \or
%<*tracing>
     \ifnum\BAtracing>\tw@\typeout{3-BAnoalign}\fi
%</tracing>
     \BA@expafter\xdef{blocktype}{\the\lastpenalty}\unpenalty
     \BA@place
     \count@=\lastpenalty\unpenalty
     \global\setbox\BA@final@box=\vbox{%
       \hsize=\wd\BA@final@box\@parboxrestore
       \vrule \@height \ht\@arstrutbox \@width \z@
       \BA@use{noalign\the\count@}
       \vrule \@width \z@ \@depth \dp \@arstrutbox
       \endgraf\unvbox\BA@final@box}%
  \or
%<*tracing>
     \ifnum\BAtracing>\tw@\typeout{4-BAnoalign*}\fi
%</tracing>
     \count@=\lastpenalty\unpenalty
     \setbox\BA@block@box=\vbox{%
       \hsize=\wd\BA@final@box \@parboxrestore
       \vrule \@height \ht\@arstrutbox \@width \z@
       \BA@use{noalign\the\count@}
       \vrule \@width \z@ \@depth \dp \@arstrutbox
       \endgraf\unvbox\BA@block@box}%
  \or
%<*tracing>
     \ifnum\BAtracing>\tw@\typeout{5-blockarray}\fi
%</tracing>
     \BA@expafter\xdef{blocktype}{10000}
     \BA@place
     \let\BA@check@pen\relax
  \fi
  \BA@check@pen}
%    \end{macrocode}
%
% Move a row of the table from the "\BA@first@box" into the block that
% is being constructed in "\BA@block@box".
%    \begin{macrocode}
\def\BA@get@row{%
  \skip@=\lastskip\unskip
  \advance\skip@\lastskip\unskip
  \setbox\@tempboxa=\lastbox
  \setbox\BA@block@box=\vbox{%
     \box\@tempboxa
     \vskip\skip@
     \unvbox\BA@block@box}}
%    \end{macrocode}
%
% Place the block that has been constructed in "\BA@block@box", together
% with any delimiters, or spanning entries which have been assembled
% into "\BA@delrow", into the final table, which is being constructed in
% "\BA@final@box".
%    \begin{macrocode}
\def\BA@place{%
  \global\setbox\BA@final@box=\vbox{\hbox{%
    \m@th\nulldelimiterspace=\z@
    \dimen\z@=\ht\BA@block@box
    \advance\dimen\z@ by \dp\BA@block@box
    \divide\dimen\z@\tw@
    \dimen\tw@=\dimen\z@
    \advance\dimen\z@ by\fontdimen22 \textfont\tw@
    \advance\dimen2 by-\fontdimen22 \textfont\tw@
    \global\BA@col=\z@
    \delimitershortfall=10pt
    \delimiterfactor=800
    \BA@delrow
    \kern-\wd\BA@block@box
    \ht\BA@block@box=\dimen\z@ \dp\BA@block@box=\dimen\tw@
    \box\BA@block@box}
  \unvbox\BA@final@box}}
%    \end{macrocode}
%
%
% Place the delimiters or spanning entries in position for one column of
% the current block.
%    \begin{macrocode}
\def\BA@lr#1{%
 \global\advance\BA@col\@ne\relax
 \BA@col@use{left}%
 \BA@col@expafter\ifx{mid}\@empty
   \kern#1
 \else
   \hbox to #1{%
      \setbox\BA@tempbox@a
        \hbox{\let\BA@mrow@bslash\@gobble\BA@col@use{u}\BA@edollar}%
      \setbox\BA@tempbox@b
        \hbox{\BA@bdollar\BA@col@use{v}}%
     \kern\wd\BA@tempbox@a
     $\vcenter{%
      \hsize=#1
      \advance\hsize-\wd\BA@tempbox@a
      \advance\hsize-\wd\BA@tempbox@b
      \@parboxrestore\BA@col@use{mid}}$%
     \kern\wd\BA@tempbox@b}%
 \fi
 \BA@col@use{right}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@leftdel#1#2#3{%
  \llap{%
    {#1}$\left#2\vrule height \dimen\z@ width\z@ \right.$\kern-#3}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@rightdel#1#2#3{%
  \rlap{%
    \kern-#3$\left.\vrule height \dimen\z@ width\z@ \right#1${#2}}}%
%    \end{macrocode}
%
% \subsection{Parsing the Column Specifications}
%
% A token "x" in the column specification, is interpreted by "\BA@parse"
% as "\BA@<x>". This command is then expanded, which may take further
% tokens as arguments.
% The expansion of "\BA@<x>" is supposed to end with a call to
% "\BA@parse" which will convert the token following any arguments to a
% control sequence name. The process is terminated by the token
% "\BA@parseend" as the coresponding command "\BA@<\BA@parseend>" does
% some `finishing off', but does not call "\BA@parse".
%
% There are two commands to help in defining column types.\\
% "\BA@defcolumntype" This takes its parameter specification in the
% primitive "\def" syntax, and allows the replacement text to be
% anything.\\
% "\BAnewcolumntype" This takes its parameter specification in \LaTeX's
% "\newcommand" syntax, and applies "\BA@parse" to the {\em front\/} of
% the replacement text. This is intended for users to define their own
% column types in terms of primitive column types, rather than in terms
% of arbitrary \TeX\ expressions.
%
% The preamble argument build up various macros as as follows:
%
% Each entry in the "\halign" preamble is of the form\\
% "\BA@upart#\BA@vpart"\\
% "\BA@upart" increments "\BA@col", and then expands
% "\BA@col@use{u}", similarly "\BA@vpart" expands
% "\BA@col@use{v}".
%
% "\BA@col@use{u}" is a macro considered local to the current block
% and column, it is always accessed via "\BA@col@use" or
% "\BA@col@expafter". So the preamble entries must result in
% "\BA@col@use{u}" and "\BA@col@use{v}" being defined to enter
% any text specified in "@"-expressions, the inter-column space (in the
% \LaTeX\ tradition, not "\tabskip"), and any declarations in ">" and
% "<" expressions. Delimiters are not added to these macros as they
% correspond to the whole block, they are left in the macros
% "\BA@col@use{left}" and "\BA@col@use{right}" spanning entries from
% "\BAmultirow" are considered like delimiters, and left in
% "\BA@col@use{mid}".
%
% If the test "\testBA@upart" is true, then the \meta{u-part} is being
% built. This consists of three different sections.\\
% 1) The left inter-column text, declared in "!"- and "@"-expressions\\
% 2) The left inter-column skip.\\
% 3) Any declarations specified in ">" expressions.
%
% Suppose "X" is a column type, which may itself be defined in terms of
% other column types, then the (equivalent) specifications:\\
% "@{aaa}>{\foo}X" and ">{\foo}@{aaa}X"\\
% must result in "aaa", surrounded by
% {\tt\protect\bslash bgroup}\ldots{\tt\protect\bslash egroup} or
% {\tt\$}\ldots{\tt\$},  being prepended to the
% {\em front\/} of the u-part, and "\foo" being appended to the end, so
% that it is the innermost declaration to be applied to the entries in
% that column.
%
% In order to achieve this, ">" expressions are directly added to the
% u-part, using "\GC@add@to@front", "@"- and "!"- expressions (and rules
% from "|") are added to a scratch macro, "\BA@l@expr", using
% "\GC@add@to@end".
%
% When the next "#" column specifier is reached, the "\BA@l@expr" is
% added to the front of the u-part, It is separated from the
% ">"-expressions by a \meta{hskip} unless an "@"-expression has
% occured, either while building the current u-part, or the previous
% v-part.
%
%  Building the v-part is similar.
%
% This procedure has certain consequences,
% \begin{itemize}
%  \item "@{a}@{b}" is equivalent to "@{ab}", or more correctly
%  "@{{a}{b}}".
%  \item ">{\a}>{\b}" is equivalent to ">{\b\a}".
% \item If any "@"-expression occurs between two columns, all
% "!"-expressions between those columns will be treated identically to
% "@"-expressions. This differs from {\tt array.sty} where two
% "!"-expressions are separated by the same skip as the rules specified
%   by "||".
%  \item If any rule "|" occurs, then a following rule will be preceded
%  by the doubleruleskip, unless a "@" or "!"-expression comes between
%  them. In particular "|&|" specifies a double rule, which looks the
%  same as "||", but "\multicolumn" commands can be used to remove one
%  or other of the rules for certain entries.
% \end{itemize}
%
% Create a macro name from a column specifier.
%    \begin{macrocode}
\def\BA@stringafter#1#2{\expandafter#1\csname BA@<\string#2>\endcsname}
%    \end{macrocode}
%
% Execute the specifier, or discard an unknown one, and try the next
% token.
%    \begin{macrocode}
\def\BA@parse#1{%
  \BA@stringafter\testGC@x{#1}\relax
    {\@latexerr {Unknown column type, \string#1}\@ehc\BA@parse}%
    {\csname BA@<\string#1>\endcsname}}
%    \end{macrocode}
%
% "\def" for column types.
%    \begin{macrocode}
\def\BA@defcolumntype#1{%
  \BA@stringafter\def{#1}}
%    \end{macrocode}
%
% "\newcommand" for column types.\footnote{Currently does not check that
% the type is new.}
%    \begin{macrocode}
\def\BAnewcolumntype{\@ifnextchar[{\BA@nct}{\BA@nct[0]}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@nct[#1]#2#3{%
  \BA@stringafter\@reargdef{#2}[#1]{\BA@parse#3}}
%    \end{macrocode}
%
% These "\if"s will be true if their associated skips are to be added in
% the current column.
%    \begin{macrocode}
\newif\ifBA@colsep
\newif\ifBA@rulesep
%    \end{macrocode}
%
% This is true if we do not need to come back up the array.
%    \begin{macrocode}
\GC@newtest{BA@quick}
%    \end{macrocode}
%

% This will be true if building the \meta{u-part}, and false if building
% the \meta{v-part}.
%    \begin{macrocode}
\GC@newtest{BA@upart}
%    \end{macrocode}
%
%
% \subsection{`Internal' Column-Type Definitions}
%
% ">" expressions:\\
%  If we are building the v-part, add a "&", and try
% again, so that "c<{\a}>{\b}c" is equivalent to "c<{\a}&>{\b}c".\\
% Otherwise add the expression to the front of the u-part, i.e., the
% list being built in "\BA@col@use{u}". Note that no grouping is added
% so that the scope of any declaration includes the column entry.
%    \begin{macrocode}
\BA@defcolumntype{>}#1{%
  \testBA@upart
   {\BA@col@expafter\GC@add@to@front{u}{#1}%
    \BA@parse}%
   {\BA@parse &>{#1}}}
%    \end{macrocode}
%
% Left delimiters:\\
% Again add a "&" if required, otherwise just save the delimiter and
% label as the first two arguments of "\BA@left@del" in the macro
% "\BA@col@use{left}".
%    \begin{macrocode}
\BA@defcolumntype{\Left}#1#2{%
  \testBA@upart
   {\global\BA@quickfalse
    \BA@col@expafter\gdef{left}{\BA@leftdel{#1}{#2}}\BA@parse}%
   {\BA@parse &\Left{#1}{#2}}}
%    \end{macrocode}
%
% Right delimiters: As for Left.
%    \begin{macrocode}
\BA@defcolumntype{\Right}#1#2{%
  \testBA@upart
   {\BA@parse ##\Right{#1}{#2}}
   {\global\BA@quickfalse
    \BA@col@expafter\gdef{right}{\BA@rightdel{#1}{#2}}\BA@parse}}%
%    \end{macrocode}
%
% "&" The end of each column specification is terminated by "&", either
% by the user explicitly entering "&", or one being added by one of the
% other rewrites.\\
% If we are still in the u-part, finish it off with "#".\\
% Otherwise add another column to the blank row, advance the column
% counter by one. Finally reset the variables
% $"\BA@use{u"|"v"|"left"|"mid"|"right}"$
%    \begin{macrocode}
\BA@defcolumntype{&}{%
  \testBA@upart
   {\BA@parse ##&}%
   {%
    \BA@expafter\xdef{blank@row}{\BA@use{blank@row}\omit&}%
    \global\advance\BA@col\@ne
    \BA@clear@entry
    \BA@parse}}
%    \end{macrocode}
%
% "#" Add a "&" if required.\\
% Otherwise make the u-part of the current column, and the v-part of the
% previous one.
%
%    \begin{macrocode}
\BA@defcolumntype{#}{%
  \testBA@upart
   {%
%    \end{macrocode}
% Add the intercolumn skips unless a "@" expression has occured since
% the last "#" entry.
%    \begin{macrocode}
    \ifBA@colsep
       \GC@add@to@front\BA@r@expr{\BA@edollar\hskip\BA@colsep}%
       \GC@add@to@end\BA@l@expr{\hskip\BA@colsep\BA@bdollar}%
    \else
       \GC@add@to@front\BA@r@expr{\BA@edollar}%
       \GC@add@to@end\BA@l@expr{\BA@bdollar}%
    \fi
%    \end{macrocode}
% Go back to the previous column. Add "\BA@r@expr" to the end of
% "\BA@col@use{v}".
%    \begin{macrocode}
    \global\advance\BA@col\m@ne
    \BA@col@expafter\GC@add@to@end{v\expandafter}\expandafter
           {\BA@r@expr}%
%    \end{macrocode}
% Add the total width of any "@" expressions as the third argument in
% the right delimiter macro, this will be used to move the delimiters
% past any inter-column material.
%    \begin{macrocode}
    \BA@add@rskip
%    \end{macrocode}
% Repeat for the u-part, and left delimiter of the current column.
%    \begin{macrocode}
    \global\advance\BA@col\@ne
    \BA@col@expafter\GC@add@to@front{u\expandafter}\expandafter
           {\BA@l@expr}%
     \BA@add@lskip
%    \end{macrocode}
% Clear these scratch macros ready for the next column.
%    \begin{macrocode}
    \global\let\BA@l@expr\@empty\global\let\BA@r@expr\@empty
%    \end{macrocode}
% Reset these tests and ifs, ready for the next inter-column material.
%    \begin{macrocode}
    \BA@upartfalse
    \BA@rulesepfalse
    \BA@colseptrue
%    \end{macrocode}
% Finally look at the next specifier.
%    \begin{macrocode}
    \BA@parse}%
   {\BA@parse &##}}
%    \end{macrocode}
%
% "<" Just like ">".
%    \begin{macrocode}
\BA@defcolumntype{<}#1{%
  \testBA@upart
   {\BA@parse ##<{#1}}%
   {\BA@col@expafter\GC@add@to@front{v}{#1}\BA@parse}}
%    \end{macrocode}
%
% "BA" version of "\vline".
%    \begin{macrocode}
\def\BA@vline{\vrule \@width \BAarrayrulewidth}
%    \end{macrocode}
%
% "|" like "!", except that a "\hskip\BAdoublerulesep" is added for
% consecutive pairs.
%    \begin{macrocode}
\BA@defcolumntype{|}{%
  \testBA@upart
   {\ifBA@rulesep
      \GC@add@to@end\BA@l@expr{\hskip\BAdoublerulesep\BA@vline}%
    \else
      \GC@add@to@end\BA@l@expr{\BA@vline}%
    \fi}%
   {\ifBA@rulesep
      \GC@add@to@end\BA@r@expr{\hskip\BAdoublerulesep\BA@vline}%
    \else
      \GC@add@to@end\BA@r@expr{\BA@vline}%
    \fi}%
  \BA@ruleseptrue
  \BA@parse}
%    \end{macrocode}
%
% "@" identical to "!", but set "\BA@colsepfalse".
%    \begin{macrocode}
\BA@defcolumntype{@}#1{%
  \testBA@upart
   {\GC@add@to@end\BA@l@expr{\BA@bdollar#1\BA@edollar}}%
   {\GC@add@to@end\BA@r@expr{\BA@bdollar#1\BA@edollar}}%
  \BA@colsepfalse
  \BA@rulesepfalse
  \BA@parse}
%    \end{macrocode}
%
% "!" Just save the expression, and make "\BA@rulesepfalse" so that the
% next "|" is not preceded by a skip.
%    \begin{macrocode}
\BA@defcolumntype{!}#1{%
  \testBA@upart
   {\GC@add@to@end\BA@l@expr{\BA@bdollar#1\BA@edollar}}%
   {\GC@add@to@end\BA@r@expr{\BA@bdollar#1\BA@edollar}}%
  \BA@rulesepfalse
  \BA@parse}
%    \end{macrocode}
%
% "*": "*{3}{xyz}" just produces "xyz*{2}{xyz}" which is then re-parsed.
%    \begin{macrocode}
\BA@defcolumntype{*}#1#2{%
 \count@=#1\relax
 \ifnum\count@>\z@
    \advance\count@\m@ne
    \edef\@tempa##1{\noexpand\BA@parse##1*{\the\count@}{##1}}%
 \else
    \def\@tempa##1{\BA@parse}%
 \fi
 \@tempa{#2}}
%    \end{macrocode}
%
% "\BA@parseend" this is added to the end of the users preamble, it acts
% like a cross between "#" and "&". It terminates the preamble building
% as it does not call "\BA@parse".
%    \begin{macrocode}
\BA@defcolumntype{\BA@parseend}{%
  \testBA@upart
   {\BA@parse ##\BA@parseend}%
   {%
    \ifBA@colsep
       \GC@add@to@front\BA@r@expr{\BA@edollar\hskip\BA@colsep}%
    \else
       \GC@add@to@front\BA@r@expr{\BA@edollar}%
    \fi
    \BA@expafter\xdef{blank@row}{\BA@use{blank@row}\omit\cr}%
    \BA@add@rskip
    \BA@col@expafter\GC@add@to@end{v\expandafter}\expandafter
           {\BA@r@expr}}}
%    \end{macrocode}
%
% Like {\tt array.sty}
%    \begin{macrocode}
\def\BA@startpbox#1{\bgroup
  \hsize #1 \@arrayparboxrestore
   \vrule \@height \ht\@arstrutbox \@width \z@}

\def\BA@endpbox{\vrule \@width \z@ \@depth \dp \@arstrutbox \egroup}
%    \end{macrocode}
%
% Save the "&" and "#" macros, so they can be restored after a
% multicolumn, which redefines them.
%    \begin{macrocode}
\BA@stringafter{\let\expandafter\BA@save@amp}{&}
\BA@stringafter{\let\expandafter\BA@save@hash}{#}
%    \end{macrocode}
%
% A column specification of "\BAmulticolumn{3}{c}" is re-written to:\\
% "c\BA@MC@end", except that the definition of "#" has been changed so
% that it expands to:\\
% ">{\null\span\span}\BA@MC@restore@hash&@{}&@{}\BA@MC@switch@amp"\\
% The 2 "\span"s in the u-part make the entry span 3 columns, the 2
% "&@{}" increment "\BA@col" without adding any intercolumn skips.
% The "\BA@MC@restore@hash" specifier just restores "#" to its normal
% meaning. "\BA@MC@switch@amp" then causes a specifier "&" to generate
% an error, as the argument to multicolumn may only specify one column.
% Finally when "\BA@MC@end" is reached, "&" is restored.
%
% "\BA@MC@restore@hash" restore the meaning of "#".
%    \begin{macrocode}
\BA@defcolumntype{\BA@MC@restore@hash}{%
  \BA@stringafter\let{##}\BA@save@hash
  \BA@parse}
%    \end{macrocode}
%
% Switch the meaning of "&" so it generates an error, and skips all
% specifiers up to "\BA@MC@end"
%    \begin{macrocode}
\BA@defcolumntype{\BA@MC@switch@amp}{%
  \BA@stringafter\let{&}\BA@extra@amp
  \BA@parse}
%    \end{macrocode}
%
% Restore "&".
%    \begin{macrocode}
\BA@defcolumntype{\BA@MC@end}{%
  \BA@stringafter\let{&}\BA@save@amp
  \BA@parse}
%    \end{macrocode}
%
% The special definition of "&" while parsing the multicolumn argument.
%    \begin{macrocode}
\def\BA@mc@extra@amp#1\BA@MC@end{%
     \@latexerr{\string& in multicolumn!}\@ehc\BA@parse\BA@MC@end}%
%    \end{macrocode}
%
% Putting it all together!
%    \begin{macrocode}
\BA@defcolumntype{\BAmulticolumn}#1#2{%
  \BA@make@mc{#1}%
  \BA@stringafter\let{##}\BA@mc@hash
  \BA@parse#2\BA@MC@end}
%    \end{macrocode}
%
% As explained above, in order to position the delimiters on the way
% back we need the widths of the inter-column texts.
%    \begin{macrocode}
\def\BA@add@rskip{%
  \BA@col@expafter\ifx{right}\relax\else
    \setbox\BA@tempbox@a\hbox{\BA@bdollar\BA@r@expr}%
    \BA@col@expafter\GC@add@to@end{right\expandafter}\expandafter
       {\expandafter{\the\wd\BA@tempbox@a}}\fi}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@add@lskip{%
  \BA@col@expafter\ifx{left}\relax\else
    \setbox\BA@tempbox@a\hbox{\BA@l@expr\BA@edollar}%
    \BA@col@expafter\GC@add@to@end{left\expandafter}\expandafter
      {\expandafter{\the\wd\BA@tempbox@a}}\fi}
%    \end{macrocode}
%
% \subsection{User Level Column-Type Definitions}
%
%    \begin{macrocode}
\BAnewcolumntype{c}   {>{\hfil}<{\hfil}}
\BAnewcolumntype{l}   {>{}<{\hfil}}
\BAnewcolumntype{r}   {>{\hfil}<{}}
%    \end{macrocode}
%
%    \begin{macrocode}
\BAnewcolumntype[1]{p}{>{\vtop\BA@startpbox{#1}}c<{\BA@endpbox}}
\BAnewcolumntype[1]{m}{>{$\vcenter\BA@startpbox{#1}}c<{\BA@endpbox$}}
\BAnewcolumntype[1]{b}{>{\vbox\BA@startpbox{#1}}c<{\BA@endpbox}}
%    \end{macrocode}
%
%    \begin{macrocode}
\BAnewcolumntype{(}  {\Left{}{(}}
\BAnewcolumntype{)}  {\Right{)}{}}
\BAnewcolumntype{\{} {\Left{}{\{}}
\BAnewcolumntype{\}} {\Right{\}}{}}
\BAnewcolumntype{[}  {\Left{}{[}}
\BAnewcolumntype{]}  {\Right{]}{}}
%    \end{macrocode}
%
%    \begin{macrocode}
\BAnewcolumntype{\BAenum}  {%
  !{%
    {\def\protect{\noexpand\protect\noexpand}%
     \xdef\@currentlabel{\p@BAenumi\theBAenumi}}
    \hbox to 2em{%
    \hfil\theBAenumi}}}
%    \end{macrocode}
%
%    \begin{macrocode}
\BAnewcolumntype[1]{\BAmultirow}{>{\BA@mrow@bslash{#1}}##}
%    \end{macrocode}
%
% \subsection{Footnotes}
%
% This test is true if footnote texts are to be displayed at the end of
% the table.
%    \begin{macrocode}
\GC@newtest{BAtablenotes}
\BAtablenotestrue
%    \end{macrocode}
%
% Inside the alignment just save up the footnote text in a token
% register.
%    \begin{macrocode}
\long\def\BA@ftntext#1{%
  \edef\@tempa{\the\BA@ftn\noexpand\footnotetext
                    [\the\csname c@\@mpfn\endcsname]}%
  \global\BA@ftn\expandafter{\@tempa{#1}}}%
%    \end{macrocode}
%
%    \begin{macrocode}
\long\def\BA@xftntext[#1]#2{%
  \global\BA@ftn\expandafter{\the\BA@ftn\footnotetext[#1]{#2}}}
%    \end{macrocode}

% \subsection{Hline and Hhline}
% The standard "\hline" command would work fine `on the way down' but on
% the way back it throws me into an infinite loop as there is no
% "\lastrule" to move the rule into the final box. I could just make
% "\hline" leave a code penalty, and put in the rule on the way back,
% but this would mean that every array with an "\hline" needs to be
% taken apart. I hope to make `most' arrays be possible without comming
% back up the array via "\lastbox". I could do something with
% "\leaders" which are removable, but for now, I just make "\hline" and
% "\hline\hline" just call "\hhline" with the appropriate argument.
% The "\hhline" from {\tt hhline.sty} does work, but needs extra options
% to deal with "&" etc, but here is a re-implementation, more in the
% spirit of this style.
%
%    \begin{macrocode}
\def\BAhline{%
  \noalign{\ifnum0=`}\fi
   \futurelet\@tempa\BA@hline}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@hline{%
  \ifx\@tempa\BAhline
    \gdef\BA@hline@@##1{\BAhhline{*{\BA@col@max}{=}}}%
  \else
    \gdef\BA@hline@@{\BAhhline{*{\BA@col@max}{-}}}%
  \fi
  \ifnum0=`{\fi}%
  \BA@hline@@}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BAhhline#1{%
  \omit
%    \end{macrocode}
% First set up the boxes used in "\leaders".
%    \begin{macrocode}
\global\setbox\BA@ddashbox=\BA@HHbox\BAarrayrulewidth\BAarrayrulewidth
\global\setbox\BA@dashbox=\hbox to \GC@six\BAarrayrulewidth{%
  \hss
  \vrule\@height\BAarrayrulewidth \@width\BAarrayrulewidth \@depth\z@
  \hss}%
%    \end{macrocode}
%
%    \begin{macrocode}
  \global\let\BA@strut\BA@strutB
  \global\BA@rulesepfalse
  \global\BA@uparttrue
  \BA@HHparse#1\BA@HHend}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@HHexp#1#2{\expandafter#1\csname aa\string#2\endcsname}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@HHparse{{\ifnum0=`}\fi\BA@HHparsex}
\def\BA@HHparsex#1{\BA@HHexp\aftergroup{#1}\ifnum0=`{\fi}}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def\BA@HHend{%
  \cr}
%    \end{macrocode}
%
%    \begin{macrocode}
\newbox\BA@dashbox
\newbox\BA@ddashbox
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def|{%
  \ifBA@rulesep\hskip\BAdoublerulesep\fi
  \global\BA@ruleseptrue
  \vrule\@width\BAarrayrulewidth
  \BA@HHparse}
%    \end{macrocode}
%
% ":" denotes a broken vertical rule, as in "hhline.sty". If the double
% dots \hbox{\leaders\hbox {\,:\,}\hskip3em} currently produced by
% \verb|"| turn out to be useful, it might be better to use ":" for
% them, and something else, perhaps "!" for this feature.
%    \begin{macrocode}
\BA@HHexp\def:{%
  \ifBA@rulesep\hskip\BAdoublerulesep\fi
  \global\BA@ruleseptrue
  \copy\BA@ddashbox
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def-{%
  \testBA@upart{}{&\omit\global\BA@uparttrue}%
  \leaders\hrule\@height\BAarrayrulewidth\hfil
  \global\BA@upartfalse
  \global\BA@rulesepfalse
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def.{%
  \testBA@upart{}{&\omit\global\BA@uparttrue}%
  \copy\BA@dashbox\xleaders\copy\BA@dashbox\hfil\copy\BA@dashbox
  \global\BA@rulesepfalse
  \global\BA@upartfalse
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def"{%
  \testBA@upart{}{&\omit\global\BA@uparttrue}%
  \setbox\z@\hbox to \GC@six\BAarrayrulewidth
       {\hss\copy\BA@ddashbox\hss}%
  \copy\z@\xleaders\copy\z@\hfil\copy\z@
  \global\BA@rulesepfalse
  \global\BA@upartfalse
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def={%
  \testBA@upart{}{&\omit\global\BA@uparttrue}%
  \copy\BA@ddashbox\xleaders\copy\BA@ddashbox\hfil\copy\BA@ddashbox
  \global\BA@rulesepfalse
  \global\BA@upartfalse
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def~{%
  \testBA@upart{}{&\omit\global\BA@uparttrue}%
  \hfill
  \global\BA@rulesepfalse
  \global\BA@upartfalse
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def#{%
  \ifBA@rulesep\hskip\BAdoublerulesep\fi
  \global\BA@ruleseptrue
  \vrule\@width\BAarrayrulewidth
  \BA@HHbox\BAdoublerulesep\BAdoublerulesep
  \vrule\@width\BAarrayrulewidth
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def{t}{%
  \rlap{\BA@HHbox\BAdoublerulesep\z@}%
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def{b}{%
  \rlap{\BA@HHbox\z@\BAdoublerulesep}%
  \BA@HHparse}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\BA@HHbox#1#2{\vbox{%
  \hrule \@height \BAarrayrulewidth \@width #1
  \vskip \BAdoublerulesep
  \hrule \@height \BAarrayrulewidth \@width #2}}
%    \end{macrocode}
%
%    \begin{macrocode}
\BA@HHexp\def&{&\omit\global\BA@uparttrue\BA@HHparse}
%    \end{macrocode}
%
%
%    \begin{macrocode}
\BA@HHexp\def{*}#1#2{%
 \count@=#1\relax
 \ifnum\count@>\z@
    \advance\count@\m@ne
    \edef\next##1{\noexpand\BA@HHparse##1*{\the\count@}{##1}}%
 \else
    \def\next##1{\BA@HHparse}%
 \fi
 \next{#2}}
%    \end{macrocode}
%
% \end{document}
\endinput