diff --git a/tex/applications.tex b/tex/applications.tex index 1e3a0813ee5d60d34514ac90279f0dcd766adc55..50d822840b3cce24f340d98c5794cb1deacc6f46 100644 --- a/tex/applications.tex +++ b/tex/applications.tex @@ -6,4 +6,7 @@ - prioritize many definitions / theorems - refactoring advice - assoc / comm normalization -- term indexing techniques \ No newline at end of file +- term indexing techniques +- use existing views in $\cL$ (compositions of views are vivews) to give Jane more + information about her beautiful subsets, e.g. that matroids (and thus beautiful sets) + form a generalization of the notion of linear independence from linear algebra. \ No newline at end of file diff --git a/tex/beautysource.png b/tex/beautysource.png new file mode 100644 index 0000000000000000000000000000000000000000..984026628e3e3593d9804ef65c2ecd7c780d0376 Binary files /dev/null and b/tex/beautysource.png differ diff --git a/tex/intro.tex b/tex/intro.tex index a926dfb458e4a0b7a52deafa079e1096049f92ff..6309552dedf4abe3d5ba464dad8dd7cdced3f47b 100644 --- a/tex/intro.tex +++ b/tex/intro.tex @@ -19,13 +19,7 @@ To see what is known about beautiful sets, she types these three conditions into classifier, which interprets them as a \MMT theory $Q$, computes all (total) views from $Q$ into a library $\cL$, and returns presentations of target theories and the assignments made by the views. In our example we have the situation in -Figure~\ref{fig:theory-classification-ex}\ednote{MK: Maybe better do this in jEdit and use - screenshots} \ednote{Interesting: the $\emptyset$ clause could also be ``$\exists S$ - beautiful'', which is equivalent via the subset clause, maybe use that in the example: - define Matroid with that and have a theorem that says that $\emptyset$ is beautiful. Just - see what the viewfinder catches.\\ - DM: It's not going to be a ``proper'' theorem because it will be difficult to construct a proof. - Apart from that it should still match Base, beautiful and the other axioms.} In the base use case, Jane learns that her +Figure~\ref{fig:theory-classification-ex}. In the base use case, Jane learns that her ``beautiful sets'' correspond to the well-known structure of matroids~\cite{wikipedia:matroid}, so she can directly apply matroid theory to her problems. diff --git a/tex/matroids.png b/tex/matroids.png new file mode 100644 index 0000000000000000000000000000000000000000..eb2eb882f91dd2510b4d23eb97ebcb20d448a286 Binary files /dev/null and b/tex/matroids.png differ diff --git a/tex/results.png b/tex/results.png new file mode 100644 index 0000000000000000000000000000000000000000..bcc9b82f4c020852d073d4c88ef195b508edb03f Binary files /dev/null and b/tex/results.png differ diff --git a/tex/usecase.tex b/tex/usecase.tex index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..982088edc2355742f07f3058764210e17bbf9ce9 100644 --- a/tex/usecase.tex +++ b/tex/usecase.tex @@ -0,0 +1,24 @@ +The Viewfinder algorithm is implemented in the MMT system and exposed within the jEdit-IDE, allowing us to realize the use case +stated in the introduction. A screenshot of Jane's theory of beautiful sets is given in Figure \ref{fig:use:source}; it +is based on the (basic higher-order logic) foundation of the Math-in-the-Middle\ednote{cite} library developed natively in MMT. + +\begin{figure}[ht]\centering + \fbox{\includegraphics[width=0.6\textwidth]{beautysource}} + \fbox{\includegraphics[width=\textwidth]{results}} +\caption{A Theory of ``Beautiful Sets'' in MMT Surface Syntax and Results of the Viewfinder}\label{fig:use:source} +\end{figure} + +Right-clicking anywhere within the theory allows Jane to select \cn{MMT} $\to$ \cn{Find\ Views\ to...} $\to$ \cn{MitM/smglom} (the main Math-in-the-Middle library), telling her (within less than one second) that 11 Views have been found, the most promising of which points to the theory +\cn{matroid\_theory} (see Figure \ref{fig:use:target}) in the library. + +\begin{figure}[ht]\centering + \fbox{\includegraphics[width=0.6\textwidth]{matroids}} +\caption{The Theory of Matroids in the MitM Library}\label{fig:use:target} +\end{figure} + +\paragraph{} Using a different library as target, we can for example quickly write down a theory for a commutative binary operator (still using the Math-in-the-Middle foundation), allowing us to search e.g. the PVS Prelude library for any commutative operators, as in Figure \ref{fig:use:pvs}. + +\begin{figure} +Hier könnte Ihre Werbung stehen +\caption{Searching for Commutative Operators in PVS}\label{fig:use:pvs} +\end{figure} \ No newline at end of file