path: root/macros/lamstex/doc/wiz3.tex

\part Particular\\Constructions\\Allowing Labels\\ \noalign{\vskip 8pt}
{}\quad\hskip-3pt
 {\eighteenbfit and their associates}
\endpart


\chapter Displayed formulas\label{DF}\endchapter

The next part of \lamstex\ is concerned with displayed formulas and the
*\tag* mechanism;  it is the first place where we define *\thelabel@*
\dots. However,  numerous special considerations for
*\tag* are also required, and
sections~\Sref{LOCL} and~\Sref{maketag} are the only ones specifically related
to the *\label* mechanism.

\section{\label{pretend1}Invisibility}
An 
``invisible'' construction following a
display, in a case like
**
$$ 
 . . .
$$\label{...}" more text
**
or  even
**
$$
 . . . 
$$" \label{...}" more text
**
presents the same problem as an invisible construction following
*\noindent* (section~\Sref{ZZZ}): The *\prevanish@* sets *\saveskip@*
to *0pt* (even in the second case, because \tex\ ignores a space after the
*$$* that end a display).  Consequently, the *\postvanish@* does not skip
the space following the *\label{...}*, and we end up with an extra space
before `*more text*'.

There doesn't seem to be any correction that we can add to *\prevanish@*
to address this problem,
because there is apparently
 no way to tell when a \tex\ construction happens to appear
 immediately after a
display.
To get around this problem,  
whenever \lamstex\ encounters the *$$*
that begin a display, it calls a control sequence that 
reads in everything up to the closing
*$$* as its argument, and then  puts back both this argument and
 the closing *$$*, together with the proper compensating mechanism:
**
\everydisplay{\csname displaymath \endcsname}
\expandafter\def\csname displaymath \endcsname#1$${%
 #1$$\FNSS@\pretendspace@}
**
Note that here we need *\FNSS@* (section~\Sref{FIX}), not just
*\futurelet\next*, since we have to skip over any space after the final
*$$*.

We will  introduce the abbreviation
\C**
\def\FNSSP@{\FNSS@\pretendspace@} "8DEFFNSSP"8
**
not only because it will save numerous tokens, but also because at one point
(section~\Sref{VF}), 
it will be essential to have it. So we use
\C**
\everydisplay{\csname displaymath \endcsname}
\expandafter\def\csname displaymath \endcsname#1$${%
 #1$$\FNSSP@}
**

\small
The control sequence
**
\csname displaymath \endcsname
**
(compare *\csname align \endcsname* etc., as explained in *amstex.doc*)
shows up on the screen as
**
\displaymath" "0
**
so if a blank line occurs before the closing *$$*, we will
get the error message
**
! Paragraph ended before \displaymath" " was complete.
**
[If we defined `*\displaymath" *' to be *\long*, we would get
basically the same error message that \tex\ normally gives,
**
! Missing $ inserted.
** 
but it would  be presented
in a much more confusing way, since  ``context lines'',
involving the argument of `*\displaymath" *', would also be presented.]

\andsmall! Notice that a construction like \pagelabel{BADOUTER}
**
$$ . . .$$
\bye
**
will  eventually *\let\next=\bye* and then call *\pretendspace@*, which
uses the test *\ismember@\vanishlist@\next*. If *\bye* were *\outer* we would
get an error message
**
! Forbidden control sequence found while scanning use of \ismember@.
**

\andsmall! Unlike the situation for *\noindent* (section~\Sref{ZZZ}),
which is presumably used only when some text is going to follow, if we have
something like
**
A line of text.
$$
 . . .
$$
\label{...}

Another line of text.
**
the *\hskip-1pt\hskip1pt* added by the *\prevanish@* in *\label* will have
a dire effect: it will cause a {\it blank line\/} to be typeset after
the display. Since there will be *\baselineskip* glue before this
blank line, the next line, `Another line
of text.' will be separated from the display by too much space.

But there's really nothing that can be done about this.  Even in *plain*
\tex@, 
\setbox0\hbox{\it\, n\,}
**
A line of text.
$$
 . . .
$$
\write"box0{...}

Another line of text.
**
will create a spurious blank line after the display.  So users just have to
be warned against using ``invisible'' constructions after a display that ends
a paragraph.\pagelabel{WARNPAR}
\endsmall




Because of this (admittedly convoluted) approach to this (admittedly
rather special) problem, constructions that change category codes
won't work within a displayed formula. If that needs to be allowed
(as it sometimes was for the \lamstex~Manual), one can
**
\def\Math{\begingroup\everydisplay{}$$}
\def\endMath{$$\endgroup\futurelet\next\pretendspace@}
**
and then use *\Math...\endMath* instead of *$$...$$*. (We don't need
*\FNSS@* here, since there won't be a space token after the control
sequence *\endMath*.)\pagelabel{DDD}

Some people,
of course, might argue that this
is really the ``logical'' way to do things
anyway.
If such a definition were to be instituted permanently, then the basic
\amstex\ definition of *\tag* (see ({\bf A}) below) would have to be
changed, so that the argument of *\tag* is delimited by *\endMath* rather
than by *$$*. (When the \lamstex~Manual required literal mode in a
displayed formula with a *\tag*, the literal mode material was first
set in a box, which was then used within the usual *$$...\tag$$* 
construction.)
It should also be noted that the \amstex\ construction
*\align....\endalign* must read in *...* as an argument, in which
case category code changes within *...* will still be ignored. The same
is true of the \lamstex\ *\CD"allowbreak..."allowbreak\endCD* construction.
So, all in all, *\Math..\endMath* should be reserved for special effects.



\small There is a way of allowing category changes within
a display *$$...$$* if we are willing to change the category code of *$*
itself:
**
\let\dollar@=$
\newif\ifindisplay@
\catcode`\$=\active
"2
\def${\futurelet\next\dollar@@}
"2
\def\dollar@@{%
 \ifx\next$%
  \ifindisplay@
   \def\next@${\dollar@\dollar@\FNSSP@}%
"2
  \else
   \def\next@${\dollar@\dollar@\indisplay@true}%
  \fi
"2
 \else
  \let\next@=\dollar@
 \fi
 \next@}
**
(We never need to set *\indisplay@false*, since our
*\indisplay@true* occurs within the display, which \tex\ implicitly
encloses within a group.)  

I wanted to
avoid additional
category changes as much as possible, but perhaps this approach is
really preferable.

If such definitions were made,
we would also have to restate any definitions
that involved *$* as part of their syntax. For example, we would have
to restate \amstex's definition of *\tag*,
\Litbox0=**
\def\tag#1$${\iftagsleft@\leqno\else\eqno\fi 
 \maektag@#1\maketag$$}
**
$$\vcenter{\box0}\tag"\style{\bf A}"$$
at some point after  *$* has been made active. 

It would naturally also be sensible to replace any *$...$* combinations
in macros 
by *\dollar@...\dollar@* (many such appear in the \amstex\ macros, or
their replacements in \lamstex@, e.g., those in sections~\Sref{relax} and~
\Sref{relax2}).

 But a *$* in an *\xdef*
(e.g., as on page~\ref{Xdefs})
 would instead have to be replaced by *\noexpand$*. Moreover,
we would have to add `*\let$=\relax*' to *\noexpandtoks@* (or,
equivalently, state *\Nonexpanding$*).

\andsmall
One advantage of this approach, by the way, is that one could modify
the definition of *\dollar@@* to be:
**
\def\dollar@@{%
 \ifx\next$%
   . . . 
 \else
"2
  \ifhmode
   \def\next@{\saveskip@=\lastskip\unskip\/%
    \ifdim\saveskip@>0pt \hskip\saveskip@\fi\dollar@}%
  \else
"2
   \let\next@=\dollar@
  \fi
 \fi
 \next@}
**
With such a definition, something like
\setbox0\hbox{(1)}\setbox1\hbox{(2)}
**
"copy0  If $|x|<3$, then ...
**
would be treated as if it had been typed
**
"copy1  If\/ $|x|<3$, then ...
**
(On the other hand, input (2) would remain as is, since *\/* has no
effect except after a character or ligature.)

This arrangement is quite useful if the current
font is slanted or italic, as in the statement of
a *\claim*, because 
\medskip
\centerline{\tenpoint\cmtensl
  If\hskip3.3333pt $|x|<3$,\hskip3.3333pt then\hskip3.333pt\null
   \dots\null}
\medskip
\noindent looks much better if the italic correction is added:
\medskip
\centerline{\tenpoint\cmtensl
 If\/\hskip3.3333pt $|x|<3$,\hskip3.3333pt then\hskip3.3333pt\null
 \dots\null}
\medskip
\noindent
(See page~\ref{SAMP} for other examples  where the
italic correction seems called for.) I used this approach in the
style file for the Publish or Perish
{\it Mathematics Lecture Series}.


As far as I can tell, there is no other way of achieving this: *\everymath*
doesn't do any good, because a *$* puts a `*\mathon*' on the horizontal
list, and one can't remove it, in order to *\unskip*.
\endsmall


\section{Localizing labels\label{LOCL}} As already
mentioned in section~\Sref{bl},
 \lamstex\ uses
*\thelabel@*, \dots, for the values of *\ref*, \dots, *\pref* associated to a
 \<label\>,
 and any \lamstex\ construction that can be given a \<label\>
must define these control sequences. It turns out that these four components
will always have to be defined {\it globally}, because they have to be made
within a group beginning with *\noexpands@*---compare
page~\ref{plex}---even though we want *\thelabel@*, \dots, to be defined
only locally.
So \lamstex\ uses *\Thelabel@*, \dots,
*\Thelabel@@@@* for the four components that it defines globally,
 and then uses the
constructions
\setbox0\hbox{\,, \dots}
**
\let\thelabel@=\Thelabel@"box0
**
to create locally defined ones.  Since this is used so often, we abbreviate
it: 
\C**
\def\locallabel@{\let\thelabel@=\Thelabel@
 \let\thelabel@@=\Thelabel@@\let\thelabel@@@=\Thelabel@@@
 \let\thelabel@@@@=\Thelabel@@@@}
**



\section{{\tt\bs tag}\label{maketag}}
We introduce the counter *\tag@C* 
for *\tag*, and the initial values for the other associated things for
labelling: 
\C**
\newcount\tag@C
\tag@C=0
\let\tag@P=\empty
\let\tag@Q=\empty
\def\tag@S#1{{\rm(}#1\/{\rm)}}  "8tagit"8
\let\tag@N=\arabic
\def\tag@F{\rm}
**

As in the case of
 *\page@F* (page~\ref{pagef}), we use *\def\tag@F{\rm}* rather than
*\let\tag@F=\rm*, so that *\fontstyle\tag* will work correctly.
In *\tag@S*
we specified roman parentheses 
even if *\tag@F* is changed\pagelabel{BB}
(compare page~\ref{CCC}); of course, *\tag@S* could  be changed 
if we didn't want this.

Unlike the situation for *\page@N*, we can *\let\tag@N=\arabic*,
because *\tag@N* appears only in certain *\xdef*'s (page~\ref{Xdefsa}),
and then this value of *\tag@N* will simply disappear,\pagelabel{TAGATN}
resulting in a shorter string than if we kept *\arabic* unexpanded.

\medskip
\noindent{\bf NOTE: 
Nevertheless, we must use *\def* instead of *\let* for 
other numbering styles.} Note that *\newnumstyle* does this
(Chapter~\ref{acces}).

\medbreak
\amstex\ already defines the combination *\tag#1$$* 
to be *\leqno* or
*\eqno* followed by *\maketag@#1\maketag$$*, and we just have to
redefine *\maketag@* for \lamstex@, although the argument *#1* will
now have a rather different significance: in \amstex@, *#1* would be the
tag number that we want to use, but now *#1* could instead involve things
like *\label* or *\pagelabel*, or even *\Reset\tag* (to affect the next
*\tag*), as well as a ``quoted'' tag number
 *""...""*, again followed by things
like *\label* or *\pagelabel*. 


The action of *\maketag@* will
depend on whether or not it is followed by a *""*  for 
a ``quoted'' *\tag*. 
\C**
\def\maketag@{\futurelet\next\maketag@@}
**
 However, for reasons that will be explained
in section~\Sref{relax}, if
*\maketag@* is followed by *\relax""...""* we will want to get
the same result as if it were followed simply by *""...""*.
So we will call *\maketag@@@*
if *\maketag@* is followed by *""*  and *\maketag@@@@* if it is
followed by anything else other than *\relax*.
But if *\maketag@* is followed by *\relax*, we call a control sequence
that swallows this *\relax* and then reiterates the process:
\C**
\def\maketag@@{\ifx\next\relax
 \def\next@\relax{\futurelet\next\maketag@@}\else
 \ifx\next""\let\next@=\maketag@@@\else
 \let\next@=\maketag@@@@\fi\fi\next@}
**

The definition of *\maketag@@@@* (when *\tag* is not followed by a
*""*) illustrates the general scheme by which \lamstex\ deals with labels.
\list
\item
First we globally advance the *\tag* counter, *\tag@C*, by one.
\item\label{xdeft}
Then we *\xdef* the values of
 *\Thelabel@*, \dots, *\Thelabel@@@@*
appropriately, using the current values of *\tag@C*, *\tag@P*, etc.
\item
Then we use *\locallabel@* to (locally) set the values of
 *\thelabel@*, \dots,
*\thelabel@@@@*.
\item
Then we actually typeset the tag, using *\tag@S* for the style, and
in the font *\tag@F* (which will be irrelevant if we have *\TagsAsMath*).
\endlist

In step~\nref{xdeft} we will be doing something like
**
{\noexpands@
 \xdef\Thelabel@@@{\number\tag@C} 
 \xdef\Thelabel@{\tag@N{\Thelabel@@@}}
"2
 \xdef\Thelabel@@@@{\ifmathtags@$\tag@P\Thelabel@\tag@Q$\else
  \tag@P\Thelabel@\tag@Q\fi} 
 \xdef\Thelabel@@{\tag@S{\Thelabel@@@@}}
}
**

All of the \lamstex\ constructions that can be given a \<label\>
will define *\Thelabel@*, \dots, *\Thelabel@@@@* in much the same
way 
(with *\tag@C* replaced by the suitable
*\...@C* counter, etc.). Consequently, it is worth introducing an
abbreviation for the steps defining *\Thelabel@* and *\Thelabel@@*:
\C**
\def\xdefThelabel@#1{\xdef\Thelabel@{#1{\Thelabel@@@}}}
\def\xdefThelabel@@#1{\xdef\Thelabel@@{#1{\Thelabel@@@@}}}
**

Thus, we define *\maketag@@@@* by
\C**
\def\maketag@@@@#1\maketag@{\global\advance\tag@C by 1
"2
 {\noexpands@
  \xdef\Thelabel@@@{\number\tag@C}%
  \xdefThelabel@\tag@N  "8Xdefsa"8
"2
  \xdef\Thelabel@@@@{\ifmathtags@
   $\tag@P\Thelabel@\tag@Q$\else  "8Xdefs"8
   \tag@P\Thelabel@\tag@Q\fi}%
"2
  \xdefThelabel@@\tag@S
 }%
"2
 \locallabel@
 \hbox{\tag@F\thelabel@@}%
 #1}
**


\medskip

When *\tag* is followed by *""*, it might occur in constructions like
\setbox0\hbox{or}\setbox1\hbox{etc.,}
**
\tag ""\style{...}""  "box0  \tag ""\style{\pre 3}""   "box1
**
involving any of
*\pre*, *\post*, *\style*, or *\numstyle*.  In such
situations, *\pre* must be interpreted as *\tag@P*, etc., when the
tag is printed,
**
{\let\pre=\tag@P \let\post=\tag@Q
 \let\style=\tag@S \let\numstyle=\tag@N
 \hbox{\tag@F...}
**
Moreover, *\Thelabel@*, \dots, *\Thelabel@@@@* must
be suitably interpreted.


For this we use a routine that
 is also used by many other constructions:\pagelabel{ql}
\C**
\def\Qlabel@#1{{\noexpands@\xdef\Thelabel@@{#1}%
 \let\style=\empty\xdef\Thelabel@@@@{#1}%
 \let\pre=\empty\let\post=\empty\xdef\Thelabel@{#1}%
 \let\numstyle=\empty\xdef\Thelabel@@@{#1}}}
**
For example,
*\Qlabel@{#1}* for *\tag""#1""* will be used after we have
*\let\pre=\tag@P*,
etc. 
So
\list
\item *\Thelabel@@* (which is what *\Ref* is supposed to produce),
 will give 
*#1*, with *\pre* interpreted as *\tag@P*, etc.
\item *\Thelabel@@@@* (what
*\pref* is supposed to produce), will be the same, except *\style* will
be ignored if it appears, since *\pref* is supposed to produce what
*\Ref* produces, but without any of the *\style* formatting.
\item *\Thelabel@* (what *\ref* is supposed to produce), also ignores
*\pre* and *\post* if they appear.
\item
*\Thelabel@@@* (what *\nref* is supposed to produce), also ignores
*\numstyle* if it appears.
\endlist

\C**
\def\maketag@@@""#1""#2\maketag@{%
 {\let\pre=\tag@P \let\post=\tag@Q
  \let\style=\tag@S \let\numstyle=\tag@N
  \hbox{\tag@F#1}%
  \noexpands@
  \Qlabel@{#1}%
  }%
 \locallabel@
 #2}
**

\small It might seem  unlikely that any one would use a *\label*
for a ``quoted'' *\tag*, since then the tag is already known.  
But the label
mechanism is provided nevertheless,
 and might even be of some use.  For example,
**
$$ ... \tag""\style{\pre A}"" \label{tagA}$$
**
might be used to produce the tag `(3.A)', where the user wouldn't know
what  precedes the `A'.
  In this case, *\Ref{tagA}*
  or *\pref{tagA}*
would be needed to print `(3.A)' or `3.A' in the text.

\andsmall!
Because of the *\xdef*'s in *\Qlabel*, any ``quoted'' number *""...""*
following
 *\tag* (or any other construction that allows a \<label\>) must contain
only things that can safely be used in *\xdef*'s when *\noexpands@*
is in force. 

As a far-fetched example,
in this manual Chapter~\ref{LBL1} was labelled `*STARTLABEL*' and
Chapter~\ref{RAF} was labelled `*ENDLABEL*'. If the next chapter were
commentary on these chapters, and for some reason we wanted this commentary
to be called 
\bigskip
\centerline{\bf Chapter \ref{LBL1}$'$--\ref{RAF}$'$. Remarks on Labels
 and Cross References}
\bigskip\noindent
we wouldn't be able to type
**
\chapter ""\nref{STARTLABEL}$'$--\nref{ENDLABEL}$'$"" Remarks ...
**
Instead, we would have to use something like
**
\Evaluatenref{STARTLABEL}
\edef\startlabel{\Nref}
\Evaluatenref{ENDLABEL}
\edef\endlabel{\Nref}
\chapter ""\startlabel$'$--\endlabel$'$"" Alternate ...
**

In such a case, we might even use a *\label* with this ``quoted'' number,
**
\chapter  ""...""  . . . \label{...} \endchapter
**
in order to refer to this new chapter later on.
\endsmall




\section{{\tt\bs align}\label{relax}} This section presumes familiarity with
\amstex's *\align* construction (see *amstex.doc*).
Before considering this
 construction in detail, we need to consider one aspect of
 the general scheme.

\setbox0\hbox{\<formula$_{\text1}$\>}
\setbox1\hbox{\<formula$_{\text2}$\>}
\setbox2\hbox{\<formula number\>}
When \amstex\ sees something like
**
\align 
"copy0 & "copy1 \tag "box2 \\
 . . .
**
the *\align* 
is an *\halign* whose preamble contains three *&*'s,
of the form
{\advance\litindent-10pt
**
\halign{ ...#...  &  ...#...  &  ... \maketag@#\maketag@ ... \cr
 . . .
**
Within the *\align*, 
a *\tag* is simply interpreted as an *&*.}
But this means that
after a *\tag*, \tex\ will examine the next token, {\it
expanding if necessary},
to see if a *\noalign* or *\omit* follows ({\it The \tex book}, page
~240). So if
**
"copy0  & "copy1 \tag ""..."" \\
**
appears, the first *""* {\it will already be
expanded out\/} to *\futurelet\next\quote@*  before being submitted to
*\maketag@*.  Consequently, *\maketag@* will think that the next
token is *\futurelet*, rather than *""*\,!  

To get around this, we will instead have *\tag* interpreted as *&\relax*,
to insure that the *""* is not expanded out.  Thus, *\tag""...""* will
lead to
**
\maketag@\relax""...""\maketag@
**
and  we have already
arranged for this to give the same result as if the *\relax* weren't there
(section~\Sref{maketag}).

\def\p.{\vphantom{p}}

The definition of *\tag* for *\align* is made by \amstex's control
sequence *\align@*, which is now redefined to include the *\relax*,
together with other changes that will be explained later.
\C**
\def\align@{\inalign@true\inany@true
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \def\tag{\global\tag@true\ifnum\and@=0 "8deftag"8
  \def\next@{&"9\omit"p."9","9\global\rwidth@=0pt"9&"9\relax"p."9}\else
   \def\next@{&"9\relax"9}\fi\next@}%
 \iftagsleft@\def\next@{\csname align \endcsname}\else
  \def\next@{\csname align \space\endcsname}\fi\next@}
**

Still further changes to the rest of the
\amstex\ *\align*  construction itself are also required, because
the remainder of this construction
first calls *\measure@*
to measure all the formulas, before actually setting them.  Even in \amstex@,
this can produce problems: if a user puts a constructed
*\box* within an *\align*, it
will be emptied out by *\measure@* and hence produce nothing at all when the
typesetting is done (this means  that the user needs
 to use *\copy* rather than *\box*).

 In \lamstex@,
the problem is that
we want to  ignore any *\Reset\tag* and *\Offset\tag* constructions
during the *\measure@*, since these globally change the *\tag* counter,
and we don't want to do that twice
 (*\Reset* and *\Offset* are described in Chapter~\ref{acces}).

We introduce a special abbreviation for a more general construction that
disables *\Offset* and *\Reset* (but keeps them invisible):
\C**
\def\noset@{\def\Offset##1##2{\prevanish@\postvanish@}%
 \def\Reset##1##2{\prevanish@\postvanish@}}
**

Now we  redefine *\measure@* so that *\noset@* is used:
\C**
\def\measure@#1\endalign{%
 \global\lwidth@=0pt \global\rwidth@=0pt
 \global\maxlwidth@=0pt \global\maxrwidth@=0pt 
 \global\and@=0
"2
 \setbox0=\vbox
  {"9\noset@"9\everycr{\noalign{\global\tag@false
  \global\and@=0}}\Let@
"2
  \halign{\setbox0=\hbox{$\m@th\displaystyle{\@lign##}$}%  "8measure"8
   \global\lwidth@=\wd0
   \ifdim\lwidth@>\maxlwidth@ \global\maxlwidth@=\lwidth@\fi
   \global\advance\and@ by 1
"2
   &\setbox0=\hbox{$\m@th\displaystyle{{}\@lign##}$}%
    \global\rwidth@=\wd0
   \ifdim\rwidth@>\maxrwidth@ \global\maxrwidth@=\rwidth@\fi
   \global\advance\and@ by 1
   &\Tag@\eat@{##}\crcr#1\crcr}}%
 \totwidth@=\maxlwidth@ \advance\totwidth@ by \maxrwidth@}
**
(Here *\eat@* from \amstex\ is defined by *\def\eat@#1{}*, see
section~\Sref{AC}.) The assignments of *\lwdith@*, \dots\  at
the beginning of the definition don't really have to be *\global*, but
they do have to be *\global* later in the definition, so we make them
*\global* at all times (compare section~\Sref{LANDG}).

Now, in the definition of `*\align" *' and `*\align" " *' (called by
*\align*), after we *\measure@*
 we can allow *\Offset* and *\Reset* to have their
usual meanings, but there is a different problem. When we have something
like
\setbox1\hbox{\<formula$_{\text1}$\>}\setbox2\hbox{\<formula$_{\text2}$\>}
**
"box1 & "box2 \Offset\tag0 \newpost\tag{$'$} \tag \\
**
the new values of *\tag@C* and
*\tag@P* created by *\Offset* and *\newpost* are processed as
part of \<formula$_{\text2}$\> (since the *&* that ends this formula is supplied
by the *\tag*).  But the new value  of *\tag@P*
is created only {\it locally}, so it will not
be known when *\tag* has to do its work. To get around this problem,
 we need to pass such information
through by means of two new globally defined
 control sequences, *\tag@P@* and *\tag@Q@*, and we make a special
abbreviation for this:
\C**
\def\prepost@{\global\let\tag@P@=\tag@P
 \global\let\tag@Q@=\tag@Q}
**

We also have an abbreviation for the construction that (locally) sets
*\tag@P* and *\tag@Q* to the globally defined *\tag@P@* and
*\tag@Q@*:
\C**
\def\reprepost@{\let\tag@P=\tag@P@\let\tag@Q=\tag@Q@}
**

Now we redefine  *\align" *  and *\align" " *
from \amstex\ using *\prepost@* within the
formulas, and using *\reprepost@* when the formula number is
being printed; note that we use *\prepost@* at the {\it end\/} of each
formula, so that any *\newpre* or *\newpost* will have been discovered,
but *\reprepost@* at the {\it beginning\/} of each formula number.
(These maneuvers aren't needed for *\measure@*, since we simply *\eat@*
each formula number.)


First comes `*\align" " *':
\C**
\expandafter\def\csname align \space\endcsname#1\endalign
 {\measure@#1\endalign\global\and@=0
"2
 \ifingather@\everycr{\noalign{\global\and@=0}}\else
  \displ@y@\fi
"2
 \Let@\tabskip\centering@
"2
 \halign to\displaywidth
  {\hfil\strut@\setbox0=\hbox{$\m@th\displaystyle
   {\@lign##"9\prepost@"9}$}%
  \box0 \global\advance\and@ by 1
  \tabskip\z@skip&
"2
  \setbox0=\hbox{$\m@th\displaystyle{{}\@lign##"9\prepost@"9}$}%
  \global\rwidth@=\wd0 
  \box0 \hfil \global\advance\and@ by 1
  \tabskip\centering@ & 
"2
   \setbox0=\hbox{\@lign\strut@"9\reprepost@"9
   \maketag@##\maketag@}%
"2
  \dimen@=\displaywidth \advance\dimen@ by -\totwidth@
  \divide\dimen@ by 2 \advance\dimen@ by \maxrwidth@
  \advance\dimen@ by -\rwidth@
"2
  \ifdim\dimen@<2\wd0 
   \llap{\vtop{\normalbaselines\null\box0}}%
"2
  \else\llap{\box0}\fi
"2
  \tabskip\z@skip
  \crcr#1\crcr
  \black@\totwidth@}}
**

Note that in a formula like
\setbox0\hbox{\<formula\>}
**
\align 
 . . .
"copy0 \newpre\tag{a}\tag ... \\
 . . .
**
where there is a
 line without any *&*, the definition of *\tag* in *\align@*
(page~\ref{deftag})
means that this line will be interpreted as
**
"copy0 \newpre\tag{a}& "9\omit"p."9","9\global\rwidth@=0pt"9 &\relax
 \reprepost@ \maketag@...\maketag@ \cr
**
 The *\prepost@* 
in the first part of the
preamble for *\align* globally defines *\tag@P@* to
be `*a*', and the *\reprepost@* then makes
*\tag@P*  properly defined for 
 *\maketag@*.  But
 if the *\omit* were not inserted, then the *\prepost@*
for the {\it second\/} part of the preamble would globally redefine
*\tag@P@* to be the default value of *\tag@P*, so that the new value
would not be properly
propagated to the *\maketag@* part of the preamble.

Since we've added the *\omit*,
we also have to add *\global\rwidth@=0pt*, which would normally be set
by an empty formula.  The extra clause
**
\ifdim\rwidth@>\maxrwidth@ \global\maxrwidth@=\rwidth@\fi
**
appearing in the definition of *\measure@* doesn't have to be duplicated,
since it would be inoperative for an empty formula.

The *\tabskip\centering@* also appears after the
first *&* in the preamble, but we don't have to worry about that: once
the preamble has been read, the various *\tabskip* glues are determined, and
they remain the same for any row, even those that have *\omit*'s in them.

(The `*\global\advance\and@ by 1*' will also be omitted because of the
*\omit*, but this is irrelevant, since the current value 
of *\and@* has already been used to determine properly the meaning
of *\tag*.)


The re-definition of `*\align" *' is  exactly analogous:
\C**
\expandafter\def\csname align \endcsname#1\endalign
 {\measure@#1\endalign\global\and@=0
"2
 \ifdim\totwidth@>\displaywidth\let\displaywidth@=\totwidth@
  \else\let\displaywidth@=\displaywidth\fi
"2
 \ifingather@\everycr{\noalign{\global\and@=0}}\else
  \displ@y@\fi
"2
 \Let@\tabskip\centering@
 \halign to\displaywidth
  {\hfil\strut@\setbox0=\hbox{$\m@th\displaystyle
    {\@lign##"9\prepost@"9}$}%
   \global\lwidth@=\wd0 \global\lineht@=\ht0
   \box0 \global\advance\and@ by 1
  \tabskip\z@skip&\setbox0=\hbox{$\m@th\displaystyle{{}\@lign
    ##"9\prepost@"9}$}%
  \ifdim\ht0>\lineht@ \global\lineht@=\ht0 \fi
  \box0 \hfil \global\advance\and@ by 1
  \tabskip\centering@ & \kern-\displaywidth@
  \setbox0=\hbox{\@lign\strut@"9\reprepost@"9
   \maketag@##\maketag@}%
  \dimen@=\displaywidth \advance\dimen@ by -\totwidth@
  \divide\dimen@ by 2 \advance\dimen@ by \maxlwidth@
  \advance\dimen@ by -\lwidth@
  \ifdim\dimen@<2\wd0 
   \rlap{\vbox{\normalbaselines\box0 \vbox to\lineht@{}}}%
  \else\rlap{\box0}\fi
  \tabskip\displaywidth@\crcr#1\crcr
  \black@\totwidth@}}
**
The extra clause 
**
\ifdim\ht0>\lineht@ \global\lineht@=\ht0 \fi
**
appearing in the second part of the preamble
doesn't have to be added to the definition of *\tag* in
*\align@*, along with the *\omit*, since
it would always be inoperative for a blank formula.

\section{\CS{alignat} and \CS{xalignat}\label{relax2}}
This section presumes familiarity with \amstex's *\alignat* and
*\xalignat* constructions, which also require changes (no changes
are required for *\xxalignat*, which doesn't allow *\tag*'s).

*\alignat* and *\xalignat* process their arguments twice, like
*\align*, although the initial processing provides much less information.
In these constructions a *\tag* might even end up
overlapping a formula,
but
at least a black box is produced
 at the end, to indicate such overlapping
(which is easy to miss when proofreading). The initial processing
is done with empty *\tag*'s, but
as if the *\tag*'s were set at their
minimum distance from the formula (i.e., at a distance equal to their
widths), and the result is
saved in *\box\savealignat@*. During the second processing
 the only role played by this box
is in the
**
\black@{\wd\savealignat@}
**
that is appended after the *\halign*, to give a black box if the whole
construction turns out to be too wide.

Unlike the situation for *\align*, where we specify the preamble for
the first process in *\measure@*,
the \amstex\  routine *\attag@* is used  to produce  
the preambles for both processes of *\alignat* and *\xalignat*,
 using a flag *\ifmeasuring@* to
determine whether we are making a preamble for the first process or for
the second,
 as well as the flag *\ifxat@* to determine
whether we are making preambles for *\alignat* or for *\xalignat*.

The definition of *\attag@* from \amstex\  has to be modified 
in the same way as the definitions of *\measure@*, `*\align" *' and
`*\align" " *', by inserting *\prepost@* and *\reprepost@* in the 
appropriate places:
\C**
\def\attag@#1{\let\Maketag@=\maketag@\let\TAG@=\Tag@
 "9\let\Prepost@=\prepost@"9","9\let\Reprepost@=\reprepost@"9
 \let\Tag@=\relax\let\maketag@=\relax
 "9\let\prepost@=\relax"9","9\let\reprepost@=\relax"9
"2
 \ifmeasuring@
 \def\llap@##1{\setbox0=\hbox{##1}\hbox to2\wd0{}}%
 \def\rlap@##1{\setbox0=\hbox{##1}\hbox to2\wd0{}}%
 \else\let\llap@=\llap\let\rlap@=\rlap\fi
"2
 \toks@={\hfil\strut@
  $\m@th\displaystyle{\@lign\the\hashtoks@"9prepost@"9}$%
  \tabskip\z@skip\global\advance\and@ by 1 &
  $\m@th\displaystyle{{}\@lign\the\hashtoks@"9\prepost"9}$\hfil
  \ifxat@\tabskip\centering@\fi\global\advance\and@ by 1}%
"2
 \iftagsleft@
  \toks@@={\tabskip\centering@&\Tag@\kern-\displaywidth
   \rlap@{\@lign"9\reprepost@"9
    \maketag@\the\hashtoks@\maketag@}%
   \global\advance\and@ by 1 \tabskip\displaywidth}\else
  \toks@@={\tabskip\centering@&\Tag@
   \llap@{\@lign"9\reprepost@"9\maketag@
   \the\hashtoks@\maketag@}\global\advance\and@ by 1 
  \tabskip\z@skip}\fi
"2
 \atcount@#1\relax\advance\atcount@ by -1
 \loop\ifnum\atcount@>0
 \toks@=\expandafter{\the\toks@&\hfil
  $\m@th\displaystyle{\@lign\the\hashtoks@"9\prepost@"9}$%
  \global\advance\and@ by 1 \tabskip\z@skip&
  $\m@th\displaystyle{{}\@lign\the\hashtoks@
    "9\prepost@"9}$\hfil
 \ifxat@\tabskip\centering@\fi\global\advance\and@ by 1}%
  \advance\atcount@ by -1
 \repeat
"2
 \xdef\preamble@{\the\toks@\the\toks@@}%
 \xdef\preamble@@{\preamble@}%
 \let\maketag@=\Maketag@\let\Tag@=\TAG@
 "9\let\prepost@=\Prepost@"9","9\let\reprepost@=\Reprepost@"9}
**

Now we must modify 
the definition of `*\alignat" *', which is called by *\alignat*, 
in several ways:
\list
\item *\tag* must mean *&\relax*;
\item More generally, *\tag* must mean *&\omit&\relax* if used
when one *&* has been omitted, or *&\omit&\omit&\relax* if
used when two *&*'s have been omitted, etc. 
\endlist


Fortunately, when we define *\tag* for *\alignat* and *\xalignat*
we don't
have to worry about additional things appearing in the preamble,
as was necessary for *\align*.
On the other hand,  whereas the first pass for *\align* simply 
had *\eat@{#}* in the preamble for the *\tag* part, *\alignat* and
*\xalignat* have *\maketag@#\maketag@*. 

\keepitem
\list
\item
This means that the tag counter
*\tag@C* will be incremented during the first pass. So we will first
store the current value of *\tag@C* in a new counter *\tag@CC*, and
then restore *\tag@C* to this value before doing the second pass.

\item
Moreover, we want to disable *\label* during the first pass (or we will
be using the same \<label\> twice during the second pass,
 and get an error message).

We could use *\let\label=\eat@* for this purpose, but we will instead call
*\unlabel@*, defined by
**
\def\unlabel@{\def\label##1{\prevanish@\postvanish@}%
 \def\pagelabel##1{\prevanish@\postvanish@}}
**
since this construction will be needed later anyway (section~\Sref{FMTC}).
\endlist


\C**
\def\unlabel@{\def\label##1{\prevanish@\postvanish@}%
 \def\pagelabel##1{\prevanish@\postvanish@}}
\newcount\tag@CC
"slip
\expandafter\def\csname alignat \endcsname#1#2\endalignat
 {\inany@true\xat@false
"2
 \gdef\tag{\global\tag@true
  \count@=#1\relax\multiply\count@ by 2 
    "9\advance\count@ by -1"9
  "9\gdef\tag@{&}"9\loop\ifnum\count@>\and@
  \xdef\tag@{&"9\omit"9\tag@}\advance\count@ by -1
  \repeat\tag@"9\relax"9}%
"2
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y@\measuring@true"9\tag@CC=\tag@C"9
"2
"slop
 \setbox\savealignat@=\hbox{"9\noset@"9","9\unlabel@"9%
   $\m@th\displaystyle\Let@
  \attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
"2
 \measuring@false
 \Let@\attag@{#1}"9\tag@C=\tag@CC"9
 \tabskip\centering@\halign to\displaywidth
  {\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
**

Similar changes are made for `*\xalignat" *':
\C**
\expandafter\def\csname xalignat \endcsname#1#2\endxalignat
 {\inany@true\xat@true
"2
 \def\tag{\global\tag@true
  \count@=#1\relax\multiply\count@ by 2 
    "9\advance\count@ by -1"9
  "9\def\tag@{&}"9\loop\ifnum\count@>\and@
  \xdef\tag@{&"9\omit"9\tag@}\advance\count@ by -1 
 \repeat\tag@"9\relax"9}%
"2
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y@\measuring@true"9\tag@CC=\tag@C"9
"2
"slop
 \setbox\savealignat@=\hbox{"9\noset@"9","9\unlabel@"9%
  $\m@th\displaystyle\Let@
  \attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
"2
 \measuring@false
 \Let@\attag@{#1}"9\tag@C=\tag@CC"9
 \tabskip\centering@\halign to\displaywidth
 {\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
**

\section{\tt\bs gather}
Finally, the \amstex\ construction *\gather*
also has a *\def\tag{&}* clause,
which  must be changed to *\def\tag{&\relax}*:
\C**
\def\gather{\relax\ifmmode\ifinner
 \def\next@{\onlydmatherr@\gather}\else
 \ingather@true\inany@true"9\def\tag{&\relax}"9%
 \vspace@\allowdisplaybreak@\displaybreak@\intertext@
 \displ@y\Let@
 \iftagsleft@\def\next@{\csname gather \endcsname}\else
  \def\next@{\csname gather \space\endcsname}\fi\fi
 \else\def\next@{\onlydmatherr@\gather}\fi\next@}
**


\chapter New counters\label{NEWC}\endchapter

Having seen how *\tag* deals with *\label*, we are now in a position
to consider \lamstex's *\newcounter*
construction for creating a new counter.
\footnote{In  version *1*  of \lamstex@, this was called
*\counter*, because *\newcounter* seemed too close to \tex's
 *\newcount* primitive for comfort, but it actually seems unlikely
that anyone (except perhaps \tex perts!)\ %
would mistakenly type *\newcount* instead of *\newcounter*,
and *\newcounter* fits much better with all the other \lamstex\  names.}


\section{{\tt\bs newcounter}\label{CNT}}
We introduce a very frequently used abbreviation
\C**
\def\exstring@{\expandafter\eat@\string} "8EXSTRING"8
**
where *\eat@* from \amstex\ is simply defined (section~\Sref{AC}) as 
**
\def\eat@#1{}
**
Note that if *#1* is a control sequence, say *\tag*, then something like
**
\csname\exstring@#1@C\endcsname
**
just becomes *\tag@C* (the *\eat@* eats the *\* at the beginning
of *\string\tag*).


The first thing *\newcounter\foo* will do is to
**
\define\foo{}
**
to give an error message if *\foo* has already been defined.


Since *\foo\label{*\<label\>*}* is supposed to work, albeit not by the
general mechanism for *\label*'s, *\foo* needs to be defined in terms of
a *\futurelet*:
**
\def\foo{\futurelet\next\foo@Z}
**
We use *\foo@Z* because no control sequence from \amstex\ or \lamstex\
ends with *@Z*.

The name `*\foo@Z*' will be created with
**
\csname\exstring@\foo @Z\endcsname
**
and to define *\foo* we use the same strategy that was used 
in section~\Sref{ATDEF}:
**
\edef\next@{\def\noexpand\foo{\futurelet\noexpand\next
 \csname\exstring@\foo @Z\endcsname}}
\next@
**

Now  *\foo@Z* should increase the counter *\foo@C* by 1, and print
the properly formatted number, in the proper font:
**
\def\foo@Z{\global\advance\foo@C by 1
 {\foo@F\foo@S{\foo@P{\foo@N{\number\foo@C}}\foo@Q}}
**
(for the moment, let's not worry about how *\foo@C*, \dots are to
be defined). 

Moreover, if *\foo*
 is followed by *\label{...}*, then we need a way of getting this
*\label{...}* properly recorded.
To do this, we can simply use the code
**
{\noexpands@\xdef\Thelabel@{...}...}
{\locallabel@\label{...}}
**
The *\label* in the second
 group will make sense, because the *\locallabel@*
will define *\thelabel@*; this *\label* will thus write to the
*.lax* file, and append to *\laxlist@*.
After the group containing *\locallabel@*
is finished, however, any values
of *\thelabel@*, \dots will be restored to their previous values, 
so another *\label* will
 give an error message (unless
 *\foo* happens to appear within some other construction that itself
allows a
*\label*).
**
\def\foo@Z{\global\advance\foo@C by 1
 {\foo@F\foo@S{\foo@P{\foo@N{\number\foo@C}}\foo@Q}}%
 \ifx\next\label
  \def\next@\label##1{%
   {\noexpands@
   \xdef\Thelabel@{...}...\xdef\Thelabel@@@@{....}}%
   {\locallabel@\label{##1}}}%
 \else
  \let\next@=\relax
 \fi
 \next@}
**

Of course, these *##*'s will all have to be *####*'s, since this
whole definition appears within the definition of *\newcounter*.
But that's only a minor problem.
We are also going to have to treat this whole thing with an
*\edef\next@*  (compare page~\Sref{ADDCSNAME}),
 so it is going to look pretty complicated
(in particular, now our *####*'s will all have to be *########*'s, since
an *\edef* changes *##* to *#*).

The control sequence *\foo@C* will be specified within this *\edef\next@*
as
**
\csname\exstring@\foo @C\endcsname
**
and similarly for *\foo@P*, \dots. In all cases, \tex\ will make these
equivalent to *\relax*, so they will not be expanded further.

Finally, after all this,
we can create *\foo@C*, \dots with their proper meanings,
**
\expandafter\newcount@\csname\exsting@\foo@ C\endcsname
\expandafter\let\csname\exstring@\foo @N\endcsname=\arabic
. . .
**
Note that here we use *\newcount@* (section~\Sref{NEWNEW}),
 since it appears within a definition,
and thus might be used after *\alloc@* has been returned to its old
definition.\pagelabel{NWNW}
Note also that  we use *\let* rather than *\def*, just as with
*\tag* (page~\ref{TAGATN}),
 but *\def* would be required for anything other than
*\arabic* (and is supplied whenever *\newnumstyle* is used).



In the following
 code for *\newcounter*, note that *\noexpand* is required before 
*\number*, *\ifx*, *\else* and *\fi* because these primitives are
``expanded'' in an *\edef*:
\C**
\def\newcounter#1{\define#1{}%
 \edef\next@{\def\noexpand#1{\futurelet
  \noexpand\next\csname\exstring@#1@Z\endcsname}}\next@
"2
 \edef\next@{\def\csname\exstring@#1@Z\endcsname
  {\global\advance\csname\exstring@#1@C\endcsname by 1
"2
  {\csname\exstring@#1@F\endcsname
   \csname\exstring@#1@S\endcsname{\csname\exstring@
   #1@P\endcsname\csname\exstring@#1@N\endcsname
   {\noexpand\number\csname\exstring@#1@C\endcsname}%
   \csname\exstring@#1@Q\endcsname}}%
"2
  \noexpand\ifx\noexpand\next\noexpand\label
"2
   \def\noexpand\next@\noexpand\label########1{%
    {\noexpand\noexpands@
"2
    \xdef\noexpand\Thelabel@
     {\csname\exstring@#1@N\endcsname
     {\noexpand\number\csname\exstring@#1@C\endcsname}}%
"2
    \xdef\noexpand\Thelabel@@@
     {\noexpand\number\csname\exstring@#1@C\endcsname}%
"2
    \xdef\noexpand\Thelabel@@
     {\csname\exstring@#1@S\endcsname
     {\csname\exstring@#1@P\endcsname
     \csname\exstring@#1@N\endcsname
     {\noexpand\number\csname\exstring@#1@C\endcsname}%
     \csname\exstring@#1@Q\endcsname}}%
"2
    \xdef\noexpand\Thelabel@@@@
     {\csname\exstring@#1@P\endcsname
     \csname\exstring@#1@N\endcsname
     {\noexpand\number\csname\exstring@#1@C\endcsname}%
     \csname\exstring@#1@Q\endcsname}}%
"2
    {\noexpand\locallabel@\noexpand\label{########1}}%
"2
   \noexpand\else\let\noexpand\next@=\relax\noexpand\fi
   \noexpand\next@}}%
 \next@
"2
 \expandafter\newcount@\csname\exstring@#1@C\endcsname
"2
 \expandafter\let\csname\exstring@#1@N\endcsname=\arabic
"2
 \expandafter\def\csname\exstring@#1@S\endcsname##1{##1\/}%
"2
 \expandafter\let\csname\exstring@#1@P\endcsname=\empty
"2
 \expandafter\let\csname\exstring@#1@Q\endcsname=\empty
"2
 \expandafter\def\csname\exstring@#1@F\endcsname{\rm}%
 }
**



\section{{\tt\bs usecounter}} To follow through the definition of
*\usecounter*, it helps to consider a specific case, like the following
simplification of an example from the \lamstex~Manual (page~78):
\Litbox0=**
\usecounter\exno\example#1{{\it Example #1.}" }
**
$$
\box0 \tag"\style{\hbox{\lower2pt\hbox{\bf\ast}}}"
$$
Here we want
\setbox1\hbox{*\example*}
\setbox2\hbox{*{\it Example \exno.}" *}
\setbox3\hbox{*\example""...""*}
\setbox4\hbox{*{\it Example {\exno@F_",_",_",...}.}" *}
\setbox5\hbox{*\example\label{...}*}
\setbox6\hbox{*{\it Example \exno\label{...}.}" *}
$$
\centerline{\vbox{\advance\baselineskip\jot
\halign{#\hfil&\ \ to give\ \ #\hfil\cr
\copy1&\copy2\cr
\copy3&\copy4\cr
\copy5&\copy6\cr}}}
$$
where *_",_",_* stands for 
**
\let\pre=\exno@P ... \let\numstyle=\exno@N
**
In the third case, the combination
*\exno\label{...}* will itself take care of printing
the right number, and labelling it.


Page 79 of the \lamstex~Manual suggest that the user should modify 
\style\tag{\hbox{\lower2pt\hbox{\bf\ast}}} to read
**
\usecounter\exno\example#1{{\it Example #1.}" \ignorespaces}
**
But that's silly---it's clearly better to have *\usecounter* automatically
add
the
*\ignorespaces*. Actually, we really need to add *\FNSSP@*
(page~\ref{DEFFNSSP}) 
for cases where *" * doesn't appear at the end of the definition, but
an invisible construction, like *\pagelabel*, occurs after the use of
the construction being defined.

So we really want
\setbox1\hbox{({\bf E1}) *\example*}
\setbox2\hbox{*{\it Example \exno.}" \FNSSP@*}
\setbox3\hbox{({\bf E2}) *\example""...""*}
\setbox4\hbox{*{\it Example {\exno@F_",_",_",...}.}" \FNSSP@*}
\setbox5\hbox{({\bf E3}) *\example\label{...}*}
\setbox6\hbox{*{\it Example \exno\label{...}.}" \FNSSP@*}
$$
\leftline{\vbox{\advance\baselineskip\jot
\halign{#\hfil\cr
\copy1\cr
\hbox{\hskip30pt to give \copy2}\cr
\copy3\cr
\hbox{\hskip30pt to give \copy4}\cr
\copy5\cr
\hbox{\hskip30pt to give\copy6}\cr}}}
$$

 \medskip

Clearly, *\example* is going to involve a *\futurelet*, so we expect
that *\usecounter\exno\example* should expand out to something like
**
\def\example{\futurelet\next\exno@@Z}
 . . .
 . . .
**
[Note that the
 subsidiary control sequence *\exno@@Z* is written entirely in terms of
*\exno*. So if we later type
**
\usecounter\exno\otherexample
**
*\otherexample* will then be defined exactly the same way, as
**
\futurelet\next\exno@@Z
**
---though of course *\exno@@Z* will now end up being defined differently.
\pagelabel{ZZ}
This is a reasonable arrangement, since the same counter *\exno* shouldn't
be allowed for two different constructions.]


In the use
**
\usecounter\exno\example#1{{\it Example #1.}" }
**
we also have to somehow capture the \<parameter text\>
and \<replacement text\>.
This suggests
that *\usecounter\exno\example* should expand out as
**
\def\example{\futurelet\next\exno@@Z}
 . . .
 . . .
\def\exno@@Z@
**
where the *\def\exno@@Z@* at the end will then swallow up the
subsequent \<parameter text\> and \<replacement text\>, and thus,
in our case,
\setbox1\hbox{*\def\exno@@Z@#1{{\it Example #1.}" *}
$$\overfullrule=0pt\boxed{\box1}$$

Once we have *\exno@@Z@*,
it is easy to say what *\exno@@Z* should do:

\Pitem If *\next* is neither *\label* nor *""*, then ({\bf E1}) we want
**
{\it Example \exno.}" \FNSSP@
**
which can obtained as
**
\exno@@Z@{\exno}\FNSSP@
**

\pitem
If *\next* is *""*, so that we have *\example""...""*, then ({\bf E2})
 we
want 
**
{\it Example {\exno@F \let\pre=\exno@P ...
 \let\numstyle=\exno@N ... }.}" \FNSSP@
**
which can be obtained as
**
\exno@@Z@{{\exno@F \let\pre=\exno@P ...
 ...\let\numstyle=\exno@N ...}}\FNSSP@
**

\pitem
If *\next* is *\label*, so that we have *\example\label{...}*,
then ({\bf E3}) we want
**
{\it Example \exno\label{...}.}" \FNSSP@
**
which can be obtained as
**
\exno@@Z@{\exno\label{...}}\FNSSP@
**

Thus, we want *\usecounter\exno\example* to expand as
**
\def\example{\futurelet\next\exno@@Z}
\def\exno@@Z{\ifx\next\label
 \def\next@\label##1{\exno@@Z@
  {\exno\label{##1}\FNSSP@}
 \else
 \ifx\next""\def\next@""##1""{\exno@@Z@
  {{\exno@F_",_",_##1}}\FNSSP@}
 \else
 \def\next@{\exno@@Z@{\exno}\FNSSP@}
 \fi\fi\next@}
\def\exno@@Z@
**


The general definition of *\usecounter*
has  the same features as that for *\newcounter*,
with several *\edef\next@*'s. But there are some complications.

First, we need a way of inserting the 
**
\exno@F
**
which we will specify as
**
\csname\exstring@#1@F\endcsname
**
except that after this is expanded to *\exno@F*, which is now {\it not\/}
*\relax*, we need to inhibit further expansion of this *\exno@F*.  This
can be done with
**
\expandafter\noexpand\csname\exstring@#1@F\endcsname
**
because the primitive *\expandafter* is ``expanded'' in an *\edef*:
\pagelabel{EXNE} the *\csname"allowbreak..."allowbreak
\endcsname* is first expanded to
*\exno@F*, and then this expansion is placed in front of *\noexpand*, and
consequently {\it not\/} expanded in the *\edef*\,!


Similar maneuvers are needed for *\exno@P* \dots; our *\edef\next@* will
**
\let\noexpand\pre=
 \expandafter\noexpand\csname\exstring@#1@P\endcsname
 . . .
**

In addition,
 the control sequences
*\exno@@Z* and *\exno@@Z@*
 might already exist, if `*\usecounter\exno*'
has already appeared (compare page~\ref{ZZ}).
 In this case, the control sequences
**
\csname\exstring@#1@@Z\endcsname
\csname\exstring@#1@@Z@\endcsname
**
would also {\it not\/} be *\relax*, and therefore they would be expanded
in *\edef*'s, probably with disastrous results.
  So we will  
simply *\let* them be *\relax* to begin with.

Finally,
 we want to add an
error message at the beginning if the first argument of *\usecounter* hasn't
already been created by *\newcounter*.

\C**
\def\usecounter#1#2{\expandafter
 \ifx\csname\exstring@#1@Z\endcsname\relax
  \Err@{\noexpand#1not created with \string\newcounter}\fi
 \expandafter\let\csname\exstring@#1@@Z\endcsname=\relax
 \expandafter\let\csname\exstring@#1@@Z@\endcsname=\relax
"2
 \edef\next@{\def\noexpand#2{\futurelet\noexpand\next
  \csname\exstring@#1@@Z\endcsname}}%
 \next@
"2
 \edef\next@{\def\csname\exstring@#1@@Z\endcsname
  {\noexpand\ifx\noexpand\next\noexpand\label
  \def\noexpand\next@\noexpand\label
   ########1{\csname\exstring@#1@@Z@\endcsname
   {\noexpand#1\noexpand\label{########1}}\noexpand\FNSSP@}%
    \noexpand\else
"2
  \noexpand\ifx\noexpand\next\noexpand""%
"2
  \def\noexpand\next@\noexpand""########1\noexpand""%
   {\csname\exstring@#1@@Z@\endcsname{{\expandafter\noexpand
    \csname\exstring@#1@F\endcsname
"2
   \let\noexpand\pre=
    \expandafter\noexpand\csname\exstring@#1@P\endcsname
"2
   \let\noexpand\post=
    \expandafter\noexpand\csname\exstring@#1@Q\endcsname
"2
   \let\noexpand\style=
    \expandafter\noexpand\csname\exstring@#1@S\endcsname
"2
   \let\noexpand\numstyle=
    \expandafter\noexpand\csname\exstring@#1@N\endcsname
   ########1}}\noexpand\FNSSP@}%
"2
  \noexpand\else
"2
   \def\noexpand\next@{\csname\exstring@#1@@Z@\endcsname
    {\noexpand#1}\noexpand\FNSSP@}%
   \noexpand\fi\noexpand\fi\noexpand\next@}}%
 \next@
 \expandafter\def\csname\exstring@#1@@Z@\endcsname}
**


\chapter Lists\endchapter

Now that we've discussed *\tag*, with just one counter *\tag@C*, it
seems appropriate to discuss *\list*, because it has five~counters
`*\list@C1*', \dots,\linebreak
`*\list@C5*', corresponding to the five~levels of a
list (Chapter~\ref{acces} explains  how this is handled by the 
 *\pre*, *\newpre*,
\dots, constructions). As on pages~\ref{QTS1}, \ref{QTS2} and~\ref{QTS3},
\pagelabel{QTS4}
 we will always use quotation marks around control
sequence names like `*\list@C1*', which really have to be 
named in the file by means of *\csname"allowbreak..."allowbreak\endcsname*.


\newcounter\Exno
\newnumstyle\Exno{\Alph}
\newfontstyle\Exno{\bf}
\usecounter\Exno\Topic#1{\medbreak\flushpar{\bf #1.\enspace}\ignorespaces}

\section{Style choices\label{liststy}}
Lists require four different style decisions, each 
in five versions, for the five different levels of a list.

\newpre\list1{A.}
\Topic
First, 
\list
\item
*\listbi@* will be the material (usually vertical
spacing and/or penalties)
that goes before
the first *\item* at the first level of a list.
\item
*\listbii@* will be the material that goes before the
first *\item* at the second level.
\endlist

\lamstex\ begins by setting the default values
\C**
\def\listbi@{\penalty50 \medskip}
\def\listbii@{\penalty100 \smallskip}
\let\listbiii@=\relax
\let\listbiv@=\relax
\let\listbv@=\relax
**

Thus,
\list
\item  *\listbi@* 
will produce a *\penalty50 \medskip* before the very first
 *\item*  at the top level of a *\list*
(when we define *\item* we will use
*\listbi@* only for the first *\item* at the top level [and
after the previous paragraph has been ended], 
so 
this penalty and space will not apply to later *\item*'s at the top level).
\item
Similarly, *\listbii@* 
produces   *\penalty100 \smallskip* before the first
item at the second level of a list.
\item In the default style, nothing is added before the first item
at the third through fifth levels.
\endlist

\newpre\list1{B.}
\Topic
Next,
\list
\item *\listmi@* will be the  changes to be made in the
 midst of  *\item*'s at the first level
 (usually changing the left and/or right indentations).
\item *\listmii@* will be the changes to be made in the midst
of *\item*'s at the second level.
\item"" . . .
\endlist




\lamstex\ sets the default values
\C**
\def\listmi@{\advance\leftskip by 30pt}
\let\listmii@=\listmi@
\let\listmiii@=\listmi@
\let\listmiv@=\listmi@
\let\listmv@=\listmi@
**

Thus, 
\list \item *\listmi@* will indent the text for *\item*'s at the
top level by *30pt*;
\item *\listmii@* will indent the text for *\item*'s at the second
level by yet another *30pt*;
\item"" . . .
\endlist

As we will see later (page~\ref{btework}), although 
*\listbiii@*,
\dots can be left 
undefined, it is important to have definitions
for *\listmii@*, \dots, even if they are just the same as 
*\listmi@*.

\newpre\list1{C.}
\Topic
Next, 
\list\item
*\itemi@* will specify the 
formatting of the  *\item*
numbers at the first level;
\item
*\itemii@* will specify the formatting of the  *\item*
numbers at the second level;
\item"" . . .
\endlist

\lamstex\ sets the default values
\C**
\def\itemi@#1{\noindent@@\llap{#1\hskip5pt}}
\let\itemii@=\itemi@
\let\itemiii@=\itemi@
\let\itemiv@=\itemi@
\let\itemv@=\itemi@
**
For the use of *\noindent@@*, see Chapter~\ref{EVPAR}. Notice that
if *\everypar* is non-empty, then new paragraphs within an *\item*
(like the one shown on page~17 of the \lamstex~Manual),
will have this *\everpar* material before them.
\pagelabel{NOAT}
(If we wanted to prohibit that, we could simply set *\everypar={}* 
right after the *\begingroup* in the definition of *\list* to follow,
and use *\noindent@* instead of *\noindent@@* at this point.)


Thus, 
\list\item
*\itemi@* will format an *\item* number *#1* as\pagelabel{ITEMIAT}
**
\noindent@@\llap{#1\hskip5pt}
**
The
*\llap{#1\hskip5pt}*
simply causes the *\item* number
 to appear *5pt* to the left
of the rest of the text;
\item Similarly, 
  *\itemii@* formats an *\item* number at
the second level in exactly the same way;
\item"" . . .
\endlist


\newpre\list1{D.}
\Topic
Finally, we have some control sequences that are numbered differently:
\list
\item *\liste@* will be the formatting (usually vertical spacing
and/or penalties) that goes at the end of the last *\item* at the {\it
first\/} 
level;
\item *\listei@* will be the formatting that goes at the end of
the last *\item* at the {\it second\/} level; 
\item""  . . .
\Reset\list15
\item *\listeiv@* will be the formatting that goes at the end of
the last *\item* at the {\it fifth\/} level.
\endlist\pagelabel{EE}


Thus, for reasons that will become clear (page~\ref{oneless})
these control sequences are ``numbered'' one less than the level to
which they apply.

\lamstex\ sets the default values
\C**
\def\liste@{\penalty-50 \medskip}
\def\listei@{\penalty-100 \smallskip}
\let\listeii@=\relax
\let\listeiii@=\relax
\let\listeiv@=\relax
**

Thus,
\list \item
*\liste@* will produce *\penalty-50 \medskip* 
at the end of
the list;
\item *\listei@* will produce *\penalty-100 \smallskip* when we go
from the end of the second level of the list back to the first level;
\endlist
but nothing will be added when we go from the end of the third level back
to the second level, etc.


\newpre\list1{}

\nopunct\section{Counters, \label{liststy2}etc.}
Next we must create the counters `*\list@C1*', \dots,\linebreak
 `*\list@C5*', which
we initialize to *0*:
\C**
\expandafter\newcount\csname list@C1\endcsname
\csname list@C1\endcsname=0
 . . .
**
We want `*\list@C1*', `*\list@C2*', \dots, in conformity with
a general
\lamstex\ principle for handling constructions with more than one
counter (see Chapter~\ref{acces}),
but we use *\listbi@*, *\listbii@*, \dots, because
there are a fixed number of such control sequences, which we will usually
be
mentioning explicitly, so there's no need to complicate matters by using
names that combine letters and numbers.


Just as we use `*\...@C1*', \dots, `*\...C5*' to indicate counters at
various levels, we also use `*\...@P1*', \dots for the pre-material at the
various levels, and `*\...@Q1*', \dots for the post-material at the various
levels.
We initialize all of these to be empty:
\C**
\expandafter\let\csname list@P1\endcsname=\empty
 . . .
\expandafter\let\csname list@Q1\endcsname=\empty
 . . .
**

Then come the styles at each level (compare page~\ref{CCC}): 
\C**
\expandafter\def\csname list@S1\endcsname#1{{\rm(}#1\/{\rm)}}
 . . .
**

Note that these styles determine the formatting of an item number, but the
spacing after the formatted number is determined by *\itemi@*, \dots\ (page
~\ref{ITEMIAT}).  In conformity with this,  style control sequences in
\lamstex\ never address the question of the spacing after the formatted
number, which has to be handled separately.\pagelabel{SPACESEP}


Then come the numbering styles at each level:
\C**
\expandafter\let\csname list@N1\endcsname=\arabic
 . . .
**
Note that here we once again
use *\let* rather than *\def*, just as with
*\tag* (page~\ref{TAGATN}),
 but *\def* would be required for anything other than
*\arabic*.

Finally, we also need the font styles at each level:
\C**
\expandafter\def\csname list@F1\endcsname{\rm}
 . . .
**

There will  be occasions when we want to refer to
the list counter, etc., for the current level, without having to
know or to
specify this level explicitly.  
For this purpose, we first create a
counter, 
\C**
\newcount\listlevel@
\listlevel@=0
** 
which will always hold the current list level, and  then we
\C**
\def\list@@C{\csname list@C\number\listlevel@\endcsname}
\def\list@@P{\csname list@P\number\listlevel@\endcsname}
\def\list@@Q{\csname list@Q\number\listlevel@\endcsname}
\def\list@@S{\csname list@S\number\listlevel@\endcsname}
\def\list@@N{\csname list@N\number\listlevel@\endcsname}
\def\list@@F{\csname list@F\number\listlevel@\endcsname}
**
so that, for example, *\list@@C* will be `*\list@C1*' if we are
at the first level, `*\list@C2*' if we are at the second level, etc.




\section{Other preliminaries\label{llevel}}
Since, as we've already indicated in section~\Sref{liststy},
 the first *\item* at each level needs
to be treated specially, we need flags
\C**
\newif\iffirstitemi@
\newif\iffirstitemii@
\newif\iffirstitemiii@
\newif\iffirstitemiv@
\newif\iffirstitemv@
**
Moreover, we need ways of setting the flag for each level true or false
without explicitly mentioning the level:
\C**
\def\Firstitem@true{\csname 
 firstitem\romannumeral\listlevel@ @true\endcsname}
\def\Firstitem@false{\csname
 firstitem\romannumeral\listlevel@ @false\endcsname}
**
We will also need to refer to *\listm...@*,
*\item...@*, and *\liste...@* without having to
specify the level `*...*'. So we define
\C**
\def\Listm@{\csname 
 listm\romannumeral\listlevel@ @\endcsname}
\def\Item@{\csname 
 listformatt\romannumeral\listlevel@ @\endcsname}
\def\Liste@{\csname 
 listformate\romannumeral\listlevel@ @\endcsname}
**
(For this to work, we must have *\listm...@*,
*\item...@*, defined for all levels;
*\Liste@* will be applied only for $1\le\hbox{*\listlevel@*} 
\allowbreak<\hbox{5}$.)\pagelabel{btework}


\medskip

Version *1* of \lamstex\ had *\continuelist*, 
which was meant to be used as
**
\continuelist
\list
 . . .
\endlist
**
although the \lamstex~Manual mistakenly indicated the usage
**
\continuelist
\item  
 . . . 
\endlist
**
(which would conflict with the general `*\foo ... \endfoo*' convention
for \lamstex\ constructions). This was a natural mistake to make, however, so
now `*\continuelist*'  has been replaced by `*\keepitem*'. 

 *\keepitem* itself will simply set a flag,
\C**
\newif\iflistcontinue@
\def\keepitem{\listcontinue@true}
**
while
*\endlist* will always reset *\listcontinue@false*.


\section{\CS{list}\label{list}}
Unlike the case of *\tag*,
whenever we start a *\list* we want to reset 
the list counters `*\list@C1*', \dots\ to~ *0*,
except if *\keeplisting* is in force, in which case
`*\list@C1*'  will not be changed.\pagelabel{reset}
Then we want to begin a group,
set *\firstitemi@true*,  set the list 
level counter to~*1*, and define *\item* in terms of a *\futurelet*,
since it needs to see if a ``quoted'' number follows:
\footnote{An *\item* outside a *\list* will continue to have its usual
meaning from *plain* \tex@, though it might be preferable to 
specify *\Invalid@\item* (see section~\Sref{K})
and to *\let\itemitem="allowbreak\undefined*, since that
usage more or less conflicts with \lamstex\ usage.}
**
\def\list{%
 \iflistcontinue@\else
  \global\csname list@C1\endcsname=0 
 \fi
"2
 \global\csname list@C2\endcsname=0
"2
 \global\csname list@C3\endcsname=0
"2
 \global\csname list@C4\endcsname=0
"2
 \global\csname list@C5\endcsname=0
"2
 \begingroup
 \firstitemi@true
 \listlevel@=1
"2
 \def\item{\futurelet\next\item@}
**



At this point it might seem  like it's time to end the previous paragraph, 
and get down to work.
But we need a slight diversion, because
we are also going to allow the possibility that
*\list* is followed by *\runinitem* instead of *\item*, as in \amstex@.
So we
also need a *\futurelet* for that:
\C**
\def\list{%
 \iflistcontinue@\else
  \global\csname list@C1\endcsname=0 
 \fi
 \global\csname list@C2\endcsname=0
 \global\csname list@C3\endcsname=0
 \global\csname list@C4\endcsname=0
 \global\csname list@C5\endcsname=0
 \begingroup
 \firstitemi@true
 \listlevel@=1
 \def\item{\futurelet\next\item@}%
 \futurelet\next\list@}
**

*\runinitem* has no role except to serve as an indicator after
*\list* [or after *\inlevel*, since we also allow *\runinitem* to be
used instead of the first *\item* at each level],
so (compare section~\Sref{K}) we first state
\C**
\Invalid@\runinitem
**

In the definition of *\list@*, the test *\ifx\next\runinitem* can be used
to detect if *\list* is followed by *\runinitem*.  
If *\list@*  detects a *\runinitem*, it will then swallow this
*\runinitem*
and  do yet another *\futurelet* (to see if *\runinitem* is followed
by a quoted number).

Otherwise, the first thing *\list@* should do is to end the current
paragraph. 
At this point, however,
 the default style adds some adjustment for the
space between paragraphs, since paragraphs are allowed within each *\item*.
 If our style does leave some space, say *1pt*,
between paragraphs, we probably want to do the same for paragraphs within
each *\item*.  Normally, however, *\parskip* is something like `*0pt
plus 1pt*', with only stretchable space. In this situation, it is inadvisable
to leave the stretchability, for, on a page requiring a fair amount of
vertical stretching, this interparagraph stretch might easily end up looking
too big compared to the other spacing that the style selects for *\list*'s
(I speak from experience!).  This stretchability can be eliminated with the
code 
**
\dimen@=\parskip \parskip=\dimen@  "8ELIM"8
**
(since *\dimen@* is a
dimension, the first assignment sets *\dimen@* to the non-stretchable part
of *\parskip*, and the second assignment resets *\parskip* to this
non-stretchable part).

So the definition of *\list@* might be
**
\def\list@{\ifx\next\runinitem
  \def\next@\runinitem{\futurelet\next\runinitem@}\else
  \def\next@{\par \dimen@=\parskip \parskip=\dimen@}\fi\next@}
**

That's not quite good enough however, because we also want  to allow a
blank line before the *\runinitem*, since blank lines are generally allowed
before *\item*'s. 
\footnote{On the other hand, there's no way we can allow a blank
line to occur
 before *\list* in a
  `*\list\runinitem*' combination; when a run-in *\item* is
required, the *\list* must appear in the same paragraph
as the previous text.}

So if *\next* happens to be *\par*, we will call a construction that
swallows this *\par* and then repeats the *\futurelet\next\list@*:
\C**
\def\list@{\ifx\next\par
 \def\next@\par{\futurelet\next\list@}\else
 \ifx\next\runinitem
  \def\next@\runinitem{\futurelet\next\runinitem@}\else
  \def\next@{\par \dimen@=\parskip \parskip=\dimen@}%
 \fi\fi\next@}
**


Leaving aside the definition   of *\runinitem@* for the moment, we
consider the case where *\item* occurs next.


\section{\CS{item}\label{item}}
*\item* has already been set to *\futurelet\next\item@*.
Before worrying about whether a quoted
*\item* number follows,
*\item@* will take care of any needed formatting.
This will involve two new flags
\C**
\newif\ifoutlevel@
\newif\ifrunin@
**
The first will be true if the *\item* was preceded by *\outlevel*
(so that *\item*'s at a higher level have just been completed). The 
second will be true if the present *\item* follows a *\runinitem* at the
same level.\pagelabel{runin}.
 In either of these cases, the appropriate flag for first *\item*'s
at this level
(*\iffirstitemi@* or *\iffirstitemii@* or \dots) will be {\it false}.

The first thing *\item@* adds is
**
\ifoutlevel@\Liste@\outlevel@false\fi
**
So, for example, 
if our *\item* occurs at the top level ($
\hbox{*\listlevel@*}=\hbox{1}$), and we have just completed *\item*'s
at the second level,
we will add *\listei@*---recall
(page~\ref{EE}) that this is the formatting that goes at the end of the 
last *\item* at the {\it second\/} level.\pagelabel{oneless}

The reason for this approach is that in a situation like
**
\list
\item ...
"2
 \inlevel 
  \item ...
"2
   \inlevel
"2
    \item ...
    \item ...
   "9\outlevel"9
 "9\outlevel"9
\item ...
**
where we go from third level *\item*'s right 
back to first level *\item*'s,
the spacing before that next *\item* at the first level should be
the spacing that goes after {\it second\/} level items, not the spacing
 that goes
after third level items (and certainly not the sum of the spacing that
goes after
the second and third levels). So
we don't want the spacing to be put in by the *\outlevel*'s; instead
*\outlevel* will just  set *\outlevel@true*, for use by *\item*.
\pagelabel{outlevel}

Next, we consider the case where *\ifrunin@* is true.
In this case, we simply want to set *\runin@false*, 
end the current paragraph (which contains the previous *\runinitem*, which
 has not been indented any extra amount), add the same adjustments that were
made for *\list@*, in case we are at the first level,
and then
add *\Listm@* (the 
*\listm...@* for the current level)  to apply to the remaining
*\item*'s at the current level:
**
 \ifrunin@\runin@false\par
 \dimen@=\parskip \parskip=\dimen@
 \Listm@\fi
**


If neither of these cases occurs, we have to consider the possibility
that the *\item* was the first at its level. At the first level,
this means that we will add
**
\listbi@ \listmi@ 
**
if *\iffirstitemi@* is true,
 also setting *\firstitemi@false*, 
but simply add a *\par* for other items:
**
 \iffirstitemi@
  \listbi@\listmi@\firstitemi@false
 \else\par\fi
**
Note that *\listbi@* will be occurring after a *\par* supplied
by *\list*, via *\list@*, or by *\outlevel* (section~\Sref{Outlevel}).

  Analogous code is added for the situation where we are at the
second level (*\iffirstitemii@...\fi*); in this case, *\listbii@*
will be occurring after the *\par* supplied by the previous code.
And similarly for the third through fifth levels.

Each of these *\iffirstitem...@* tests has to be made separately, and
*\listbi@*, \dots\ appear only in such constructions; that is why
there is no point having a `*\Listb@*' construction.


We will use compressed format, as well as the K-method, for *\item@*, 
 so that the definition ends
**
\ifx\next""\expandafter\next@\else\expandafter\nextii@\fi
**
with *\next@*  and *\nextii@* defined first.%\pagelabel{a\ b}

The definitions of *\next@* and *\nextii@* are
 quite similar to the definitions of
*\maketag@@@* and *\maketag@@@@*,
using *\Qlabel@* from section~\Sref{maketag}
 for ``quoted'' *\item* numbers, 
but
 with some additions:
**
 \def\next@""##1""{{\let\pre=\list@@P \let\post=\list@@Q
  \let\style=\list@@S \let\numstyle=\list@@N
  "9\vskip-\parskip"9
  \Item@{\list@@F##1}%
  \noexpands@
  \Qlabel@{##1}}%
  \locallabel@
  "9\FNSSP@"9}%
"slip
 \def\nextii@{\global\advance\list@@C by 1
  {\noexpands@
   \xdef\Thelabel@@@{\number\list@@C}%
   \xdefThelabel@\list@@N
   \xdef\Thelabel@@@@{\list@@P\Thelabel@\list@@Q}}%
   \xdefThelabel@@\list@@S
  }%
  \locallabel@
  "9\vskip-\parskip"9
  \Item@{\list@@F\thelabel@@}%
  "9\futurelet\next\pretendspace@"9}%
**

We add the
*\vskip-\parskip* because *\Item@* will normally
start a new paragraph, and we want the spacing before the *\item* to be
explicitly specified by *\listbi@*, \dots, and not involve any
*\parskip*, which is easy to forget about.

And we add the *\FNSSP@* and
*\futurelet\next\pretendspace@*'s because
 *\Item@* puts us into horizontal mode\pagelabel{NEEDFP}
 (in the default style it also produces some space
after the
*\item* number---the *\hskip5pt* at the end of the
*\llap* in the definition of *\item...@*---but
this space is ``hidden''
inside the *\llap*, and will not be discovered by *\lastskip*). 
  So  (compare section~\Sref{ZZZ})
**
\item \label{...}" Text ...
**
would leave an extra space before the ``Text \dots''. 
The *\pretendspaces@*'s
take care of this.
  In the case of
*\nextii@* we don't need *FNSSP@*, since a space
token won't appear after *\item* (compare  *\endMath*, page~\ref{DDD}).


It should perhaps also be noted that something like *\let\pre=\list@@P*
does not actually make *\pre* have the value of the appropriate
`*\list@P1*' or `*\list@P2*' or \dots, but simply makes *\pre* expand out to
the definition of *\list@@P*, i.e., to
**
\csname list@P\number\listlevel@\endcsname
**
This is adequate, however, since we are not storing this value of *\pre* for
later use:\pagelabel{ADEQ}
 when this *\pre* gets used, either in printing the number,
**
{\list@@F##1}
**
or in the *\xdef*'s involved in
**
\Qlabel@{##1}
**
the current value of `*\list@P1*' or `*\list@P2*' or \dots, will be inserted.

Thus, the definition of *\item@* is:
\C**
\def\item@{%
 \ifoutlevel@\Liste@\outlevel@false\fi
"2
 \ifrunin@\runin@false\par
 \dimen@=\parskip \parskip=\dimen@ \Listm@\fi
"2
 \iffirstitemi@
   \listbi@\listmi@\firstitemi@false
  \else\par\fi
"2
 \iffirstitemii@
   \listbii@\listmii@\firstitemii@false
  \else\par\fi
"2
 \iffirstitemiii@
   \listbiii@\listmiii@\firstitemiii@false
  \else\par\fi
"2
 \iffirstitemiv@
   \listbiv@\listmiv@\firstitemiv@false
  \else\par\fi
"2
 \iffirstitemv@
   \listbv@\listmv@\firstitemv@false
  \else\par\fi
"2
 \def\next@""##1""{{\let\pre=\list@@P \let\post=\list@@Q   "8LISTQ"8
  \let\style=\list@@S \let\numstyle=\list@@N
"2
  \vskip-\parskip
  \Item@{\list@@F##1}
"2
  \noexpands@
  \Qlabel@{##1}}%
"2
  \locallabel@
  \FNSSP@}%
"2
 \def\nextii@{\global\advance\list@@C by 1
  {\noexpands@
"2
   \xdef\Thelabel@@@{\number\list@@C}%
   \xdefThelabel@\list@@N
"2
   \xdef\Thelabel@@@@{\list@@P\Thelabel@\list@@Q}}%
   \xdefThelabel@@\list@@S
  }% 
"2
  \locallabel@
"2
  \vskip-\parskip
  \Item@{\list@@F\thelabel@@}%
"2
  \futurelet\next\pretendspace@}%
 \ifx\next""\expandafter\next@\else\expandafter\nextii@\fi}
**

\section{\CS{runinitem\@}}
*\runinitem@* is  similar to, but simpler than, *\item@*.

First, *\runinitem@* sets *\ifrunin@true* and *\Firstitem@false*
(to be used by the next
*\item* [page~\ref{runin}]). The preliminary formatting of *\item@* isn't
necessary, so *\runinitem@*
 then immediately defines *\next@* and\linebreak *\nextii@* for
the compressed format:
**
  \def\next@""##1""{{\let\pre=\list@@P \let\post=\list@@Q
   \let\style=\list@@S \let\numstyle=\list@@N
   \unskip\space{\list@@F##1}"9" "9%
   \noexpands@
   \Qlabel@{##1}}%
   \locallable@
   \ignorespaces}
"slip
  \def\nextii@{\global\advance\list@@C by 1
   {\noexpands@
"2
    \xdef\Thelabel@@@{\number\list@@C}%
    \xdefThelabel@\list@@N
"2
    \xdef\Thelabel@@@@{\list@@P\Thelabel@\list@@Q}}%
    \xdefThelabel@@\list@@S
   }% 
   \locallabel@
   \unskip\space{\list@@F\thelabel@@}"9" "9}
**
In other words, after suitably defining *\thelabel@*, \dots, we leave
a space after the preceding text, and then print the *\item* number,
either as explicitly quoted, or as supplied automatically, 
and then add a space.  In the case of *\runinitem""...""* we have to ignore
any space that follows the *""...""*. Notice, however, that in neither case
do we have to worry about invisible constructions that follow, since now
a real space has been inserted.

Thus, the definition of *\runinitem@* reads:
\C**
\def\runinitem@{%
  \runin@true
  \Firstitem@false
"2
  \def\next@"##1"{{\let\pre=\list@@P \let\post=\list@@Q
   \let\style=\list@@S \let\numstyle=\list@@N
   \unskip\space{\list@@F##1}" %
   \noexpands@
   \Qlabel@{##1}}%
   \locallabel@
   \ignorespaces}%
"2
  \def\nextii@{\global\advance\list@@C by 1
   {\noexpands@
"2
    \xdef\Thelabel@@@{\number\list@@C}%
"2
    \xdefThelabel@\list@@N
"2
    \xdef\Thelabel@@@@{\list@@P\Thelabel@\list@@Q}}%
    \xdefThelabel@@\list@@S
   }%
"2
   \locallabel@
   \unskip\space{\list@@F\thelabel@@}" }%
   \ifx\next""\expandafter\next@\else\expandafter\nextii@\fi}
**



\section{\CS{inlevel}\label{inlevel}}
We will keep each level of a list within its own group, to
localize *\listlevel@*, etc.

 *\inlevel* will simply produce an error message if *\listlevel@*
is already ~*5*. Otherwise it will
 provide a *\begingroup* and advance *\listlevel@* by~ 1; notice
that this is  {\it not\/} a *\global\advance*: the value of
*\listlevel@* will be different within the different groups provided by
different levels.
Then we will set *\Firstitem@true* (i.e., set *\firstitemii@true* if we 
are
at now at the second level,
 *\firstitemiii@true* if we are now at the third level,
etc.).  
 No special formatting has to be done by *\inlevel*, because,
once *\listlevel@* has been correctly set, each *\item* will take care of
all necessary formatting.  But we are not quite done, because we need a 
*\futurelet* to see if a *\runinitem* follows:
\C**
\def\inlevel{\ifnum\listlevel@=5
 \def\next@{\Err@{Already 5 levels down}}\else
 \def\next@{\begingroup\advance\listlevel@ by 1 
 \Firstitem@true\futurelet\next\inlevel@}\fi\next@}
**

If *\inlevel@* detects a *\runinitem*, it just has to swallow
this *\runinitem* and call *\futurelet\next\runinitem@*, exactly
like *\list*; otherwise nothing remains to be done at all.  However,
just as in the case of *\list@*, we must also allow the possibility 
that  a *\par* precedes a *\runinitem*
\footnote{As in the case of *\list*, there's no way we can allow a blank
line to occur
  before *\inlevel* in  an `*\inlevel\runinitem*'
combination; 
 when a run-in *\item* is
required at a new level,
 the 
*\inlevel* must appear in the same paragraph
as the previous text.}:
\C**
\def\inlevel@{\ifx\next\par
 \def\next@\par{\futurelet\next\inlevel@}\else
 \ifx\next\runinitem
  \def\next@\runinitem{\futurelet\next\runinitem@}\else
 \let\next@=\relax\fi\fi\next@}
**


\section{\CS{outlevel}\label{Outlevel}}
Similarly, *\outlevel* gives an error message if we are at level~1.
Otherwise, we
want to end the paragraph and provide an *\endgroup* to match the
*\begingroup* provided by the previous *\inlevel*. 
 Nothing has to be
done to *\listlevel@*, since it will simply return to the value it was
already given before this new group had been entered.\pagelabel{ebeforee}
Note that it
is important to end the paragraph before the *\endgroup*; otherwise, the
current value of *\leftskip* provided by *\Listm@* would no longer
be in force when the paragraph ended.
In addition, before the *\endgroup*
 we need to globally
reset the counter for the current level back to ~0 (in case
we go down to this level by another *\inlevel*).\pagelabel{OUT}
  Finally, we want to
set *\outlevel@true*, for use by the next *\item*
 (page~\ref{runin}~ff.).
\C**
\def\outlevel{\ifnum\listlevel@=1
 \Err@{At top level}\else
 \par\global\list@@C=0 \endgroup\outlevel@true\fi}
**

\section{\CS{endlist}\label{ENDLIST}}
*\endlist* 
first ends the current paragraph:
**
\def\endlist{\par . . .
** 

Note that it's quite
possible for *\endlist* to occur after several consecutive
*\inlevel*'s---there may not be *\outlevel*'s to match all these
*\inlevel*'s. Consequently, *\endlist* must not
only supply an
*\endgroup* to match the *\begingroup* supplied
by *\list*,  but it must also supply enough
 *\endgroup*'s to match any
*\inlevel*'s that do not having matching *\outlevel*'s; this is
accomplished by the following code:
**
\global\toks1={}%
\count@=\listlevel@
{\loop
"2
 \ifnum\count@>0 \global\toks1=\expandafter{\the\toks1 \endgroup}%
 \advance\count@ by -1
 \repeat}
\the\toks1
**
(The possibility that an
*\inlevel* does not have a matching *\outlevel*
is the reason why we
 reset the counters for all levels at the beginning of a *\list*
[page~\ref{reset}], even though *\outlevel* resets the counter for its
level [\recentpageref{OUT}{see above}{see the previous
page}{page~\value\page}].) 
The *\loop* is enclosed within a group for the
unlikely eventuality that some *\list"allowbreak..."allowbreak\endlist*
 occurs within a *\loop* construction (compare page~\ref{POSSLOOP}).
Because of this, we need a *\global* assignment of the token list, so we
use *\toks1* (compare section~\Sref{LANDG}); and for consistency,
we begin with the *\global* assignment *\global\toks1={}*. We don't make
an abbreviation for *\toks1* because it is used so infrequently.

The *\endgroup*'s are followed by  
**
\liste@
**
(page~\ref{EE}), and then 
by
**
\listcontinue@false
**
since *\listcontinue@true* is set by
*\keeplisting*, which appears before a *\list*.


The final step is to take care of the fact that
 a *\list...\endlist* is not supposed to start a new
paragraph at the end, unless a new paragraph actually appears
in the file. For this
we
add\pagelabel{listnopar}
**
\vskip-\parskip
\noindent@@
**
If text follows immediately after the *\endlist*, it will start an
unindented paragraph, with no extra space, except that provided
by *\liste* 
(and so it will appear that the *\list...\endlist*
has merely ``interrupted'' the paragraph).


On the other hand, when *\endlist* is followed by a *\par* or blank line
before
new text, so that we have
**
\vskip-\parskip
\noindent@@
\par
 . . .
**
the ``empty paragraph'' *\noindent@@...\par* doesn't produce a blank line,
but we do get
*\parskip* glue inserted before the *\noindent@@* and {\it also\/}
before the text following the *\par*.  Together with the
*\vskip-\parskip*, this means that the   following text, which will
start a new paragraph,
 will have the usual *\parskip* glue before it. 


There is just one further detail: We need to add\pagelabel{ADDFNP}
**
\futurelet\next\pretendspace@
**
in case an invisible construction like *\pagelabel* happens to appear
after the *\endlist* (compare page~\ref{NEEDFP}).


Thus, the definition of *\endlist*   is:
\C**
\def\endlist{\par
"2
 \global\toks1={}%
 \count@=\listlevel@
"2
 {\loop
  \ifnum\count@>0 
   \global\toks1=\expandafter{\the\toks1 \endgroup}%
  \advance\count@ by -1
  \repeat}%
"2
 \the\toks1
"2
 \liste@
"2
 \listcontinue@false
"2
 \vskip-\parskip
 \noindent@@
 \futurelet\next\pretendspace@}
**

\small! As on page~\ref{BADOUTER}, \pagelabel{BADOUTER2} note
that if *\bye* were *\outer*, then *\endlist\bye* would give an error
message. \endsmall


Notice that a *\par* after *\endlist*
doesn't have to appear explicitly for all this to work.
For example, something like
**
\list
 . . .
\endlist
\section{...}
**
where *\section* starts a new paragraph, will behave correctly.
Consequently, this approach is preferable to one that would use
 a *\futurelet*
to see if a  *\par* comes next (such uses of *\futurelet* in sections
~\Sref{list} and~\Sref{inlevel} were quite different---they were meant only
to {\it skip over\/} any *\par*'s that might appear).  If somewhat
different design decisions are required for the spacing after the
*\endlist*, we could, for example, use
\setbox0\hbox{\<dimen$_{\text1}$\>}%
**
\edef\parskip@{\parskip=\the\parskip}
\parskip="box0
\noindent@@
\futurelet\next\pretendspace@
**
[The construction
**
\edef\parskip@{\parskip=\the\parskip} "8=the"8
**
is similar to the construction
**
\edef\@sf{\spacefactor\the\spacefactor}
**
used in *plain* \tex@: the primitive *\parskip*
is not expanded in the *\edef*,  but `*\the*' {\it is\/} expanded, so
*\parskip@* means
\setbox0\hbox{\<current value of *\parskip*\>}%
\setbox1\hbox{`}\setbox2\hbox{'}
**
"box1\parskip="box0"box2
**
after the *\edef* is finished.]


\chapter\CS{describe} and \CS{margins}\endchapter

Although *\describe* and *\margins* don't really come next by any logical
imperative, they come next in \lamstex\ because they are so similar to 
*\list*.

\section{\CS{describe}}
Since *\describe* has only one level, it is simplest to incorporate all
 necessary style decisions 
 directly into the definition, without using 
 subsidiary
 control sequences like *\listbi@*, etc.  In addition,
*\describe* is much less complicated than *\list* because
nothing gets numbered,
*\describe* doesn't have to check for a *\runinitem*, and
*\item*'s in a *\describe* don't have to check to see if a *""* follows.


We require 
just one flag, for the first *\item* in a *\describe*:
\C**
\newif\iffirstdescribe@
**

*\describe* can immediately end the previous paragraph (unlike *\list*,
which has to worry about a *\runinitem* following); then, like *\list*,
it begins a group and sets *\firstdescribe@true*. 
(The default style doesn't bother adding `*\dimen@=\parskip
\parskip=\dimen@*', but other styles might want to add that here.)  Then
it simply has to define *\item* within *\describe*, which is simply a
control sequence with an argument:
\C**
\def\describe{\par
 \begingroup
 \firstdescribe@true
"2
 \def\item##1{%
  \iffirstdescribe@
  \penalty50 \medskip \vskip-\parskip
  \firstdescribe@false\else\par\fi
  \hangindent2pc \hangafter1
  \noindent@@{\bf##1}\hskip.5em}
**
(compare page~\ref{NOAT} for the use of *\noindent@@*).

In the definition of *\item*, the 
**
\penalty50 \medskip \vskip-parskip
\hangindent2pc \hangafter1 \noindent
\noindent@@{\bf##1}\hskip.5em
**
represent  style decisions, which might be changed for other styles.


*\enddescribe* is also much simpler than *\endlist*: we simply end the
previous paragraph, add spacing and penalties (style decisions) and
end the group started by *\describe*:
\C**
\def\enddescribe{\par
 \penalty-50 \medskip\vskip-\parskip
 \endgroup}
** 

Since
*\describe...\enddescribe* {\it is\/} supposed to start a new paragraph at
the end (at least in the default style), we don't need the special
machinations that were used for *\endlist* (page~\ref{listnopar}); of
course, they could always be added for a style that wants to handle this
question differently.


\section{\CS{margins}}
The *\margins* construction uses the commands
*\pullin* and *\pullinmore*, rather
than *\item*.  We might as well have these give error messages outside of
a *\margins...\endmargins* construction (see section~\Sref{K}),
\C**
\Invalid@\pullin
\Invalid@\pullinmore
**

There is no special formatting before the first paragraph of a
*\margins* construction.  Nevertheless, we still need a flag
\C**
\newif\iffirstpull@
**
but this flag will  play quite a different role than the analogous
flag in *\describe*:  Each *\pullin* command
is going to start a new group, within which *\leftskip* and *\rightskip*
will be determined by the arguments of this command;  since a *\pullin*
is usually followed by yet another *\pullin*, this means that each
*\pullin* will  also have to provide the *\endgroup* that matches
the *\begingroup* from the previous *\pullin*, except that the
 {\it first\/} *\pullin* should not provide this extra *\endgroup*.

*\margins*, like *\describe*, will end the previous paragraph,
begin a group, set *\firstpull@true*, and then define *\pullin* and
*\pullinmore*:
**
\def\margins{\par\begingroup\firstpull@true
 \def\pullin##1##2{...}%
 \def\pullinmore##1##2{...}}
**

*\pullin* will end the previous paragraph, and supply an *\endgroup*,
except for the first *\pullin*, as already indicated, and then start
yet another group:
**
\def\pullin##1##2{\par
 \iffirstpull@\firstpull@false\else\endgroup\fi
 \begingroup
**
(Notice that it is important to have the *\par* before the
*\endgroup*, compare page~\ref{ebeforee}.)

In this new group we want to set *\leftskip=##1* and *\rightskip=##2*.
But we want 
\setbox0\hbox{or}
**
\pullin{}{...}  "box0  \pullin{" }{...}
**
to yield *\leftskip=0pt*, and similarly for the second argument, so we
explicitly have to check for these possibilities:
**
\def\next@{##1}%
\ifx\next@\empty\leftskip=0pt\else
 \ifx\next@\space\leftskip=0pt\else
  \leftskip=##1\fi\fi
\def\next@{##2}%
\ifx\next@\empty\rightskip=0pt\else
 \ifx\next@\space\rightskip=0pt\else
  \rightskip=##1\fi\fi\ignorespaces}
**
The final
*\ignorespaces* is needed to get rid of any spaces following the
*\pullin{...}{...}*.

Normally, *\margins* is meant to be used as
**
\margins
 \pullin{...}{...}
 . . .
\endmargins
**
but our definition allows text to intervene between the `*\margins*'
command and the first `*\pullin*'; such text will just be treated as a
paragraph with no special indentations.


Note that this definition of *\pullin*
regards the  arguments as `absolute'
dimensions, rather than as
 dimensions relative to values of *\leftskip* and
*\rightskip* that may have already been set. Indeed, when one of the
arguments is *{}* or *{ }*, we explicitly set the value of *\leftskip*
or *\rightskip* to *0pt*, instead of simply leaving it alone.

 Since no other \lamstex\
macros fool with *\leftskip* and *\rightskip*, this seems like a
reasonable design decision; a sophisticated
user who knows about *\leftskip* and
*\rightskip* will presumably have the sense either to adjust the
arguments of *\pullin* appropriately (or to use *\pullinmore*), or to
first
set *\leftskip* and *\rightskip* to *0pt* before using *\margins*.


To make the arguments of *\pullin* relative dimensions, it would suffice
 to replace the `*\leftskip*' and `*\rightskip*' with
`*\advance\leftskip*' and `*\advance\rightskip*', respectively. In this
case, we could simply omit
the `*\leftskip=0pt\relax*' and `*\rightskip=0pt\relax*' 
 both times.

The definition of *\pullinmore* follows just such a scheme, except that
we must store the current values of *\leftskip* and *\rightskip* before 
ending the  previous group:
**
\xdef\Next@{\leftskip=\the\leftskip
 \rightskip=\the\rightskip}
**
The effect of this *\xdef* (compare page~\ref{=the}) is to make
*\Next@* mean
\setbox0\hbox{\<current value of *\leftskip*\>}
\setbox1\hbox{\<current value of *\rightskip*\>}
**
\leftskip="box0
\rightskip="box1
**
We need *\xdef* rather than *\edef*, because this will be followed by
an *\endgroup*; then, after the following *\begingroup* we can reinstate
these values, before using the arguments of *\pullinmore* to decide
how much to
*\advance\leftskip* or *\advance\rightskip*:
**
\def\pullinmore##1##2{\par
 \xdef\Next@{\leftskip=\the\leftskip
  \rightskip=\the\rightskip}%
"2
 \iffirstpull@\firstpull@false\else\endgroup\fi
"2
 \begingroup
"2
 \Next@
 \def\next@{##1}%
 \ifx\next@\empty\else\ifx\next@\space\else
  \advance\leftskip by ##1\fi\fi
"2
 \def\next@{##2}%
 \ifx\next@\empty\else\ifx\next@\space\else
  \advance\rightskip by ##1\fi\fi
 \ignorespaces}
**
We use the scratch token *\Next@* here, because it
has been reserved for *\global*
assignments (page~\ref{GNXT}).

Thus, the definition of *\margins* is
\C**
\def\margins{\par\begingroup\firstpull@true
 \def\pullin##1##2{\par
  \iffirstpull@\firstpull@false\else\endgroup\fi
"2
  \begingroup
  \def\next{##1}%
  \ifx\next@\empty\leftskip=0pt\else
  \ifx\next@\space\leftskip=0pt\else
  \leftskip=##1\fi
"2
  \def\next{##2}%
  \ifx\next@\empty\rightskip=0pt\else
  \ifx\next@\space\rightskip=0pt\else
  \rightskip=##2\fi\fi
  \ignorespaces}%
"2
 \def\pullinmore##1##2{\par
  \xdef\Next@{\leftskip=\the\leftskip
   \rightskip=\the\rightskip}%
"2
  \iffirstpull@\firstpull@false\else\endgroup\fi
"2
  \begingroup
  \Next@
  \def\next@{##1}%
  \ifx\next@\empty\else\ifx\next@\space\else
  \advance\leftskip by ##1\fi\fi
"2
  \def\next@{##2}%
  \ifx\next@\empty\else\ifx\next@\space\else
  \advance\rightskip by ##2\fi\fi
  \ignorespaces}}
**

And *\endmargins* simply has to end the current paragraph, and supply
two *\endgroup*'s (one to match the *\begingroup*
from the previous *\pullin* or *\pullinmore*, and one to match the
initial *\begingroup* supplied by *\margins*):
\C**
\def\endmargins{\par\endgroup\endgroup}
**


\chapter \CS{nopunct}, \CS{nospace}, and \CS{overlong}\endchapter
In the next chapter we will consider *\demo*, because it uses some
preliminary constructions for *\claim*, the subject of the chapter after
that. Since both *\demo* and *\claim* involve punctuation and spacing that
are normally supplied by a style, but which a user might want to override,
this chapter is devoted to such considerations, which version~*1* of
\lamstex\ handled with the *\nofrills* construction.


\section{\CS{nopunct}, \CS{nospace}, and \CS{overlong}\label{AGONY}}
In \amstex's *amsppt* style, *\nofrills* was used in several, not entirely
consistent, ways (unfortunately extended yet further by the AMS in their
additions to the style), and this inconsistent usage was brought over to
version~*1* of \lamstex\ (see the small print on
page~\ref{NOFC}).

 In version~*2* of \lamstex@,
*\nofrills* has been changed to *\nopunct*, so that it  affects
 only punctuation.
It then seems silly to allow *\nopunct* to also delete the spacing after the
punctuation, with *\usualspace* required
to put this spacing back.  Instead, it seems
more consistent to have `*\nospace*' to delete the space, so that removal of
the punctuation and removal of the spacing are handled separately.

  In
addition to these two new control sequences,
 *\overlong* has been retained.  Although no construction in
the default \lamstex\ style happens to allow both *\overlong* and *\nopunct*
or *\nospace*, other style might, so our macros will allow for
the
possibility that any combination of *\nopunct*, *\nospace*, and *\overlong*
precedes some construction (however, we will assume that each of these is used
just once).


In \lamstex@,
 *\nopunct*, *\nospace*, and *\overlong* all work in the same way,
by checking whether the next control sequence after any of these is in an
appropriate list, and setting a flag to be true if it is; it is then
the prerogative of that next control sequence to deal with this information
(and to reset the flags to false at the end).

We need three flags
\C**
\newif\ifnopunct@
\newif\ifnospace@
\newif\ifoverlong@
**
a list, initialized as	
\C**
\let\nofrillslist@=\empty
**
of constructions to which both *\nopunct* and *\nospace* can apply, and
a list, initialized as
\C**
\let\overlonglist@=\empty
**
of constructions to which *\overlong* can apply.

Because each of *\nopunct*, *\nospace*, and *\overlong* has to allow the
possibility that it is followed by one or both of the others, the macros are
complicated, though in no way interesting; basically, each will set the
corresponding flag to be true, although the flag may be reset to false
if we eventually find that an appropriate control sequence doesn't follow.

First of all, each of these construction begins with a *\futurelet\next*:
\C**
\def\nopunct{\nopunct@true\futurelet\next\nopunct@}
\def\nospace{\nospace@true\futurelet\next\nospace@}
\def\overlong{\overlong@true\futurelet\next\overlong@}
**

If *\nopunct* is followed by *\nospace* or *\overlong*, it will swallow
these control sequences, set
the corresponding flags true, and then use yet another *\futurelet*:
\C**
\def\nopunct@{%
 \ifx\next\nospace
  \def\next@\nospace{\nospace@true\futurelet\next\nopnos@}%
 \else
 \ifx\next\overlong
  \def\next@\overlong{\overlong@true\futurelet\next\nopol@}%
 \else
  \let\next@=\nopunct@@
 \fi\fi\next@}
**
 
We reach *\nopunct@@* when neither *\nospace* nor *\overlong* follows
our original *\nopunct*, so now we have to check whether the control sequence
that follows is in *\nofrillslist@*.  If so, we simply execute this
control sequence (the flag *\ifnopunct@* has already been set true);
otherwise we reset *\ifnopunct@* to be false and give an error message,
and still execute the control sequence:
\C**
\def\nopunct@@#1{\ismember@\nofrillslist@#1%
 \iftest@
  \let\next@=#1%
 \else
  \def\next@{\nopunct@false
   \Err@{\noexpand\nopunct can't be used with
   \string#1}#1}$%
 \fi\next@}
**
(We use an argument *#1* for *\nopunct@@*, rather than picking up the
next control sequence with a *\futurelet\next*, so that we can
properly include *#1* in the error message.) For the use of *\noexpand*
in this, any future, error messages, compare section~\Sref{SACN}.

Temporarily leaving aside *\nopnos@* and *\nopol@*,
 the other possible outcomes
of *\nopunct@*, we use basically the same procedures for *\nospace@* and
*\overlong@*:
\C**
\def\nospace@{%
 \ifx\next\nopunct
  \def\next\nopunct{\nopunct@true\futurelet\next\nopnos@}%
 \else
 \ifx\next\overlong
  \def\next@\overlong{\overlong@true\futurelet\next\nosol@}%
 \else
  \let\next@=\nospace@@
 \fi\fi\next@}
**
(notice that we use the same *\nopnos@* that appeared in *\nopunct@*)
\C**
\def\nospace@@#1{\ismember@\nofrillslist@#1%
"2
 \iftest@
  \let\next@=#1%
"2
 \else
  \def\next@{\nospace@false
   \Err@{\noexpand\nospace can't be used with
    \string#1}#1}%
 \fi\next@}
"2
\def\overlong@{%
 \ifx\next\nopunct
  \def\next@\nopunct{\nopunct@true\futurelet\next\nopol@}%
 \else
 \ifx\next\nospace
  \def\next@\nospace{\nospace@true\futurelet\next\nosol@}%
 \else
  \let\next@=\overlong@@
 \fi\fi\next@}
**
(notice that we use the same *\nopol@* and *\nosol@* that appeared in 
*\nopunct@* and *\nospace@*)
\C**
\def\overlong@@#1{\ismember@\overlonglist@#1%
 \iftest@
  \let\next@=#1%
 \else
  \def\next@{\overlong@false
   \Err@{\noexpand\overlong can't be used with
    \string#1}#1}%
 \fi\next@}
**

Now each of *\nopnos@*, *\nopol@*, and *\nosol@* must look for the
third of the triumvirate:
\C**
\def\nopnos@{\ifx\next\overlong
 \def\next@\overlong{\overlong@true\nopnosol@}\else
 \let\next@=\nopnos@@\fi\next@}
"2
\def\nopol@{\ifx\next\nospace
 \def\next@\nospace{\nospace@true\nopnosol@}\else
 \let\next@=\nopol@@\fi\next@}
"2
\def\nosol@{\ifx\next\nopunct
 \def\next@\nopunct{\nopunct@true\nopnosol@}\else
 \let\next@=\nosol@@\fi\next@}
**

The first of the newly created possibilities, *\nopnos@@* is easy:
\C**
\def\nopnos@@#1{\ismember@\nofrillslist@#1%
 \iftest@
  \let\next@=#1%
 \else
  \def\next@{\nopunct@false\nospace@false
   \Err@{\noexpand\nopunct\noexpand\nospace
    can't be used with \string#1}#1}%
 \fi\next@}
**
Notice that we may be giving the error message
**
\nopunct \nospace can't be used with ...
**
not worrying about niceties like commas between *\nopunct* and
*\nospace*! 


For the next two, which require testing for both *\nofrillslist@* and
*\overlonglist@*, we will  *\let\nextiii@=T* or *F*, depending on whether
or not the argument is in *\nofrillslist@*, and *\let\nextiv@=T* or *F*,
depending on whether or not the argument is in *\overlonglist@*; we
use *\nextiii@* and *\nextiv@* because *\ismember@* redefines
*\next@* and *\nextii@*.  It helps to define a routine that
makes these tests, and then also sets *\iftest@* to be true
precisely when both of the tests were positive:
\C**
\def\testii@#1{\ismember@\nofrillslist@#1%
 \iftest@\let\nextiii@=T\else\let\nextiii@=F\fi
 \ismember@\overlonglist@#1%
 \iftest@\let\nextiv@=T\else\let\nextiv@=F\fi
 \test@false
 \if\nextiii@ T\if\nextiv@ T\test@true\fi\fi}
**

Then we define *\nopol@@* and *\nosol@@*:
\C**
\def\nopol@@#1{\testii@{#1}%
 \iftest@
  \let\next@=#1%
 \else\def\next@{\if\nextiii@ T\else\nopunct@false\fi
  \if\nextiv@ T\else\overlong@false\fi
  \Err@{\if\nextiii@ T\else\noexpand\nopunct\fi
  \if\nextiv@ T\else\noexpand\overlong\fi 
  can't be used with \string#1}#1}%
 \fi\next@}
"2
\def\nosol@@#1{\testii@{#1}%
 \iftest@\let\next@=#1%
 \else\def\next@{\if\nextiii@ T\else\nospace@false\fi
  \if\nextiv@ T\else\overlong@false\fi
  \Err@{\if\nextiii@ T\else\noexpand\nospace\fi
  \if\nextiv@ T\else\noexpand\overlong\fi 
  can't be used with \string#1}#1}%
\fi\next@}
**

Finally,  *\nopnosol@*---when *\nopunct*, *\nospace*,
and *\overlong* have all appeared---works almost the same:
\C**
\def\nopnosol@#1{\testii@{#1}%
 \iftest@\let\next@=#1%
 \else\def\next@{%
  \if\nextiii@ T\else\nopunct@false\nospace@false\fi
  \if\nextiv@ T\else\overlong@false\fi
  \Err@{%
   \if\nextiii@ T\else\noexpand\nopunct\noexpand\nospace\fi
   \if\nextiv@ T\else\noexpand\overlong\fi
   can't be used with \string#1}#1}%
 \fi\next@}
**


\section{Using the flags}
The additional punctuation
 for constructions that allow *\nopunct@* will be added precisely
when *\ifnopunct@* is false, so 
 we introduce an
abbreviation for that:
\C**
\def\punct@#1{\ifnopunct@\else#1\fi}
**
Similarly, we have
\C**
\def\addspace@#1{\ifnospace@\else#1\fi}
**
for adding the space.

Control sequences that allow *\overlong* are ones that normally might contain
an *\hss*, like
**
\def\centerline#1{\line{\hss#1\hss}}
**
Any such candidates will have the *\hss* replaced by *\hss@*, which is
defined by
\C**
\def\hss@{\ifoverlong@ 0pt plus1000pt minus1000pt
 \else 0pt plus1000pt\fi}
**
So both stretch and shrink will be allowed when *\ifoverlong@* has been set
true, but only stretch will be allowed otherwise.\pagelabel{HSS}



\chapter\CS{demo} \label{Demo}\endchapter
 Since *\demo* is one of the constructions to which
*\nopunct* and *\nospace* should apply, we put it in *\nofrillslist@*:
\C**
\rightadd@\demo\to\nofrillslist@
**

As in \amstex@, we will introduce a new flag,
\C**
\newif\ifclaim@
**
so that  each *\claim* can set  *\ifclaim@* to be true (within the
group that that *\claim* will begin).
Then
*\demo* can give an error message when *\ifclaim@* is true, since we
shouldn't be giving a proof within the statement of a *\claim*. (On the
other hand, *\claim* will not make
a similar check regarding *\demo*, since
we {\it could\/}
 be stating subsidiary *\claim*'s within a *\demo*.
 In fact, the flag
*\ifclaim@* is used only by *\demo*, since virtually anything other than
a *\demo* can come within a *\claim*.)


As we will see in the next chapter, whenever we have started a *\claim*,
or something like *\Thm* that has been constructed using *\newclaim* or
*\shortenclaim*, 
not only will *\ifclaim@* be true, but also *\claimtype@* will be defined
to be *\claim* or *\Thm*, etc. So we can give an error message that
mentions *\claim* when we are in the middle of a general *\claim*, but
will instead state
**
Previous \Thm has no matching \endThm
**
when we are in the middle of a *\Thm* produced with *\newclaim*, 
etc. 
We can do this with
**
\Err@{Previous \expandafter\noexpand\claimtype@ has
 no matching \string\end
 \expandafter\expandafter\expandafter\eat@\expandafter
 \string\claimtype@}
**
Here (compare
page~\ref{EXNE})\pagelabel{EXNE2}
 the *\expandafter* is expanded in the error message,
so *\claimtype@* is expanded---to *\claim*, *\Thm*, or whatever---%
 before having *\noexpand* placed in front of it, which then prevents
further expansion.
See
{\it The \tex
book}, page~374 
for the triple  *\expandafter*;\pagelabel{tEXA}
 here *\claimtype@* is expanded first,
to *\claim* or *\Thm*, etc., 
then *\string* is applied to this, and then 
 *\eat@* (section~\Sref{AC}) is applied to the result of this
*\string*, thus eating the *\* at the beginning
of the *\string\claim* or *\string\Thm* or whatever. (Finally, see section~
\Sref{SACN} for the spacing after the *\noexpand*'ed control sequence.)

{\advance\litindent-10pt The combination
**
\expandafter\expandafter\expandafter\eat@\expandafter\string
**
will} occur quite frequently, so we abbreviate it:
\C**
\def\exxx@{\expandafter\expandafter\expandafter  "8EXXX"8
  \eat@\expandafter\string}
**

Normally (i.e., when *\ifclaim@* is false),  *\demo#1* will
 end the previous paragraph 
and add a *\smallskip*
(deleting the previous skip if smaller, or using the previous skip instead,
if it is larger).

 Then it will begin a group and
start an unindented paragraph with *#1* in *\smc* (with spaces before
and after *#1* ignored, since they are presumably typing errors); we
use *\noindent@@* for this (Chapter~\ref{EVPAR}).
This will be followed
by a colon, unless *\nopunct@* preceded the demo, 
**
\punct@:
**
and an *\enspace*, unless
 *\nospace* preceded the *\demo*,
**
\addspace@\enspace
**
 Instead of typing a (type~*12*)~*:*, we
will 
\C**
\let\colon@=: "8COLONAT"8
**
and use *\colon@* instead, so that a French style that makes *:*~active 
can change *\colon@* (compare~\Sref{ALF}).  
Moreover, we will use
**
\punct@{\null\colon@} "8NULLPUNCT"8
**
just in case  *#1* happens to end with an upper-case letter (although this
will usually be irrelevant, since an *\enspace*, rather than a space,
follows). 


At this point, after
we have determined whether or not the colon and *\enspace* should be added,
we will  reset
*\ifnopunct@* and *\ifnospace@*
to be false immediately, even though 
*\enddemo* will also do this, just
  to minimize problems if the user forgets 
the *\enddemo*.

Finally, we want to switch 
to *\rm*.  However, we must also be careful to add a
 *\FNSSP@*, in case an invisible construction follows
the *\demo{...}* (this will also throw away any extraneous
space after the *}*).
We can't simply say
**
\def\demo#1{\ifclaim@ ...
 \else 
  . . . 
 \rm\FNSSP@\fi}
**
because *\next* will be *\let* equal to  the *\fi*, rather than to the
next  non-space token
after *\demo{...}*. So instead we have to use the definition
\C**
\def\demo#1{\ifclaim@
"2
  \Err@{Previous \expandafter\noexpand\claimtype@ has 
   no matching \string\end\exxx@\claimtype@}%
  \let\next@=\relax
"2
 \else
  \par
"2
  \ifdim\lastskip<\smallskipamount 
   \removelastskip\smallskip\fi
"2
  \begingroup
"2
  \noindent@@{\smc\ignorespaces#1\unskip
   \punct@{\null\colon@}\addspace@\enspace}%
"2
  \nopunct@false\nospace@false
  \rm
  \def\next@{\FNSSP@}%
 \fi
 \next@}
**

\pagebreak

*\enddemo* simply has to end the current paragraph, supply
 the *\endgroup* to match the
*\begingroup* from *\demo*, reset the flags *\ifnopunct@* and
*\ifnospace@*, 
 and insert 
a *\smallskip*:
\C**
\def\enddemo{\par\endgroup
 \nopunct@false\nospace@false\smallskip}
**


\chapter \CS{claim}'s\endchapter

Now we come to *\claim* and related constructions, one of the more
complicated complexes in \lamstex.

\section{Preliminaries}
First of all, *\claim* is another thing that can follow *\nopunct*, so
we add it to *\nofrillslist@*:
\C**
\rightadd@\claim\to\nofrillslist@
**

The fontstyle for *\claim*'s,
\C**
\def\claim@F{\smc}
**
will be needed right away, but, in fact, we will need something more general. 

In Chapter~\Sref{Demo}, we pointed out that *\claimtype@* will be defined
to be *\claim* when  we have started an ordinary *\claim*, but
*\Thm* when we have started a construction like *\Thm* that has been
constructed with *\newclaim* or *\shortenclaim*.

 Each construction like
*\Thm* will have an associated font style *\Thm@F*@. This can be named 
(see page~\ref{EXSTRING}) as
**
\csname\exstring@\Thm @F\endcsname
**
or, more generally (recall the definition of *\exxx@* on page~\ref{EXXX}),
as
**
\csname\exxx@\claimtype@ F\endcsname
**
Since we often need to refer to this general font style, we introduce the
special construction
\C**
\def\claim@@@F{\csname\exxx@\claimtype@ @F\endcsname}
**
[We use a triple *@@@*, rather than the double *@@* used in
*\list@@F* to emphasize the distinction: *\list@@F* depends on the value
of the counter *\listlevel@*,  the level of a *\list*,
while *\claim@@@F* depends on *\claimtype@*, the name of the
*\claim*.]



Now we can introduce
 *\claimformat@* to indicate the general format of a *\claim*:
\C**
\def\claimformat@#1#2#3{\medbreak
 \noindent@@{\smc#1 {\claim@@@F#2} #3%
  \punct@{\null.}\addspace@\enspace}\sl}
**
(Compare page~\ref{NULLPUNCT} for the `*\null.*'\pagelabel{QW3}
and Chapter~\ref{EVPAR} for the *\noindent@@*.)
Arguments *#1* and *#3*
for
*\claimformat@* are the two arguments that a user types in
**
\claim{...}{...}
**
while argument *#2* is the *\claim* number,
either produced automatically, or
specifically  ``quoted'' after *\claim*.



Section~\Sref{MODC} explains how a style file can modify *\claimformat@* to
deal with  numerous possibilities for formatting different sorts of
*\claim*s in different ways.

\section{\CS{claimformat\@\@}}
Since *\claimformat@* is meant to be easily modified by a style designer,
it omits several messy details: 
\list\item Any extraneous spaces at the beginning and end of arguments
*#1* and *#3* should be removed.
\item If *#3* is empty, or a space
 (which occurs if the user types
*{ }* instead of *{}*),
 then the space before it must be removed.
\item *#2* should be the properly formatted *\claim* number.  Moreover,
if this is empty (because
 the user typed *\claim""""*), then the space before it
 should be removed.
\item A space following the
*\claim{...}{...}* should be ignored; more generally, we need
*\FNSSP@*, in case an invisible construction follows.
\endlist

So instead of using *\claimformat@* directly, we will
use *\claimformat@@*, which calls *\claimformat@* with all these
details added. When we are using
*\claimformat@@*, the control sequence *\thelabel@@* will contain the
properly formatted
 claim number.
\footnote{The formatting of the *\claim* number is specified by
*\claim@S*---it should not be specified directly in *\claimformat@*.} 
 In the definition below, argument *#2* 
corresponds to argument *#3* for *\claimformat@*. Only the 
next-to-last line of
code needs further amplification.
\C**
\def\claimformat@@#1#2{%
 \claimformat@{\ignorespaces#1\unskip}%
"2
 {\ifx\thelabel@@\empty\unskip\else\thelabel@@\fi}%
"2
 {\ignorespaces#2\unskip}%
"2
 \let\Claimformat@@=\claimformat@@
 \FNSSP@}
**
Note that it wasn't necessary to add any special clause for the cases where
*#2* is empty or a space---in either case the space preceding *#2* will
end up being removed. (Section~\Sref{MODC} illustrates how modifications may
be  made to the definition of *\claimformat@*.  In some cases,
*\claimformat@@* might need some  tinkering also.)


To explain the mysterious next-to-last line of code,
 we have to confess to a little white lie.
*\claim*, and all related constructions,
 never actually use *\claimformat@@*. Instead
they use
 *\Claimformat@@*, which we will initially set to be the
same as *\claimformat@@*: 
\C**
\let\Claimformat@@=\claimformat@@
**

This indirect approach has been implemented to deal with
 constructions 
produced with *\newclaim* and *\shortenclaim*.  Suppose, for example,
that we produce *\Thm* with
**
\newclaim\Thm\c{thm}{Theorem}
**
Roughly speaking, this defines *\Thm* as
**
\def\Thm{ ...
 \def\Claimformat@@{\claimformat@@{Theorem}} ...
 \claim }
**
The *\claim* in this definition will call *\Claimformat@@*,  and hence 
**
\claimformat@@{Theorem}
**
 so that the `Theorem' label will automatically
be inserted. Although the final *\endclaim* will return
  *\Claimformat@@* to its original state,
so
 that any subsequent *\claim* will just be using
 *\claimformat@@* (unless it happens
to be called by another construction that redefines *\Claimformat@@*),
we add
**
\let\Claimformat@@=\claimformat@@
**
at this point, just to minimize problems if the user forgets the *\endclaim*.


\section{Further preliminaries}
Although we won't consider all the complications of *\newclaim* until
later, there  are several other aspects that we need to
mention before moving on.

We've already used
*\claimtype@*
to define *\claim@@@F*.
More generally, we will 
\C**
\def\claim@@@P{\csname\exxx@\claimtype@ @P\endcsname}
"2
\def\claim@@@Q{\csname\exxx@\claimtype@ @Q\endcsname}
"2
\def\claim@@@S{\csname\exxx@\claimtype@ @S\endcsname}"8atat"8
"2
\def\claim@@@N{\csname\exxx@\claimtype@ @N\endcsname}
**

The counter has to be treated differently,   however,
for the following reason.  If the user directly types something
like 
**
\claim\c{thm}
**
then the style, numbering style, pre- and post-material for this *\claim*
are just the standard ones. {\it But a new counter must be involved}, 
since such *\claim*'s are to be numbered independently from other
*\claim*'s; this new counter is required even if no *\newclaim*
construction has been used.


To keep track of these different numbering classes, we will introduce
*\claimclass@*
in addition  to *\claimtype@*.
\setbox0\hbox{\<claim class\>}
A *\claim* with a particular ``class'', produced by
**
\claim\c{"copy0}
**
defines *\claimclass@* to be this \<claim class\> (ordinary *\claim*'s,
which are equivalent  to *\claim\c{}*, define *\claimclass@* to be empty).
And  the *\newclaim* construction
**
\newclaim\Thm\c{thm}{Theorem}
**
makes *\Thm* define *\claimclass@* to be `*thm*' also.


Now, when *\claim\c{thm}* is typed, we will use
**
\claim@Cthm  
**
for the counter.  More generally, we will use
**
\csname claim@C\claimclass@\endcsname
**
(As we will see later, the construction 
**
\newclaim\Thm\c{thm}{Theorem}
**
creates *\Thm@P*, *\Thm@Q*, etc.,  directly, but it creates
*\Thm@C* 
 indirectly: first
the counter *\claim@Cthm* is created, if it doesn't already exist, and
then *\Thm@C* is made equivalent to this counter.)


Consequently, the counter *\claim@@@C* is simply defined by:
\C**
\def\claim@@@C{\csname claim@C\claimclass@\endcsname}
**

It is the *\claimclass@* of a  construction like *\Thm*, etc., that
determines its numbering.  Consequently, 
**
\newclaim\Thm\c{thm}{Theorem}
\newclaim\Lem\c{lem}{Lemma}
**
produces *\Thm*'s and *\Lem*'s that are numbered independently, while
**
\newclaim\Thm\c{thm}{Theorem}
\newclaim\Lem\c{thm}{Lemma}
**
makes *\Thm*'s  and  *\Lem*'s share the same numbering.



\section{Starting a \CS{claim}}
First we
 introduce the other components of a printed
*\claim* number:
\C**
\newcount\claim@C
\claim@C=0
\let\claim@P=\empty
\let\claim@Q=\empty
\def\claim@S#1{#1\/}
\let\claim@N=\arabic
**
Compare page~\ref{TAGATN} for the `*\let\claim@N=\arabic*'.

*\claim* initializes *\ifclaim@* to be true,
*\claimclass@* to be empty, and *\claimtype@*
 to be *\claim*, and then 
uses a *\futurelet* to see if 
we are ``quoting'' the claim number with a *""* or specifying a
claim class with *\c*:
\C**
\def\claim{\claim@true
 \let\claimclass@=\empty\def\claimtype@{\claim}%
 \futurelet\next\claim@}
**


If *\claim* is followed by *\c*, we will use *\claim@c*, and if it is
followed by~ *""* we will use *\claim@q*,
**
\def\claim@{%
 \ifx\next\c
  \let\next@=\claim@c
 \else
  \ifx\next""%
   \let\next@=\claim@q
  \else
  . . .
**
 Otherwise, we will
use
**
\begingroup
**
to begin a group.
[The definitions of *\claim@c* (section~\Sref{clc}) and *\claim@q* 
(section~\Sref{clq}) will each begin with *\begingroup* also; but we
don't simply put the *\begingroup*
into the definition of *\claim* because, as
we will see later (page~\ref{bsc}), constructions produced by
*\newclaim* or *\shortenclaim* lead us directly to *\claim@c*, without
passing through *\claim*.]

Then we will
advance the *\claim* counter by *1*, 
define
*\thelabel@*, \dots\ in the usual way, and then call
 *\Claimformat@@*. In the following, we can use *\claim@C*, \dots\ rather
than the more general *\claim@@@C*, \dots\ because, as we have just
mentioned, 
 this clause of *\claim@* will only be called directly by
*\claim*, never indirectly by something created by *\newclaim*:
\C**
\def\claim@{%
 \ifx\next\c
  \let\next@=\claim@c
"2
 \else
  \ifx\next""%
   \let\next@=\claim@q
"2
  \else
   \begingroup
   \global\advance\claim@C by 1
"2
   {\noexpands@
    \xdef\Thelabel@@@{\number\claim@C}%
    \xdefThelabel@\claim@N
    \xdef\Thelabel@@@@{\claim@P\Thelabel@\claim@Q}}%
    \xdefThelabel@@\claim@S
   }%     
   \locallabel@
   \let\next@=\Claimformat@@
  \fi
 \fi
 \next@}
**


\section{Starting a \CS{claim\@c}\label{clc}}
The definition of *\claim@c* begins
**
\def\claim@c\c#1{\claim@true\begingroup
**
so that *\claim@c*  swallows up the succeeding *\c*, sets
*\ifclaim@* to be true,
and then
begins a group. We add
the *\claim@true* even
though this appears in *\claim*, because constructions created by
*\newclaim* and *\shortenclaim* call *\claim@c* directly
(pages~\ref{EEE}~ff. and~\ref{FFF}~ff.). 


Next we have to find out if the counter 
**
\csname claim@C#1\endcsname
**
already exists (which will happen if
 *\claim\c{#1}* has already appeared); this is
easily done with the test
**
\expandafter\ifx\csname claim@C#1\endcsname\relax
**
which is true when the counter hasn't  been defined yet.
If the counter {\it has\/}
 already been defined, we simply advance it by~*1*.
If it hasn't been defined, we create it, with *\newcount@* (compare
page~\ref{NWNW}), 
 and
set it to~*1*.

 Then we define *\claimclass@* to be *#1*, and define
 *\thelabel@*, \dots; in this case, for the
preliminary construction, defining *\Thelabel@*, \dots, we do use  the
more general constructions *\claim@@@C*, \dots (page~\ref{atat});
fortunately, these definitions can all be used within *\xdef*'s.
  Finally, we need a 
*\futurelet* to see if our 
 *\claim@c\c{...}* is followed by a quoted number *""...""*, which can
happen when *\claim@c* is called by a construction created by *\newclaim*
or *\shortenclaim*. We have to allow the possibility that a space might
intervene between the *\c{...}* and a *""*, so we use *\FNSS@*
(section~\Sref{FIX}): 
\C**
\def\claim@c\c#1{\claim@true
 \begingroup
"2
 \expandafter\ifx\csname claim@C#1\endcsname\relax
  \expandafter\newcount@\csname claim@C#1\endcsname
  \global\csname claim@C#1\endcsname=1
"2
 \else
  \global\advance\csname claim@C#1\endcsname by 1
 \fi
"2
 \def\claimclass@{#1}%
"2
 {\noexpands@
  \xdef\Thelabel@@@{\number\claim@@@C}%
  \xdefThelabel@\claim@@@N
"2
  \xdef\Thelabel@@@@{\claim@@@P\Thelabel@\claim@@@Q}}%
  \xdefThelabel@@\claim@@@S
 }%
 \locallabel@
 \FNSS@\claim@c@}
**

We're not really done with *\claim@c* yet,
but  we will  return to *\claim@c@* in a moment.

\section{Starting a \CS{claim\@q}\label{clq}}
For
our definition of *\claim@q* 
 we use *\Qlabel@*
from section~\Sref{maketag} for defining *\thelabel@*, \dots,
and we add a
 *\FNSS@*,
since we have to see whether our *\claim@q* is followed by *\c{...}*
(possibly after a space):
\C**
\def\claim@q""#1""{\begingroup
 {\let\pre=\claim@@@P \let\post=\claim@@@Q
 \let\style=\claim@@@S \let\numstyle=\claim@@@N
 \noexpands@
 \Qlabel@{#1}}%       "8CLAIMQ"8
 \locallabel@
 \FNSS@\claim@q@}
**
Unlike the situations  for *\maketag@* and *\item@*, we are not yet
 ready to
actually typeset the quoted *\claim* number; however, the number that we
want to typeset has been safely stored in *\thelabel@@*, which eventually
finds its way into *\claimformat@@*.

In regard to the *\let\pre=\claim@@@P*, \dots, compare page~\ref{ADEQ}.


\section{Finishing off} Let's return to *\claim@c*, which ended with
**
\FNSS@\claim@c@
**
Here *\claim@c@*  must check to see whether *\next* is
*""*. 
If *\next* is not *""*, we just call *\Claimformat@@*.
If *\next* is *""*, we will call yet another
routine *\claim@cq*.  But we will also have to make an adjustment:
Remember that *\claim@c* has already increased the appropriate counter
*\csname claim@C\claimclass@\endcsname* by 1. If *\claim@c@* finds
a *""* next, so that the claim number is actually being quoted, then
it must counteract this change:
\C**
\def\claim@c@{\ifx\next""%
 \global\advance\claim@@@C by -1
  \let\next@=\claim@cq
 \else\let\next@=\Claimformat@@
 \fi
\next@}
**

The definition of *\claim@cq* is now fairly straightforward, using only
devices already encountered; instead of *\Claimformat@@* at the end,
we use  *\FNSS@\Claimformat@@*, just to get rid of a possible space
following the second *""*: 
\C**
\def\claim@cq""#1""{{\let\pre=\claim@@@P \let\post=\claim@@@Q
 \let\style=\claim@@@S \let\numstyle=\claim@@@N
 \noexpands@
 \Qlabel@{#1}}%
 \locallabel@
 \FNSS@\Claimformat@@}
**



Similarly, our definition of *\claim@q* ended with 
**
\FNSS@\claim@q@
**
where *\claim@q@* can simply be defined by
\C**
\def\claim@q@{\ifx\next\c\expandafter\claim@qc
 \else\expandafter\Claimformat@@\fi}
**
(the ``K-method'' again, see section~\Sref{K}).

We reach *\claim@qc* only when we have the combination
**
\claim""...""\c{...}
**
(never   via a construction that
has been created with *\newclaim*),
which is actually pretty unlikely, since there's not much point indicating
the class of a *\claim* if the number is being quoted (unless different
classes of *\claim*'s are going to be formatted differently, in which case
the style designer has presumably already used *\newclaim* to introduce
a new name), 
 but we might as well carry it through.

Before calling *\Claimformat@@*, we just have to
use the *\c{...}* part to define *\claimclass@*, 
 and, just in case this particular class
*\c{...}* of *\claim*'s has never been used before, 
 create the new counter `*\claim@...*', if necessary, 
and set it to~*0* (not to~*1*,
as in *\claim@c*, since the counter isn't going to be used now). And
finally, we must again use
*\FNSS@\Claimformat@@* to skip over any space after the *\c{...}*:
\C**
\def\claim@qc\c#1{\expandafter
 \ifx\csname claim@C#1\endcsname\relax
  \expandafter\newcount@\csname claim@C#1\endcsname
  \global\csname claim@C#1\endcsname=0 \fi
 \FNSS@\Claimformat@@}
**


\section{\CS{endclaim}}
Finally, *\endclaim* simply ends the group begun by *\claim* (or
*\claim@c* if called by something created by *\newclaim* or
*\shortenclaim*),
 sets *\ifclaim@* and *\ifnopunct@* to be
false, resets *\Claimformat@@* to be *\claimformat@@*,
and adds a *\medbreak*.
\C**
\def\endclaim{\endgroup\claim@false
 \nopunct@false\nospace@false
 \let\Claimformat@@=\claimformat@@\medbreak}
**


\section{\CS{newclaim}}
To finish off the entire *\claim* complex, we have to define
*\newclaim* and *\shortenclaim*.

 *\newclaim* allows *\claimclause* as optional syntax, and we
do the standard thing to prevent its being used at inappropriate times
(see section~\Sref{K}):
\C**
\Invalid@\claimclause
**

*\newclaim* itself will require a *\futurelet* to see if *\claimclause*
comes next:
\C**
\def\newclaim{\futurelet\next\newclaim@}
**
 If *\claimclause* does come next,
 we will swallow the *\claimclause* and incorporate
the following argument into
**
\newclaim@@{#1}
** 
otherwise, the result will be the same as if we had typed
**
\newclaim\claimclause\relax
**
so we will simply call *\newclaim@@\relax* directly:
\C**
\def\newclaim@{\ifx\next\claimclause
 \def\next@\claimclause##1{\newclaim@@{##1}}\else
 \def\next@{\newclaim@@\relax}\fi\next@}
**
Thus, we have reduced everything to the definition of *\newclaim@@*.


Several aspects of *\newclaim@@* are included for eventual use by 
the\linebreak
*\shortenclaim* construction.
For example, something like
**
\shortenclaim\Thm\thm
**
should  be allowed only if *\Thm* has already been  created with
*\newclaim*; for this reason, we are going to keep a list, *\claimlist@*,
of all such possibilities, and we initialize it as:
\C**
\def\claimlist@{\\\claim}
**
We will also need two new token lists,
\C**
\newtoks\claim@i
\newtoks\claim@v
**
and, as we'll see, one other auxiliary control sequence is going to be
defined in the process of defining *\newclaim@@*.  Finally, there will be a
situation where we {\it don't\/}  want the *\claimclause* to be inserted,
even if it has been specified.  For this purpose, we initially
\C**
\let\noclaimclause@=F
** 
In the special case where we want
to suppress the claim clause, we will *\let\noclaimclause@=T* (this
happens  only once, and is more efficient than declaring
*\ifnoclaimclause@*, which actually creates three control sequence names).
\pagelabel{EFFL}

\medskip

If \<*" *\> denotes an optional space, then 
 *\newclaim* will appear in something of the form
\setbox0\hbox{*\newclaim \claimclause {*\<claim clause\>*}*\<*" *\>%
 *\Thm \c{thm}*\<*" *\>*{Theorem}*}
$$\overfullrule=0pt\box0$$
so
*\newclaim@@* will appear in something of the form
\setbox0\hbox{*\newclaim@@ {*\<claim clause\>*}*\<*" *\>%
 *\Thm \c{thm}*\<*" *\>*{Theorem}*}
$$\box0\tag"({\bf A})"$$

Our definition of *\newclaim@@* will be of the form
**
\def\newclaim@@#1#2#3\c#4#5{ . . .
**
In case ({\bf A}), argument *#1* will be  \<claim clause\>
(which may be empty),
argument *#2* will be `*\Thm*', and argument *#3* will 
be empty. In fact, argument *#3* will {\it always\/} be empty, but by
adding the *#3* before the *\c* 
we make argument *#2* an undelimited argument, and
consequently
  argument *#2* will simply be
`*\Thm*' even in the situation where the space occurs,
**
\newclaim@@{...}" \Thm\c{thm}
**
Similarly 
argument *#4* will be
`*thm*',
 and argument *#5* will be `*Theorem*' (even if a space precedes
`*{Theorem}*', since *#5* is an undelimited argument).


The definition of *\newclaim@@* begins
**
\def\newclaim@@#1#2#3\c#4#5{\define#2{}%
 \rightadd@#2\to\claimlist@\rightadd@#2\to\nofrillslist@
**

Illustrating with case ({\bf A}) again,
the
*\define\Thm{}* is inserted simply to allow *\define* to give an error
message if *\Thm* is already defined---for in that case
we certainly don't want 
*\Thm* to be given another meaning by *\newclaim*.
Then we add *\Thm* to *\claimlist@*, for use by *\shortenclaim*, as
explained above, and
to *\nofrillslist@*, since
we will want *\nopunct\Thm* to be allowed.

Next we have to create default values for *\Thm@P*, *\Thm@Q*,
 *\Thm@S*, *\Thm@N*,
 *\Thm@F*,
which will simply be the default values for
*\claim@P*, \dots:
**
\expandafter\def\csname\exstring@#2@P\endcsname{\claim@P}
\expandafter\def\csname\exstring@#2@Q\endcsname{\claim@Q}
"2
\expandafter\def\csname\exstring@#2@S\endcsname{\claim@S}
\expandafter\def\csname\exstring@#2@N\endcsname{\claim@N}
"2
\expandafter\def\csname\exstring@#2@F\endcsname{\claim@F}
**
Notice that we use *\def*, rather than *\let*,
so that when *\newclaim\Thm* is used, *\Thm@P*, \dots\ will be
assigned the current values of *\claim@P*, \dots. These
may have been modified by some
**
\newpre\claim
\newpost\claim
\newstyle\claim
\newnumstyle\claim
\newfontstyle\claim
**
That 
was done because style files may quite well define *\claim@P* to be
something like 
\setbox0\hbox{\<chapter number\>}
\setbox1\hbox{\<section number\>}
**
"box0."box1.
**
 and we would presumably
want such a numbering scheme to be carried through for our *\Thm*. 

[A *\newpost* will usually be made only locally, so that *\claim@Q*
probably won't change, except for individual *\claim*'s. As for
*\claim@S* and *\claim@N*, if the user changes them, presumably the
change should be brought along also for *\Thm*. 
One could always change some of this code, to
**
\expandafter\let\csname\exstring@\Thm@S\endcsname=\claim@S
**
for example, if this doesn't seem like the best arrangement.]

We also make *\endThm* mean *\endclaim*:
**
\expandafter\def\csname end\exstring@#2\endcsname{\endclaim}
**


The counter *\claim@Cthm* may already exist (because of a previous\linebreak
*\claim\c{thm}*); if not, we must create it, with *\newcount@* (again, 
see page~\ref{NWNW}), 
 and,
for safety's sake, initialize it to~*0*:
**
\expandafter\ifx\csname claim@C#4\endcsname\relax
 \expandafter\newcount@\csname claim@C#4\endcsname
 \global\csname claim@C#4\endcsname=0 \fi
**

Then we have to *\let\Thm@C=\claim@Cthm*, which is accomplished by the
  code
**
\edef\next@{\let
 \csname\exstring@#2@C\endcsname
 =\csname claim@C#4\endcsname\endcsname}
\next@
**
Here the first *\csname...\endcsname* will be expanded to *\Thm@C*, which
will be made equivalent to *\relax*, since *\Thm@C* isn't already
defined; on the other hand, the second *\csname...\endcsname* will expand to
*\claim@Cthm*, which has been created with *\newcount@*, and  hence with
a *\countdef*; such control sequences aren't expanded further in an
*\edef* (compare page~\ref{CHARDEFNE}).\pagelabel{CDNE}


After all this, we will want to  define *\Thm*:
**
\def#2{ . . . 
 \def\claimtype@{#2}%
 \def\Claimformat@@{\claimformat@@{#5}}\claim@c\c{#4}}}
**
Thus, *\Thm* will not call *\claim* directly, but instead call
**
\claim@c\c{thm}  "8EEE"8
**
This is where *\claim\c{thm}* usually gets us.\pagelabel{bsc}
  The difference is that
we first take the opportunity to define *\Claimformat@@* 
as
**
\claimformat@@{Theorem}
**
so that the argument `*Theorem*' is automatically supplied, and
 we also take the opportunity to
**
\def\claimtype@{\Thm}
**

In addition, for the sake of *\shortenclaim*  we want to add
**
 \global\claim@i={#1}\gdef\claim@iv{#4}\global\claim@v={#5}
**
In situation ({\bf A}), *\Thm* will thus store
the \<claim clause\>  in the token list *\claim@i*,
the class `*thm*' in *\claim@iv*, and `*Theorem*'
 in the token list
*\claim@v*:\pagelabel{ATE}
**
\def#2{ . . .  
 \global\claim@i={#1}\gdef\claim@iv{#4}\global\claim@v={#5}
 \def\claimtype@{#2}%
 \def\Claimformat@@{\claimformat@@{#5}}\claim@c\c{#4}}}
**
In the next section we will see why we need *\global* assignments.

Finally, we want the claim clause, argument *#1*, to be executed, except
in the special case where we have *\let\noclaimclause@=T*:
**
\def#1{\ifx\noclaimclause@ T\else#1\fi
 \global\claim@i={#1}\gdef\claim@iv{#4}\global\claim@v={#5}
 \def\claimtype@{#2}%
 \def\Claimformat@@{\claimformat@@{#5}}\claim@c\c{#4}}}
**

So the full definition of *\newclaim@@* reads:
\C**
\def\newclaim@@#1#2#3\c#4#5{\define#2{}%
 \rightadd@#2\to\claimlist@\rightadd@#2\to\nofrillslist@%
"2
 \expandafter\def\csname\exstring@#2@P\endcsname{\claim@P}%
 \expandafter\def\csname\exstring@#2@Q\endcsname{\claim@Q}%
"2
 \expandafter\def\csname\exstring@#2@S\endcsname{\claim@S}%
 \expandafter\def\csname\exstring@#2@N\endcsname{\claim@N}%
"2
 \expandafter\def\csname\exstring@#2@F\endcsname{\claim@F}%
 \expandafter\def\csname end\exstring@#2\endcsname{\endclaim}%
"2
 \expandafter\ifx\csname claim@C#4\endcsname\relax
  \expandafter\newcount@\csname claim@C#4\endcsname
  \global\csname claim@C#4\endcsname=0 \fi
"2
 \edef\next@{\let
  \csname\exstring@#2@C\endcsname
  =\csname claim@C#4\endcsname}%
 \next@
"2
 \def#2{\ifx\noclaimclause@ T\else#1\fi
  \global\claim@i{#1}\gdef\claim@iv{#4}\global\claim@v{#5}%
  \def\claimtype@{#2}%
  \def\Claimformat@@{\claimformat@@{#5}}\claim@c\c{#4}}}
**

\small We *\def\endThm{\endclaim}* rather
 *\let\endThm=\endclaim* for situations where
 a style file changes *\endclaim*, and also uses
*\newclaim* to create special claims, like *\Thm*. If we used *\let*,
then the *\newclaim\Thm*
{\it would have to
 come after\/} the redefinition of *\endclaim*, or *\endThm*
would have the wrong meaning. 

On the other hand, even if *\endclaim* isn't changed, but the particular
case of *\endThm* is supposed to be different (leaving extra space perhaps, or
possibly even something more extreme, like an *\hrule* across the page),
then one might have to 
\setbox0\hbox{\<special formatting after *\Thm*\>}
**
\redefine\endThm{\endgroup\claim@false\nopunct@false
  "box0}
**

But special formatting at the beginning of *\Thm* should be handled
as in the case of *\Conj* in section~\Sref{MODC}.
\endsmall


\section{\CS{shortenclaim}}
Finally, we come to *\shortenclaim#1#2*, a typical usage of which is
**
\shortenclaim\Thm\thm
**

The first thing *\shortenclaim* will do, when called this way, is 
**
\define\thm{}
**
 to get an error message if *\thm* is already defined.

Next, *\shortenclaim* will try the test
**
\ismember@\claimlist@\Thm
**
If  this is false, we will just give an error message
**
\Thm not yet created by \newclaim.
**

Otherwise, we will
first add *\thm* to *\nofrillslist@*, and then
make *\thm@S* be  *\Thm@S*, etc:
**
\rightadd@#2\to\nofrillslist@
\expandafter\def\csname\exstring@#2@S\endcsname
  {\csname\exstring@#1@S\endcsname}
 . . .
**
(The \lamstex\ Manual incorrectly
implies, on page~45, that *\thm@S*, etc.,
 will actually
be *\claim@S*, etc., on the grounds that these constructions for
*\Thm* might be changed later on.  That would indeed be a problem if we
used *\let* instead of *\def*, but with the *\def*, any use of
*\newstyle\Thm*, etc., will automatically carry over to *\thm*.  
A problem arises only  if something like *\newstyle\thm* is ever used;
in that case, any succeeding *\newstyle\Thm*'s will no longer carry over
to *\thm*.)


Then, as with *\newclaim*, we must make *\endthm* mean
*\endclaim*, and let *\thm@C* be *\Thm@C*.

Finally, *\shortenclaim* will have to define *\thm*. The problem now
is that we would like to
\setbox0\hbox{\<claim clause\>}
**
\def\thm{"box0
 \def\claimtype@{\thm}%
 \def\Claimformat@@{\claimformat@@{Theorem}{}}%
 \claim@c\c{thm}} "8FFF"8
**
where \<claim clause\> is the claim clause for *\Thm*.  

So we need
a way of getting this \<claim clause\>, as well as the `*thm*' and
`*Theorem*' that actually go with *\Thm*. The strategy for this
is to set a box
\Litbox0=**
\setbox0=\vbox{\Thm""""\relax\endgroup}
**
$$\box0 \tag"\style{\bf A}"$$
because the globally defined token list
*\claim@i* will then contain our desired \<claim clause\>,
*\claim@iv* will be defined to be `*thm*', and the token list
*\claim@v* will contain `*Theorem*'.  We use an empty label *""""* for
the *\Thm* so that the counter won't be increased, and instead of
*\endThm*, 
we just use *\endgroup*, since the other parts of *\endThm*
will be irrelevant in this situation.


Once we have recovered these quantities, we will be in a position to
globally *\def\thm*, but again we will need a somewhat indirect route:
**
\xdef#2{\the\claim@i
 \def\noexpand\claimtype@{\noexpand#2}%
 \def\noexpand\Claimformat@@
  {\noexpand\claimformat@@{\the\claim@v}{}}%
 \noexpand\claim@c\noexpand\c{\claim@iv}}
**
This works as before, noting that for a token list like *\claim@i*, the
expansion of *\the\claim@i* is simply that token list.
(We need token lists to store the \<claim clause\> and the part of the
*\claim*  exemplified by `*Theorem*' because both of these might
contain control sequences, which should  remain unexpanded in the *\xdef*;
on the other hand, the claim class, like a \<label\>, is not supposed to have
expandable tokens in it.)

But there is still
one little fillip that  we need to add: Instead of ({\bf A}),
we really want to use
**
\setbox0=\vbox{\let\noclaimclause@=T
 \Thm""""\relax\endgroup}
**
To see why, imagine a situation (compare section~\Sref{MODC}), where we have
**
\newclaim\Cor\c{cor}{Corollary}
\newclaim\claimclause{\Reset\Cor1}\Thm\c{thm}{Theorem}
\shortenclaim\Thm\thm
**
so that each *\Thm* and *\thm*
resets the numbering of *\Cor*'s to~*1*.
If we were to declare these in a different order,
**
\newclaim\claimclause{\Reset\Cor1}\Thm\c{thm}{Theorem}
\shortenclaim\Thm\thm
\newclaim\Cor\c{cor}{Corollary}
**
then the *\shortenclaim\Thm\thm* will cause us to
**
\setbox0=\vbox{\Thm""""\relax\endgroup}
**
and if
 the \<claim clause\> *\Reset\Cor1* were executed, we would get an error
message, since *\Cor* hasn't been created yet!
So we add the
**
\let\noclaimclause@=T
**
which prevents the \<claim clause\> from being executed.

Summing up, the definition of *\shortenclaim* reads:
\C**
\def\shortenclaim#1#2{\define#2{}%
 \ismember@\claimlist@#1%
"2
 \iftest@
  \rightadd@#2\nofrillslist@%
"2
  \expandafter\def\csname\exstring@#2@S\endcsname
   {\csname\exstring@#1@S\endcsname}%
"2
  \expandafter\def\csname\exstring@#2@N\endcsname
   {\csname\exstring@#1@N\endcsname}%
"2
  \expandafter\def\csname\exstring@#2@P\endcsname
   {\csname\exstring@#1@P\endcsname}%
"2
  \expandafter\def\csname\exstring@#2@Q\endcsname
   {\csname\exstring@#1@Q\endcsname}%
"2
  \expandafter\def\csname\exstring@#2@F\endcsname
    {\csname\exstring@#1@F\endcsname}%
"2
  \expandafter\def
   \csname end\exstring@#2\endcsname{\endclaim}%
"2
  \edef\next@{\let
   \csname\exstring@#2@C\endcsname
   =\csname claim\exstring@#1@C\endcsname}%
  \next@
"2
  \setbox0=\vbox{\let\noclaimclause@=T#1""""\relax\endgroup}%
"2
  \edef#2{\the\claim@i
   \def\noexpand\claimtype@{\noexpand#2}%
   \def\noexpand\Claimformat@@
    {\noexpand\claimformat@@{\the\claim@v}\relax}%
   \noexpand\claim@c\noexpand\c{\claim@iv}}%
"2
 \else
  \Err@{\string#1 not yet created by \string\newclaim}%
 \fi}
**


{

\catcode`\@=11



\def\claimformat@#1#2#3{\medbreak\noindent
\classtest@{conj}\iftest@\llap{\cmbf?\hskip5pt}\fi
 {\smc#1 {\claim@@@F#2} #3\punct@.\addspace@\enspace}%
 \typetest@\Defn\iftest@\cmtenrm
 \else\typetest@\defn\iftest@\cmtenrm\else\cmtensl\fi\fi}

\def\claim@F{\cmbf}

\catcode`\@=\active

\newclaim\claimclause{\Reset\Cor1}\Thm\c{thm}{Theorem}
\shortenclaim\Thm\thm

\newclaim\claimclause{\Reset\Cor1}\Lem\c{thm}{Lemma}
\shortenclaim\Lem\lem

\newclaim\Cor\c{cor}{Corollary}
\shortenclaim\Cor\cor

\newclaim\Defn\c{thm}{Definition}
\shortenclaim\Defn\defn

\newclaim\Conj\c{conj}{Conjecture}
\shortenclaim\Conj\conj

\newnumstyle\Conj\Alph


\section{Customizing \CS{claim}'s\label{MODC}}
To assist in printing different sorts of *\claim*'s  in different  ways,
\lamstex\ provides two tests, 
\C**
\def\classtest@#1{\def\next@{#1}%
 \ifx\next@\claimclass@\test@true\else\test@false\fi}
\def\typetest@#1{\def\next@{#1}%
 \ifx\next@\claimtype@\test@true\else\test@false\fi}
**
Thus, for example,  *\classtest@{thm}* will set *\iftest@* to be true
 precisely
when *\claimclass@* is `*thm*', and *\typetest@\Thm* 
will set *\iftest@* to be true precisely when *\claimtype@* is *\Thm*.

To see how  these are used, let us  suppose that we want our Theorems,
Lemmas, Corollaries, Definitions and  Conjectures to be printed as follows
(temporarily  switching to Computer Modern fonts):

\Reset\Thm6

\lem  If $n$ is odd, then $n^2$ is odd; and if $n$ is even, then
$n^2$ is even.\pagelabel{SAMP}\endlem

\Cor{(Converse)} If $n^2$ is odd, then $n$ is odd; and if $n^2$ is
even, then $n$ is even.\endCor

\Thm{(Pythagoras)}  $\sqrt2$ is irrational.\endThm

\defn An integer  $x$ is a {\cmtenit perfect square\/}
 if $x=y^2$ for some integer $y$.
\enddefn

\conj If $x$ is not a perfect square, then $\sqrt x$ is irrational.\endconj

Thus, Theorems, Lemmas, and Definitions are all numbered together, but
Corollaries begin at 1 after each Theorem or Lemma.  In addition, Definitions
are in *\rm* type.  Finally, Conjectures are numbered completely
independently, as A, B, C, \dots, and they have a {\cmbf?} in the margin.

To set things  up, we first use
**
\newclaim\claimclause{\Reset\Cor1}\Thm\c{thm}{Theorem}
\shortenclaim\Thm\thm
"slip
\newclaim\claimclause{\Reset\Cor1}\Lem\c{thm}{Lemma}
\shortenclaim\Lem\lem
"slip
\newclaim\Cor\c{cor}{Corollary}
\shortenclaim\Cor\cor
"slip
\newclaim\Defn\c{thm}{Definition}
\shortenclaim\Defn\defn
"slip
\newclaim\Conj\c{conj}{Conjecture}
\shortenclaim\Conj\conj
\newnumstyle\Conj\Alph
**

Since *\Thm*, *\Lem* and  *\Defn* all have the same claim class
`*thm*', they  will be numbered together (and the numbering for *\thm*,
*\lem*, and *\defn* follow those for *\Thm*, *\Lem*, and *\Defn*,
respectively).  
 The *\claimclause*'s in
the *\newclaim*'s for *\Thm* and *\Lem* ensure that Corollary numbers
start at  1 after each one; these claim clauses  carry over to *\thm* and
*\lem*.

Finally, we just have to redefine *\claimformat@*  as follows:
**
\catcode`\@=11
"slip
\def\claimformat@#1#2#3{\medbreak\noindent@@
 \classtest@{conj}\iftest@\llap{\bf?\hskip5pt}\fi
"2
 {\smc#1 {\claim@@@F#2} #3\punct@{\null.}\addspace@\enspace}%
 \typetest@\Defn
 \iftest@\rm
 \else
 \typetest@\defn
 \iftest@\rm
 \else\sl\fi\fi}
"slip
\catcode`\@=\active
**

Then the output on page~\ref{SAMP} will be produced by
**
\lem  If $n$ is odd, ... \endlem

\Cor {(Converse)} If $n^2$ is odd ... \endCor

\Thm{(Pythagoras)}  $\sqrt2$ is irrational.\endThm

\defn An integer $x$ is a perfect square ... \enddefn

\conj If $x$ is not a perfect square, ... \endconj
**

 
} % matches { before previous \section

\chapter Heading levels\label{HLS}\endchapter

The ``heading levels''
 *\HL* and *\hl* exhibit a strange mixture of the features of
 *\list* and *\claim*. They have levels, like *\list*, but these levels
indicate separate entities, rather than parts of a single construction.
And we can create new names, like
*\chapter* and *\section* for, say, *\HL1* and *\hl1*,  but this is somewhat
different than creating new *\claim*'s with *\newclaim*, because *\chapter*
is essentially just a synonym for *\HL1*, rather than a new class of heading
levels. 

Moreover, heading levels introduce yet
another complication, since they are constructions
that get written to the table of contents file, which we need to consider
first. 

\section{The {\tt.toc} file}
In  version *1* of \lamstex@, headings  were written to the
*.toc* file, while the corresponding page numbers were written to a separate
*.tpg* file.
Now, however, the page numbers are written together with the headings in the
 *.toc* file.

On the other hand, *\island*'s, and their page numbers, will be written to a
separate file, which I can't resisting calling the *.tic* file, even though
it's not really a proper acronym.\pagelabel{TICFILE}
 Corresponding to *\indexfile*
(page~\ref{INDEXFILE}), we have
\C**
\newif\iftoc@
\def\tocfile{\iftoc@\else
 \alloc@@7\write\chardef\sixt@@n\toc@ "8ZYX"8
 \immediate\openout\toc@=\jobname.toc
 \alloc@@7\write\chardef\sixt@@n\tic@
 \immediate\openout\tic@=\jobname.tic
 \global\toc@true\fi}
**


\section{Preliminaries}
To begin with, we want to add *\hl* to *\nofrillslist@*:
\C**
\rightadd@\hl\to\nofrillslist@
**

We don't need to add *\HL* to *\nofrillslist@*, since these heading levels
don't have any punctuation in the default style (compare the small print
section on page~\ref{NOFC}).  But *\HL*
can be preceded
by *\overlong*, so we need to
\C**
\rightadd@\HL\to\overlonglist@
**


\section{Different levels of \CS{HL}}
Just as the *\list* construction used *\listlevel@* to keep track of the
*\list* level, we will use *\HLlevel@* to keep track of the *\HL*
level. But *\listlevel@* was a counter, whereas *\HLlevel@* will simply be
a control sequence that will be defined to have the proper value.
\footnote{This has the advantage that in various *\edef*'s, *\csname ...
\endcsname*'s, etc., we
 can use *\HLlevel@*
alone instead of *\number\HLlevel@*. On the other hand,
it was a little more efficient
to have *\listlevel@* be a counter, since at one point we 
*\advance\listlevel@*.}

Analogous to *\list@@C*, \dots, we have
\C**
\def\HL@@C{\csname HL@C\HLlevel@\endcsname}
"2
\def\HL@@P{\csname HL@P\HLlevel@\endcsname}
"2
\def\HL@@Q{\csname HL@Q\HLlevel@\endcsname}
"2
\def\HL@@S{\csname HL@S\HLlevel@\endcsname}
"2
\def\HL@@N{\csname HL@N\HLlevel@\endcsname}
"2
\def\HL@@F{\csname HL@F\HLlevel@\endcsname}
**

In addition, as with *\claim*, we will have *\HLtype@*, which will be
defined
to be *\chapter*  when we are using *\chapter* instead of *\HL1*, etc.
However, *\HL* itself will simply 
*\let\HLtype@=\relax*.

Corresponding  to *\claim@@@C*, etc., we define
\C**
\def\HL@@@C{\csname\exxx@\HLtype@ @C\endcsname}
"2
\def\HL@@@P{\csname\exxx@\HLtype@ @P\endcsname}
"2
\def\HL@@@Q{\csname\exxx@\HLtype@ @Q\endcsname}
"2
\def\HL@@@S{\csname\exxx@\HLtype@ @S\endcsname}
"2
\def\HL@@@N{\csname\exxx@\HLtype@ @N\endcsname}
**
all of which will only be used when *\HLtype@* is not *\relax*;
*\HL@@@F* won't be needed at all.

\section{The \CS{HL} construction\label{HLC}}
Roughly speaking, *\HL1* will translate to
`*\HL@1*' and *\HL2* will
translate to `*\HL@2*', \dots, while an error message will be given
if the corresponding control sequence `*\HL@*{\it n\/}' does not exist.
The default style defines `*\HL@1*' (section~\Sref{CHL}), and it is up to
other style files to define any further such constructions.
We use quotation marks around *\HL@*\,{\it n\/} as before (see
page~\ref{QTS4}). 


Assuming that *\HL#1* can be used, we will not call `*\HL@#1*'
 directly, but
instead store *#1* in *\HLlevel@* and  call *\HL@*, where
*\HL@* will then take care of calling `*\HL@*\,{\it n}' where {\it n\/}
is the value *\HLlevel@*.
 We do this
so that something like *\chapter* can simply define *\HLlevel@* to be
~*1* and then call *\HL@* directly.

Actually, *\HL#1* will call *\FNSS@\HL@*, because we need to
see if a quoted *\HL* number *""...""* follows, and 
we also have to skip over any 
space between the argument *#1* of *\HL#1* and the next token;
 moreover, we will 
define *\HLname@* to be *\HL{#1}*, for use when writing to the *.toc*
file (section~\Sref{WTOC}), and we initialize *\HLtype@* to be *\relax*:
\C**
\def\HL#1{\expandafter
 \ifx\csname HL@C#1\endcsname\relax
  \def\next@{\Err@{\string\HL#1 not defined in this style}}%
"2
 \else
  \def\next@{\gdef\HLlevel@{#1}\def\HLname@{\HL{#1}}%
   \let\HLtype@=\relax\FNSS@\HL@}%
 \fi
 \next@}
**
We use a *\gdef\HLlevel@* just in case *\HL* happens to be used within a
group, because the value of *\HLlevel* might be of interest after  the
*\HL* has  been  printed (compare section~\Sref{HLLEV}).



The action of *\HL@* will depend on whether a *""* follows next, so
 *\HL@* will essentially be defined as
**
\def\HL@{%
 \def\next@""##1""##2\endHL{...}
 \def\nextii@##1\endHL{...}
 \ifx\next""\expandafter\next@\else\expandafter\nextii@\fi}
**
Both *\next@* and *\nextii@* will be calling
**
\csname HL@\HLlevel@\endcsname##1\endHL
**
where things like
**
\expandafter\def\csname HL@1\endcsname#1\endHL{...}
\expandafter\def\csname HL@2\endcsname#1\endHL{...}
**
are the basic data that a style file will provide.

\medskip
{\bf(1) }%
*\next@* first stores *##2* in *\entry@*, for eventually writing to the
*.toc* file.
**
\def\next@""##1""##2\endHL{\def\entry@{##2} . . .
**
Then
 *\next@* must create
*\Thelabel@*, \dots, *\Thelabel@@@@*. The preliminary
step
**
\let\pre=... \let\post=...
**
must be divided into
two cases, depending on whether we are  using an ordinary *\HL*\<number\>, 
so that  *\HLtype@* is *\relax*, or a substituted name, like
*\chapter*, in which case *\HLtype@* will  be defined to be *\chapter*:
**
\ifx\HLtype@\relax
 \let\pre=\HL@@P \let\post=\HL@@Q
 \let\style=\HL@@S  \let\numstyle=\HL@@N
\else
 \let\pre=\HL@@@P \let\post=\HL@@@Q
 \let\style=\HL@@@S \let\numstyle=\HL@@@N
\fi
\Qlabel@{##1}
**
Note that this  would be much harder to state if  we hadn't introduced
*\HL@@@P*, \dots, and compare page~\ref{ADEQ}.


After defining *\Thelabel@*, \dots, *\Thelabel@@@@*, 
we  will want to store  the value of 
*\Thelabel@@@@*
in
*\Thepref@*.\pagelabel{STORETP} The  reason for this is that after  the 
appropriate
\setbox0\hbox{`*\HL*\<number\>'}
**
"box0 ... \endHL
**
construction, we may perform other steps using the value of
 *\Thelabel@@@@*, and it is possible  (though
unlikely) that the *\HL..."allowbreak\endHL* 
construction contains some other
construction allowing \<label\>'s, which would then create new values
for *\Thelabel@@@@*.\pagelabel{PTU}
\footnote{*\footnote*  is really the only plausible candidate for this,
aside from user-constructed counters.
(*\tag* might seem like a candidate, except  that  displayed formulas
aren't allowed in headings; actually they can easily be simulated by
setting *$\dsize...$*  on a separate line, but it would be quite strange to
expect  such a formula to have a  *\tag* over at the margin).}

But this is one other detail that we need to worry about, 
in connection with writing
information to the *.toc* file (section~\Sref{WTOC}). Normally, we will be
using *\Thelabel@@@@@* for the properly formatted heading number that we will
write to the *.toc* file.  Thus, we will be writing the number, together with
any pre- and post- material, but without extra formatting determined by the
style, so that we can use a different formatting style in the Contents
if we desire.
For example, in the text we might print *\hl1* numbers as `\Ssymbol1',
`\Ssymbol2', \dots\ (compare the small print section on page~\ref{NOFC}),
but we want the option of including or omitting the \Ssymbol\ in the Contents.

If we do decide to print the \Ssymbol\ in the Contents, then we will have a
bit of quandary when we are dealing with a ``quoted'' number, like
**
\HL1 ""B"" ... \endHL
**
In this case, the printed number will appear as `B' rather than
`\Ssymbol B', so it should presumably also appear that way in the contents;
on the other hand, *""\style B""* would appear as `\Ssymbol B', so should
continue to appear that way in the Contents.

What this means is that quoted numbers {\it should also appear quoted
in the *.toc* file}, and that any occurrence of *\style* in a quoted
number {\it should also appear in the *.toc* file}, although occurrences
of *\pre* and *\post* should simply be expanded out to their proper values.

(This is admittedly a rather piddling point; compare the small print section
on page~\ref{PIDD}.)


To handle this, we  introduce a new flag
\C**
\newif\ifquoted@
**
which we will set true right after defining *\entry@*,
and after the\linebreak *\Qlabel@{##1}* we will add
**
\let\style=\relax\xdef\Qlabel@@@@@{##1}
**
so that *\style* will remain unexpanded in *\Qlabel@@@@*; on the other
hand, *\nextii@* will set *\ifquoted@* to be false
and won't define
*\Qlabel@@@@*.



After all this, we use
**
\csname HL\HLlevel@\endcsname##2\endHL
**
to actual typeset the heading.

[We use *##2* explicitly, rather than *\entry@*, because certain style
files, like the *book* style, store the argument of `*\HL@1*'*...\endHL*
for use in running heads. In such cases, we want to store the actual heading
 that was originally typed, not simply *\entry@*, since *\entry@* may
have changed its meaning by the time the running head is typeset.]

Then
we will use
**
\csname HL@I\HLlevel@\endcsname
**
to perform the  proper ``initializations'', determined by the style file.
For example, the default style file will basically make `*\HL@I1*'  
mean
**
\Reset\hl1{1}
\newpre\hl1{\Thepref@.}
**
(recall [page~\ref{STORETP}] that *\Thepref@* holds the value of
*Thelabel@@@@*),
so that 
in the first  *\HL1*, the *\hl1* numbers will be 1.1, 1.2, \dots;  in
the second *\HL1*,  they will be 2.1, 2.2, \dots; etc. As we will see
in Chapter~\ref{acces}, a *\newpre* will essentially do an  *\edef*, so
that  the current value of
*\Thepref@* will be stored in the pre-material for  *\hl1*.
\pagelabel{NEWPREDEF} 

And after that  we will use
\setbox0\hbox{`*\HL@J1*'}
**
\csname HL@J\HLlevel@\endcsname
**
to perform ``initializations'' prescribed by the user, via *\Initialize*
(section~\Sref{ATEVERY}); as we will see  in  section~\Sref{EVERY}, 
*\Initialize*
simply defines  things  like `*\HL@J1*'.

Before performing these two routines we will 
**
\let\pref=\Thepref@
**
so that any *\pref*  that  the  user places in
an *\Initialize* will be interpreted properly (this even allows the style file
designer to use *\pref* in defining `*\HL@I1*'), and we will use *\pref@*
to restore the original definition of *\pref*:
%In this process we will want any *\newpre*'s that we encounter to have a
%{\it global\/} effect, rather  than their usual local effect.
%\pagelabel{GLNEW} 
% For this 
%purpose  (compare page~\ref{EFFL}),
%we initially
%\C**
%\let\globalnews@=F
%**
%and we will arrange (Chapter~\ref{acces}) for
% the *\new...* constructions to have a global effect 
%when we *\let\globalnews@=T*, so that we can use the group
**
\let\pref=\Thepref@
\csname HL@I\HLlevel@\endcsname
\csname HL@J\HLlevel@\endcsname}
\let\pref=\pref@
**

Then we will use
**
\HLtoc@  "8WTOCF"8
**
to write  to the *.toc* file, if necessary.
 *\HLtoc@* won't be defined until
section~\Sref{WTOC}.

After writing to the *.toc* file,  yet other steps may be required, which
we call *\aftertoc@*.  Initially we 
**
\let\aftertoc@=\relax
**
but various heading level definitions may change this (compare
section~\Sref{AFTOC}).

Finally, after that  we simply want to reset values  that may have been set
before the *\HL@*:
**
\let\aftertoc@=\relax \overlong@false
**

\medskip

{\bf(2) }%
*\nextii@* is exactly analogous, except that for defining *\Thelabel@*,
\dots, we will need
**
\ifx\HLtype@\relax
"2
 \global\advance\HL@@C by 1
"2
 \xdef\Thelabel@@@{\number\HL@@C}%
 \xdefThelabel@{\HL@@N}%
"2
 \xdef\Thelabel@@@@{\HL@@P\Thelabel@\HL@@Q}%
 \xdefThelabel@@{\HL@@S}%
"2
\else
 \global\advance\HL@@@C by 1
"2
 \xdef\Thelabel@@@{\number\HL@@@C}%
 \xdefThelabel@{\HL@@@N}% 
"2
 \xdef\Thelabel@@@@{\HL@@@P\Thelabel@\HL@@@Q}%
 \xdefThelabel@@{\HL@@@S}%
\fi
**
(and, as already mentioned,
 we set *\ifquoted@* to be false, and do not define *\Qlabel@@@@*).

The  whole  definition of *\HL@* is:
\C**
\let\aftertoc@=\relax
"slip
\def\HL@{%
 \def\next@""##1""##2\endHL{\def\entry@{##2}\quoted@true
  {\noexpands@
  \ifx\HLtype@\relax
   \let\pre=\HL@@P \let\post=\HL@@Q
   \let\style=\HL@@S \let\numstyle=\HL@@N
  \else
   \let\pre=\HL@@@P \let\post=\HL@@@Q
   \let\style=\HL@@@S \let\numstyle=\HL@@@N
  \fi
  \Qlabel@{##1}\let\style=\relax\xdef\Qlabel@@@@{##1}%
  \xdef\Thepref@{\Thelabel@@@@}}%
"2
  \csname HL@\HLlevel@\endcsname##2\endHL
"2
  \let\pref=\Thepref@
  \csname HL@I\HLlevel@\endcsname
  \csname HL@J\HLlevel@\endcsname
  \let\pref=\pref@
"2
  \HLtoc@
  \aftertoc@
"2
  \let\aftertoc@=\relax \overlong@false}%
"2
 \def\nextii@##1\endHL{\def\entry@{##1}\quoted@false
  {\noexpands@
  \ifx\HLtype@\relax
   \global\advance\HL@@C by 1 
   \xdef\Thelabel@@@{\number\HL@@C}%
   \xdefThelabel@{\HL@@N}%
   \xdef\Thelabel@@@@{\HL@@P\Thelabel@\HL@@Q}%
   \xdefThelabel@@{\HL@@S}%
  \else
   \global\advance\HL@@@C by 1  
   \xdef\Thelabel@@@{\number\HL@@@C}%
   \xdefThelabel@{\HL@@@N}% 
   \xdef\Thelabel@@@@{\HL@@@P\Thelabel@\HL@@@Q}%
   \xdefThelabel@@{\HL@@@S}%
  \fi
  \xdef\Thepref@{\Thelabel@@@@}}%
  \csname HL@\HLlevel@\endcsname##1\endHL
"2
   \let\pref=\Thepref@
   \csname HL@I\HLlevel@\endcsname
   \csname HL@J\HLlevel@\endcsname
   \let\pref=\pref@
"2
  \HLtoc@
  \aftertoc@   
"2 
 \let\aftertoc@=\relax \overlong@false}%
 \ifx\next""\expandafter\next@\else\expandafter\nextii@\fi}
**

In all these definitions, *\endHL* simply functions as syntax, so we want
to declare (see section~\Sref{K})
\C**
\Invalid@\endHL
**



As of yet, no heading level *\HL* has actually been defined.  Before
considering this, however, we first tend to *\hl*.





\section{The \CS{hl} construction}
Everything for *\hl* is almost exactly analogous to that for *\HL*:

We start with
\C**
\def\hl@@C{\csname hl@C\hllevel@\endcsname}
"2
\def\hl@@P{\csname hl@P\hllevel@\endcsname}
"2
\def\hl@@Q{\csname hl@Q\hllevel@\endcsname}
"2
\def\hl@@S{\csname hl@S\hllevel@\endcsname}
"2
\def\hl@@N{\csname hl@N\hllevel@\endcsname}
"2
\def\hl@@F{\csname hl@F\hllevel@\endcsname}
**

Then we 
define
\C**
\def\hl@@@C{\csname\exxx@\hltype@ @C\endcsname}
"2
\def\hl@@@P{\csname\exxx@\hltype@ @P\endcsname}
"2
\def\hl@@@Q{\csname\exxx@\hltype@ @Q\endcsname}
"2
\def\hl@@@S{\csname\exxx@\hltype@ @S\endcsname}
"2
\def\hl@@@N{\csname\exxx@\hltype@ @N\endcsname}
**

Similarly, we define
\C**
\def\hl#1{\expandafter
 \ifx\csname hl@C#1\endcsname\relax
  \def\next@{\Err@{\string\hl#1 not defined in this style}}%
"2
 \else
  \def\next@{\gdef\hllevel@{#1}\def\hlname@{\hl{#1}}%
   \let\hltype@=\relax\FNSS@\hl@}%
 \fi
 \next@}
**


Then we define *\hl@* as follows (see the remarks at the end regarding the
*\FNSSP@*'s): 
\C**
\def\hl@{%
 \def\next@""##1""##2{\def\entry@{##2}\quoted@true
  {\noexpands@
"2
  \ifx\hltype@\relax
   \let\pre=\hl@@P \let\post=\hl@@Q
   \let\style=\hl@@S \let\numstyle=\hl@@N
"2
  \else
    \let\pre=\hl@@@P \let\post=\hl@@@Q
   \let\style=\hl@@@S \let\numstyle=\hl@@@N
  \fi
"2
  \Qlabel@{##1}\let\style=\relax\xdef\Qlabel@@@@{##1}%
  \xdef\Thepref@{\Thelabel@@@@}}%
"2
  \csname hl@\hllevel@\endcsname{##2}}%
"2
   \let\pref=\Thepref@
   \csname hl@I\hllevel@\endcsname
   \csname hl@J\hllevel@\endcsname
   \let\pref=\pref@
"2
  \hltoc@
  \aftertoc@
  \let\aftertoc@=\relax 
  \nopunct@false \nospace@false \FNSSP@}%
"2
 \def\nextii@##1{\def\entry@{##1}\quoted@false
  {\noexpands@
"2
  \ifx\hltype@\relax
"2
   \global\advance\hl@@C by 1 
"2
   \xdef\Thelabel@@@{\number\hl@@C}%
"2   \xdefThelabel@{\hl@@N}%
   \xdef\Thelabel@@@@{\hl@@P\Thelabel@\hl@@Q}%
"2
   \xdefThelabel@@{\hl@@S}%
  \else
   \global\advance\hl@@@C by 1 
"2
   \xdef\Thelabel@@@{\number\hl@@@C}%
"2
   \xdefThelabel@{\hl@@@N}% 
"2
   \xdef\Thelabel@@@@{\hl@@@P\Thelabel@\hl@@@Q}%
   \xdefThelabel@@{\hl@@@S}%
  \fi
  \xdef\Thepref@{\Thelabel@@@@}}%
"2
  \csname hl@\hllevel@\endcsname{##1}}%
"2
   \let\pref=\Thepref@
   \csname hl@I\hllevel@\endcsname
   \csname hl@J\hllevel@\endcsname
   \let\pref=\pref@
"2
  \hltoc@
  \aftertoc@
  \let\aftertoc@=\relax 
  \nopunct@false \nospace@false \FNSSP@}%
 \ifx\next""\expandafter\next@\else\expandafter\nextii@\fi}
**
The *\FNSSP@*'s are added to deal with spaces and invisible constructions
 that might occur
after the whole
*\hl*\<number\>*{...}* combination. (It wouldn't  do any good to add the
*\FNSSP@*'s to the definitions of `*\hl@1*', \dots, since 
other material comes after them in the definition of *\hl@*.)

\section{Other elements of heading levels\label{OTHERE}}
In the default style, *\newstyle*
can be used to change the 
style for printing
 *\HL* and *\hl* numbers,  and
*\nopunct* and *\nospace* can be used to control
the punctuation and spacing that follows 
an *\hl* heading level (compare page~\ref{NEWWSTUFF}).

On the other hand, most styles will have one further element of a heading
level that we might want to control, namely,
a word like `Chapter' that is printed
before the *\HL* number.

Someone writing in German would naturally want to replace `Chapter' with
`Kapitel', etc.
Although such a replacement could easily 
be made directly within the style file, there is considerable objection to
this, on the grounds that additional style files shouldn't have to be made
for such minor changes.  

So, to the pantheon of constructions like
*\...@C*, *\...@P*, \dots, we admit one more candidate,
 *\...@W*,  the ``word''
associated with a construction.
This will be complemented by a construction
*\newword*, analogous to *\newpre*, \dots, (Chapter~\ref{acces}),  
allowing  us to change its values, as well as *\word*, to
print its value. From the point of view of the user, *\word* and *\newword*
will work just like *\pre* and *\newpre*, etc., but they will be not be 
applicable
to all constructions allowing labels, only to a select few (and also
one or two constructions that do not allow labels---see
section~\Sref{SBMACS}). 

The idea of this device is that a style file can define 
`*\HL@1*'
in terms of
`*\HL@W1*', which might initially be defined to mean *Chapter*.
 Then if the user types
**
\newword\HL1{Kapitel}
**
thereby redefining `*\HL@W1*',
the word `Kapitel' will be substituted for `Chapter' in the *\HL1* headings. 

\section{Writing long token lists\label{WLTL}} As we saw 
in section~\Sref{UNMACRO},
the construction
**
\expandafter\unmacro@\meaning\entry@\unmacro@
**
will make *\macdef@* contain the tokens of *\entry@*, but with all non-space
tokens converted to type~*12*.

This means that *\macdef@* can be used in a *\write*, without worrying about
expansions.  But we still have to worry about the fact that a heading
may be too long for a *\write*.  This may be true even for implementations of
\tex\ that allow rather long *\write*'s, since there is no theoretical limit
on the length of a heading; the problem is particular acute for
  *\caption*'s (Part~\ref{ISLANDS}), which might 
be quite long.

Consequently, we will simply arbitrarily split *\macdef@* at every sixth
space
\footnote{In version *1* of \lamstex@, lines were split at every fifth space;
but six seems safe enough, especially since, as we mention below, various
spaces that didn't count in version~*1* will count now.}
 when we *\write* to the *.toc* file; to make the *.toc* file look
better, we will add a space at the beginning of each piece.

To do this quickly, we will make a definition like
**
\def\six@#1 #2 #3 #4 #5 #6 {\def\next@{#1}%
 \ifx\next@\empty\def\next@##1\six@{}\else
 \write\toc@{" #1 #2 #3 #4 #5 #6}\let\next@=\six@\fi
 \next@}
** 
and then use
\setbox0\hbox{\<material to be split\>}
**
\six@"box0" " " " " " " " " " " " \six@
**
with 12 *" *'s added. Thus, *\six@* will  extract six
pieces, write them to the *.toc* file,
and then
 call *\six@* once again, except when
*#1* is empty (in which case *#2*, \dots, *#6* will also be
empty).
  The first time this happens, everything has
already been written, so we simply throw away everything up to and including
the final *\six@*. 
(At the next-to-last stage, *#1* might be the last piece, and thus the
 only non-empty argument of *\six@*.
Then *\six@* will use up ~6 of the inserted
*" *'s (unless this last piece of the
\<material to be split\> happened to end with a *" * itself). So we need
~6 more *" *'s, to be used up by the next call to *\six@*.)

This all fails spectacularly, however, if the \<material to be split\>
is empty, or
happens to begin with a space! So we will have to be careful about that.

Since we are going to need a similar routine to *\write* to the *.tic* file
in Chapter~\ref{PI}, the `*\toc@*' in the above definition will be replaced
by an argument *#1*, so that we define
\C**
\def\six@#1#2 #3 #4 #5 #6 #7 {\def\next@{#2}%
 \ifx\next@\empty
  \def\next@##1\six@{}%
 \else
  \write#1{ #2 #3 #4 #5 #6 #7}\def\next@{\six@#1}%
 \fi
 \next@}
**

We are going to be applying this when 
the \<material to be split\> is
stored in *\macdef@*.
If *\macdef@* happens to be empty (because of an empty heading level),
we will do nothing. Otherwise,
 we will first eliminate any initial space in *\macdef@* with
**
\def\next@#1#2\next@{\def\macdef@{#1#2}}
\expandafter\next@\macdef@\next@
**
If *\macdef@* originally
expands to *" s*$_{\text{1}}$*s*$_{\text{2}}$\dots, then
*#1* will be *s*$_{\text 1}$, since \tex\ ignores spaces in looking for
undelimited arguments, and *#2* will be *s*$_{\text2}$\dots, so the new
*\macdef@* will be the old, with any initial space deleted. 


Then we will use
**
\edef\next@
 {\noexpand\six@\toc@\macdef@ "8SEVENTOC"8
 \space\space\space\space\space\space
 \space\space\space\space\space\space\noexpand\six@}
 \next@
**
The *\edef* not only inserts 12~spaces, but it also
expands out *\macdef@* to its current value, so that the resulting
 series of (delayed) *\write*'s doesn't depend on what value *\macdef@* may
have by the time the *\write*'s are done.

Finally, we will use 
**
\let\macdef@=\relax
**
to clear up memory space, since *\macdef@* might be quite long.

The whole definition is:
\C**
\def\Sixtoc@{\ifx\macdef@\empty\else
 \def\next@##1##2\next@{\def\macdef@{##1##2}}%
 \expandafter\next@\macdef@\next@
 \edef\next@
  {\noexpand\six@\toc@\macdef@
  \space\space\space\space\space\space
  \space\space\space\space\space\space
  \noexpand\six@}%
 \next@\let\macdef@=\relax\fi}
**



\small 
Even if some argument for *\six@* is of the form *{...}*, \tex\ {\it
won't\/} remove the braces, since these are now type~*12* characters, not
real braces. (In version~*1* of \lamstex@, where this wasn't the case, a much
more complicated routine was required.)  Similarly, we don't have to worry
about braces being removed during the first stage of deleting any
initial space.

\andsmall Some remarks near the end of page~87 of the \lamstex~Manual
are now wrong.  Now spaces after control words {\it are\/}
 counted in this break-up
process (and will be inserted even if they weren't typed in the input file).
Spaces within curly braces will also count (since these type~*12* braces
won't introduce any grouping for the arguments). This has the added
advantage that one doesn't have to worry about a long group within a heading.

\andsmall If the prospect of  short lines in the *.tic* file is too
unappealing, a more complicated routine could be used, in which we selected
the pieces delimited by spaces one at a time, and stored them until we
obtained a sufficiently large aggregate; the ``size'' of a collection *#1* of
type~*12* tokens is easily computed by examining the width of
*\hbox{\tt#1}*.
\endsmall


\section{\CS{HLtoc\@} and \CS{hltoc\@}\label{WTOC}}
For *\HLtoc@*, we want to write either something like
\setbox0\hbox{\<heading level\>}
\setbox1\hbox{\<formatted *\HL* number\>}
\setbox2\hbox{\<page number\>}
\setbox3\hbox{\<word\>}
**
\HL {"box0}{"box3}{"box1}
 The heading, with line breaks after 
 every sixth space. 
\Page{"box2}{\arabic }{}{}
**
or something like
\setbox1\hbox{\<formatted *\chapter* number\>}
\setbox3\hbox{\<word\>}
**
\chapter {"box3"}{"box1} . . .
 The heading, with line breaks after 
 every sixth space. 
\Page{"box2}{\arabic }{}{}
** 
if we have created *\chapter* as a name for *\HL1*, say, using
*\NameHL* (section~\Sref{RHL}). [If the heading is empty, then we will
simply have the *\Page...* line follow the *\HL* line.]

Here \<word\> is the value of
`*\HL@W*{\it n\/}' (section~\Sref{OTHERE}).  In the default style
`*\HL@W1*' is empty, while for the book style *book.st*
*\HL1* ({\it alias\/} *\chapter*) has *\HL@W1* initially defined as *Chapter*.
Notice that the \<word\> is treated as a separate argument from the
\<formatted number\>. So, even if the heading level itself prints something
like
\medskip
\centerline{\bf Chapter 3. \dots{}}
\medskip
\flushpar
the table of contents will be able to combine these elements in different
ways, if desired.

This whole arrangement is a big change from version~*1* of \lamstex@;
 in addition
to the \<word\>,
 the page number is included, and all the other information appears
without extraneous matter that made the *.toc* file harder to read.



To handle the special case of quoted numbers, we define
\C**
\def\QorThelabel@@@@@{\ifquoted@
 \noexpand\noexpand\noexpand""\Qlabel@@@@
 \noexpand\noexpand\noexpand""\else
 \Thelabel@@@@\fi}
**
so that *\QorThelabel@@@@* will expand in 
 an *\edef* to either
\setbox0\hbox{\<expansion of *\Qlabel@@@@*\>}
\setbox1\hbox{\<expansion of *\Thelabel@@@@*\>}
**
\noexpand"""box0\noexpand""
**
or to
**
"box1
**

Our first *\write* will involve *\HLname@*, which is either *\HL {*\<heading
level\>*}* or something like *\chapter*;  the \<word\>
for the heading level;
and *\QorThelabel@@@@*, 
 the actual
\<formatted number\> (or *\Qlabel@@@@*).
 However, this will be a delayed *\write*, and the
values of *\HLname@* and 
*\Thelabel@@@@* or *\Qlabel@@@@*
may be completely different by the time
the *\write* is executed, so everything has to be expanded out.

For *\QorThelabel@@@@* we need to be in a group with *\noexpands@*;
moreover, within this group we need to *\let\style=\relax*, in case
*\style* appears in *\Qlabel@@@@*.

For *\HLname@* we need something like
**
\edef\next@{\write\toc@{\noexpand\noexpand
 \expandafter\noexpand\HLname@}}
\next@
**
In this *\edef*, the  *\toc@* is not expanded,\pagelabel{TKSNE} since it 
was created with a *\chardef* (compare page~\ref{CDNE}),
 the 
 *\noexpand\noexpand*  collapses to a single *\noexpand*, and
the *\expandafter\noexpand\HLname@* (compare pages~\ref{EXNE} and
~\ref{EXNE2}) 
inhibits expansion of a control sequence
occurring at the beginning of the expansion of *\HLname@* (i.e., either
*\HL* or *\chapter*, etc.) Thus, our *\edef* makes *\next@* mean
\setbox0\hbox{\<*\HL1* or *\chapter*, etc.\>}
**
\write\toc@{\noexpand"copy0}
**
so that *\next@* then gives us
 what we want.

The \<word\>, stored in `*\HL@W1*', etc., presents more problems,
because it may contain control sequences that shouldn't be expanded out
in the *\write*. So we will use the *\unmacro\meaning* trick of
section~\Sref{WLTL}, within the triple *\expandafter* trick
(page~\ref{tEXA}): the code
**
\expandafter\expandafter\expandafter\unmacro@
 \expandafter\meaning\csname HL@W\HLlevel@\endcsname\unmacro@
**
will make *\macdef* contain the tokens of the \<word\>, but with all
non-space tokens converted to type~*12*.\pagelabel{XXZZXX}

So, altogether, we can use
**
\expandafter\expandafter\expandafter\unmacro@
 \expandafter\meaning\csname HL@W\HLlevel@\endcsname\unmacro@
{\noexpands@\let\style=\relax
\edef\next@{\write\toc@{\noexpand\noexpand\expandafter\noexpand
 \HLname@{\macdef@}{\QorThelabel@@@@}}
\next@}
**
Note that, just as we will need to declare *\noexpands@* before
a *\shipout*,
 when the *\write* is actually done (pages~\ref{SUB1} and~\ref{SUB99}), 
 we will also need to declare
*\let\style=\relax*  before the *\shipout*.\pagelabel{SUB11}

Then we use 
**
\expandafter\unmacro@\meaning\entry@\unmacro@
\Sixtoc@
**
to write the heading, with all non-space characters of type~*12*, and line
breaks after every sixth space.

Finally, we  add
**
\write\toc@{\noexpand\Page{\number\pageno}{\page@N}%
 {\page@P}{\page@Q}^^J}
**
where the extra blank line at the end is added
to make the *.toc* file more
readable.  
\footnote{Blank lines after the *\Page...* line
 will usually create no problem, since the table of contents will be usually
be set
as a series of lines each contributed in vertical mode. But 
it's conceivable that a style file will format things in a way that
puts us into horizontal mode, and then it might be important that
we not leave horizontal mode after the page number is printed; in such
cases, the macros must scan for *\Page#1#2#3#4\par*, to eliminate the 
blank line.
Although this is an added pain, it is unlikely to occur often, so it seems
worth while adding the extra readability to the *.toc* file. 
\endgraf
In the case of the index, where an unknown number of *\Page*'s can follow
each *\Entry*, we will be careful to eliminate such *\pars*'s (section~
\Sref{BMPRE}).}

 (During the *\write* we will have
*\noexpands@* in effect, so that the numbering control sequence
*\page@N* won't be expanded, nor will any font change control sequences
in *\page@P* or *\page@Q*.)


So our final definition is:
\C**
\def\HLtoc@{%
 \iftoc@
"2
 \expandafter\expandafter\expandafter\unmacro@
  \expandafter\meaning
   \csname HL@W\HLlevel@\endcsname\unmacro@
"2
  {\noexpands@\let\style=\relax
  \edef\next@{\write\toc@{%
   \noexpand\noexpand\expandafter\noexpand\HLname@
   {\macdef@}{\QorThelabel@@@@@}}}%
  \next@}%
"2
  \expandafter\unmacro@\meaning\entry@\unmacro@
"2
  \Sixtoc@
"2
  \write\toc@{\noexpand\Page{\number\pageno}{\page@N}%
    {\page@P}{\page@Q}^^J}%
 \fi}
**

\medbreak
For *\hltoc@* we want to write something like
\setbox0\hbox{\<heading level\>}
\setbox1\hbox{\<formatted *\hl* number\>}
\setbox2\hbox{\<page number\>}
\setbox3\hbox{\<word\>}
**
\hl {"box0}{"box3"{"box1}
 The heading, with line breaks after 
 every sixth space
\Page{"box2}{\arabic }{}{}
**
or something like
\setbox1\hbox{\<formatted *\section* number\>}
\setbox2\hbox{\<page number\>}
\setbox3\hbox{\<word\>}
**
\section {"box3"}{"box1} .
 The heading, with line breaks after every
 sixth space
\Page{"box2}{\arabic }{}{}
** 
In addition, we want *\nopunct* and *\nospace*
to appear before the *\hl* or *\section*
in the *\write* if they appeared in the input file:
\C**
\def\hltoc@{%
 \iftoc@
"2
 \expandafter\expandafter\expandafter\unmacro@
  \expandafter\meaning
   \csname hl@W\hllevel@\endcsname\unmacro@
"2
  {\noexpands@\let\style=\relax
  \edef\next@{\write\toc@{%
   \ifnopunct@\noexpand\noexpand\noexpand\nopunct\fi
   \ifnospace@\noexpand\noexpand\noexpand\nospace\fi
   \noexpand\noexpand\expandafter\noexpand\hlname@
   {\macdef@}{\QorThelabel@@@@@}}}%
  \next@}%
"2
  \expandafter\unmacro@\meaning\entry@\unmacro@
"2  
  \Sixtoc@
  \write\toc@{\noexpand\Page{\number\pageno}{\page@N}%
   {\page@P}{\page@Q}^^J}%
 \fi}
**

(We didn't add the analogous clause
**
\ifoverlong@\noexpand\noexpand\noexpand\overlong\fi
**
to the definition of *\HLtoc@*, because *\overlong* will usually be 
irrelevant to the treatment of the heading level in the Contents; but
for some styles this addition might be reasonable.)

\small It's \pagelabel{PIDD}
 conceivable that a style file might need different information
in the *.toc* file that we have provided.  For example, perhaps the sections
3.1, 3.2, 3.3, \dots of Chapter~3 are simply going be numbered
1, 2, 3, \dots under the Chapter~3 entry in the Contents.  To handle such
possibilities, the *.toc* file should probably get the whole set of
information 
**
{\Thelabel@}{\Thelabel@@}{\Thelabel@@@}{\Thelabel@@@@}
**
instead of simply *{\Thelabel@@@@}*.  Then front matter style files 
(Chapter~\ref{FRONTMATTER})
could
decide which information to use. Since I've never
actually seen a book in which formatting of this sort was used,
 it seemed silly to encumber
\lamstex\ with this extra baggage.  But if such a treatment were needed,
it should be clear how to modify the definitions of *\HLtoc@* and *\hltoc@*
accordingly.
\endsmall


\section{\CS{mainfile}}When we have specified *\tocfile* in our main file,
say *paper.tex*,  the file *paper.toc* is written, but this file is
not meant to be \tex'ed directly.  Instead, we will be making a ``front 
matter'' file, say *paperfm.tex*, and since this file will need to know
the name of the original file, in order to *\input* the proper *.toc* file,
*paperfm.tex* will begin with a line like
**
\mainfile{paper}
**
We define
\C**
\def\mainfile#1{\def\mainfile@{#1}}
**
so that, at the appropriate time the macros for the front matter style can
**
\input mainfile@.toc
**
If the *\mainfile* command is omitted from *paperfm.tex*, we would like
to produce an error message when *\maketoc* is encountered. So we add
\C**
\def\checkmainfile@{\ifx\mainfile@\undefined  "8CHECKMF"8
 \Err@{No \noexpand\mainfile specified}\fi}
**
(We put these definitions directly into *lamstex.tex* so that front matter
style files don't have to worry about them.) (See section~\Sref{SACN} for
the use of *\noexpand*.)



\section{Creating heading levels\label{CHL}}
Although we now have the general mechanism for handling heading levels, no
heading levels have actually been defined.


 The default
style makes  *\HL1* and *\hl1* be
defined, which will indicate the general procedure required.


 We begin by adding  the necessary counters
and control sequences.
\C**
\expandafter\newcount@\csname HL@C1\endcsname
\csname HL@C1\endcsname=0
"2
\expandafter\def\csname HL@S1\endcsname#1{#1\null.}  "8NULLSTYLE"8
\expandafter\let\csname HL@N1\endcsname=\arabic
\expandafter\let\csname HL@P1\endcsname=\empty
\expandafter\let\csname HL@Q1\endcsname=\empty
\expandafter\def\csname HL@F1\endcsname{\bf}
\expandafter\let\csname HL@W1\endcsname=\empty
"slip
\expandafter\newcount@\csname hl@C1\endcsname
\csname hl@C1\endcsname=0
"2
\expandafter\def\csname hl@S1\endcsname#1{#1\/}
\expandafter\let\csname hl@N1\endcsname=\arabic
\expandafter\let\csname hl@P1\endcsname=\empty
\expandafter\let\csname hl@Q1\endcsname=\empty
\expandafter\def\csname hl@F1\endcsname{\bf}
\expandafter\let\csname hl@W1\endcsname=\empty
**
Using *\newcount@* (see page~\ref{NWNW}) rather than *\newcount* isn't
necessary here, since these definitions are made within the file
*lamstex.tex*, but they serve as a reminder that auxiliary files should
use *\newcount@* (unless they have stated *\let\alloc@=\alloc@@* at the
beginning).
We added the *\null* in `*\HL@S1*' in case *#1* ends with an   upper-case
letter (compare page~\ref{NULLPUNCT}).\pagelabel{QW4}
\pagelabel{ANULL} 
 (The proficient \amstex\ or \lamstex\ user would 
type `*@.*' in such a case, but *@* can't be allowed in a style command,
since that would essentially be as bad as allowing it in a \<label\>.)


Note, by the way,\pagelabel{NEWWSTUFF}
 that the period after the heading number in `*\HL@S1*'
is not
considered to be punctuation  that  can be eliminated with *\nopunct*.
There is no need for  that, since a quoted heading level could always be used
instead (and  *\newstyle\HL1* or *\newstyle\hl1* could be used to make a
permanent change).   Basically, *\nopunct* only affects
punctuation  that  the
user normally wouldn't be able to change at all, like the period after
an *\hl1* title in the default style (see page~\ref{ABCDE}).

\small In  version *1* of \lamstex@, I didn't have this principle
\pagelabel{NOFC}
clearly formulated, and the period after the heading number in *\HL1* was
considered a ``frill''.  Moreover, the default style  used to print a  \S\
before the heading number, and this `*\S*' was ``hard-wired'' into the
definition of  *\HL@1*  (except that we 
*\let\Ssymbol@=\S*
and used *\Ssymbol@*, just in case some one decided to redefine *\S*).
 If we wanted to retain this \S, then it should
really be placed within the definition of `*\HL@S1*'.

\andsmall! In that case,
however, it would also  be necessary to add *\Nonexpanding\S* (or 
*\Nonexpanding\Ssymbol@*). In view of all this, it seemed better just to
leave the damn thing out.
\endsmall

To allow *\HL1* to be defined, we must create `*\HL@1*' with
**
\expandafter\def\csname HL@1\endcsname#1\endHL{...}
**
Although that's quite a mouthful, such definitions are meant to be supplied
only by style file designers, and numerous subtleties are involved in the
definitions anyway, so there's no point trying to make this part easier.

Roughly speaking,
\lamstex's definition of the default style `*\HL@1*' is
**
\expandafter\def\csname HL@1\endcsname#1\endHL{\bigbreak
 {\locallabel@
"2
 \vbox{\Let@\tabskip\hss@
  \halign to\hsize{\bf\hfil##\hfil\cr
"2
 \csname HL@W1\endcsname\space
 {\HL@@F\thelabel@@}" #1\crcr}}
 \nobreak\medskip}
**
where
\list 
 \item
We put the whole construction in a
group with *\locallabel@*, so that a *\label* within the
**
\HL1 ... \endHL
**
will be given the values relevant to this *\HL1*.

\item We
set 
a *\vbox* consisting of centered  lines. 
*\Let@*, from \amstex@, is the device
for letting *\\* be the same as *\cr* within this *\vbox*. Normally
we would use *\tabskip\hfil* or *\tabskip\hss*
to  produce the centered  lines; 
*\tabskip\hss@* is used in case *\overlong* precedes the *\HL*
(page~\ref{HSS}). 

\item
At the beginning of the argument *#1*
we print *\thelabel@@* (the number, together with any pre- and
post-material, plus anything produced by the style), in the   proper  font.
Notice that we explicitly leave the space after *\thelabel@@*, since
the spacing is not made part of `*\HL@S1*' (compare page~\ref{SPACESEP}).
Moreover, before *\thelabel@@* we print
the \<word\> for `*\HL@1*' (empty in the default style).
\endlist

However, there are a few details that we need to  change:
\list
\item The preamble should really contain
**
\halign to\hsize{\bf\hfil\ignorespaces##\unskip\hfil\cr "8UNSKIP"8
**
to discard extraneous spaces at the beginning or end of each line of the
heading.

\item In addition, we need to replace the
**
{\HL@@F\thelabel@@} #1
**
by
**
{\HL@@F\thelabel@@} \ignorespaces#1
**
to get rid of an extraneous space at the very  beginning  of the heading.

\item Moreover, if *\thelabel@@* is empty (from a *\HL 1 """"*), then
the space before the *\ignorespaces* should be eliminated. And
if the \<word\> is empty, then the space after it should be eliminated.

\item
We don't really  want our heading to be a *\vbox*, because 
*\insert*'s (like 
*\footnote*) won't migrate out.  So we will instead globally
*\setbox1* to be the *\vbox*, and then *\unvbox1*:
\endlist
\C**
\expandafter\def\csname HL@1\endcsname#1\endHL{\bigbreak "8HLONE"8
 {\locallabel@
"2
 \global\setbox1=\vbox{\Let@\tabskip\hss@
  \halign to\hsize{\bf\hfil\ignorespaces##\unskip\hfil\cr
"2
  \expandafter\ifx\csname HL@W1\endcsname\empty\else
   \csname HL@W1\endcsname\space\fi
  {\HL@@F\ifx\thelabel@@\empty\else\thelabel@@\space\fi}%
  \ignorespaces#1\crcr}%
 }%
 \unvbox1 \nobreak\medskip} 
**
{\bf NOTE: }The *\nobreak* here is absolutely essential---see section
~\Sref{AFTOC}.

The definition of *\hl1* for the default style  is quite straightforward,
using *\punct@* and *\addspace@*, since *\hl* is on *\nofrillslist@*:
\C**
\expandafter\def\csname hl@1\endcsname#1{\medbreak\noindent@@  "8ABCDE"8
 {\locallabel@
 \bf{\hl@@F\ifx\thelabel@@\empty\else\thelabel@@\space\fi}%
 \ignorespaces#1\unskip
 \punct@{\null.}\addspace@\enspace}}
**
See Chapter~\ref{EVPAR} for the use of *\noindent@@*.
Notice that here we don't even print the \<word\>, even if it has
been changed by *\newword*.  (Generally speaking, *\HL* heading levels
will have words printed as part of them, while *\hl* levels won't.  Of course
a style file could redefine `*\hl@1*' to include the \<word\>, if necessary.)

\section{Initializations}
In addition to defining `*\HL@1*', we want  a definition like
**
\expandafter\def\csname HL@I1\endcsname{\Reset\hl1{1}%
 \newpre\hl1{\pref.}}
**
so that  these ``initializations'' are   always performed after each *\HL1*
(though they  may
be overridden if *\csname HL@J1\endcsname* has been defined by  an
*\Initialize* [section~\Sref{EVERY}]).  Recall that *\pref* will mean
*\Thepref@* during this initialization.

But there is a little subtlety involved here, since *\HL1* might be used
with an empty label *\HL1""""*. 
For
 example,
**
\HL1""""Introduction\endHL
**
might be used to get an unnumbered Introduction preceding the other
*\HL1*'s.
  In that case *\pref* would be empty, and we don't want a
lonely period preceding the *\hl1* numbers!
  So instead we use
\C**
\expandafter\def\csname HL@I1\endcsname{\Reset\hl1{1}%  "8IFXP"8
 \ifx\pref\empty\newpre\hl1{}\else\newpre\hl1{\pref.}\fi
**

No initializations are required at each  *\hl1* in the default style,
so we simply leave `*\hl@I1*' undefined.

\small In the situation on  page~\ref{AEEX}, where we used
**
\Initialize\hl1{%
 \Evaluate\HL1\edef\HLvalue{\number\Value} 
 \Evaulate\hl1
 \newpre\exno{\HLvalue.\the\Value.}}
**
to set the numbering  for *\exno*,  subtleties about empty  heading level
numbers
were not taken into
account. Actually, there's no way that they can be handled at this point,
since there's no way of determining, once we get to an  *\hl1*, whether or
not 
the
*\HL1* before it had an empty heading number. To deal with  these
possibilities, we could, for  example, have *\HL1* 
store the current value of *\Thelabel@@@@*  in another control sequence,
say
 *\HLpref*, in addition
to storing  it in
 *\Thepref@*; then *\HLpref* wouldn't change at an  *\hl1*, so it would
 give information about the
*\HL1* that comes before the current *\hl1*. 
If we were designing a style  file in which something  like
*\exno* were a standard feature, then we would probably need to do this.

A clever user could always emulate this with 
**
\Initialize\HL1{\Evaluate\HL1\xdef\HLpref{\number\Value}}
"slip
\Initialize\hl1{  . . .
 \ifx\HLpref\empty\else
  \Evaluate\HL1\edef\HLvalue{\number\Value}\fi
  . . .  }
**
(Or a new *\Initialize\HL1* could simply be given before any  *\HL1""""* is 
stated.)
\endsmall


\section{\CS{aftertoc\@}\label{AFTOC}}
Remember that *\HL1* calls 
  *\HL@*, and *\HL@* in turn will then call
`*\HL@1*'*...\endHL* 
followed by 
**
\HLtoc@
**
for writing to the *.toc* file.

\smallskip

  {\bf IT \,IS \,THEREFORE \,ESSENTIAL\/}
\,that no breaks be allowed by any material at the end of the 
definition of `*\HL@1*'*...\endHL*,
 to insure that the proper page number will be written; thus, in the
definition for the default style  (page~\ref{HLONE}), the
*\nobreak* before the *\medskip*
would be necessary
even if the style file design
weren't  particularly concerned about prohibiting a page
break here.

It is quite possible that a style file won't try to prohibit a page
break after the heading is printed. In fact, 
 a style file might even {\it demand\/} a page break at this
point. For example, the style file for the \lamstex~Manual uses *\HL0*
for the Part pages,
and in the definition of `*\HL@0*', we want a page break after typesetting
the Part~page; and then we want to *\Offset\page2*, since the next page is
supposed to be blank.
It would certainly not do to
\setbox0\hbox{\<instructions for typesetting the Part page\>} 
**
\expandafter\def\csname HL@0\endcsname#1\endHL{%
  "box0
 \vfil\break\Offset\page2}
** 
because in the *.toc* file
the page number for this
Part page would then be 1~more than it should be!
Instead, the definition  has the additional clause
**
\def\aftertoc@{\vfil\break\Offset\page2} "8AFTERTOC"8
**
---then 
the proper page is written by the *\HLtoc@* command before we increase
the page numbering by~1.




\sectiong{Order of  heading levels\label{HLLEV}}
The  default style allows an *\hl1* to appear before an *\HL1*, but we
could easily disallow this. For example, we could first
**
\def\HLlevel@{0}
**
and then use
**
\expandafter\def\csname hl@1\endcsname{%
 \ifnum\HLlevel@=0
  \Err@{\string\hl1 not allowed before some \string\HL}
**
  Similarly, if we created *\hl2*, we could
**
\def\hllevel@{0}
**
and then
**
\expandafter\def\csname hl@2\endcsname#1{%
 \ifnum\hllevel@=0
  \Err@{\string\hl2 not allowed before some \string\hl1}
 . . . } 
**
For this to work properly, 
 we should also add
**
\def\hllevel@{0}
**
to our definition of `*\HL@I1*'.

Note, by the way,  that there's really  no necessity for  ``higher''
heading levels to have smaller numbers.
\footnote{Actually, a heading  level doesn't even
have to be a  number (but it's probably best not to exploit that  fact).}

\endsmall




\section{Naming header levels\label{RHL}}
Now we come to the
*\NameHL* and *\Namehl* mechanisms, by which, for
example, 
**
\NameHL1\chapter
**
makes *\chapter...\endchapter* function like *\HL1...\endHL*,
and 
**
\Namehl1\section
**
makes *\section{...}* function like *\hl1{...}*.
As the uppercase ~`*N*' suggests, *\NameHL* and *\Namehl* will act
globally. 
\footnote{*\NameHL* and  *\Namehl* replace the *\newHL* and
*\newhl* constructions from  version~*1* of \lamstex.}

As a special case of
**
\NameHL#1#2
**
let us consider *\NameHL1 \chapter*.

First we will want to
**
\define\chapter{}
**
to get an error message if *\chapter* is already defined.

We will also want to 
**
\rightadd@\chapter\to\overlonglist@
**

And we will want to  let *\chapter@C* be `*\HL@C1*', 
and *\chapter@P* be `*\HL@P1*',
etc. For this we will need the old *\edef* trick (see, for example,
page~\ref{ADDCSNAME} and Chapter~\ref{NEWC}, and
see  pages~\ref{EXNE} and ~\ref{EXNE2}
for the use of the
`*\expandafter\noexpand*'):\pagelabel{TOMF}
**
\edef\next@{\let\csname\exstring@#2@C\endcsname
 =\expandafter\noexpand\csname HL@C#1\endcsname}\next@ 
**

\noindent{\bf NOTE: }Since we *\let\chapter@C=*`*\HL@C1*', etc., 
 it is therefore
essential that *\NameHL*\,{\it n\/} be used {\it only after\/}
`*\HL@C1*', \dots, `*\HL@F1*' have been defined.
\pagelabel{NameNOTE}

Then we want to
**
\def\chapter##1\endchapter
 {\def\HLtype@{\chapter}
  \def\HLname@{\chapter}
  \gdef\HLlevel@{#1}
  \FNSS@\HL@##1\endHL}
**

This definition will have to be done with an *\edef* also:
{\litindent=0pt
**
\edef\next@{\def\noexpand#2####1\expandafter\noexpand
 \csname end\exstring@#2\endcsname
 {\def\noexpand\HLtype@{\noexpand#2}
  \def\noexpand\HLname@{\noexpand#2}
  \gdef\noexpand\HLlevel@{#1}
  \noexpand\FNSS@\noexpand\HL@####1\noexpand\endHL}}
 \next@
**
}
[We used *\FNSS@* rather than *\futurelet\next* simply because
it takes fewer tokens, especially with the *\noexpand* required before it.]

We also want to state `*\Invalid@\endchapter*' so that an improper use of
*\endchapter* will give an error message (see section~\Sref{K}),
**
\edef\next@{\noexpand\Invalid@\expandafter\noexpand
 \csname end\exstring@#2\endcsname}
\next@
**  


That is the main outline of the definition, but additional details are needed.
With this much of the  definition, *\chapter* would still not function
just like *\HL1*, because, for example, *\newpre\chapter* and
*\newpre\HL1* would have entirely different effects: one would change
*\chapter@P*, while the other would change `*\HL@P1*'---if a user typed
*\newpre\HL1* this would not affect the pre-material for *\chapter*.   
That might not seem like such a terrible problem---users could just
be warned not to use *\newpre\HL1* instead of *\chapter*---until we
realize that our definition of `*\HL@I1*' has a
*\newpre\hl1* clause: if the user of the default style decided to 
**
\NameHL 1 \chapter
\Namehl 1 \section
**
then *\section*'s would not have the proper pre-material determined
by the *\chapter* in which they were used. (Similarly,
*\newfontstyle\chapter* and *\newfontstyle\section* would have no
effect.) 


To get around this problem, we need a way of passing special information to
the *\new...* constructions of Chapter~\ref{acces},  so that, for example,
*\newpre\chapter* and *\newpre\HL1* will each change
{\it both\/} *\chapter@P* and `*\HL@P1*'.
 This will be done by
means of two *R*eplacement control sequences:
\setbox0\hbox{will be defined to have the value *\chapter*}
\setbox1\hbox{will be defined to have as value the pair *{HL}{1}*}
\setbox2\hbox{*\chapter@R*}
\setbox3\hbox to\wd2{`*\HL@R1*'\hfil}
**
"box3   "box0
"box2   "box1
**
So we will add
**
\expandafter\gdef\csname HL@R#1\endcsname{#2}
\expandafter\gdef\csname\exstring@#2@R\endcsname{{HL}{#1}}
**

In some cases,
some of this information must also  be passed to the  *.toc* file.
For example, the default front matter style  file  *lamstex.stf* contains
instructions for typesetting entries  that begin
**
\HL {1}
**
but if *\NameHL1\chapter*  appears in the main file,
then *\chapter*  will produces entries in the *.toc* file
beginning
**
\chapter
**

In order for the *lamstex.stf* file  to be able to
deal with these lines, the
information
**
\NameHL1\chapter
**
must be passed to it:
**
\iftoc@
\immediate\write\toc@{\noexpand\NameHL#1\noexpand#2^^J}
\fi
**
with a *^^J* to give 
 a blank line afterwards, to separate this
from an entry line that might come next.

For all this to work properly when we get to front matter style 
files (Chapter~\ref{FRONTMATTER}), it will be
 essential, of course,   that the user has placed the *\tocfile*  command
 {\it before\/} any *\NameHL*  commands. Actually, in addition to 
its invocation by a user who wants names for heading levels that a 
style hasn't given names to, 
*\NameHL* can
also be used by a style file designer.
In the latter case, we really don't want any extra information written to the
*.toc* file, since the style file designer will presumably also write special
code for the front matter style files to deal with lines that begin
with something like
**
\chapter
**
As we will see in Part~\ref{SFPART},\pagelabel{USESFPART}
 special precautions will be taken to
insure that nothing is written to the *.toc* file even if
a file contains *\tocfile* before the *\docstyle* command.


\medskip

A style file might well want to *\NameHL1* twice.  For example, in the *book*
style file, the control sequence
**
\appendices
**
calls *\NameHL1\appendix* to make 
**
\appendix ... \endappendix
**
work just like *\chapter...\endchapter*.
\footnote{In this style
`*\HL@1*' uses
 `*\HL@W1*' (section~\Sref{OTHERE}),
 which is initially defined to be
 `*Chapter*', but which is then changed  to~`*Appendix*' by
the *\appendices* command.
Similarly, *\appendices* also uses *\Reset\HL1{1}*, to 
start the numbering of Appendices at~1.}

Once *\appendices* has used *\NameHL1\appendix*, we want a previous name for
*\HL1*, say
*\chapter*, to
become undefined, \pagelabel{NHLUD}
and we also want *\endchapter* to become undefined, and we
want *\Offset\chapter*, etc., to be disallowed. 
To test whether *\NameHL1* has already appeared, we simply use the test
**
\expandafter\ifx\csname HL@R1\endcsname\relax
**
If this test is false, we want to *\let*
{\def\,{{\rm,}}
**
\...@C", \...@P", \...@Q", \...@S", \...@N", \...@F,", \...@W,
**
all be *\relax*}, where *...*
 is the value of the control sequence *\csname HL@R#1\endcsname*, since, 
as we'll see in Chapter~\ref{acces}, this will disallow the corresponding
*\Reset*, \dots,
constructions. 

Unfortunately, *\csname...\endcsname* is quite unsuitable for use in
\linebreak
*\expandafter* constructions, which is  just how we will need it, so we will
first  use  the code
**
\def\nextiv@{\let\nextiii@=}   "8LNIII"8
\expandafter\nextiv@\csname HL@R#1\endcsname
**
which makes the ``nameable''  control sequence *\nextiii@* have the same
value as `*\HL@R#1*'.
Then we can use
**
\expandafter\let\nextiii@\undefined
\expandafter\let\csname\exxx@\nextiii@ @C\endcsname=\relax
 . . .
\expandafter\let\csname end\exxx@\nextiii@\endcsname=\undefined
**


So our whole definition is:
\C**
\def\NameHL#1#2{\define#2{}%
"2
 \expandafter\ifx\csname HL@R#1\endcsname\relax
 \else
  \def\nextiv@{\let\nextiii@=}%
  \expandafter\nextiv@\csname HL@R#1\endcsname
"2
  \expandafter\let\nextiii@\undefined
"2
  \expandafter\let\csname\exxx@\nextiii@ @C\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @P\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @Q\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @S\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @N\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @F\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @W\endcsname=\relax
"2
  \expandafter\let\csname 
   end\exxx@\nextiii@\endcsname=\undefined
 \fi
"2
 \expandafter\gdef\csname HL@R#1\endcsname{#2}%
 \expandafter\gdef\csname\exstring@#2@R\endcsname{{HL}{#1}}%
"2
 \iftoc@
  \immediate\write\toc@{\noexpand\NameHL#1\noexpand#2^^J}%
 \fi
"2
 \rightadd@#2\to\overlonglist@
"2
"2
 \edef\next@{\let\csname\exstring@#2@C\endcsname
  =\expandafter\noexpand\csname HL@C#1\endcsname}\next@  "8NameHLcounter"8
"2
 \edef\next@{\let\csname\exstring@#2@P\endcsname
  =\expandafter\noexpand\csname HL@P#1\endcsname}\next@ 
"2
 \edef\next@{\let\csname\exstring@#2@Q\endcsname
  =\expandafter\noexpand\csname HL@Q#1\endcsname}\next@ 
"2
 \edef\next@{\let\csname\exstring@#2@S\endcsname
  =\expandafter\noexpand\csname HL@S#1\endcsname}\next@ 
"2
 \edef\next@{\let\csname\exstring@#2@N\endcsname
  =\expandafter\noexpand\csname HL@N#1\endcsname}\next@ 
"2
 \edef\next@{\let\csname\exstring@#2@F\endcsname
  =\expandafter\noexpand\csname HL@F#1\endcsname}\next@ 
"2
 \edef\next@{\let\csname\exstring@#2@W\endcsname
  =\expandafter\noexpand\csname HL@W#1\endcsname}\next@ 
"2
 \edef\next@{\def\noexpand#2####1\expandafter\noexpand
  \csname end\exstring@#2\endcsname 
"2
  {\def\noexpand\HLtype@{\noexpand#2}%
"2
   \def\noexpand\HLname@{\noexpand#2}%
"2
   \gdef\noexpand\HLlevel@{#1}%
"2
   \noexpand\FNSS@\noexpand\HL@####1\noexpand\endHL}}%
"2
 \next@
"2
 \edef\next@{\noexpand\Invalid@\expandafter\noexpand
  \csname end\exstring@#2\endcsname}%
 \next@
}
**

For *\Namehl* we don't have to worry about an *\end...* construction.
Moreover, *\Namehl* doesn't worry about *\...@W* constructions, since
words are seldom added to such heading levels.
\C**
\def\Namehl#1#2{\define#2{}
"2
 \expandafter\ifx\csname hl@R#1\endcsname\relax
 \else
  \def\nextiv@{\let\nextiii@}%
  \expandafter\nextiv@\csname hl@R#1\endcsname
"2
  \expandafter\let\nextiii@=\undefined
"2
  \expandafter\let\csname\exxx@\nextiii@ @C\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @P\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @Q\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @S\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @N\endcsname=\relax
"2
  \expandafter\let\csname\exxx@\nextiii@ @F\endcsname=\relax
 \fi
"2
 \expandafter\gdef\csname hl@R#1\endcsname{#2}%
 \expandafter\gdef\csname\exstring@#2@R\endcsname{{hl}{#1}}
"2
 \iftoc@
  \immediate\write\toc@{\noexpand\Namehl#1\noexpand#2^^J}%
 \fi
"2
 \rightadd@#2\to\nopunctlist@%
"2
 \edef\next@{\let\csname\exstring@#2@C\endcsname=
  \expandafter\noexpand\csname hl@C#1\endcsname}\next@
"2
 \edef\next@{\let\csname\exstring@#2@P\endcsname=
  \expandafter\noexpand\csname hl@P#1\endcsname}\next@
"2
 \edef\next@{\let\csname\exstring@#2@Q\endcsname=
  \expandafter\noexpand\csname hl@Q#1\endcsname}\next@
"2
 \edef\next@{\let\csname\exstring@#2@S\endcsname=
  \expandafter\noexpand\csname hl@S#1\endcsname}\next@
"2
 \edef\next@{\let\csname\exstring@#2@N\endcsname=
  \expandafter\noexpand\csname hl@N#1\endcsname}\next@
"2
 \edef\next@{\let\csname\exstring@#2@F\endcsname=
  \expandafter\noexpand\csname hl@F#1\endcsname}\next@
"2
 \edef\next@{\def\noexpand#2{%
"2
  \def\noexpand\hltype@{\noexpand#2}%
  \def\noexpand\hlname@{\noexpand#2}%
  \gdef\noexpand\hllevel@{#1}%
"2
  \noexpand\FNSS@\noexpand\hl@}}%
 \next@}
**


\section{\CS{Initialize}\label{EVERY}}Finally, we want to consider
*\Initialize*, which allows the user to prescribe additional
``initializations'' that are  done at a heading level.

We want  *\Initialize\HL*\<number\>
 and *\Initialize\hl*\<number\> to be allowed, and
also *\Initialize\chapter* if *\chapter* has  been created using 
*\NameHL*.
So
we will use one routine, *\InitH@*, if  *\Initialize* is followed by
a header level *\HL* or *\hl*, and another routine, *\InitS@*, if
it is followed by a single  name  like *\chapter*:
\C**
\def\Initialize{\futurelet\next\Init@}
"2
\def\Init@{\ifx\next\HL\let\next@=\InitH@
 \else\ifx\next\hl\let\next@=\InitH@
 \else\let\next@=\InitS@\fi\fi\next@}
**
The definition of *\InitH@* is quite straightforward.  For example,
**
\InitH@ \HL 1 {...}
**
is supposed to (globally) define `*\HL@J1*' to be `*...*'. But we
want to give an error message if the corresponding heading level hasn't been
defined: 
\C**
\def\InitH@#1#2{\expandafter
 \ifx\csname\exstring@#1@C#2\endcsname\relax
"2
  \def\next@{\Err@{\noexpand#1level #2 not defined 
   in this style}}%
"2
 \else
  \def\next@{\expandafter
   \gdef\csname\exstring@#1@J#2\endcsname}%
 \fi
 \next@} 
**

Now we have to reduce *\InitS@* to *\InitH@*. 
Let's
suppose the argument of *\InitS@*
is *\chapter*, which has been
created by 
**
\NameHL1\chapter
**
 so that *\chapter@R* has the value
*{HL}{1}*.  
We introduce the combining construction
\C**
\def\InitC@#1#2{\edef\nextii@{\expandafter\noexpand
 \csname\csname#1\endcsname#2}}
**
(again compare pages~\ref{EXNE} and~ \ref{EXNE2}
for the *\expandafter\noexpand*),
so that
\setbox0\hbox{*\InitC@{HL}{1}*}
$$\box0 \tag"\style{\bf A}"$$
makes *\nextii@* mean *\HL1*; the  point of this is  that we can then use
**
\expandafter\InitH@\nextii@
**

Actually, things are not that direct. To get ({\bf A}) we need
**
\expandafter\InitC@\chapter@R
**
except that `*\chapter@R*' will actually have to be specified as
**
\csname\exstring@#1@R\endcsname
**
which  cannot be used directly in this *\expandafter*. As 
on page~\ref{LNIII}, we will actually use the combination
**
\def\next@{\let\next@=}    "8USELNIII"8
\expandafter\next@\csname\exstring@#1@R\endcsname
\expandafter\InitC@\next@
**
The  first two lines make the ``nameable'' control sequence *\next@* 
have the save value as *\chapter@R*, and then the third line
makes *\nextii@* mean *\HL1*.


Putting  this all together, our final definition is
\C**
\def\InitS@#1#2{\expandafter
 \ifx\csname\exstring@#1@R\endcsname\relax
  \Err@{\noexpand#1not defined in this  style}%
  \let\next@=\relax
 \else
  \def\next@{\let\next@=}%
  \expandafter\next@\csname\exstring@#1@R\endcsname
  \expandafter\InitC@\next@
  \def\next@{\expandafter\InitH@\nextii@}%
 \fi
 \next@}
**





\chapter Accessing and controlling counters, styles, etc.\label{acces}
\endchapter

We are finally ready to examine the various constructions that allow us to
access and manipulate the
 values that *\ref* and its relatives give us.


First we will consider the constructions that allow us to access the values:
 *\value*, *\Evaluate*,
*\pre*, *\post*, *\style*, *\numstyle*, and
*\fontstyle*. 

The definition of *\value* illustrates the basic strategy required:
\hskip-.77pt
*\value\tag* should make sense, and if we *\NameHL1\chapter*, then
*\value\chapter* should make sense;  on the other hand,
*\value\list* and *value\HL* should make sense
only when followed by an appropriate number.
These two different cases are easily distinguished, because 
*\tag@C* and *\chapter@C* are defined, but  *\list@C* and *\HL@C*
are not defined, while things like `*\list@C1*' and `*\HL@C1*'
 are defined.


The definition of *\value#1* first uses the test
**
\ifx\csname\exstring@#1@C\endcsname\relax
**
to see whether *#1* is a construction like *\tag*
 with a single counter.
If this *\ifx* test is false, so that the counter in question does exist,
 it simply prints
**
\number\csname\exstring@#1@C\endcsname
**


If the *\ifx* test gives a 
positive result, we want to use the test
**
\ifx\csname\exstring#@#1@C1\endcsname\relax
**
to see if *#1* is a construction like *\list* with several counters.
If this test also gives a positive result, we want to give an error message,
**
\noexpand\value can't be used with \string#1
**
(see section~ \Sref{SACN} for the use of *\noexpand*)
but if this second test is false, we want to call 
*\value@#1*, where *\value@#1#2* tests whether 
**
\csname\exstring@#1@C#2\endcsname
**
exists, giving an error message if it doesn't, and typesetting 
the value of this counter if it does:
\C**
\def\value#1{\expandafter
 \ifx\csname\exstring@#1@C\endcsname\relax
  \expandafter\ifx\csname\exstring@#1@C1\endcsname\relax
   \def\next@{\Err@{\noexpand\value can't be used with 
    \string#1}}%
  \else
   \def\next@{\value@#1}%
  \fi
 \else
  \def\next@{\number\csname\exstring@#1@C\endcsname\relax}%
 \fi
 \next@}
"slip
\def\value@#1#2{\expandafter
 \ifx\csname\exstring@#1@C#2\endcsname\relax
  \def\next@{\Err@{\string\value\string#1 can't be followed 
   by \string#2}}%
 \else
  \def\next@{\number\csname\exstring@#1@C#2\endcsname\relax}%
 \fi
 \next@}
**
{\bf NOTE: }%
In order for this to work properly, it is thus essential that any
construction having any `*\...@C*{\it\, n\/}'
 counter should always have at 
least 
the counter `*\...@C1*'.  In particular, *\HL1* 
should always
be defined if any *\HL* level  is defined, and similarly for *\hl*.


In the error message for *\value@*, we used *\string\value* 
since it will generally look better not to have a space after *\value*, and
*\string#1" * rather than *\noexpand#1*, since *#1* may not be (and usually
won't be) a control sequence.



\medskip
We introduce the counter *\Value*, which holds the value for *\Evaluate*,
\C**
\newcount\Value
**
but we won't bother printing the code for
*\Evaluate*, because it is strictly analogous,
 except that it globally sets the value of 
the counter *\Value*, instead of printing  a number.


The definition of *\pre#1* is quite similar,
 except that instead of typesetting
**
\number\csname\exstring@#1@C\endcsname
**
we  typeset 
**
{\csname\exstring@#1@P\endcsname}
**
(we enclose this material inside braces, in case a
font change instruction is involved).

 Only the first part of the definition
will be given:
\C**
\def\pre#1{\expandafter
 \ifx\csname\exstring@#1@P\endcsname\relax
"2
  \expandafter\ifx\csname\exstring@#1@P1\endcsname\relax
"2
   \def\next@{\Err@{\noexpand\pre can't be used 
    with \string#1}}%
"2
  \else
   \def\next@{\pre@#1}%
  \fi
"2
 \else
  \def\next@{{\csname\exstring@#1@P\endcsname}}%
 \fi
 \next@}
**
Notice that we now use *\foo@P* and `*\foo@P1*' rather than
*\foo@C* and `*\foo@C1*' to determine whether *\pre* can be used with
*\foo*. So it is possible for *\Reset\foo* to be allowed but not
*\pre\foo* and vice versa.  This generality will extend to all our
constructions, and will even be of some importance in Chapter~\ref{foot}.


The definition of *\post* is strictly analogous to that for *\pre*, but
with `*Q*' replacing `*P*' in the tests.


The definition of *\style*  is also  analogous, except that we don't
have the extra set of braces, i.e., we have the clause
**
\def\next@{\csname\exstring@#1@S\endcsname}
**
Nevertheless, this definition functions quite differently, because
 the *\next@* that we call will actually be a control sequence that will
process its argument (the following input).

And exactly the same  remarks hold for *\numstyle*.

\medskip
On the other hand, *\fontstyle* has to be handled differently, because we 
want something like
**
\fontstyle\claim{...}
**
to expand to
**
{\claim@F...}  "8FS"8
**
so *\fontstyle#1* must itself be a control sequence with an argument:
\C**
\def\fontstyle#1{\expandafter
 \ifx\csname\exstring@#1@F\endcsname\relax
"2
  \expandafter\ifx\csname\exstring@#1@F1\endcsname\relax
"2
   \def\next@{\Err@{\noexpand\fontstyle can't be used 
    with \string#1}}%
"2
  \else
"2
   \def\next@{\fontstyle@#1}%
  \fi
"2
 \else
  \def\next@##1{{\csname\exstring@#1@F\endcsname##1}}%
 \fi
 \next@}
"slip
\def\fontstyle@#1#2{\expandafter
 \ifx\csname\exstring@#1@F#2\endcsname\relax
  \def\next@{\Err@{\string\fontstyle\string#1 can't be 
   followed by \string#2}}%
 \else
  \def\next@##1{{\csname\exstring@#1@F#2\endcsname##1}}%
 \fi
 \next@}
**

\medbreak
Next we come to the constructions that allow us to manipulate the values,
namely *\Reset*, *\Offset*, and the *\new...* constructions.

*\Reset*  is similar to *\fontstyle*, in that *\Reset\tag*, for
example, must be a control sequence with an argument, namely the number
following *\Reset\tag*.

There is also
 one new wrinkle.
If we *\Reset\tag5*, for example, then we want to set the *\tag* counter,
*\tag@C*, to *4* (since the next use of *\tag* increases this counter
by~*1* before printing the *\tag*). But if we *\Reset\page5*, then we
simply want to set *\pageno=5*;
\footnote{Of course, *\Reset\page* should only be used at a reasonable
place, e.g., after a construction, like *\chapter*, that has started a new
page.} 
 this special case is handled by the boxed
code: 
\C**
\def\Reset#1{\expandafter
 \ifx\csname\exstring@#1@C\endcsname\relax
  \expandafter\ifx\csname\exstring@#1@C1\endcsname\relax
   \def\next@{\Err@{\noexpand\Reset can't be used
    with \string#1}}%
"2
  \else
   \def\next@{\Reset@#1}%
  \fi
"2
 \else
"2
  \def\next@##1{\count@=##1\relax
"2
   "9\ifx#1\page\else\advance\count@ by -1 \fi"9
"2
   \global\csname\exstring@#1@C\endcsname=\count@}%
 \fi
 \next@}
"slip
\def\Reset@#1#2{\expandafter
 \ifx\csname\exstring@#1@C#2\endcsname\relax
  \def\next@{\Err@{\string\Reset\string#1 can't be
    followed by \string#2}}%
"2
 \else
  \def\next@##1{\count@=##1\relax\advance\count@ by -1
   \global\csname\exstring@#1@C#2\endcsname=\count@}%
 \fi
 \next@}
**

We won't repeat the code for
*\Offset*, which is analogous to that for
*\Reset*, except that we don't need any special compensation for *\page*.
However, there is an important point to be made about both *\Reset* and
*\Offset*. Suppose that we have used
**
\NameHL1\chapter
**
(see Chapter~\ref{HLS}).
Then *\Reset\chapter* sets the value of the counter\linebreak
 *\chapter@C*, while
*\Reset\HL1* sets the value  of the counter `*\HL@C1*'. But when we 
look at the definition of
**
\NameHL1\chapter
** 
we see (page~\ref{NameHLcounter})\pagelabel{useNameHLcounter}
that it 
basically involves
\setbox0\hbox{`*\HL@C1*'}
**
\let\chapter@C="box0
**
and this means that *\chapter@C* and `*\HL@C1*' are simply two different
names for the {\it same counter\/} (e.g., *\count47*).  Consequently,
*\Reset\chapter* and *\Reset\HL1* have exactly the same significance, and
the same is true of *\Offset*.


\medskip
This fortunate circumstance will not extend to
*\newpre*, which introduces numerous new problems. 
First of all, *\newpre* is used in a construction like
\setbox0\hbox{\<new pre material\>}
**
\newpre\tag{"box0}
**
So *\newpre\tag* should essentially define *\next@* to be
**
\def\tag@P
**
and then call *\next@*, so that we will obtain
\setbox0\hbox{\<new pre material\>}
**
\def\tag@P{"box0}
**
allowing the *\def* to do the work of scanning the *{*\<new pre
material\>*}*. 


As a first attempt we might use 
**
\def\newpre#1{\expandafter
 \ifx\csname\exstring@#1@P\endcsname\relax
  \expandafter\ifx\csname\exstring@#1@P1\endcsname\relax
   \def\next@{\Err@{\noexpand\newpre can't be used
     with \string#1}}%
  \else
   \def\next@{\newpre@#1}%
  \fi
"2
 \else
  \def\next@{\expandafter
   \def\csname\exstring@#1@P\endcsname}%
 \fi
 \next@}
**
However, there are two features that need to be added to this definition:
\list
\item As  mentioned on page~\ref{NEWPREDEF}, we really want an *\edef*
rather than a *\def*.
%\item And, as  mentioned on page~\ref{GLNEW}, we want the *\edef* to be
%global when *\globalnews@* is *T*.
\item If we have used *\NameHL1\chapter*, then,
unlike the situation with *\Offset* and *\Reset* discussed above,
 *\chapter@P* and `*\HL@P1*' are
two independent control sequences, and special efforts are required to 
insure that
*\newpre\chapter* and *\newpre\HL1* will each change {\it both\/}
*\chapter@P* and `*\HL@P1*'. 
\endlist


\medskip
For (1) it would appear that we simply have to replace
the 
**
\expandafter\def\csname\exstring@#1@P\endcsname
**
with
**
\expandafter\edef\csname\exstring@#1@P\endcsname
**
Unfortunately, things are not quite that simple, because, although
*\newpre* should involve an *\edef*, we still want this *\edef* to be
carried out while *\noexpands@* is in force! 

This would seem to require something like 
**
\begingroup\noexpands@
\expandafter\edef\csname\exstring@#1@P\endcsname
**
But that means
\list\newnumstyle\list1\alph
\item
We need to supply an *\endgroup* after the *\edef* is completed.
\item
This *\edef* must therefore be an *\xdef* in order to survive the
grouping. 
\endlist

We can attack these two problems at once by saying
\Litbox0=**
\def\next@{%
 \def\nextii@{\endgroup
  \expandafter\let\csname\exstring@#1@P\endcsname
   =\Next@}
 \begingroup\noexpands@\afterassignment\nextii@
  \xdef\Next@}
\next@
**
$$\vcenter{\box0}\tag"({\bf A})"$$
Thus, *\next@*
\list\newnumstyle\list1\roman
\item first supplies *\begingroup\noexpands@*,
\item and then it *\xdef*'s 
*\Next@* to be the following text;
\item after that assignment is completed, it supplies an *\endgroup*, and
\item then it (locally) 
lets *\...@P* be this (globally defined) *\Next@*.
\endlist
We use *\Next* for this globally assigned scratch token (page~\ref{GNXT}).

For (2)
we  have to worry about the fact that a single control sequence to
which *\newpre* applies, like *\chapter*, might have an associated pair
*\HL1*
to which *\newpre* should apply, and conversely, a pair like *\HL1* might
have an associated control sequence *\chapter*.

In section~\Sref{RHL}, we already noted that if *\chapter* is created by
**
\NameHL1\chapter
**
then `*\HL@R1*' will be defined, with
*\chapter* as its value, and *\chapter@R* will be defined and
have as value the pair
*{HL}{1}*. 

On   page~\ref{LNIII} of that section,  one of the problems associated with
this *\...@R...* mechanism was handled with the code
**
\def\nextiv@{\let\nextiii@=}
\expandafter\nextiv@\csname HL@R1\endcsname
**
which makes  the ``nameable'' control sequence *\nextiii@* have the same
value as `*\HL@R1*'.
  
More generally, we will define
\C**
\def\getR@#1#2{\def\nextiv@{\let\nextiii@=}%
 \expandafter\nextiv@\csname\exstring@#1@R#2\endcsname}
**
which can be  used in two ways.
\smallskip

\noindent{\bf 1.\enspace}First of all
**
\getR@\chapter{}
**
will make *\nextiii@* be *\chapter@R*.
We will also define
\C**
\def\letR@#1#2#3{\expandafter
 \let\csname#1@#3#2\endcsname=\Next@}
**
Then the effect of
**
\getR@\chapter{}
\expandafter\letR@\nextiii@ P
**
\setbox1\hbox{\<expansion of *\chapter@R*\>}
\setbox0\hbox{\ \ \ \ \ i.e.,\ \ \ \ \ }
is
**
\letR@"box1P"box0 \letR@{HL}{1}P
**
hence
\setbox1\hbox{`*\HL@P1*'}
**
\let"box1=\Next@
**

\noindent{\bf 2.\enspace}On the other hand,
**
\getR@\HL1
**
will make *\nextiii@* be `*\HL@R1*'.
We will also define
\C**
\def\letR@@#1#2{\expandafter
 \let\csname\exstring@#1@#2\endcsname=\Next@}
**
Then the effect of
**
\getR@\HL1
\expandafter\letR@@\nextiii@ P
**
\setbox0\hbox{\ \ \ \ \ i.e.,\ \ \ \ \ }
\setbox1\hbox{\<expansion of `*\HL@R1*'\>}
is
**
\letR@@"box1P"box0\letR@@\chapter P
**
hence
\setbox0\hbox{[*\let* or *\global\let*]}
**
\let\chapter@P=\Next@
**

Putting this all together, we can define *\newpre* as follows:
\C**
\def\newpre#1{\expandafter
 \ifx\csname\exstring@#1@P\endcsname\relax
"2
  \expandafter\ifx\csname\exstring@#1@P1\endcsname\relax
   \def\next@{\Err@{\noexpand\newpre can't be used 
     with \string#1}}%
"2
  \else
   \def\next@{\newpre@#1}%
  \fi
"2
 \else
  \def\next@{%
   \def\nextii@{%
    \endgroup
"2
    \expandafter\let\csname\exstring@#1@P\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R\endcsname\relax
    \else
    \getR@#1{}\expandafter\letR@\nextiii@ P\fi}%
   \begingroup\noexpands@\afterassignment\nextii@
    \xdef\Next@}%
 \fi
 \next@}
"slip
\def\newpre@#1#2{\expandafter
 \ifx\csname\exstring@#1@P#2\endcsname\relax
"2
  \def\next@{\Err@{\string\newpre\string#1 can't be 
   followed by \string#2}}%
"2
 \else
  \def\next@{%
   \def\nextii@{%
    \endgroup
"2
    \expandafter\let\csname\exstring@#1@P#2\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R#2\endcsname\relax
"2
    \else
"2
    \getR@#1{#2}\expandafter\letR@@\nextiii@ P\fi}%
"2
   \begingroup\noexpands@\afterassignment\nextii@
    \xdef\Next@}%
"2
 \fi
 \next@}
**


Of course, *\newpost* is strictly analogous, so we won't write out any of
the code.

The *\newstyle* command is used in
 slightly more complicated situations like
\setbox0\hbox{\<parameter text\>}\setbox1\hbox{\<replacement text\>}
**
\newstyle\tag"box0{"box1}
**
but this can be handled in much the same way as *\newpre*.
  For example, we want
*\newstyle\tag*
 to define *\next@*
to be 
**
\def\tag@S
**
and then call *\next@*, so that we will obtain
\setbox0\hbox{\<parameter text\>}\setbox1\hbox{\<replacement text\>}
**
\def\tag@S"box0{"box1}
**

In this case, we want a *\def*, rather than an *\edef*, and we don't need
to enter a group with *\noexpands@*. Aside from these differences, however,
we simply copy  the code for *\newpre*:
\C**
\def\newstyle#1{\expandafter
 \ifx\csname\exstring@#1@S\endcsname\relax
  \expandafter\ifx\csname\exstring@#1@S1\endcsname\relax
   \def\next@{\Err@{\noexpand\newstyle can't be used 
    with \string#1}}%
"2
  \else
   \def\next@{\newstyle@#1}%
  \fi
"2
 \else
  \def\next@{%
   \def\nextii@{%
    \expandafter\let\csname\exstring@#1@S\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R\endcsname\relax
    \else
     \getR@#1{}\expandafter\letR@\nextiii@ S\fi}%
   \afterassignment\nextii@\gdef\Next@}%
 \fi
 \next@}
"slip
\def\newstyle@#1#2{\expandafter
 \ifx\csname\exstring@#1@S#2\endcsname\relax
"2
  \def\next@{\Err@{\string\newstyle\string#1 can't be 
   followed by \string#2}}%
"2
 \else
  \def\next@{%
   \def\nextii@{%
    \expandafter\let\csname\exstring@#1@S#2\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R#2\endcsname\relax
"2
    \else
"2
    \getR@#1{#2}\expandafter\letR@@\nextiii@ S\fi}%
"2
   \afterassignment\nextii@\gdef\Next@}%
"2
 \fi
 \next@}
**

*\newnumstyle* will be handled a bit differently from *\newstyle*
because
*\newnumstyle* will usually be used with a single numbering style
control sequence, like
**
\newnumstyle\tag{\roman}
**
and 
 it is natural for the user
to think that *\roman* is simply the
second argument to *\newnumstyle*,
 and thus doesn't need the braces (I~
kept making this mistake all the time
in  version~*1* of \lamstex@, 
with disastrous consequences).
So we will  make *\next@* be
a control sequence with an argument---this
works whether or not the user has added the braces.  In this case, instead of
having *\def\next@* at the end of our definition of *\next@*, we 
have it at the beginning:
\C**
\def\newnumstyle#1{\expandafter
 \ifx\csname\exstring@#1@N\endcsname\relax
"2
  \expandafter\ifx\csname\exstring@#1@N1\endcsname\relax
   \def\next@{\Err@{\noexpand\newnumstyle can't be used 
    with \string#1}}%
"2
  \else
   \def\next@{\newnumstyle@#1}%
  \fi
"2
 \else
  \def\next@##1{%
   \gdef\Next@{##1}%
    \expandafter\let\csname\exstring@#1@N\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R\endcsname\relax
    \else
    \getR@#1{}\expandafter\letR@\nextiii@ N\fi}%
 \fi
 \next@}
"slip
\def\newnumstyle@#1#2{\expandafter
 \ifx\csname\exstring@#1@N#2\endcsname\relax
  \def\next@{\Err@{\string\newnumstyle\string#1 can't be 
   followed by \string#2}}%
"2
 \else
  \def\next@##1{%
   \gdef\Next@{##1}% 
    \expandafter\let\csname\exstring@#1@N#2\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R#2\endcsname\relax
    \else
    \getR@#1{#2}\expandafter\letR@@\nextiii@ N\fi}%
  \fi
 \next@}
**

\medskip

*\newfontstyle* is exactly analogous to *\newnumstyle*, so we won't
bother repeating the code.

\medskip

The definition of *\word* is strictly analogous to that of
*\pre*, etc., with *W* substituted for~ *P* everywhere, and *word*
substituted for~ *pre* everywhere.


The definition of *\newword* follows that for *\newstyle*, where we want a
*\def*, rather than an *\edef*, and don't need to enter a group with
*\noexpands@*. 

\pagebreak

\C**
\def\newword#1{\expandafter
 \ifx\csname\exstring@#1@W\endcsname\relax
"2
  \expandafter\ifx\csname\exstring@#1@W1\endcsname\relax
   \def\next@{\Err@{\noexpand\newword can't be used  
    with \string#1}}%
"2
  \else
   \def\next@{\newword@#1}%
  \fi
"2
 \else
  \def\next@{%
   \def\nextii@{%
    \expandafter\let\csname\exstring@#1@W\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R\endcsname\relax
    \else
     \getR@#1{}\expandafter\letR@\nextiii@ W\fi}%
   \afterassignment\nextii@\gdef\Next@}%
 \fi
 \next@}
"slip
\def\newword@#1#2{\expandafter
"2
 \ifx\csname\exstring@#1@W#2\endcsname\relax
  \def\next@{\Err@{\string\newword\noexpand#1can't 
    be followed by \string#2}}%
"2
 \else
  \def\next@{%
   \def\nextii@{%
    \expandafter\let\csname\exstring@#1@W#2\endcsname
     =\Next@
"2
    \expandafter\ifx\csname\exstring@#1@R#2\endcsname\relax
"displaybreak
    \else
     \getR@#1{#2}\expandafter\letR@@\nextiii@ W\fi
    }%
"2
   \afterassignment\nextii@\gdef\Next@}%
 \fi
 \next@}
**









\chapter Footnotes\label{foot}\endchapter


\section{Preliminaries\label{FNP}}In addition to *\footnote*, \lamstex\ has
*\footmark* and *\foottext*, for special situations like the one
indicated on page~52 of the \lamstex~Manual. 
Because of the  ways that these three control sequences interact
(page~\ref{INA}),
we will need a flag
\C**
\newif\iffn@
**
which will be set true at the beginning of  *\footnote* and then
false again at the end.

Next we declare certain
constructions associated with *\footmark*:
\C**
\newcount\footmark@C
\footmark@C=0
\def\footmark@S#1{$^{#1}$}
\let\footmark@N=\arabic
\def\footmark@F{\rm}
**
No definitions  were given for
`*\footmark@P*' and `*\footmark@Q*' because footnote markers
  almost never
have pre-  or  post- material in their numbers. Consequently,
*\pre\footmark*, *\newpre\footmark*, etc., will give error messages.   Of
 course, a style file could always change  this arrangement if it were
necessary. 

With this default definition of *\footmark@S*, the value of
*\footmark@F* is  actually quite irrelevant, but it might be significant
if *\newstyle\footmark* were used.


We  will also define
\C**
\def\foottext@S#1{$^{#1}$}
\def\foottext@F{\rm}
**
This will allow
*\newstyle\foottext* and  *\newfontstyle\foottext*
 to change   things about the numbers in the *\foottext*;
as mentioned on  page~54 of the \lamstex~Manual, it is possible  to have
a different style for printing the marks within the footnote marker and
within the footnote itself.  On the other hand, we  don't want to
have a separate
 counter `*\foottext@C*', since the numbers in the marker and in the
footnote certainly have to be the same.  (Since  *\foottext@N* is
undefined, we also can't have different numbering styles. If, for some
weird reason, a style wanted something like
a footnote mark of~3 referring to  a footnote beginning
 with~iii,  the necessary
 modifications should be pretty obvious.)


\section{\CS{vfootnote\@}\label{VF}}
In  *plain* tex@, the *\footnote* macro
is defined in terms of *\vfootnote*
(footnote in vertical mode), which does the main  work of producing
an *\insert*.  \lamstex\  uses *\vfootnote@* for this purpose,
to avoid any possible conflict (*\vfootnote@* will also work 
rather differently from *\vfootnote*).

In  \lamstex@,  
**
\vfootnote@#1{_",_",_}
**
will  be called when *#1* represents something like the footnote marker,
which has already been determined by other \lamstex\ constructions, while
`*_",_",_*' is the  text that we  want  to appear at the bottom of the page.


A straightforward definition of  *\vfootnote@*
 would be
**
\def\vfootnote@#1#2{\insert\footins
 {\floatingpenalty=20000
  \interlinepenalty=\interfootnotelinepenalty
  \leftskip=0pt \rightskip=0pt
  \spaceskip=0pt \xspaceskip=0pt
  \rm \splittopskip=\ht\strutbox \splitmaxdepth=\dp\strutbox
  \locallabel@\noindent@@{\footmark@F#1}
  \strut#2\strut}%
 }
**
(using *\noindent@@*, see Chapter~\ref{EVPAR}).

The *\locallabel@* defines *\thelabel@*, \dots, in terms of
*\Thelabel@*, \dots, which  have been set by the constructions that will
call *\vfootnote@* (either *\footnote*  or *\foottext*); this is
for the use of any *\label* in  *#2*.
 And *#1* will be  something like
*\foottext@S{\thelabel@@}*, 
which we set at the beginning of an unindented paragraph
(in the font *\footmark@F*, if that's relevant). Then  the rest of the
footnote is typeset in *\rm*. 


\small  The large value of *\floatingpenalty*,
 which is
 the penalty added to a page when  
there is a split *\insert* on it, discourages footnotes from breaking across
a page.
*\interlinepenalty* is the penalty for page breaks between two arbitrary
lines of a paragraph. It is normally *0*, but  is here temporarily set equal
 to
  *\interfootnotelinepenalty*, which
*plain* \tex\ gives the value~ *200*; so
if a footnote must split across a page, it will be more likely to split
between 
 paragraphs.
 Other styles might
set  other values for *\interfootnotelinepenalty*.


*\leftskip* and  *\rightskip* must be set to~ *0pt* within the
*\insert* in  case it occurs within text where other values are in force
(paragraphs indented on the left or  right), and similarly for
*\spaceskip* and *\xspaceskip* (paragraphs set *\raggedright*, for
example). 

\andsmall!
If a style had a construction that
did something else strange, like changing the value
of *\parfillskip*, then this would normally
also  have to be changed back  within
the *\vfootnote@*.

\andsmall
The *\strut#2\strut* adds a strut to the first and last line of the
footnote (compare the footnote on page~\ref{STRUTINSERT}).
*\strut* is defined by *plain* \tex\ 
in terms of *\strutbox*, which contains a vertical rule
of zero width and the desired height and depth of a *\strut*;
in the default style a *\strut* has 
 height ~*8.5pt* and depth~*3.5pt*.
 And
*\splittopskip* is made the height of  *\strutbox* so that the space
before the first line of 
 a split
footnote will be just the same as if there were a *\strut* on this line also;
similarly, the value of
*\splitmaxdepth* allows
footnotes to go below the bottom of the page only by the depth of
*\strutbox*. 
 Normally any point-size  command, like *\tenpoint*,
*\ninepoint*, etc., will redefine *\strutbox*; in  the 
paper and book styles, *\rm* is replaced by
*\eightpoint*, so that
 the *\strutbox* then  has  a smaller height appropriate for 8~point type;
the *\rm* in this definition has been placed before the assignments of
*\splittopskip* and *\splitmaxdepth*, to emphasize that in general, font size
commands must precede them.

Actually, *plain* \tex\ uses
**
\footstrut#2\strut
**
where *\footstrut* is defined as *\vbox to\splittopskip{}*, which thus
has height *\ht\strutbox*, but no depth.  This will
 be important for a two-line
footnote, whenever *\lineskiplimit* happens to have been chosen to
 be greater than~*0pt*: If a full *\strut*
appeared on both lines, so that the first line has depth~*3.5pt* while the
second line has height~*8.5pt*, then these two lines could not be placed
together with *0pt* glue between them because they would then be closer
together than *\lineskiplimit*;\pagelabel{LIMITPROB} consequently,
 additional *\lineskip* glue
would intrude.

\lamstex\ also replaces the second *\strut* by 
**
\lower\dp\strutbox\vbox to\dp\strutbox{}
**
which has the proper depth, but zero height.

(By the way,
Appendix E of {\it The \tex book}, page~416, illustrates a more complicated
arrangement; the *\strut* for the eight-point footnote has a height
of ~*7pt*, but a *\smallskip* ($={}$*\vskip 3pt plus 1pt minus 1pt*)
precedes each footnote, so *\splittopskip* is set to the sum,
*10pt plus 1pt minus 1pt*.) 


\andsmall! Aside from being aesthetically unpleasing,
 struts don't actually give  the right results. For example,
*plain* \tex@, with *\baselineskip=12pt*, defines a *\strut* to have height
~*8.5pt* and depth~*3.5pt*.
If the last line of one footnote actually has depth ~*0pt*, while the
first line of the next footnote contains a tall symbol having
a height of *9pt*, there should still be
*12pt* between the baselines (assuming a reasonably small value
of *\lineskiplimit*).
  But the last line of the first footnote will be artificially
increased to ~*3.5pt* by the strut, 
so the
baselines will be separated by
a total of $\hbox{*3.5pt*}+\hbox{*9pt*}=\hbox{*12.5pt*}$. Of
course, when there are large symbols of this sort, the extra space probably
won't be considered too extravagant.

\andsmall!
A  more disquieting disadvantage of struts is the fact that
the proper definition of a *\strut* for any particular point size is
{\it font-dependent}.\pagelabel{FONTDEP}
 In the Computer Modern  fonts, the parentheses
are usually the tallest and deepest characters;
 in *cmr8*, for example,
 their height
is~ *6pt* and their depth is~*2pt*. Thus, for eight point type and
a *\baselineskip* of ~*9pt*,
 a *\strut*
of height~*7pt* and depth~*2pt*  is appropriate
(compare {\it The \tex book}, page~415).  For this manual, which uses
a *\baselineskip* of~*10pt* for the *\eightpoint* footnotes, I 
originally 
chose a *\strut* of height~*8pt* and depth~*2pt*. But this
 sometimes
gave strange inconsistent line spacing; it turns out
that some characters (not parentheses) were deeper than *2pt*, 
and the  dimensions had to be changed
to~ *7.5pt* and ~*2.5pt* to work with the Baskerville fonts used here.
\endsmall


Instead of using the straightforward definition,
we will follow *plain* \tex\ and
 use a more complicated construction, which
doesn't consider the group *{_",_",_}* as an  argument to
*\vfootnote@*, thus
 allowing category changes within `*_",_",_*'.
In *plain* \tex\ this 
 virtuoso performance  was provided so that
literal mode constructions could appear in footnotes.  In version~*1* of
\lamstex@, this was needed to allow invisible index entries within a
footnote, since such entries involved category changes. 
That's no longer necessary, but we might as well allow category changes
anyway, since *plain* \tex\ already supplies most of the necessary machinery,
and it is a nice feature to have.
\footnote{It sure  made this manual easier!} 

So  the actual definition is  more sophisticated, using the ``implicit''
left brace
*\bgroup*. 
Basically, we would like to 
**
\def\vfootnote@#1{\insert\footins
 \bgroup . . .
"2
 \noindent@@{\foottext@F#1}\footstrut
 \aftergroup\@foot
 \bgroup
 \let\next@=}
"slip
\def\@foot{\lower\dp\strutbox\vbox to\dp\strutbox{}\egroup}
**
Then when we have
**
\vfootnote@#1{_",_",_}
**
the *\let\next@=* is followed by *{*, so that we *\let\next@={*, thereby
{\it removing\/}
 the~ *{*.  Consequently, 
we now have
**
\insert\footins
 \bgroup . . .
 \noindent@@{\foottext@F#1}\footstrut \bgroup _",_",_}
**
with the *}*  matching  the  second *\bgroup*.
And after that *}*, \tex\ inserts the *\aftergroup* token,
*\@foot*, which gives  the *\strut*
and the *\egroup* that matches the  remaining first *\bgroup*. 

Notice that the `*{_",_",_}*' ends  up staying in a group---the 
*\bgroup_",_",_}*---which 
wouldn't happen if we had read in it as an argument.\pagelabel{BFN}
As we will see later (page~\ref{UBFN}),
this is {\it not\/} irrelevant: it introduces complications, which
are most easily dealt with if the *{\foottext@F#1}* is followed by
 an additional
control sequence, `*\modifyfootnote@*'
 which is initially
*\relax*:
\C**
\let\modifyfootnote@=\relax
**
and which the user can change with *\modifyfootnote*,
\C**
\def\modifyfootnote#1{\def\modifyfootnote@{#1}}
**

We've now essentially established the required definition, except that
 there's always the horrid possibility of a footnote only one token long,
which has been typed without braces, so we actually need a
*\futurelet\next* to  worry about this:
\C**
\def\vfootnote@#1{\insert\footins
 \bgroup
 \floatingpenalty=20000
 \interlinepenalty=\interfootnotelinepenalty
 \leftskip=0pt \rightskip=0pt
 \spaceskip=0pt \xspaceskip=0pt
 \rm \splittopskip=\ht\strutbox \splitmaxdepth=\dp\strutbox
 \locallabel@\noindent@@{\foottext@F#1}\modifyfootnote@
 \footstrut\futurelet\next\fo@t}
**

Here *\fo@t*
 calls *\f@@t*
when a group follows, but *\f@t* otherwise:
\C**
\def\fo@t{\ifcat\bgroup\noexpand\next\expandafter\f@@t\else
 \expandafter\f@t\fi}
**
(this  is a slight redefinition from *plain*, 
using  the K-method).
Since *\f@t* is called when we have a single token following instead of
a group, we just insert that token, followed by *\@foot*, to be 
defined presently.
\C**
\def\f@t#1{#1\@foot}
**
*\f@@t* is also slightly changed from *plain* \tex@:
\C**
\def\f@@t{\bgroup\aftergroup\@foot
 \afterassignment\FNSSP@\let\next@=}
**
Here the *\afterassignment\FNSSP@* adds *\FNSSP@*
right after the
*{* that the *\let\next@=*  swallows, thereby discarding any space that
might come after the~ *{*, and also taking care of the possibility  that
an invisible construction follows the~ *{*.
\footnote{Since *\afterassignment* works on single  tokens, this is the
situation where we {\it  must\/} have a single control sequence that is
defined to mean *\FNSS@\pretendspace@*.}

Finally, *\@foot* will  be changed in two ways. First,
we change *\strut* to 
**
\lower\dp\strutbox\vbox to\dp\strutbox{}
**
and
we add an *\unskip* before this, in case a mistaken space appears
before the closing *}*. In addition, as we will see in sections
~\Sref{FT} and ~\Sref{FNS},
\setbox0\hbox{ and calls }%
\setbox1\hbox to\wd0{\hfil calls\hfil}%
\setbox2\hbox to\wd0{\hfil sets\hfil}%
**
\foottext "box1 \vfootnote@
**
while
**
\footnote "box2 \fn@true   
          "box0 \footmark \vfootnote@  "8INA"8
**
Note that although a *\footnote* is essentially like a *\footmark*,  
*\foottext* combination, nevertheless, *\foottext*  is never  called
indirectly, but is   used only when  it actually appears in the input file,
presumably matching a previous *\footmark* that appears directly in  the
input file.

Now
*\foottext*, which leaves *\iffn@* false, 
begins with *\prevanish@*, since  it is  supposed to
be  invisible.
Consequently, if *\iffn@* is false, we 
want 
 to end with a *\postvanish@*, but if *\iffn@* is true,
we  simply want to reset *\iffn@* false:
\C**
\def\@foot{\unskip
 \lower\dp\strutbox\vbox to\dp\strutbox{}\egroup
 \iffn@\expandafter\fn@false\else
  \expandafter\postvanish@\fi}
**

\small!  A style file might replace the *\rm* in the definition of
*\vfootnote@* by\linebreak
 *\eightpoint*, for example, so that footnotes would be set in 8~point type
with, say, *\baselineskip=10pt*.
 But a user who tries to change
things on the fly, 
**
\footnote{\baselineskip10pt . . . }
**
will be sorely disappointed!\pagelabel{UBFN} As noted on page~\ref{BFN},
this construction produces
**
\insert\footins\bgroup . . . "9{"9\baselineskip10pt . . ."9}"9\egroup
**
and *. . .* won't be typeset in paragraphs until the *\egroup*
is encountered, by which time
 the value of *\baselineskip* will have been restored to its old value!
(This same difficulty occurs in *plain* \tex)@.

On the other hand,
**
\modifyfootnote{\baselineskip10pt}
\footnote{...}
**
will have the desired effect, so a user can easily arrange for *\footnote*'s
to be treated specially within certain constructions.
\endsmall

\section{Fancy footnote numbering\label{FFN}}Footnotes differ from all other
automatically numbered \lamstex\ constructions because of the possibility of
``fancy footnote numbering'', whereby footnote numbers begin anew 
 on each page.  This section explains the basic strategy to be  used in that
case. 

We will introduce the flag
\C**
\newif\ifplainfn@
\plainfn@true
\def\fancyfootnotes{\plainfn@false}
**
whose default true value indicates that we are using ``plain'' rather than
``fancy'' footnote numbering.


When we are using fancy  footnote numbering,
*\footmark@C*
will continue to be incremented by~*1* at each footnote.  But we 
will have a separate counter
\C**
\newcount\fancyfootmarkcount@
\fancyfootmarkcount@=0
**
in which we store the latest fancy footnote number.
We also need a counter in which to  store the number of the most recent page
on which a footnote appeared:
\C**
\newcount\lastfnpage@
**
Initially this should not have the value of any page that has appeared.
So we will initialize it to *-10000*, presuming that no one will ever start
something  at  that page number:
\C**
\lastfnpage@=-10000
**

Remember (Chapter~\ref{BD})
that when *\fancyfootnotes* is in force, \lamstex\ will  write
lines of the form
\setbox0\hbox{\<number\>$_{\text1}$}
\setbox1\hbox{\<number\>$_{\text2}$}
\setbox2\hbox{\<number\>$_{\text3}$}
**
F"box0
F"box1
F"box2
 . . .
**
to the *.lax* file, 
where \<number\>$_{\text1}$ is the page  number on which the first  footnote occurs,
\<number\>$_{\text2}$ the number  on which the second footnote occurs, etc.
And the next time the file is \tex'ed, 
 *\document* will  use  these lines  to
define
 *\fnpages@* to be 
\setbox0\hbox{\<number\>$_{\text1}$}
\setbox1\hbox{\<number\>$_{\text2}$}
\setbox2\hbox{\<number\>$_{\text3}$}
**
\\"box0\\"box1\\"box2 ...
**



Now  suppose  that we have come to the {\it k}$^{\text{th}}$
 footnote. By  looking through
*\fnpages@*, we can determine the number {\it K\/} of the  page on
which it 
occurs (which might not be
the  same  as  the  current  value of *\pageno*). 
If {\it K\/} is greater than *\lastfnpage@*, the number of the page on
which the previous footnote occurs, then  the current footnote is 
the  first on the page.
In this case, we will set *\fancyfootmarkcount@* to~ *1*,
and use this value for the number  of  the current footnote.
Moreover,  we will also change *\lastfnpage@* to {\it  K}.
But  if {\it K\/} equals  *\lastfnpage@*, so that  the previous footnote
occurs on this  same  page, we  will just
increase *\fancyfootmarkcount@* by 1, and use that value
for the  number of the  current footnote (in this case, we don't have
to bother changing *\lastfnpage@*). 

If *\footmark@C* has the value {\it k}, 
the following code efficiently
sets  *\Next@*  to the corresponding page number {\it K},
 or to *-10000* if there are
fewer than {\it k\/} numbers on the list (we use *\Next@* because of
the global *\xdef* [see page~\ref{GNXT}]):
\setbox0\hbox{\it k}
\Litbox0=**
{\let\\=\or
 \xdef\Next@{\ifcase\number\footmark@C\fnpages@
  \else -10000 \fi}
}
**
$$\vcenter{\box0} \tag"\style{\bf A}"\pagelabel{kK}$$
Roughly speaking, the *\xdef* makes *\Next@* mean
\setbox0\hbox{\<number\>$_{\text1}$}
\setbox1\hbox{\<number\>$_{\text2}$}
\setbox2\hbox{\<number\>$_{\text3}$}
\setbox3\hbox{\it k}
**
\ifcase "box3\or"box0\or"box1\or"box2...\else -10000 \fi
**
which immediately picks out either \<number\>$_{\text{\it k}}$ or *-10000 *.
In reality, however, things are trickier, and this code works only by
a fluke: As \tex\ expands *\number\footmark@C*, it will have to
expand out *\fnpages@* (since this might stand for another digit of the
final number that it is looking for); consequently, all the *\\*'s in
*\fnpages@* will be revealed, so that \tex\ will know how many *\or*'s the
*\ifcase* actually has.  If we had been ``careful'' and used
**
\ifcase\number\footmark@C\relax\fnpages@\else -10000 \fi
**
then we would always get the case *-10000* (being sloppy pays off), so
a more intricate scheme would be needed.  This observation will also
be important
when we read in data from a *.dat* file for tables (Volume 2).



\section{\CS{footmark}}
In section~\Sref{FNP}, we introduced the flag  *\iffn@*, which is true
when we are processing a
*\footnote*. 

When *\footmark* is not called indirectly by
*\footnote*, but is called directly
(so that the flag *\iffn@* will be  false),
we will have to  store
\setbox1\hbox{V$_{\text{1}}$}
\setbox2\hbox{V$_{\text{2}}$}
\setbox3\hbox{V$_{\text{3}}$}
\setbox4\hbox{V$_{\text{4}}$}
**
{"box1}{"box2}{"box3}{"box4}
**
where V$_{\text{1}}$, \dots, V$_{\text{4}}$ have their  usual significance
(Chapter~\ref{LBL1} et seq.), because this  information will  have to be
used  by some   subsequent *\foottext* (a *\label* might appear
in the *\foottext* part, and  V$_{\text{2}}$ will be  the marker that
will appear at  the beginning of the *\foottext*).

This information will be stored in *\justfootmarklist@*,  initially
defined  to be empty,
\C**
\let\justfootmarklist@=\empty
**
In this case it will be more convenient for *\justfootmarklist@* to be a list
of the type introduced in {\it The \tex book}, page~378, so we will be 
 using *\rightappend@*
(c.f.~section~\Sref{LISTS}) to append to it.


The definition of *\footmark* begins with some of the same constructions
used by *\footnote* in *plain* to save the space factor (compare
page~\ref{=the}), and add the italic correction to the previous letter:
**
\let\@sf=\empty
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
**
Notice that *\/* has already been redefined by \amstex\ to include an
*\unskip* before the italic correction; so a space before a *\footmark*
(and hence, eventually, before a *\footnote*) is ignored.

We are  going to be  using a modified compressed format,
**
\def\footmark{\let\@sf=\empty
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
\def\next@{\ifx""\expandafter\nextii@\else
 \expandafter\footmark@\fi}
\def\nextii@""#1""{...}
\futurelet\next\next@}
**
where we will define *\footmark@* separately (instead of using
*\nextiii@*, which  we would temporarily  define within *\footmark*).
We use this procedure simply  because *\footmark@* will turn out to be
quite involved, and we don't want *\footmark* to have  to make such
a complicated definition for *\nextiii@* each time it is used.

The first attempt for defining *\nextii@* might be
**
\def\nextii@""#1""{%
 {\let\style=\footmark@S \let\numstyle=\footmark@N
"2
  \footmark@F#1
"2
  \noexpands@
"2
  \let\style=\foottext@S
  \Qlabel@{#1}
  }
"2
 \iffn@\else
"2  
  {\noexpands@\xdef\Next@{{\Thelabel@}{\Thelabel@@}
   {\Thelabel@@@}{\Thelabel@@@@}}
"2
  \expandafter\rightappend@\Next@\to\justfootmarklist@
 \fi
 \@sf\relax}
**

Here we use *\Qlabel@*  to create *\Thelabel@*, \dots,
*\Thelabel@@@@*.   If our *\footmark* came from a *\footnote*, which
calls the pair *\footmark*, *\vfootnote@* (see page~\ref{INA})
then any *\label*'s within the *\footnote* will actually end
in  the *\vfootnote@* part  of the  construction, and
 these values will then be used by the *\vfootnote@*.
However,  before  using  *\Qlabel@*, we
first change   the meaning of
 *\style* from *\footmark@S* to *\foottext@S*, 
so that *\Ref* within  a  *\footnote{...}* will refer  to the  style of
the numbering that is used within the note  itself, rather   than to the
style used for the footmark.



If our *\footmark* was used directly, so  that the flag
*\iffn@* is  false, then
the *\iffn@\else...\fi* clause  stores the appropriate information.
In this case, it is essential  that *\Thelabel@@*  use the value  
of *\foottext@S*  rather than *\footmark@S*, since *\Thelabel@@* is
what  we  will print   at the beginning  of the corresponding *\foottext*.

And then, finally, we restore the space factor with 
**
\@sf\relax
**
The *\relax* is necessary, because *\@sf* expands out to
\setbox0\hbox{\<number\>}
**
\spacefactor="box0
**
and a digit could follow.

Unfortunately, there is problem here, of a type already addressed by \amstex\
for the *amsppt.sty* file: If *\footmark* is invoked within
*\text* (as in the example on
page~52 of the \lamstex~Manual), we don't want  to add things
to *\justfootmarklist@* 4~times, even  though *\text* sets things 4~times.
So \amstex\
has a flag *\iffirstchoice@*, which is usually true, but which is set to
false within the second, third, and  fourth choices of the  *\mathchoice*
involved in the definition of *\text*.  We will therefore use
**
\def\nextii@""#1""{%
 \iffirstchoice@
"2
  {\let\style=\footmark@S \let\numstyle=\footmark@N
  \footmark@F#1
"2
  \noexpands@
  \let\style=\foottext@S
  \Qlabel@{#1}
  }
"2
  \iffn@\else
   {\noexpands@
"2
   \xdef\Next@{{\Thelabel@}{\Thelabel@@}
    {\Thelabel@@@}{\Thelabel@@@@}}
   }
"2
   \expandafter\rightappend@\Next@\to\justfootmarklist@
  \fi
 \fi
 \@sf\relax}
**

The definition of *\footmark@*, the routine
when  *\footmark* is not followed 
by a quoted number *""...""*, 
will be quite a bit more complicated.

First, we want to  advance  *\footmark@C* by ~*1*, 
**
\global\advance\footmark@C by 1
**

Next we want to  define *\adjustedfootmark@*, which will simply be 
the value of *\footmark@C* for non-fancy footnotes, but which will
be  the properly
adjusted value when *\fancyfootnotes*  is in force. For the latter case, we
 use the strategy explained in section~\Sref{FFN}. Note that if
the test ({\bf A}) on page~\ref{kK} makes *\Next@*  have the value
*-10000*, then we presumably have
  some new footnotes, not recorded on the last run;
in this case we just use *\footmark@C* for
determining the value of *\adjustedfootmark@* (another run will be
necessary to get everything right): 
**
\ifplainfn@
 \xdef\adjustedfootmark@{\number\footmark@C}
"2
\else 
 {\let\\=\or
  \xdef\Next@{\ifcase\number\footmark@C\fnpages@\else-10000 \fi}}
"2
 \ifnum\Next@=-10000 
  \xdef\adjustedfootmark@{\number\footmark@C}
"2
 \else
  \ifnum\Next@=\lastfnpage@
   \global\advance\fancyfootmarkcount@ by 1
  \else
   \global\fancyfootmarkcount@=1
   \global\lastfnpage@=\Next@
  \fi
  \xdef\adjustedfootmark@{\number\fancyfootmarkcount@}
 \fi
\fi
**

Then we define *\Thelabel@*, \dots, *\Thelabel@@@@*, in case it will be
needed by a succeeding *\vfootnote@*. Since there is no pre- or post-
material, *\Thelabel@@@@* will just be the same as *\Thelabel@*:
**
{\noexpands@
 \xdef\Thelabel@@@{\adjustedfootmark@}
 \xdefThelabel@\footmark@N
 \xdef\Thelabel@@@@{\Thelabel@}
 \xdefThelabel@@\foottext@S
 }
**
Notice that in  the last  step we used *\foottext@S* instead of
*\footmark@S*, for  the same reasons as with the definition of *\nextii@*.

As before, we then add information to *\justfootmarklist@* unless\linebreak
*\iffn@* is  true:
**
\iffn@\else
 {\noexpands@
"2
  \xdef\Next@{{{\Thelabel@}{\Thelabel@@}
   {\Thelabel@@@}{\Thelabel@@@@}}
"2
  \expandafter\rightappend@\Next@\to\justfootmarklist@
\fi
**
Finally, if we have fancy footnote numbering, we want to write
an  appropriate  line
\setbox0\hbox{\<current page  number\>}
**
F"box0
**
to the  *.lax* file.
To do this we will  use
**
\ifplainfn@\else
 \edef\next@{\write\laxwrite@{F\noexpand\the\pageno}}
 \next@
\fi
**
In this *\edef*, the  *\laxwrite@* is not expanded  because it was
created with *\newwrite* and  thus  with *\chardef*  (compare
page~\ref{CHARDEFNE}), and
*plain* \tex's *\pageno* is also not expanded, since it was created with
a *\countdef* (compare page~\ref{CDNE}). Consequently, the  *\edef* makes
 *\next@* mean
**
\write\laxwrite@{F\the\pageno}
**
When this (delayed) write is executed, it will consequently print the
proper page number.

And, finally, *\footmark@* will end  with *\@sf\relax*,  just  like
*\nextii@*.  

But again, we have to perform most of this definition only when\linebreak
*\iffirstchoice@* is true, since we don't want to increase the counter
4~times, etc.

Thus, the whole definition of *\footmark* reads:
\C**
\def\footmark{\let\@sf=\empty
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
"2
 \def\next@{\ifx""\next\expandafter\nextii@\else
  \expandafter\footmark@\fi}
"2
 \def\nextii@""##1""{%
  \iffirstchoice
   {\let\style=\footmark@S \let\numstyle=\footmark@N
   \footmark@F##1%
"2
   \noexpands@
   \let\style=\foottext@S
   \Qlabel@{##1}%
   }%
"2
   \iffn@\else
    {\noexpands@
    \xdef\Next@{{\Thelabel@}{\Thelabel@@}%
     {\Thelabel@@@}{\Thelabel@@@@}}%
    }% 
    \expandafter\rightappend@\Next@\to\justfootmarklist@
   \fi
  \fi
  \@sf\relax}%
 \futurelet\next\next@}
"slip
\def\footmark@{%
 \iffirstchoice@
  \global\advance\footmark@C by 1
"2
  \ifplainfn@
   \xdef\adjustedfootmark@{\number\footmark@C}%
"2
  \else
   {\let\\=\or
    \xdef\Next@{\ifcase\number\footmark@C\fnpages@
    \else-10000 \fi}}%
"2
   \ifnum\Next@=-10000
    \xdef\adjustedfootmark@{\number\footmark@C}%
"2
   \else
    \ifnum\Next@=\lastfnpage@
     \global\advance\fancyfootmarkcount by 1
"2
    \else
     \global\fancyfootmarkcount@=1
     \global\lastfnpage@=\Next@
    \fi
"2
    \xdef\adjustedfootmark@{\number\fancyfootmarkcount@}%
   \fi
  \fi
"2
  {\noexpands@
  \xdef\Thelabel@@@{\adjustedfootmark@}%
  \xdefThelabel@\footmark@N
"2
  \xdef\Thelabel@@@@{\Thelabel@}%
  \xdefThelabel@@\foottext@S
  }%
"2
  \iffn@\else
   {\noexpands@\xdef\Next@{{\Thelabel@}{\Thelabel@@}%
    {\Thelabel@@@}{\Thelabel@@@@}}}%
"2
   \expandafter\rightappend@\Next@\to\justfootmarklist@
  \fi
"2
  \ifplainfn@
  \else
   \edef\next@{\write\laxwrite@{F\noexpand\the\pageno}}\next@
  \fi
 \fi 
"2
 \footmark@S{\footmark@N{\adjustedfootmark@}}%
 \@sf\relax}
**

\section{\CS{foottext}\label{FT}} The *\foottext* construction has to get its
information from *\justfootmarklist@*, since (compare page~\ref{INA})
*\footext*'s should only occur after sufficiently many *\footmark*'s have
been used. If *\justfootmarklist@* is
\setbox0\hbox{\<stuff\>$_{\text1}$}
\setbox1\hbox{\<stuff\>$_{\text2}$}
**
\\{"copy0}\\{"copy1}\\...
**
and we define
**
"hskip-40pt\def\next@\\#1#2\next@{\def\next@{#1}\gdef\justfootmarklist@{#2}}
**
then 
**
\expandafter\next@\justfootmarklist@\next@
**
defines *\next@* to be \box0, while *\justfootmarklist@* is redefined as
*\\{"copy1}...*\,.

The definition of *\foottext* will begin with *\prevanish@*. Then we will
first test whether *\justfootmarklist@* is empty, and if so, we will issue an
error message
**
There is no \footmark for this \foottext.
**
Assuming this hasn't happened, we will use the process just described to make
*\next@* be the first thing on *\justfootmarklist@*, and to redefine
*\justfootmarklist@* to be the remainder.

And then we will use
**
\expandafter\foottext@\next@
**
so that *\foottext@* can use the four values of *\next@*:
\C**
\def\foottext{\prevanish@
 \ifx\justfootmarklist@\empty
  \Err@{There is no \noexpand\footmark for this 
   \string\foottext}\fi
 \def\next@\\##1##2\next@{\def\next@{##1}%
  \gdef\justfootmarklist@{##2}}%
 \expandafter\next@\justfootmarklist@\next@
 \expandafter\foottext@\next@}
**
Once again, for the *\noexpand* in the error message, see section
~\Sref{SACN}.

*\foottext@* simply uses the next four values for defining *\Thelabel@*,
\dots, *\Thelabel@@@@*, and then calls *\vfootnote@* with the value of
*\thelabel@@* (the *\locallabel@* part of *\vfootnote@* sets this to the
current value of\linebreak
*\Thelabel@@*, namely the second value of *\next@*):
\C**
\def\foottext@#1#2#3#4{{\noexpands@
  \xdef\Thelabel@{#1}\xdef\Thelabel@@{#2}%
  \xdef\Thelabel@@@{#3}\xdef\Thelabel@@@@{#4}}%
  \vfootnote@{\thelabel@@}}
**

The *\vfootnote@* will put in a *\postvanish@* at the end, to match the
*\prevanish@* at the beginning, since *\iffn@* will not be true when
*\foottext* is processed.  The only thing left to do now, is to
\C**
\rightadd@\foottext\to\vanishlist@
**

\section{\CS{footnote}\label{FNS}}Finally,
 the definition of *\footnote* holds no
special surprises. It is practically the same as the combination *\footmark*,
*\foottext*, except that we use *\vfootnote@* explicitly instead of
*\foottext*, so that the flag *\iffn@*, which we now set to be true, will
function properly:
\C**
\def\footnote{\fn@true
 \let\@sf=\empty
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
 \def\next@{\ifx""\next\expandafter\nextii@
  \else\expandafter\nextiii@\fi}%
 \def\nextii@""##1""{\footmark""##1""%
  \vfootnote@{\let\style=\foottext@S
   \let\numstyle=\footmark@N##1}}%
 \def\nextiii@{\footmark
  \vfootnote@{\foottext@S{\footmark@N{\adjustedfootmark@}}}}%
 \futurelet\next\next@}
**