% $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: Isabelle and \isac}

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

 \begin{frame}

   \frametitle{Isabelle and \isac}

 The task of this ``Projektpraktikum'' (6 ECTS) was to

 \begin{itemize}

 \item study the concept of ``context'' in the theorem prover \textbf{Isabelle} from TU Munich

 \item study basic concepts of the math assistant \sisac{} from TU Graz

 \pause

 \item redesign \sisac{} with respect to contexts

   \begin{itemize}

   \item use contexts for type inference of user input

   \item handle preconditions of specifications

   \item clarify the transfer of context data from sub-programs to the calling program

   \end{itemize}

 \pause

 \item introduce contexts to \sisac{} according to the new design

 \item use the coding standards of Isabelle2011 for new code.

 \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 to \isac}

 \subsection[Contexts]{Isabelle's Contexts, advantages and use}

 \begin{frame}

   \frametitle{Advantages of Isabelle's Contexts}

 Isabelle's context replaced theories because \dots:

 \begin{itemize}

 \item theories are static containers of \textit{all} logical data

 \item contexts are \textit{dynamic} containers of logical data:

   \begin{itemize}

   \item functions for storing and retrieving various logical data

   \item functions for type inference

   \item provide data for Isabelle's automated provers

   \end{itemize}

 %\item e.g. theories have no direct functions for type inference

 %\item replace function \texttt{parseNEW}

 %\item assumptions \& environment $\rightarrow$ context

 \item allow to conform with scopes for subprograms.

 \end{itemize}

 \end{frame}

 \begin{frame}

   \frametitle{Isabelle's context mechanism}

     \texttt{\small{

       \begin{tabbing}

 xx\=xx\=in\=\kill

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

 %datatype Isac\_Ctxt =\\

 %\>\>Env of term * term\\

 %\>| Asm of term;\\

 %\\

 structure ContextData =  \alert{Proof\_Data}\\

 \>~(\alert{type T} = term list\\

 \>\>\alert{fun init \_} = []);\\

 \\

 %local\\

 %\>fun insert\_ctxt data = ContextData\alert{.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\\

 fun insert\_assumptions asms = \\

 \>\>\>ContextData\alert{.map} (fn xs => distinct (asms@xs));\\

 \\

 %local\\

 %\>fun unpack\_asms (Asm t::ts) = t::(unpack\_asms ts)\\

 %\>\>| unpack\_asms (Env \_::ts) = unpack\_asms ts\\

 %\>\>| unpack\_asms [] = [];\\

 %\>fun unpack\_envs (Env t::ts) = t::(unpack\_envs ts)\\

 %\>\>| unpack\_envs (Asm \_::ts) = unpack\_envs ts\\

 %\>\>| unpack\_envs [] = [];\\

 %in\\

 %\>fun get\_assumptions ctxt = ContextData.get ctxt |> unpack\_asms;\\

 %\>fun get\_environments ctxt = ContextData.get ctxt |> unpack\_envs;\\

 %end

 fun get\_assumptions ctxt = ContextData\alert{.get} ctxt;\\

 \\

 \\

 val declare\_constraints : \\

 \>\>\>term -> Proof.context -> Proof.context

       \end{tabbing}

     }}

 \end{frame}

 \begin{frame}

   \frametitle{Usage of Contexts}

     \texttt{\footnotesize{

       \begin{tabbing}

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

 fun transfer\_asms\_from\_to from\_ctxt to\_ctxt =\\

 \>  let\\

 \>\>    val to\_vars = get\_assumptions to\_ctxt |> map vars |> flat\\

 \>\>    fun transfer [] to\_ctxt = to\_ctxt\\

 \>\>\>      | transfer (from\_asm::fas) to\_ctxt =\\

 \>\>\>\>\>          if inter op = (vars from\_asm) to\_vars = []\\

 \>\>\>\>\>         then transfer fas to\_ctxt\\

 \>\>\>\>\>          else transfer fas (insert\_assumptions [from\_asm] to\_ctxt)\\

 \>  in transfer (get\_assumptions from\_ctxt) to\_ctxt end\\

 \\

 fun parse thy str =\\

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

 \>\>\>\>(\alert{Syntax.read\_term\_global thy} str)\\

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

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

 \\

 fun parseNEW ctxt str = \\

 \>\>\>SOME (\alert{Syntax.read\_term ctxt} str |> numbers\_to\_string)\\

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

       \end{tabbing}

     }}

 \end{frame}

 \subsection[Redesign]{Redesign of \isac{} using contexts}

 \begin{frame}

   \frametitle{Redesign of \isac{} using contexts}

 \begin{center} DEMO \end{center}

 \end{frame}

 \begin{frame}

   \frametitle{Deduction simplifies computation}

 \small{

 %\begin{onehalfspace}

 \begin{tabbing}

 xxx\=xxx\=\kill

      \`$\mathit{(some)}\;\mathit{assumptions}$\\

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

 %     \`$x ^ 2 - 6 * x + 9\not=0\land x ^ 2 - 3 * x\not=0$\\

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

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

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

      \`$x\not=3\land x\not=0$\\

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

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

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

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

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

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

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

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

      \`$x = 0\land x = \frac{6}{5}$\\

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

      \`\alert{$\mathit{Check\_Elementwise}\;\mathit{Assumptions}:x\not=0\land x = 0$}\\

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

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

 \end{tabbing}

 }

 %\end{onehalfspace}

 \end{frame}

 \begin{frame}

   \frametitle{More ``deduction'', \\less ``computation''}

 \footnotesize{\tt

 \begin{tabbing}

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

 Script Solve\_root\_equation (e\_e::bool) (v\_v::real) =      \\

 \> (let e\_e = ((Try (Rewrite\_Set norm\_equation False)) \@\@   \\

 \>\>\>            (Try (Rewrite\_Set Test\_simplify False))) e\_e; \\

 \>\>     (L\_L::bool list) =                                   \\

 \>\>\>            (SubProblem (Test',                           \\

 \>\>\>\>                         [linear,univariate,equation,test]\\

 \>\>\>\>                         [Test,solve\_linear])             \\

 \>\>\>\>                        [BOOL e\_e, REAL v\_v])             \\

 \>  in \alert{Check\_elementwise L\_L \{(v\_v::real). Assumptions\}})\\      

 \end{tabbing}

 }

 \small{

 ``Deductive'' part of Lucas-Interpretation relives the ``computational'' part: \alert{one statement becomes obsolete~!}

 }

 \end{frame}

 \begin{frame}

   \frametitle{Redesign of \isac{} using contexts}

 Advantages of the redesign:

 \begin{itemize}

 \item type inference by \textit{local} contexts\\

 \pause

      \alert{now user-input without type constraints~!}

 \pause

 \item consistent handling of logical data

   \begin{itemize}

   \item preconditions and partiality conditions in contexts

   \item transfer of context data into subprograms clarified

   \item transfer of context data from subprograms clarified

   \end{itemize}

 \pause

      \alert{now some statements become obsolete.}\\

 \end{itemize}

 \pause

 Now Lucas-interpretation shifts efforts from ``computation'' further to ``deduction''.

 \end{frame}

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

 \begin{frame}

   \frametitle{Improvement of functional code}

   \begin{itemize}

   \item \textbf{code conventions}: Isabelle2011 published coding standards first time

   \item \textbf{combinators}: Isabelle2011 introduced a library containing the following combinators:

 \\\vspace{0.2cm}

 \tiny{\tt%

   val |$>$ : 'a * ('a -$>$ 'b) -$>$ 'b\\

   val |-$>$ : ('c * 'a) * ('c -$>$ 'a -$>$ 'b) -$>$ 'b\\

   val |$>>$ : ('a * 'c) * ('a -$>$ 'b) -$>$ 'b * 'c\\

   val ||$>$ : ('c * 'a) * ('a -$>$ 'b) -$>$ 'c * 'b\\

   val ||$>>$ : ('c * 'a) * ('a -$>$ 'd * 'b) -$>$ ('c * 'd) * 'b\\

   val \#$>$ : ('a -$>$ 'b) * ('b -$>$ 'c) -$>$ 'a -$>$ 'c\\

   val \#-$>$ : ('a -$>$ 'c * 'b) * ('c -$>$ 'b -$>$ 'd) -$>$ 'a -$>$ 'd\\

   val \#$>>$ : ('a -$>$ 'c * 'b) * ('c -$>$ 'd) -$>$ 'a -$>$ 'd * 'b\\

   val \#\#$>$ : ('a -$>$ 'c * 'b) * ('b -$>$ 'd) -$>$ 'a -$>$ 'c * 'd\\

   val \#\#$>>$ : ('a -$>$ 'c * 'b) * ('b -$>$ 'e * 'd) -$>$ 'a -$>$ ('c * 'e) * 'd\\

 }

   \end{itemize}

 \end{frame}

 \begin{frame}

   \frametitle{Example with combinators}

     \texttt{\footnotesize{

       \begin{tabbing}

 xx\=xx\=xx\=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}

     }}

 \dots which probably can be further polished.

 \end{frame}

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

 %\begin{frame}

 %  \frametitle{Preparation of Future Development}

 %

 %%  "Script Solve_root_equation (e_e::bool) (v_v::real) =       " ^

 %%  " (let e_e = ((Try (Rewrite_Set norm_equation False)) @@    " ^

 %%  "            (Try (Rewrite_Set Test_simplify False))) e_e;  " ^

 %%  "     (L_L::bool list) =                                    " ^

 %%  "            (SubProblem (Test',                            " ^

 %%  "                         [linear,univariate,equation,test]," ^

 %%  "                         [Test,solve_linear])              " ^

 %%  "                        [BOOL e_e, REAL v_v])              " ^

 %%  "  in Check_elementwise L_L {(v_v::real). Assumptions})     "

 %\end{frame}

 %

 %\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 new Isabelle release in February 2011: update \sisac{} first

 \pause

     \item lines of code (LOC) in Isabelle and \sisac{}\\ \vspace{0.2cm}

 \textit{

     \begin{tabular}{lrl}

       src/ & 1700 & $\,$k LOC\\

       src/Pure/ & 70 & k LOC\\

       src/Provers/ & 8 & k LOC\\

       src/Tools/ & 800 & k LOC\\

       src/Tools/isac/ & 37 & k LOC\\

       src/Tools/isac/Knowledge & 16 & k LOC

     \end{tabular}

 }

 \pause

     \item changes scattered throughout the code ($\rightarrow$ grep)

 \pause

     \item documentation of Isabelle very ``technical'' (no API)

 \pause

    \item documentation of \sisac{} not up to date

     \end{itemize}

 \end{frame}

 %\begin{frame}

 %  \frametitle{Lines of Code}

 %    \begin{tabular}{lr}

 %      src/ & 1700 k \\

 %      src/Pure/ & 70 k \\

 %      src/Provers/ & 8 k \\

 %      src/Tools/ & 800 k \\

 %      src/Tools/isac/ & 37 k \\

 %      src/Tools/isac/Knowledge & 16 k \\

 %    \end{tabular}

 %\end{frame}

 \section{Summary}

 \begin{frame}

   \frametitle{Summary}

 The project succeeded in all goals:

 \begin{itemize}

 \item implemented Isabelle's contexts in \sisac{} such that

 \item user input requires no type constraints anymore

 \item consistent logical data is prepared for Isabelle's provers

 \end{itemize}

 \pause

 The course of the project was close to the plan:

 \begin{itemize}

 \item faster in writing new code

 \item slower in integrating the code into \sisac

 \end{itemize}

 \pause

 The project provided essential prerequisites for further development of the Lucas-interpreter.

 \end{frame}

 \end{document}