This directory contains the version of the SML implementation of
TeX Maths Layout algorithms. It has been updated to allow for changes
to the specification of SML from '90 to '97.

Further to the minimal changes needed to work with SML-97 there are
two sorts of change here. One is a collection of upgrades worked on
by Zach Hauser that implement support for accents, delimiters and
radicals. The second are some basically grotty cganges made by ACN that
re-work this code to use less of the "clever" features of SML. Specifically
the plan is to avoid use of ML modules (ie signatures and structures). To
avoid higher order functions as much as reasonably possible, and to use
function definitions with a definite number of arguments in place of
curried ones. The motivation for these changes is to make mapping the
SML code onto other languages easier.
(1) The signature/structure scheme protects name-spaces and helps keep the
    code modular. But the code here is only around 2500 lines long anyway
    and that is not large enough to run terrible risks of name clashes.
    Getting rid of the modules avoids the need to support the module-style
    namespace protection in any re-write. I observe that there are only
    a very few clashes anyway. Ha ha - when one removes the module stuff
    you end up with only 1500 lines of code!
(2) There seem to be remarkably few uses of higher order functions in the
    original code. The only uses of FOLD are in a prologue. There are only
    half a dozen uses of map. Cleaning them away does not do much damage
    to the code structure and avoids need for full support for static
    scoping of synamic variables and worries about closures in a translation.
(3) Most of the functions in the original are defined as Curried but are
    never partially applied. There are a number of cases where this is not
    so, but merely making the extra arguments explicit sorts that out
    rather easily. As with the other changes this will ease translation.
    Making the change is a mess, but the SML type-checker can ensure that
    I do not end up messing things up! Hmmm - on further thought this is not
    necessary - in any translation I can treat "f x y" as if it has been
    "f(x,y)" and so provided no partial application is used all will be well.
    And any partial application would show up as functions being called with
    the wrong number of args - an easy case to spot.
    The original code contains a number of cases of
       fun F x y = ...;
       val G = F X;
    that I can turn into
       fun G y = F X y;
    without significant loss of clarity, and I should make that conversion.
(4) There was one instance of a use of an "infix" directive, which is used
    with purely local scope and was easy to remove.
(5) I would probably like to end up with symbol names all distinct even if
    handled in a case-insensitive manner.


Thanks are due to Heckmann and Wilhelm for this code.

                                               ACN February 2015
                                                   June 2016





=====================================================================
The following exchanges of emails confirm permission to make use of the
files here.



From heckmann@absint.com Thu Apr 15 17:25:43 2010
Date: Thu, 15 Apr 2010 18:25:14 +0200
From: Reinhold Heckmann <heckmann@absint.com>
To: Arthur Norman <acn1@cam.ac.uk>
Cc: wilhelm@cs.uni-sb.de
Subject: Re: TeX in SML from around 1997

Arthur Norman wrote:
> Hi! I have just come across that paper and so let me start by saying
> what fun it is.
That's nice to hear.

> I had been considering what would be involved with
> re-creating exactly the formula layout that TeX uses for display of
> formulae for the Reduce algebra system (check reduce-algebra at
> Sourceforge). At present the way I display formula there is to use code
> that maps Reduce onto TeX-format textual stuff like $\int \sqrt ...$, I
> pass that to some C++ code that I wrote that instantly turns it back
> from textual form into an internal representation, then box structures.
> I then have code that paints direct from the boxes on the screen. I use
> cmr10, cmmi10, cmsy10 and cmex10 when painting. But I do not use any
> code from TeX itself and the exact layout and spacing I have is my own
> thoughtless code - it is a maths display but purists fuss that it is not
> as good as it should be... specifically that TeX gets the spacing a lot
> better!

Parts of this can be usefully combined with our layouter, I think.
We never created a parser from $\int \sqrt ...$ to SML terms.
On the other side, I programmed a translator from box terms to dvi,
but painting the box terms directly may also be useful.

> I might also add that a few years ago I taight the SML course at
> Cambridge - Larry Paulson has been doing that for a while, but I gave it
> before im and stood in for him a few years back when he went on leave.
>
> There are three ways your work really encourages me - one is that SML
> code is so much nicer than the Web/Pascal TeX original. The second is
> that you concentrate on just the maths mode layout, and for my purposes
> at present I do not care about the rest! And finally your code
> demonstrates that the guts of the TeX maths layout stuff can fit in
> under 2500 lines of code (albeit SML - a *NOTABLY* concise language) and
> that is a nice size body of code to work on individually or with one or
> two friends... it is feasible to look at.

> OK, so after the above introduction, a couple of questions:
>
> (1) I have fetched your code from the ftp server as mentioned in your
> paper. It does not have any explicit license terms attached. In a spirit
> of caution before I look much further I should ask your permission to
> use the code you have, hack at it, use it as a basis for other
> experiments etc etc... if anything derived from it weher to end up in
> Reduce I note that we have the rest of Reduce under the 2-clause BSD
> license (which in effect says "do what you like with this, but you may
> not blame me if it bits you"), so I should explicitly check your
> reaction to using it in that context.

For my part, I think you can use it since I stopped working with it long ago.

> (2) The things you list as incomplete in the version in the FTP server
> are (a) radicals such as \sqrt (b) huge delimiters built up out of
> towers and (c) accented symbols. I guess also a box that embeds
> text-mode TeX inside a formula could also go beyond your scope! I
> presume that you stopped work on the project soon after the paper and
> that you do not have a version that is more complete, but I ought to ask!

Yes, that's true.

> And do you believe that the things that need finishing off
> introduce real new serious issues or do you view them as just "more of
> the same"? Any hints or advice there would be interesting.

I think (b) and (c) are more of the same.
\sqrt might be a bit more tricky since the V-like part of it varies in size
according to the size of the argument,
and has to fit exactly to the overline-like part.

What we did to derive our SML code was to study Knuth's TeX book
and to translate the Pascal code to SML, applying the simplifications
offered by this more powerful language.
So you should look at Knuth's implementation of \sqrt and translate it, too.

> I do not know if I will find the energy or time to make serious use of
> your work to replace or improve the layout of my display, but you can
> probably see why it interests me!

> I am sending this email in the immediate run up to Easter (so Happy
> Easter!), and I will then be away from Cambridge and email for around a
> fortnight, so do not need an instant response... And at this stage I
> have downloaded your code and read the paper and a few lines of the code
> itself, but e.g. not tried it... this message is so I know where I am
> before I invest real time...

I was also away a few days ...

Best wishes for your work
Reinhold Heckmann

From wilhelm@gigasun.cs.uni-sb.de Thu Apr 15 17:38:26 2010
Date: Thu, 15 Apr 2010 18:38:21 +0200 (CEST)
From: wilhelm@gigasun.cs.uni-sb.de
To: Reinhold Heckmann <heckmann@absint.com>
Cc: Arthur Norman <acn1@cam.ac.uk>, wilhelm@cs.uni-sb.de
Subject: Re: TeX in SML from around 1997

Hi,
I also agree to you using the code without formal license agreement.
It would be nice, though, if you would acknowledge the paper and the
origin of the SML code if you extend it and integrate it somewhere.

Cheers,  Reinhard Wilhelm



=====================================================================


This directory contains a re-implementation of TeX's formula layout
written in Standard ML of New Jersey, version 109.2
by Reinhold Heckmann, Universitaet des Saarlandes,
following suggestions by Reinhard Wilhelm, Universitaet des Saarlandes.

WARNING:  The system is still in the status of development.
-------   This distribution may contain errors of any kind.

The present system can typeset nearly all formulae
by translating them from formula terms (see MathTypes.sml)
into box terms (see BoxTypes.sml).
The only exceptions are accents, roots, and big delimiters.
The resulting box terms can be translated into dvi output.
At present, there is no good way to enter formulae;
a parser is needed which can read TeX input and build formula terms from it.
Also, the testing possibilities and user friendliness
are not yet well developed.

To install:
   get formulae.tar.gz
   zcat formulae.tar.gz | tar -xf -
This gives a directory called `formulae'.
Go into this directory.
Start sml (best: Standard ML of New Jersey, version 109.2).
   use "edit.m";
   U "all";
... and everything is read in and translated (hopefully).

At the moment, the system provides two test functions (see test.sml)
  test1, test2: unit -> unit
which, when executed, typeset certain fixed formulae,
translate them to dvi and write them into file  "das.dvi".
(Sorry, this file name is built in.)
As an example, the distributed system contains
the file "das.dvi" resulting from running test1.
It also contains a TeX file "dastex.tex" which contains the formulae
of test2 to allow comparing TeX layout with our system's layout.
More tests can be programmed by editing or augmenting file "test.sml".

The typesetting system itself is contained in files "----.sml".
For a rough description of their organization, see file "OVERVIEW".
In addition, there are files RM05 ... RM10 MI05 ... MI10 SY05 ... SY10 EX09 EX10
which contain condensed font information (height, depth, and width of characters).
These files have been derived from TeX's TFM files.

File "edit.m" contains functions which provide access to the Unix editor "vi"
from within sml.
   E "xxx";
runs the editor on file "xxx.sml" (note the addition of the suffix).
After leaving the editor, the file is reloaded
if there have been any changes to it.
A call
   U "xxx";
loads file "xxx.sml" without editing.
Both functions store the file name internally;
if the same file is to be edited / loaded again,
it suffices to call
   E "";
and likewise with U.

File "all.sml" contains a sequence of U's
which load the files containing the system in their proper order.
(Sorry, there is no "make" or any other kind of source code management.)

Documentation:
The core system is described in the paper
"A Functional Description of TeX's Formula Layout"
submitted to Journal of Functional Programming.
Unfortunately, there is no documentation of the usage of the system
other than the remarks in this file
(mainly because we have not yet implemented a nice user interface).