[Axiom-developer] Design of Semantic Latex

[Tim Daly]

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The referenced paper only looked at the DLMF Airy functions. The results are:

"Of the 17 sections in the DLMF sample chapter on Airy functions we can handle the mathematical

formulas completely in 6, partially in 5 (without the transformation to MathML), and 6 remain

incomplete.

The grammar currently contains approximately 1000 productions, of which ca. 350 are dictionaries.

There are about 550 rewrite rules. There are fewer rewrite rules than grammar rules, partly because

dictionaries can be treated uniformly by manipulating literals, and partly because it is still incomplete

with respect to the grammar.

Our project shows that parsing mathematics in the form of LATEX documents written to project-specific

rules is feasible, but due to the variations in notation the grammar needs to be engineered specifically

for the project, or even for different chapters written by different mathematicians (e.g. the chapter on

elementary transcendental functions and on Airy functions)."

Many have tried to parse DLMF but there is not sufficient information in the latex. This 

effort used many rules to try to decide if w(x+y) is a multiplication or a function application.

There are rules to decide if sin a/b means (sin a)/b or sin(a/b), either of which is trivial to

distinguish if the latex read {sin a}/b or sin{a/b}

Trivial amounts of semantic markup in the DLMF would communicate semantics without using

1000 productions which still get wrong answers.