For tl;dr: look at https://github.com/leftaroundabout/Symbolic-math-HaTeX/blob/master/EXAMPLES.md.
This is an attempt to get convenient math syntax in HaTeX (i.e., in data structures
compatible / convertable to those from http://hackage.haskell.org/package/HaTeX).
The idea is to combine these features:
Full access to the math-typesetting power of LaTeX. It should be possible to express
any formula that might be found in a typical mathematics or physics journal article.
This should also include expression which are not quite well-defined from a programming
point of view, but are clear to the intended audience.
Idiomatic Haskell syntax. Who wants to bother with unreadable expressions involving
either hundreds of double-backslashes or extra syntax overhead in wrapping them
explicitly into HaTeX?
Ideally, one would write expressions as if only meaning Haskell to calculate them,
but get the result back as a full pretty-printing LaTeX math string. /And the actual
calculated result as well/, if possible!
To this end, we use a minimal symbolic-manipulation EDSL, namely
dumb-cas, set up in a way so the
leaves of the syntax tree, i.e. the individual symbols, are represented by LaTeX
expressions in memory and by single-letter variables in the Haskell code.
These can then be combined with operators corresponding to LaTeX's maths operators,
to obtain a very compact and almost WYSIWYG-like code appearance, while retaining
the ability to apply any LaTeX-specific tweaks whenever necessary. At the same
time, because the AST is fully precedence-aware, it is safely possible to transform
the expressions via e.g. Template Haskell, to actually compute concrete numerical
results, or apply exact symbolic-manipulation techniques.
