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%  macros
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% version comments
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%========================================
%  settings
%=========================================
\newcommand{\cd}{\textsc{CD}}
\newcommand{\cocoa}{\textsl{CoCoA}}
\newcommand{\coq}{\textsc{Coq}}
\newcommand{\gap}{\textsf{GAP}}
\newcommand{\ida}{{\it Algebra Interactive!\/}}
\newcommand{\mml}{\textsc{MathML}}
\newcommand{\mathematica}{\textsl{Mathematica}}
\newcommand{\MathBook}{\textsc{MathBook}}
\newcommand{\mod}{\,\textrm{mod}\,}
\newcommand{\oma}{\textbf{application}}
\newcommand{\Phr}{phrasebook}
\newcommand{\Phrs}{phrasebooks}
\newcommand{\xhtml}{\textsc{XHtml}}
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\newcommand{\DocBook}{{\rm DocBook }}
\newcommand{\Gap}{{\rm Gap }}
\newcommand{\Mathematica}{{\rm Mathematca }}
\newcommand{\Maple}{{\rm Maple }}

\newcommand{\nl}{\smallskip\noindent}
\newcommand{\np}{\bigskip\noindent}

\newcommand{\wsdl}{\textsc{wsdl}}

\newcommand{\html}{\textsc{HTML}}
\newcommand{\jsp}{\textsc{JSP}}
\newcommand{\latex}{\textsc{LaTex}}
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\newcommand{\soap}{\textsc{soap}}
\newcommand{\java}{\textsc{Java}}
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\newcommand{\mathml}{\textsc{MathML}}
\newcommand{\CAS}{\textsc{CAS}}

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\newcommand{\monet}{\textsc{MONET}}
\newcommand{\HTTP}{\textsc{HTTP}}
\newcommand{\web}{\textsc{WEB}}
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\newcommand{\lambdacal}{$\lambda$-calculus}
\newcommand{\lambdaterm}{$\lambda$-term}


%========================================
%  Context abbreviations
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\newcommand{\ecds}{Extended-Formal CDs}
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\newcommand{\crossref}{\mathfrak{R}}

\newcommand{\Var}   {Variable}
\newcommand{\Vars}  {Variables}
\newcommand{\var}   {variable}
\newcommand{\vars}  {variables}


\newcommand{\taglib}  {Tag Library}
\newcommand{\fmp}     {FMP}
\newcommand{\fmpl}    {Formal Mathematical Property}
\newcommand{\cmp}     {CMP}
\newcommand{\cmpl}    {Commented Mathematical Property}

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%  XML abbreviations
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\newcommand{\BET}[1]{$<$#1/$>$}
\newcommand{\attr}[1]{{\bf#1}}
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\newcommand{\attrval}[1]{{\em #1}}
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\newtheorem {question}{Question}[section]
\newtheorem {TODO}{TODO}[section]

\newtheorem {remark}{Remark}[section]
\newtheorem {remarks}{Remarks}[section]
\newtheorem {example}{Example}[section]
\newtheorem {Definition}{Definition}[section]

%---------------------------------------------------
\title{\Large Meaninful Mathematical Messages}
\author{E. Reinaldo Barreiro\\
RIACA, Eindhoven University of Technology\\
Eindhoven, The Netherlands\\
\texttt{ereinald@win.tue.nl}
}

%-----------------------------------------------------

\begin{document}
\maketitle

\newpage

{
\huge
\begin{itemize}
    \item Project Objectives.
    \item Meaningful Mathematical Messages.
    \item OmDoc.
    \item MBase.
    \item MathBook
    \item Content Management in MathBook.
    \item Implementations.
\end{itemize}
}


\newpage

{
\huge

\center{Project Objectives} \\

\begin{itemize}
    \item ``...developing tools and software
to facilitate and enhance the communication of `Meaningful
Mathematical Messages' over World Wide Web.  The emphasis is on
\emph{interactive} communication, as opposed to the one-way
communication that occurs via journals. The results should lead to a
better computer environment for mathematical activity than is
presently available.''

    \item ``The main activity of this project ({\sl viz.}, creating a rigorous
notion of `meaningful mathematical object')
is an essential step toward the overall goal of the IMD project: {\em a
better computer environment for conducting mathematics}''.

    \item ``Other projects envisaged within the IMD project
are building an authoring tool for the mathematical objects and 
interfaces with applications, and adaptivity for 
interactive documents.''

\end{itemize}


}

\newpage

{
\huge 

\center{Meaningful Mathematical Messages} \\ 

\begin{itemize}
    \item A mathematical message is meaningful when 
          the entities communicating the message agree 
          on a meaning.

    \item The meaning of a message depends on the context
          on which the message is produced and received. 
          To agree in a meaning the producer and sender 
          should share the same context.

    \item OpenMath CDs as a form of context: 

    \begin{itemize}
        \item Contain intentional declaration of OM symbols.
        \item Machine readable but not machine understandable.
        \item No support for Complex Mathematical Theories or 
              Formal Mathematics.
    \end{itemize}                    
\end{itemize}
}

\newpage


{
\huge 

\center{OmDoc} \\ 

{
\large
(Developed under the direction of M. Kohlhasse at Saarbruecken).
http://www.mathweb.org/omdoc/
}

\begin{itemize}
    \item OmDoc is a XML markup format and data model for Open Mathematical 
          Documents on the Web. 

    \item  It concentrates on representing the meaning of mathematical 
           formulae instead of their appearance.

    \item It is build upon Algebraic Specification Theory.


    \item Extension of the OpenMath and MathML standards. It extends these 
          formats by adding markup for the document and theory level 
          of mathematical documents. 
     
   
    \item Limited support for presentation and interactivity.

\end{itemize}
}

\newpage

{
\huge 

\center{MBase} \\ 

{
\large
    Saabruecken.
    http://www.mathweb.org/mbase/.
}

\begin{itemize}

    \item The MBase System is a web-based, distributed mathematical knowledge 
          base. 
          
    \item This system is realized as a mathematical service in the MathWeb system, 
          an implementation of a mathematical software bus for distributed 
          theorem proving. 

    \item It offers a universal repository of formalized mathematics where the 
          formal representation allows semantics-based retrieval of distributed 
          mathematical facts. (OmDoc used as underlying representation 
          language).
    

    \item (Platform dependent: Linux, Solaris).
        
\end{itemize}

\begin{center} MBase + OmDoc = support for context\end{center}

}

\newpage

{
\huge 

\center{MathBook} \\ 

\begin{quote}
    MathBook is a framework for the development of interactive 
    mathematical documents.
    
\end{quote} 

\nl
{
\large
    Developed at RIACA.
    http://riaca.win.tue.nl/mathbook/
}

\begin{center}MathBook's main features\end{center}


\begin{itemize}
    \item It is inspired on OmDoc (support for theories) and on DocBook
          (presentation issues).  

    \item Full support for interactivity and programming constructs. 


    \item Good interface with RIACA's Mathematical Services (Mathematica, Gap, 
          Maple).

    \item Lightweight context management.

    \item Platform independent (all the technology is Java based).

    \item Extensible.

\end{itemize}
}

\newpage

{
\huge 

\center{Context management in MathBook} \\ 

\begin{itemize}
    \item It offers support for theories (organized in the so called 
          extended CDs).

    \item Theories signatures are modeled as ``classes''. Classes are 
          entities containing different kinds of methods (symbols, 
          axioms, definitions, assertions, etc). 

    \item Theory imports (via morphisms) are modeled as class inheritance  
           (via morphism).
          
    \item  Class (theory) methods are (locally) parameterized to make then 
           presentation independent.

     \item Support for Theory parameterization (e.g. finite 
           dimensional vector spaces are parameterized by an integer 
           (the dimension) and a field (the base field)).

\end{itemize}
}

\newpage

{
\huge 
\center{Practical Implementations} \\ 

\begin{itemize}
    \item RIACA phrasebooks and mathematical services (in collaboration with M. Riem).

    \item OpenMath CD editor: Java GUI editor for OpenMath CDs.

    \item RIACA's JSP Tag Libraries. A group of OpenMath related tag 
          libraries. Web Interface to RIACA phrasebooks and services. 

    \item IDA II: Main MathBook application. Java based Web Application
          (Servlets, JSP Tag Libraries, XSLT transformations, etc).
    
    \item Partial implementation of context for IDA: as a combination of 
          servlets and tag libraries.

    \item Full implementation of a context service (in progress). It uses 
          Jelly (Executable XML) among other Java Web Technologies.
    
\end{itemize}
}

\newpage

\begin{thebibliography}{99}
\bibitem{RIACATAGLIB} RIACA's Tag Libraries. http://riaca.wi.tue.nl/taglib/.
\end{thebibliography}

\bibliographystyle{plain} \bibliography{}
\end{document}

