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authorNorbert Preining <norbert@preining.info>2022-05-25 03:01:13 +0000
committerNorbert Preining <norbert@preining.info>2022-05-25 03:01:13 +0000
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treeefb861dfafff09d4bef8024c85a11f8c8deaba76 /macros/latex/contrib/stex/doc/packages/stex-metatheory.tex
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-\textcolor{red}{TODO: metatheory documentation} \ No newline at end of file
+The \pkg{stex-metatheory} package contains \sTeX symbols so ubiquitous, that it is
+virtually impossible to describe any flexiformal content without them, or that are
+required to annotate even the most primitive symbols with meaningful
+(foundation-independent) ``type''-annotations, or required for basic structuring
+principles (theorems, definitions). As such, it serves as the default meta theory for any
+\sTeX module.
+
+We can also see the \pkg{stex-metatheory} as a foundation of mathematics in the sense of
+\cite{rabe:future:15}, albeit an informal one (the ones discussed there are all formal
+foundations). The state of the \pkg{stex-metatheory} is necessarily incomplete, and will
+stay so for a long while: It arises as a collection of empirically useful symbols that are
+collected as more and more mathematics are encoded in \sTeX and are classified as
+foundational.
+
+Formal foundations should ideally instantiate these symbols with their formal counterparts,
+e.g. |isa| corresponds to a typing operation in typed setting, or the $\in$-operator in
+set-theoretic contexts; |bind| corresponds to a universal quantifier in ($n$th-order)
+logic, or a $\Pi$ in dependent type theories.
+
+We make this theory part of the \sTeX collection due to the obiquity
+of the symbols involved. Note however, that the metatheory is
+for all practical purposes a ``normal'' \sTeX module, and the
+symbols contained ``normal'' \sTeX symbols.
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "../stex-manual"
+%%% End:
+
+% LocalWords: stex-metatheory th-order