\centerline{\bf Formulator}
\medskip
\noindent
{\it Formulator} is an equation processor
for the Macintosh which allows  {\it wysiwyg}
creation of displayed equations, through selection
from pull-down menus (or, for the more skilled)
the Mac's command-key sequences. The interesting
feature of {\it Formulator} is that it was clearly
inspired by \TeX, and that one of its options
is to create a \TeX-version of the equation.
The writer of this software, Bob Pollard, was
also responsible for much of {\it MacAuthor}, and
the two applications were clearly designed to live
together.

Icon Technology generously sent me a pre-release version
of {\it Formulator} (with a neat time expiry on
it, so that I have to reset the date on my Mac in order
to use it). What I have is version 0.7. My comments
should therefore be read in the light of 
this not being the `final' version. There were also
some bits of the {\it Formulator Reference}, which
summarised many of the possible commands, and a
stack for use with HyperCard. In passing, this is
a very valuable approach adopted by Apple: almost
all software now comes with a hypertext stack or two which
almost replaces a manual. Since every new Mac comes
with HyperCard, this is obviously the beginning of
a new growth industry --- writing hypertext stacks.

Perhaps I am not the best person to use {\it wysiwyg}
software. I'm rather fond of mark-up, and I find
the buildup of an equation through menus rather
laborious and exhausting. By now I know \TeX\ well
enough to be able to tackle problems up to at
least \TeX pert level. My preconceptions get in the way.
But lets try it anyway. After a few false starts ---
well it is user-friendly and intuitive, or so I thought ---
I looked through the stacks and read the reference pages.
The first thing I tried was one of the examples
from {\it Icon Technology's} flyer, and given here as
a Macintosh screen dump after construction through
{\it Formulator}:
\smallskip
\noindent{\overfullrule0pt
\scaledpicture 141truemm by 21truemm (icontech scaled 400)
}\par
\noindent
(Some of the lumpiness in the example is due to scaling
it to fit the page. {\it Formulator\/} itself permits
you to work in one of two scales. The smaller is close
to `true' size, while the larger is the one which allows
more control.)
The \TeX\ which this generated is
\smallskip
\begintt
$${1\over{2\pi}}
{\int^{\sqrt{}y}_{-\infty}}
{\left({\sum^n_{k=1}}
{\sin^2}{x_t}(t)\right)}
(f(t)+g(t))dt\hbox{}$$
\end
\endtt
\smallskip\noindent
It generated the |\end| itself too. In the original
this was one continuous line, which is impossible to
print here, so I have broken it up into more
digestible units. The first thing that strikes me is
the multiplicity of braces. No bad thing, although
it does reduce the human readability. However, just
as we would expect machine generated \PS\ to be
machine rather than human readable, we should not
expect this to be easy to understand. The real problem
seems to me to be the mistake. Did you spot it?
What does |\sqrt{}y| give? It gives  $\sqrt{}y$, 
rather than $\sqrt y$. In this context it is not
ambiguous, but neither is it what appeared when
we manipulated the symbols through {\it Formulator}.
Therefore any claim to {\it wysiwyg\/}ness is dashed.

Perhaps the feature I liked best in {\it Formulator}
was the ease with which you could edit the {\it wysiwyg}
version. This is a major advance over something like
Mac$\Sigma$qn, where editing really means doing things
over. On the other hand I did find selection of the elements
very sensitive. It took some care to mark the part of
the equation you wanted to deal with. If you do not
make sure that you have finished the parts of an equation
off correctly (usually by pressing {\it enter}), and
try to shortcut by placing the cursor, you can generate
fallacious \TeX. A nice feature is the automatic
balancing of brackets. But it was not clear to me just how
you could choose a particular size of parentheses, for
those times when \TeX\ does not know best.

But let's tackle a more interesting equation,
whose {\it Formulator} version is:
\par
\vskip-0.8truein
\noindent
\picture 150truemm by 36truemm (bezier.pic scaled 400)
\par
\noindent
 My main interest here was to see
how the limits on the summation would be handled.
I, of course, was expecting to handle them through
|\atop|, with some lip service to |\scriptstyle|.
{\it Formulator} very sensibly makes no mention of
|\over| as a way of creating fractions (surely one
of Don's little mistakes), but uses
a Fraction selection instead. But in doing so we have lost
|\atop|. So instead, we use a subscripted one column matrix.
Now, in the {\it Formulator} version of this, the
subscripts are  nicely displayed at a smaller size.
The \TeX\ produced looks like\smallskip
\begintt
$$\phi({\zeta_1},
{\zeta_2},
{\zeta_3})=
{\sum^{}_\matrix{{i+j+k=2}\cr
{i,j,k\geq0}\cr}}
{{2!}\over{i!j!k!}}
{\zeta^i_1}
{\zeta^j_2}{\zeta^k_3}\
{\phi_{ijk}}
\hbox{}$$ 
\end
\endtt
\smallskip\noindent
Unfortunately, this doesn't work. In order to
subscript a matrix, you have to group, writing
something like
\begintt
\sum_{\matrix i+j+k=2\cr
i,j,k\geq0\cr}
\endtt
As we all know, \TeX's error messages are not always
easy to understand. This one was a real mare's nest.
And naturally, when you subscript a matrix, the
elements do not appear at a smaller size.

At this point, I was getting a little despondent,
and I stopped. I have no doubt that these bugs will have
been ironed out by the final release. But one
or two things do still worry me.
\item{$\bullet$}Who is this intended for?
If you have {\it MacAuthor}, and are happy with it
--- it is after all a very powerful {\it wysiwyg}
processor --- would you be using \TeX\ at all?
\item{$\bullet$}It is only a \TeX\ generator, 
not an \AmSTeX\ or
\LaTeX\ generator, nor does it seem to be
able to be extended to take account of your own
macros. I'm not at all clear how you could reference
a control sequence which was not part of the menus.
Say you had a special relational
operator, constructed through |\buildrel|, 
how would you use it?
\item{$\bullet$}Is this for unskilled hands, those who do
not know the names of the symbols? Would they know
to use Matrix in order to get multiple subscripts?
And would they be surprised when the {\it Formulator}
version and the \TeX\ version were rather different?
The Symbols menu also gives a few symbols (like
therefore) not in |plain|\TeX; these come through
as question marks. 
\smallskip
I can't see how it makes things
already tricky in \TeX\ any easier; and easy things
seem more roundabout.
The benefits are probably mostly from \TeX\
to {\it Formulator}, which has been able
to absorb \TeX's mathematical
sophistication.

I feel very iffy about the whole thing. {\it Formulator}
clearly has an appeal, because \TeX\ is in there somewhere,
but I don't think it is something which existing
\TeX\ users will adopt, nor can I see its use bringing
any more users into the \TeX\ fold. I would like to
be wrong.

{\it Formulator} may be obtained from
{\obeylines
Icon Technology
9 Jarrom Street
Leicester LE2 7DH
tel: 0533 546225
}

\rightline{\sl Malcolm W. Clark}
