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\title{An encoding proposal: YAASP\\Yet Another Aston Proposal\\This
  is not a finished document}

\author{Justin Ziegler \\ 
   \texttt{\small
    ziegler@goofy.zdv.uni-mainz.de} \\ \texttt{\small
    ziegler@educ.emse.fr} }

\date{\small Started: 3 July\\ Printed:
  \today \\Last change: 18 August. \\Version 2.00 \\Filename:
  yaasp.tex with NSFF2}

\maketitle






\begin{abstract}
  The idea here is to put on paper what could be the backbone or the
  skeleton of the new math encoding. This is not the complete
  description of an encoding, but a sort of grid, or global picture of
  what things could look like. This document refers to glyph groups
  that are defined in ``Towards a list of math glyphs''. Same author.
\end{abstract}






\section{Lets start with a few definitions}

\noindent \textbf{An ``encoding table'':} this conveys the
traditional meaning of an encoding. That is to say a set of 256
glyphs in a given order. The expression ``encoding table'' is usually
abbreviated with encoding.

\vskip .5cm
\noindent \textbf{A ``slot'':} is the usual word we use for referring
to a position in an encoding, that can contain a glyph. It usually is
an integer between 0 and 255. A slot is
certainly not a family, or anything to do with it.

\vskip .5cm
\noindent \textbf{A ``math kernel'':} this terminology is used to
specify the fonts that are necessary for the math facility to work
as it is described in most \TeX\ documentation\footnote{documentation
on LA\TeX, AMS\TeX, etc, also fits in here.}.
In DEK's implementation of math the math kernel consists of the
families from 0 to 3. On top of the kernel, many other fonts with
whatever encoding is available, could be optionally loaded and used.

\vskip .5cm
\noindent\textbf{A ``math encoding'':} the way it is considered here, is
as a whole. Not just one 256-glyph encoding table, but a set of $x$
encoding tables, where $x$ is the number of fonts in the math kernel.
We will refer to this concept with the abbreviation ``M-encoding''.

% jz -- recent change. I did not like alan proposition at all !
\vskip .5cm
\noindent\textbf{The ``core symbols'':} core symbols are made of two
groups. The group of symbols that must live with the default alphabet
for kerning reasons, and the group of symbols that must live with the
default alphabet for design reasons.


\vskip .5cm
\noindent\textbf{The ``default alphabet'':} it is the alphabet that is
used  when a user types \texttt{\$abc\$}. In the present encoding that
produces $abc$.








\section{Global policy}
  \subsection{Grouping all \TeX\ specific glyphs in one font encoding}
  The present \texttt{cmex} font contains glyphs that can not be used
  by other typesetting systems, because they are set in a strange way.

  The present \texttt{cmsy} font contains one glyph that is set in a
  strange way --- the radical sign, and thus makes that whole font
  unusable for the outer world. I think it is a good idea to make sure
  that this does not happen again.

  We are hopping to set a new standard, that will not only be used by
  \TeX, but by all systems that typeset mathematical formulae. If
  every thing goes according to plan, in the next few years many math
  fonts will exist, for many different systems, and they will all use
  the same encoding. The fact that they all use the same encoding,
  means that it will be very easy to exchange fonts from one system to
  another. So one day a \TeX\ user will be able to take a math font
  used by Microsoft Word, and convert it easily in order to use it
  with \TeX.

  If \TeX\ specific glyphs are grouped in one font, there will only be
  one problematic font. As it happens, all \TeX\ specific glyphs are
  more or less geometric, so they could be used with more than one
  math font.

  On the other hand, if \TeX\ specific glyphs are spread around in
  many fonts, then many ``imported'' fonts will not be usable by \TeX\ 
  without major messing around.

  Concerning this problem, I think that the real question is: are we
  setting a real standard for the next few years, or are we just
  making another \TeX\ encoding?

  If the answer to that question is: we are setting a real standard
  for the next few years! Then \TeX\ specific glyphs must be grouped
  in one font. If that is not possible, and I mean really not
  possible, then we can consider putting them in two fonts.

  \subsection{Grouping all Plain and \LaTeX\ glyphs in 4 fonts}
  The main reason for this, is compatibility. Lets consider a user
  that has typed a document with the present math encoding, and has
  saturated the families for this document. If the new math encoding
  does not garanty Plain and \LaTeX\ glyph compatibility with a
  minimum of 4 fonts, then that document can't run with the new math
  encoding: not enough families. 

  \subsection{Grouping all AMS\TeX\ and AMS\LaTeX\ glyphs in less than
    6 fonts} The main reason for this, is compatibility. Lets consider
  a user that has typed a document with the existant AMS\TeX\ or
  \LaTeX\ package, and has saturated the families for this document.
  If the new math encoding does not garanty AMS\LaTeX\ and AMS\TeX\ 
  glyph compatibility with less than 6 fonts, then that document can't
  run with the new math encoding: not enough families.



\section{The base: a Cork encoded text font}

Main use: things like \texttt{\string\log}. This would generably be a
Latin font. 

If it is a Latin upright font, it would probably also be used by
physicists\footnote{I guess I should also  mention chemists.} for
operator, and more generally whenever upright letters are needed. 

\textbf{Separating this set from the rest,} enables the user to
have `log' and `sin', etc typeset in many different ways. Thus the
multiletter operators can by compatible with the text font, or
with the rest of the math glyphs, or even set in yet another font.

\note {this font is not for typesetting words. That must be done in
text mode.}








\section{The ``text symbol'' encoding: the TS encoding} 
Here we would put the old style numerals, and most of what we have
agreed to take out of the present math encoding. Other symbols could
be added. The Text Symbol encoding is definetly \textem{not part of
  the math kernel.} But seeing as it will contain symbols that
previously were accessed via the math fonts, we must supply its
encoding. This font will not be loaded in a family. It will just be
loaded as a normal text font\footnote{If some users realy feel the
  need to load it in a math family they can.}.








\section{The core: the MC encoding (256)}
Counting: 1+10+1 + 54+6 + 124+12 + 13+23+12 = 256 glyphs

The accents are no longer here. They had no real reason to be here.
Most of them are geometrics anyway. But they do have reasons to be
else where. One of the main consequences of taking these accents out
is that the core can be made more coherent, and more complete.  The MC
encoding would contain:
  \begin{itemize}

  \item The skewchar in position 0: 1
  \item The core digits: 10
  \item The space character in position 32: 1

  \item The core Latin alphabet, which is the default alphabet, in
    uppercase, and lowercase, together with the dotless i and j: 54

  \item The Latin friends: 6

  \item All the Greek material: 124

  \item The Greek friends, next to the Greek: 12

  \item The core symbols for kerning reasons (punctuation and
    delimiters): 13

  \item The core symbols for design reasons: 23

    More for kerning reasons:
  \item The basic geometric delimiters: 12 

    Some new stuff:
  \item New basic delimiters: 

  \end{itemize}











\section{The extensibles: the MX encoding}

Count up: 1+1+ 77+8 + 8 + 24+6 + 7+7 + 16+26 + 60 = 241

The usual extensible characters, together with some new ones would
live here.  We include here any characters that have strange
\TeX\ features like big descenders. Thus grouping glyphs that are not
compatible with the outer world. 

The MX encoding, will be designed in such a way, that if it is loaded
in one size (for compatibility with the present \TeX), every thing
works OK, and the user can still have access to the new symbols. On
the other hand, the MX encoding is best loaded in three sizes, and
produces better quality typesetting.

We are left with the following:
  \begin{itemize}

  \item Maybe a skewchar: 1

    I guess the space is questionnable here, because MX will not be usable by
    other typesetting systems, see comment:
  \item Maybe a space: 1

  \item All existant delimiters including the pieces needed for
    constructing the extensible versions, this includes the single and
    double vertical bar. There are 4 sizes per delimiter: 77

  \item Any characters that have strange \TeX\ features like big
    descenders. Radicals including the one from CMSY'160: \quad 8.

  \item Horizontal curly braces: 8 

  \item All existant big and small ``bigops'' except the integrals: 24

  \item The single and double vertical arrows: 6


    Have to limit the number of wide accents, otherwise not enough place.
  \item The wide tildes, and the wide hats: 16

  New stuff:

    I am a little concerned about the fact that these will be separated from
    the small versions, but there is nothing much to do about it:
  \item The big ``big integral'' family: 7
  \item The small ``big integral'' family: 7

  \item The new big and small `bigops': 26
  \item New multisized and extensible delimiters: 60


  \end{itemize}








\section{The math symbol `privilege' font ``MSP'': 256}
 1+1+ 54 + 19+7+3 + 23 + 8+4+2+4+4 + 20+7+ 10 + 8+8+12 +  24 + 6+4+4+4 + 8+2
 + 16= 256
  \begin{itemize}

  \item A skewchar in position 0: 1
  \item A spacechar in position 32: 1

  \item The script/calligraphic Latin letter set:54

    Because according to AMS statistics, the script/cal are
    used more often than the Bbb. 

    Another reason is so that we can achieve backward compatibility
    with the existing \TeX\ without loading MS1 and MS2. 

  \item The basic accents: 19   %  all basic accents should stay here  
  \item The double accents: 7   %  could go else where
  \item The underaccents: 3     %  could go else where

    This must stay here:
  \item The ``Basic symbols'' group: 23

    The next 5 are needed for compatibility with plain:
  \item The ``Greater than plain'' group: 8
  \item The ``Subset plain'' group: 4
  \item The ``In / ni plain'' group: 2
  \item The ``Sqsubset plain \& ams'' group: 4
  \item The ``Succ without sim plain'' group: 4

  \item The ``Small binops plain'' group: 20
  \item The small ints: 7
    I feel these should live with the other `succ' members for design
    reasons:
  \item The ``Succ without sim ams'' group: 10

    The next three make a homogenous group, and must live with sim.
    Sim itself must live here because of compatibility with Plain:
  \item The ``Greater than with sim'' group: 8
  \item The ``Succ with sim'' group: 8
  \item The ``Sim'' group: 12

    The arrows, for compatibility, (improved a little though):
  \item ``Plain horizontal arrows'': 24
  \item ``Plain vertical arrows'' does not include the extensible ones: 6
  \item ``Plain oblique arrows'': 4
  \item ``Latex arrow heads'': 4
  \item Plain miscellaneous geometric symbols: 4

    The lasy triangles completed with the ones from AMS:
  \item AMS left right open triangles: 8

    Should live with the ``Plain oblique arrows'':
  \item ``AMS obliques'':2

    Some new stuff: Some of these could come out.
  \item Wide accents bar: 8

\end{itemize}







\section{The MS1, MS2, Math-Symbol encodings}
Each of these encodings will contain a set of Latin letters, like for
instance fraktur or black board bold, in uppercase or lowercase or
both. In some cases a place should be reserved for a set of matching
numbers too (i.e. Open). The rest would be filled up with symbols. We
need an MS$_i$ encoding for:

\begin{itemize}
\item An extra script/calligraphic, (see below comment on script and
  calligraphic) the default caligraphic is in the MSP encoding.
\item Open + (Arrows or relations) + other geometrics.
\item Old german,
\end{itemize}


\textbf{Note:} Barbara Beeton ``regarding script vs.  calligraphic, i do
understand the difference; however, at AMS I believe we only very
rarely get a request to use both styles in the same paper''.

For that we have two possibilities:\\ 1) We design one encoding table
where the position A-Z (and probably a-z and 0-9 even if they aren't
all filled) are supposed to contain a ``calligraphy/script'' set of
characters.  Then there would be instances of that encoding that would
contain script chars and others that would contain calligraphic chars.
Suppose our standard would say that this encoding is to be used as
fam4.  A designer would then choose one such font with this encoding
for fam4 (thereby effectively deciding how \texttt{\string\cal} and a
lot of other symbols look like (the ones whose mathchardef points into
fam4)). For those who in addition would like to use another
script/call math alphabet: they can then just allocate one of the free
families. Access to this would then be trivial.

\noindent
2) We have two different encodings one for cal and one for script. The
remaining symbols in both encodings would be different too. Thus both
encodings would need to be part of the standard suite of math encoding
tables.

Which solution to prefer depends a bit on the the number of symbols
that we want to put into the standard.

>From J\"org: I strongly support to have two different encodings, one
for cal and one for script. Why? If the user's have the choice between
cal and script, they prefer script (at least here in
Mainz\footnote{Maybe American style/taste prefer it the other way
  round.}). On the other hand, the old calligraphic alphabet still
needs to be supported for compatibility reasons.









\section{The MS1 encoding: 232}
Counting: 1 1 54 10  32  36 30 12 10 21 10 15,= 232
  \begin{enumerate}
    
    \item A skewchar in position 0: 1
    \item A spacechar in position 32: 1
    \item The BBB alphabet uppercase and lowercase: 54
    \item The BBB digits: 10
    \item The last WIDE ACCENTS: arc, back to front vector, and double
      sided vector, normal vector: 32

      For ams inclusion:
    \item The ``Ams arrows'' group: 36
    \item The ``Greater than AMS'' group: 30
    \item The ``subset ams'' group: 12
    \item AMS equals friends: 10
    \item Ams miscellaneous geometric symbols: 21
    \item Ams Vdash group: 10
    \item AMS boxes and friends: 15



      For fantasie if we have place to spair:
    \item Alan arrow construction set: 

  \end{enumerate}








\section{And the rest ?}
  \begin{itemize}

  \item In general, users may want MC fonts in arbitrary styles (bold
    sans MC for instance) in order to get the Greek letters in their
    favourite styles.

  \item A ``text-like'' italic or slanted for computer science
    identifier names and the like.  This would be Cork encoded and
    optionally loaded.

  \item A ``bold upright'' for use as variables -- e.g. vectors in
    physics notation rather than the arrow over an italic letter. This
    would be Cork encoded, and optionally loaded or accessed via the
    \texttt{\string\boldsymbol} concept in that case no family is
    required.

  \item Bold italic for use as variables: either optionally loaded as
    a second font with MC or cork encoding (using only variable fam
    symbols) or accessed via something like
    \texttt{\string\boldsymbol}.

  \item Bold Old german (occasional) suggested
    \texttt{\string\boldsymbol} approach.

  \item Bold script (occasional) suggested \texttt{\string\boldsymbol}
    approach.

  \item Sans serif lightface (occasional): optionally loaded cork
    encoded font.

  \item Sans serif boldface (occasional): optionally loaded cork
    encoded font.

  \item Bold symbols: either \texttt{\string\boldsymbol} or optionally
    loaded in remaining slots.

  \item Ultra bold symbols: either \texttt{\string\boldsymbol} or
    optionally loaded in remaining slots.

  \item An MC-encoded bold font containing upright bold Latin glyphs,
    plus bold upright and bold slanted Greek.  This would contain all
    of the most commonly requested bold glyphs in one font (rather
    than many more).
  \end{itemize}





\section{Summarising the families used by the proposed YAASP M-encoding}
\begin{enumerate}
\item Family $0$: A Cork encoded upright text font.

\item Family $2$: An MC encoded font containing the default latin and
  Greek italic+upright, and core symbols...

\item Family $1$: An MSP encoded font containing cal/script and accents...

\item Family $3$: An MX encoded font including all extensible glyphs,
  and double sized operators...

\item Family $y$: An MS$1$ encoded symbol font for Open, and arrows
  or relations.

\item Family $z$: An MS$2$ encoded symbol font for Old german.
\end{enumerate}

This leaves 10 families free for anything else, (like bold or sans...)
and makes many symbols available.

\textbf{What's more:} The first four give total \TeX, La\TeX\ compatibility.

\textbf{Still more:} The first six give total \TeX, \LaTeX, AMS\TeX,
AMS\LaTeX, LAMS\TeX compatibility.

\textbf{The six put together:} make wonders, using no more font families than
the present AMS\TeX.




\section{Discussion}

\subsection{Advantages}

For MC: A big advantage here, is kerning. In this encoding kerning
is possible between the Latin default alphabet, and both italic and
upright Greek alphabets. This is necessary for compatibility, and for
tidyness. On top of this both letter sets (in actual fact there are
three) can be kerned with the core symbols that are in the MC
encoding. That last point is the most important, and gives new and
better automatic math spacing. (For compatibility reasons, we must kern
the Greek italic with the period, the comma, and the slash.)

The bold version of the MC encoding gives the user access to a lot of
bold letter sets in one go. The global family consumtion is therefore
largely reduced: 1 bold font instead of 2 or 3.

Taking the accents away from the letters, means that the accents do
not change when the text face changes. i.e. bold letters, and medium
letters get the same accents.

Putting all the wide accents together, goes in the way of orthogonal
grouping. Thus all the accents could be metafonted together, and have
a few variables for adjustment.

One can get more than compatibility with plain TeX using 4 families
(the same number as standard \TeX\ currently uses).

One can get more than compatibility with AMS\TeX\ using 6 families.
This is less or equal than the number of families used by AMS\TeX.

The calligraphic alphabet is more used that the open, so putting it
with the accents is a step towards grouping most used stuff together.

This proposal gives a little room in the MC for free space, and good
core material.

With the MSP encoding concept, the MSi encodings can really be
considered as (optionnnal) extensions. Thus somebody who knows he
doesn't need the arrow kit and the Blackboard bold letter set does not
have to load them. Same for Fraktur.

All the \TeX\ specific glyphs are grouped in MX. Thus all the other fonts
could be used by other typesetting systems.

Using the Cork encoded font in fam 0 for things like \cn{log} and
\cn{sin}, means that the Greek users can replace it by a Greek font.
(I have been told that Greek mathematicians set those function names
in Greek).



\subsection{Disadvantages}

If there is not enough space for all the symbols we want to get in, I
suggest that we make an MS3 encoding, that would contain the other
version of script/cal, and extra symbols.


\subsection{Comments}

Now the core is really made of two fonts, and the kernel is made of four.

Comment from Alan about the space is MX:
\begin{quote}
  MX will be used by TeX, and the dvi drivers may be outputting to a
  device that doesn't accept anything but a space in position 32.  So
  if you don't include a space here, then the MX-encoded fonts have to
  be split into two device fonts by the drivers.
\end{quote}

Comment from Alan about the Cork encoded font:
\begin{quote} 
  I think it would be good to specify that this is family 0, for
  compatiblity with current \TeX\ documents containing explicit \cn{fam0}
  (naughty them!) and in order that we've filled up slots 0--3 rather
  than leaving a gap in family 0.
\end{quote}




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