% $Header: /cvsroot/latex-beamer/latex-beamer/solutions/conference-talks/conference-ornate-20min.en.tex,v 1.7 2007/01/28 20:48:23 tantau Exp $

\documentclass{beamer}

% This file is a solution template for:

% - Talk at a conference/colloquium.

% - Talk length is about 20min.

% - Style is ornate.

% Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.

%

% In principle, this file can be redistributed and/or modified under

% the terms of the GNU Public License, version 2.

%

% However, this file is supposed to be a template to be modified

% for your own needs. For this reason, if you use this file as a

% template and not specifically distribute it as part of a another

% package/program, I grant the extra permission to freely copy and

% modify this file as you see fit and even to delete this copyright

% notice.

\mode<presentation>

{

  \usetheme{Hannover}

  % or ...

  \setbeamercovered{transparent}

  % or whatever (possibly just delete it)

}

%\usepackage{setspace} %for "\begin{onehalfspace}"

\usepackage[english]{babel}

% or whatever

\usepackage[utf8]{inputenc}

% or whatever

\usepackage{times}

\usepackage[T1]{fontenc}

% Or whatever. Note that the encoding and the font should match. If T1

% does not look nice, try deleting the line with the fontenc.

\def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}

\def\sisac{{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}}

\title[\isac: Computation \& Deduction] % (optional, use only with long paper titles)

{Integrating Computation and Deduction\\

  in the \isac-System}

\subtitle{Projektpraktikum: Introducing Isabelle's Contexts}

\author[Lehnfeld] % (optional, use only with lots of authors)

{Mathias~Lehnfeld}

% - Give the names in the same order as the appear in the paper.

% - Use the \inst{?} command only if the authors have different

%   affiliation.

\institute % (optional, but mostly needed)

{

  Vienna University of Technology\\

  Institute of Computer Languages

}

% - Use the \inst command only if there are several affiliations.

% - Keep it simple, no one is interested in your street address.

% \date[CFP 2003] % (optional, should be abbreviation of conference name)

% {Conference on Fabulous Presentations, 2003}

% - Either use conference name or its abbreviation.

% - Not really informative to the audience, more for people (including

%   yourself) who are reading the slides online

% \subject{Theoretical Computer Science}

% This is only inserted into the PDF information catalog. Can be left

% out.

% If you have a file called "university-logo-filename.xxx", where xxx

% is a graphic format that can be processed by latex or pdflatex,

% resp., then you can add a logo as follows:

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}

% \logo{\pgfuseimage{university-logo}}

% Delete this, if you do not want the table of contents to pop up at

% the beginning of each subsection:

\AtBeginSubsection[]

{

  \begin{frame}<beamer>{Outline}

    \tableofcontents[currentsection,currentsubsection]

  \end{frame}

}

% If you wish to uncover everything in a step-wise fashion, uncomment

% the following command:

%\beamerdefaultoverlayspecification{<+->}

\begin{document}

\begin{frame}

  \titlepage

\end{frame}

\begin{frame}{Outline}

  \tableofcontents

  % You might wish to add the option [pausesections]

\end{frame}

% Structuring a talk is a difficult task and the following structure

% may not be suitable. Here are some rules that apply for this

% solution:

% - Exactly two or three sections (other than the summary).

% - At *most* three subsections per section.

% - Talk about 30s to 2min per frame. So there should be between about

%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you

%   are going to talk about. So *simplify*!

% - In a 20min talk, getting the main ideas across is hard

%   enough. Leave out details, even if it means being less precise than

%   you think necessary.

% - If you omit details that are vital to the proof/implementation,

%   just say so once. Everybody will be happy with that.

\section[Introduction]{Introduction}

\subsection[Isabelle \& \isac]{Isabelle and \isac}

\begin{frame}

  \frametitle{Isabelle and \isac}

    \begin{itemize}

    \item Computer Theorem Prover Isabelle

    \item Math Learning Assistent \isac

    \end{itemize}

\end{frame}

\subsection[Computation \& Deduction]{Computation and Deduction in a Lucas-Interpreter}

\begin{frame}

  \frametitle{Computation and Deduction in a Lucas-Interpreter}

    \includegraphics[width=100mm]{overview.pdf}

\end{frame}

\section[Contributions]{Contributions of the project}

\subsection[Contexts]{Introduction of Isabelle Contexts}

\begin{frame}

  \frametitle{Introduction of Isabelle Contexts}

    \begin{itemize}

    \item theories too general

    \item not capable of type inference

    \item replace function \texttt{parseNEW}

    \end{itemize}

\end{frame}

\begin{frame}

  \frametitle{Introduction of Isabelle Contexts}

    \texttt{\tiny{

      \begin{tabbing}

xx\=xx\=xx\=xx\=\kill

fun parse thy str =\\

\>(let val t = (typ\_a2real o numbers\_to\_string)\\

\>\>\>\>(Syntax.read\_term\_global thy str)\\

\>\>in SOME (cterm\_of thy t) end)\\

\>\>\>handle \_ => NONE;

\\~\\~\\

fun parseNEW ctxt str = SOME (Syntax.read\_term ctxt str |> numbers\_to\_string)\\

\>\>\>handle \_ => NONE;

\\~\\~\\

local\\

\>fun insert\_ctxt data = ContextData.map (fn xs => distinct (data@xs));\\

in\\

\>fun insert\_assumptions asms = map (fn t => Asm t) asms |> insert\_ctxt;\\

\>fun insert\_environments envs = map (fn t => Env t) envs |> insert\_ctxt;\\

end

      \end{tabbing}

    }}

\end{frame}

\subsection[Redesign]{Redesign of Type Inference in \isac}

\begin{frame}

  \frametitle{Redesign of type inference in \isac}

    \begin{itemize}

    \item use context type inference

    \item parsing input (specification \& user input)

    \item specification with polymorphic types

    \item etc.

    \end{itemize}

\end{frame}

\subsection[Code Improvement]{Improvement of functional code}

\begin{frame}

  \frametitle{Improvement of functional code}

  \begin{itemize}

  \item combinators

  \item code conventions

  \end{itemize}

\end{frame}

\begin{frame}

  \frametitle{Combinators \& Code Conventions}

    \texttt{\tiny{

      \begin{tabbing}

xx\=xx\=xx\=xx\=xx\=\kill

fun prep\_ori [] \_ \_ = ([], e\_ctxt)\\

\>| prep\_ori fmz thy pbt =\\

\>\>\>let\\

\>\>\>\>val ctxt = ProofContext.init\_global thy |> fold declare\_constraints fmz\\

\>\>\>\>val ori = map (add\_field thy pbt o split\_dts o the o parseNEW ctxt) fmz\\

\>\>\>\>\>|> add\_variants\\

\>\>\>\>val maxv = map fst ori |> max\\

\>\>\>\>val maxv = if maxv = 0 then 1 else maxv\\

\>\>\>\>val oris = coll\_variants ori\\

\>\>\>\>\>|> map (replace\_0 maxv |> apfst)\\

\>\>\>\>\>|> add\_id\\

\>\>\>\>\>|> map flattup\\

\>\>\>in (oris, ctxt) end;

      \end{tabbing}

    }}

\end{frame}

\begin{frame}

  \frametitle{Drop \tt{Check\_Elementwise}!}

\small{

%\begin{onehalfspace}

\begin{tabbing}

xxx\=xxx\=\kill

$\mathit{solve}\;(\frac{x}{x ^ 2 - 6 * x + 9} - \frac{1}{x ^ 2 - 3 * x} = \frac{1}{x}, x)$\\ \\

\>$\frac{x}{x ^ 2 - 6 * x + 9} - \frac{1}{x ^ 2 - 3 * x} = \frac{1}{x}$ \\ \\

\>$\frac{x}{x ^ 2 + -1 * (6 * x) + 9} + \frac{-1 * 1}{x ^ 2 + -1 * (3 * x)} = \frac{1}{x}$ \\ \\

%\>$\frac{3 + -1 * x + x ^ 2}{9 * x + -6 * x ^ 2 + x ^ 3} = \frac{1}{x}$ \\ \\

\>$(3 + -1 * x + x ^ 2) * x = 1 * (9 * x + -6 * x ^ 2 + x ^ 3)$ \\

\>$\mathit{solve}\;((3 + -1 * x + x ^ 2) * x = 1 * (9 * x + -6 * x ^ 2 + x ^ 3), x)$ \\

\>\>$(3 + -1 * x + x ^ 2) * x = 1 * (9 * x + -6 * x ^ 2 + x ^ 3)$ \\

%\>\>$(3 + -1 * x + x ^ 2) * x - 1 * (9 * x + -6 * x ^ 2 + x ^ 3) = 0$ \\

\>\>$(3 + -1 * x + x ^ 2) * x - (9 * x + -6 * x ^ 2 + x ^ 3) = 0$ \\

\>\>$-6 * x + 5 * x ^ 2 = 0$ \\

\>\>$\mathit{solve}\;(-6 * x + 5 * x ^ 2 = 0, x)$ \\

\>\>$[x = 0, x = \frac{6}{5}]$ \\

\>$[x = 0, x = \frac{6}{5}]$ \\

                                          \`\alert{$\mathit{Check\_Elementwise}\;\mathit{Assumptions}$}\\

\>$[x = \frac{6}{5}]$ \\

$[x = \frac{6}{5}]$

\end{tabbing}

}

%\end{onehalfspace}

\end{frame}

\subsection[Future Development]{Preparation of Future Development}

\begin{frame}

  \frametitle{Preparation of Future Development}

    \begin{itemize}

    \item logical data for Isabelle provers in contexts

    \item \isac programming language more compact\\

      $\rightarrow$ context built automatically

    \end{itemize}

\end{frame}

\section[Problems]{Problems encountered in the project}

\begin{frame}

  \frametitle{Problems encountered in the project}

    \begin{itemize}

    \item publication of new Isabelle release

    \item amount of code in Isabelle and \isac

    \item changes scattered throughout the code

    \end{itemize}

\end{frame}

\section{Summary}

\begin{frame}

  \frametitle{Summary}

TODO

\end{frame}

\end{document}