reconsidering the size of the leap; a literature search for related efforts
Published 2020-07-27T17:38:00.001Z by Physics Derivation Graph
A pure graph-based approach is far from what is standard (sequential presentation in PDFs). The value isn't sufficient for content creators (Physics researchers) to cross the entry barrier. I needed to learn this lesson:
Improving on tradition is good, but ignoring tradition is stupid.
More specifically,
Focus on formalization of actual mathematical practice, and not also try to ‘improve’ on the way that people currently do mathematics.
If a graph-based semantically-encoded representation is too much, what are the more incremental options? Non-graph options for sequential content with semantic decoration:
start the workflow of document creation in a CAS (e.g., Sympy) and generate .tex from that.
create documents in Latex, then check the .tex file using a CAS
We could ignore both graphs and validation and focus merely on semantically meaningful expressions. That alone would constitute an evolutionary step.
This semantic representation is a necessary dependency for validation and for a rigorous graph.
A mathematically-linked graph that has edges which are not rigorously checked is closer to Wikipedia's hyperlinked text pages.
Semantic text in Latex
"SALT – Semantically Annotated LATEX for Scientific Publications."
Groza, Tudor, Handschuh, Siegfried, Möller, Knud, Decker, Stefan
In Franconi, Enrico, Kifer, Michael, May, Wolfgang (eds.) ESWC 2007. LNCS vol. 4519, pp. 518–532. Springer, Heidelberg (2007)
MCML appears focused on the structure of proofs rather than expressions.
No source code available.
sTeX: An Infrastructure for Semantic Preloading of LaTeX Documents
sTeX handles expressions and proofs. Most relevant to the PDG is "cmathml" which provides a method for concise Content MathML that gets converted to Latex for display.
An amalgamation of the above summary plus the PDFs for each package
Sub-packages in sTeX
https://tools.ietf.org/doc/texlive-doc/latex/stex/cmathml/cmathml.pdf "cmathml.sty: A TEX/LATEX-based Syntax for Content MathML" (2012)
"This package provides a collection of semantic macros for content MathML and their LATEXML bindings. These macros form the basis of a naive translation from semantically preloaded LATEX formulae into the content MathML formulae via the LATEXML system." content --> presentation (Latex or Presentation MathML)
"statements" in sTeX https://ctan.math.illinois.edu/macros/latex/contrib/stex/sty/statements/statements.pdf "Semantic Markup for Mathematical Statements" (2019)
abstract: "This package provides semantic markup facilities for mathematical statements like Theorems, Lemmata, Axioms, Definitions, etc. in STEX files. This structure can be used by MKM systems for added-value services, either directly from the STEX sources, or after translation."