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W. F. Hammond: The GELLMU Archive
A Silly Little <abbr>GELLMU</abbr> Article
William F. Hammond
revised March 25, 2006
This is the simplest possible type of article Its body
consists of just a few paragraphs It is a GELLMU
document GELLMU stands for Generalized Extensible
Like Markup.
GELLMU is designed to admit completely
automated translation into many document languages
Classical does not have that property; but some
documents do when imported under GELLMU
Yet GELLMU is really no more difficult to edit than .
It is relatively easy for a sophisticated GELLMU
user with freely available software to add like commands to
GELLMU.
There is no organization of this article into sections The
content model for this type of document (GELLMU
article) provides that the document body be organized
either into one or more sections, which may be preceded and followed
by paragraphs outside those sections, or that the document body simply
be organized into one or more paragraphs
One thing to notice is that the generalized markup allows
new paragraphs to be opened with the appearance of a blank line in
the marked up document
Another thing to notice is that
beginpar ... endpar
and par ...
are essentially equivalent forms of markup in GELLMU That is,
GELLMU markup, which is essentially a markup under SGML
does not provide its own concept of environment although
it supports like environmental markup
Just as with or it is easy to provide a mathematical
formula, such as y x^{3}(x^{2} 1) either inline or displayed
This paragraph contains a math display involving the same
formula:
y x^{3}x^{2} 1
Here is a gratuitous inline radical: 32
The current version of the didactic GELLMU article
definition supports simple mathematical commands such as frac,
sum, int, and prod, and provides some
table support Table models are close adaptations
of the early HTML table model, and there is near emulation of
s tabular model
The square root of a compound fraction:
abcd
This math display was marked up with:
sqrtfracfracabfraccdeos
The markup eos for endofsentence is used instead of
. in order to signal a semantic parser that it is not part of
the mathematical content of the display
Next we present the formula for solving the general quadratic equation:
a x^{2} b x c 0
Its solution is marked up with:
xfracbpmsqrtb24ac2aeos
to give
x b b^{2} 4 a c2 a
And we offer the Taylor series of the exponential function:
e^{t} _{k 0}^{} t^{k}k
which is created with the markup:
etsumk0inftyfractkkcma
To be sure that frac is working recursively, we try
frac1sqrt52
1frac11frac11frac11frac11ldots;eos
for the continued fraction expansion of the golden mean, and this
yields:
1 52
1 11111111
It is important to understand what is or is not happening here The
mathematical markup is rather like In fact, only
the markup for sum is slightly different from the
mathematical markup used with That is because it is
essential in GELLMU to have a precise location for the end of
that which is being summed
The reason is that the exact end location for sum is
not deducible merely from the syntax of its markup but requires
a knowledge of the command name sum This is always the case
for a command with more than one argument For some such commands it is
inconsequential because the location of the end is determined automatically
at the second stage of processing with sufficient precision Where greater
precision is needed, however, it must be provided in input markup since the
first stage of processing is allowed to know only syntax
One way for a mathematician to view the difference between
GELLMU, and HTML is to think about
rational maps of algebraic surfaces If one wishes to
have an automatic translator from to HTML (or even to
HTML with provision for mathematical notation), there will be
places where the transformation is singular and fails Such
singularities may be resolved by moving to a markup designed to
dominate both targets
I never intend to provide more than a didactic definition of
article inasmuch as it is my opinion that each author or
work group of authors will ultimately find it essential, just as now
they find essential the newcommand feature of ,
to be able to provide customization Customization is
ever so much more important in GELLMU than in because
under this design there will never be a full set of ultimate target
formats With customization is primarily a matter of
authoring convenience; under GELLMU customization is required
in order to be able to service all of the desired target formats
Beyond that an author or work group may hope to design a definition
of article (or of another document type) that is robust
for almost any conceivable target format by thinking carefully
about all possible content distinctions relevant to
his, her, or its current authoring context To the extent that this
design meets that goal, the author or work group will have no need
to revisit old documents in order to be able to have automatic
processing to new formats