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-\documentclass{omdoc}
-\usepackage{amssymb}
-\usepackage{alltt}
-\usepackage{hyperref}
-\usepackage{listings}
-\def\omdoc{OMDoc}
-\def\latexml{LaTeXML}
-\defpath{backmods}{../background}
-%% defining the author metadata
-\WAperson[id=miko,
- affiliation=JUB,
- url=http://kwarc.info/kohlhase]
- {Michael Kohlhase}
-\WAinstitution[id=JUB,
- url=http://jacobs-university.de,
- streetaddress={Campus Ring 1},
- townzip={28759 Bremen},
- countryshort=D,
- country=Germany,
- type=University,
- acronym=JACU,
- shortname=Jacobs Univ.]
- {Jacobs University Bremen}
-
-\begin{document}
-
-% metadata and title page
-% \begin{DCmetadata}[maketitle]
-% \DCMcreators{miko}
-% \DCMrights{Copyright (c) 2009 Michael Kohlhase}
-% \DCMtitle{An example of semantic Markup in {\sTeX}}
-% \DCMabstract{In this note we give an example of semantic markup in {\sTeX}:
-% Continuous and differentiable functions are introduced using real numbers, sets and
-% functions as an assumed background.}
-% \end{DCmetadata}
-
-\inputref{intro}
-
-\begin{omgroup}[id=sec.math]{Mathematical Content}
- \begin{omgroup}{Calculus}
- We present some standard mathematical definitions, here from calculus.
- \inputref{continuous}
- \inputref{differentiable}
-\end{omgroup}
-
-\begin{omgroup}[id=sec.math]{A Theory Graph for Elementary Algebra}
- Here we show an example for more advanced theory graph manipulations, in particular
- imports via morphisms.
-
-\begin{module}[id=magma]
- \importmodule[load=\backmods{functions}]{functions}
- \symdef{magbase}{G}
- \symdef[name=magmaop]{magmaopOp}{\circ}
- \symdef{magmaop}[2]{\infix\magmaopOp{#1}{#2}}
- \begin{definition}[id=magma.def]
- A \defi{magma} is a structure $\tup{\magbase,\magmaopOp}$, such that $\magbase$ is
- closed under the operation $\fun\magmaopOp{\cart{\magbase,\magbase}}\magbase$.
- \end{definition}
-\end{module}
-
-\begin{module}[id=semigroup]
- \importmodule{magma}
- \begin{definition}[id=semigroup.def]
- A \trefi[magma]{magma} $\tup{\magbase,\magmaopOp}$, is called a \defi{semigroup}, iff
- $\magmaopOp$ is associative.
- \end{definition}
-\end{module}
-
-\begin{module}[id=monoid]
- \importmodule{semigroup}
- \symdef{monneut}{e}
- \symdef{noneut}[1]{#1^*}
- \begin{definition}[id=monoid.def]
- A \defi{monoid} is a structure $\tup{\magbase,\magmaopOp,\monneut}$, such that
- $\tup{\magbase,\magmaopOp}$ is a \trefi[semigroup]{semigroup} and $\monneut$ is a
- \defii{neutral}{element}, i.e. that $\magmaop{x}\monneut=x$ for all $\inset{x}\magbase$.
- \end{definition}
-
- \begin{definition}[id=noneut.def]
- In a monoid $\tup{\magbase,\magmaopOp,\monneut}$, we use denote the set
- $\setst{\inset{x}S}{x\ne\monneut}$ with $\noneut{S}$.
- \end{definition}
-\end{module}
-
-\begin{module}[id=group]
- \importmodule{monoid}
- \symdef{ginvOp}{i}
- \symdef{ginv}[1]{\prefix\ginvOp{#1}}
- \begin{definition}[id=group.def]
- A \defi{group} is a structure $\tup{\magbase,\magmaopOp,\monneut,\ginvOp}$, such that
- $\tup{\magbase,\magmaopOp,\monneut}$ is a \trefi[monoid]{monoid} and $\ginvOp$ acts as
- a \defi{inverse}, i.e. that $\magmaop{x}{\ginv{x}}=\monneut$ for all
- $\inset{x}\magbase$.
- \end{definition}
-\end{module}
-
-\begin{module}[id=cgroup]
-\importmodule{group}
-\begin{definition}[id=cgroup.def]
- We call a \trefi[group]{group} $\tup{\magbase,\magmaopOp,\monneut,\ginvOp}$ a
- \defii{commutative}{group}, iff $\magmaopOp$ is commutative.
-\end{definition}
-\end{module}
-
-\begin{module}[id=ring]
-\symdef{rbase}{R}
-\symdef[name=rtimes]{rtimesOp}{\cdot}
-\symdef{rtimes}[2]{\infix\rtimesOp{#1}{#2}}
-\symdef{rone}{1}
-\begin{importmodulevia}{monoid}
- \vassign{rbase}\magbase
- \vassign{rtimesOp}\magmaopOp
- \vassign{rone}\monneut
-\end{importmodulevia}
-\symdef[name=rplus]{rplusOp}{+}
-\symdef{rplus}[2]{\infix\rplusOp{#1}{#2}}
-\symdef{rzero}{0}
-\symdef[name=rminus]{rminusOp}{-}
-\symdef{rminus}[1]{\prefix\rminusOp{#1}}
-\begin{importmodulevia}{cgroup}
- \vassign{rplus}\magmaopOp
- \vassign{rzero}\monneut
- \vassign{rminusOp}\ginvOp
-\end{importmodulevia}
-\begin{definition}
- A \defi{ring} is a structure $\tup{\rbase,\rplusOp,\rzero,\rtimesOp,\rone,\rminusOp}$,
- such that $\tup{\noneut\rbase,\rtimesOp,\rone}$ is a monoid and
- $\tup{\rbase,\rplusOp,\rzero,\rminusOp}$ is a commutative group.
-\end{definition}
-\end{module}
-\end{omgroup}
-\end{omgroup}
-
-\begin{omgroup}[id=concl]{Conclusion}
- In this note we have given an example of standard mathematical markup and shown how a a
- {\sTeX} collection can be set up for automation.
-\end{omgroup}
-\bibliographystyle{alpha}
-\bibliography{kwarc}
-\end{document}
-
-%%% Local Variables:
-%%% mode: LaTeX
-%%% TeX-master: t
-%%% End:
-
-% LocalWords: miko Makefiles tex contfuncs modf sms pdflatex latexml Makefile
-% LocalWords: latexmlpost omdoc STEXDIR BUTFILES DIRS