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.From "The QED manifesto revisited" (2007)
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.
- create a .tex document using semantically enriching domain-specific language
- see https://github.com/slatex/sTeX and specifically the cmathml package
- see "mathematical content markup language" referenced in https://pdfs.semanticscholar.org/6139/579ab589c62397ef4ba6728da42f519c9b8c.pdf
- https://arxiv.org/abs/1707.01271 -- requires DSL like \giacinputmath{factor(x^10-1)}
- create a .tex document with standard Latex, then decorate the expressions with semantics (using context present in the document).
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)
--> focuses on decorators like "claim" and "explanation." No suggestion of handling mathematics.
QED v2: Mathropolis and mathematical content markup language
"The QED Manifesto after Two Decades -- Version 2.0"
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.
Most relevant to the PDG is "cmathml" which provides a method for concise Content MathML that gets converted to Latex for display.
https://kwarc.info/systems/sTeX/ - sTeX homepage
https://github.com/slatex/sTeX - sTeX source code
https://ctan.org/pkg/stex?lang=en - sTeX package for Latex
https://github.com/slatex/sTeX/blob/master/sty/stex/stex.pdf "Semantic Markup in Tex/Latex" (2019)
This document advises that github is the best source since CTAN is tedious to update and thus not current.
http://ctan.math.utah.edu/ctan/tex-archive/macros/latex/contrib/stex/sty/stex/stex.pdf "Semantic Markup in Tex/Latex" (2019)
https://caligari.dartmouth.edu/doc/texmf-dist/doc/latex/stex/stex.pdf (2010)
Overview of packages in sTeX.
Overview of packages in sTeX.
An amalgamation of the above summary plus the PDFs for each package
"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."
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."
"omtext" in sTeX
http://mirrors.ibiblio.org/CTAN/macros/latex/contrib/stex/sty/omtext/omtext.pdf "omtext: Semantic Markup for Mathematical Text Fragments in LATEX" (2019)
abstract: "This package supplies an infrastructure for writing OMDoc text fragments in LATEX."
Latex packages which are not relevant
A package for common math commands: COntent Oriented LaTeXhttps://www.ctan.org/pkg/cool
http://ftp.math.purdue.edu/mirrors/ctan.org/macros/latex/contrib/cool/Content_LaTeX_Package_Demo.pdf
There are tools for performing arithmetic calculations in Latex,
- http://latexcalc.sourceforge.net/
- https://ctan.org/pkg/calc?lang=en and https://texdoc.net/texmf-dist/doc/latex/tools/calc.pdf
There's no math support on https://schema.org/ for webpages.
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