Commit 4e6d5cd5 authored by Florian Rabe's avatar Florian Rabe
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\paragraph{Motivation}
``Semantic Search'' -- a very suggestive term, which is alas seriously under-defined --
has often been touted as the ``killer application'' of semantic technologies. With a view
finder, we can add another possible interpretation: searching mathematical ontologies
......@@ -65,3 +66,22 @@ theory matroid : F?MitM
\end{tabular}
\caption{Theory Classification for beautiful sets}\label{fig:theory-classification-ex}
\end{figure}
\paragraph{Approach and Contribution}
We have developed the MMT language \cite{RK:mmt} and the concrete syntax of the OMDoc XML format \cite{omdoc} as a uniform representation language for mathematical knowledge.
Moreover, we have exported multiple proof assistant libraries into this format, including the ones of PVS in \cite{KMOR:pvs:17} and HOL Light in \cite{RK:hollight:15}.
This enables us, for the first time, to apply generic methods --- i.e., methods that work at the MMT level --- to search for theory morphisms in these libraries.
Our contribution is twofold.
Firstly, we present such a generic theory morphism finder.\ednote{add 2 sentences about how it works}
Secondly, we apply this view finder in two concrete case studies. \ednote{add 1-2 sentences for each case study}
\paragraph{Related Work}
Existing systems have so far only worked with explicitly given theory morphisms, e.g., in IMPS \cite{imps} or Isabelle \cite{isabelle}.
Automatically and systematically searching for new theory morphisms, let alone doing so generically, is entirely novel as far as we know.
\ednote{FR: I really don't know any related work. Is there anything?}
\paragraph{Overview}
In Section~\ref{sec:prelim}, we revise the basics of MMT and the PVS and the representations of the HOL Light libraries
......@@ -63,6 +63,8 @@
\input{macros}
\setcounter{tocdepth}{2}
\begin{document}
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......@@ -87,19 +89,21 @@
avoiding duplication of work or suggesting an opportunity for refactoring.
\end{abstract}
\setcounter{tocdepth}{2}\tableofcontents\newpage
\section{Introduction}\label{sec:intro}\input{intro}
\section{Introduction}\label{sec:intro}
\input{intro}
\section{Preliminaries}\label{sec:prelim}\input{prelim}
\section{Preliminaries}\label{sec:prelim}
\input{prelim}
\section{Viewfinder}\label{sec:viewfinder}\input{viewfinder}
\section{Finding Theory Morphisms}\label{sec:viewfinder}
\input{viewfinder}
\section{Extended Use Case}\label{sec:usecase}\input{usecase}
\section{Applications}\label{sec:usecase}
\input{usecase}
\section{Conclusion}\label{sec:concl}
\subsubsection*{Acknowledgements}
\paragraph{Acknowledgements}
The authors gratefully acknowledge financial support from the OpenDreamKit Horizon 2020
European Research Infrastructures project (\#676541) and the DFG-funded project OAF: An
Open Archive for Formalizations (KO 2428/13-1).
......
MMT theories, flat, bla
\subsection{MMT Grammar}
\subsection{The MMT Language}
For the purposes of this paper, we will work with the (only slightly simplified) grammar given in Figure \ref{fig:mmtgrammar}.
......@@ -43,6 +42,6 @@ We can eliminate all includes in a theory $T$ by simply copying over the constan
An assignment in a view $V:T_1\to T_2$ is syntactically well-formed if for any assignment $C=t$ contained, $C$ is a constant declared in the flattened domain $T_1$ and $t$ is a syntactically well-formed term in the codomain $T_2$. We call a view \emph{total} if all \emph{undefined} constants in the domain have a corresponding assignment and \emph{partial} otherwise.
\subsection{Theory Graphs and Library Encoding}
\subsection{Proof Assistant Libraries in MMT}
OAF?, Meta-Theories, Logical Frameworks / LF, HOAS, Judgments-as-Types
\ No newline at end of file
OAF: PVS, HOL Light
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