1.1 --- a/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Tue Oct 18 23:30:37 2011 +0200
1.2 +++ b/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Wed Oct 19 23:11:45 2011 +0200
1.3 @@ -32,6 +32,7 @@
1.4 \def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
1.5 \def\sisac{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
1.6
1.7 +
1.8 %----------// BEGIN DOCUMENT \\----------%
1.9
1.10 \begin{document}
1.11 @@ -78,71 +79,48 @@
1.12 %----------// ABSTRACT \\----------%
1.13
1.14 \begin{abstract}
1.15 -The Baccalaureate Thesis creates interactive course material for Signal Processing based on the experimental math assistant Isabelle/\sisac.
1.16 -
1.17 -The content of the course material is defined together with the Signal Processing and Speech Communication Laboratory (SPSC Lab) of Graz University of Technology (TUG). The content is planned to be used in specific lectures and labs of the SPSC and thus is thoroughly concerned with underlying mathematical and physical theory.
1.18 -
1.19 +The Baccalaureate Thesis creates interactive course material for Signal Processing based on the experimental math assistant Isabelle and provides it within {\sisac} (Isabelle for Calculations).
1.20 +\par The content of the course material is defined together with the Signal Processing and Speech Communication Laboratory (SPSC Lab) of Graz University of Technology (TUG). The content is planned to be used in specific lectures and labs of the SPSC and thus is thoroughly concerned with underlying mathematical and physical theory.
1.21 One challenge of this thesis is, that theory is not yet mechanized in Computer Theorem Provers (CTP); so this thesis will provide preliminary definitions in so-called \emph{theories} of the CTP Isabelle and theorems without proofs.
1.22 -
1.23 -Another callenge is the implementation of interactive courses: this is done within the educational math assistant Isabelle/\sisac, which is under development at TU Graz. The present state of \sisac{} happens to provide the {\em first} occasion for authoring by a non-member of the \sisac{} developer team. So this challenge involves alpha-testing of the underlying ``CTP-based programming language'', because error messages are still not user-friendly and need frequent contact with \sisac-developers.
1.24 -
1.25 +\par Another callenge is the implementation of interactive courses: this is done within the educational math assistant Isabelle/{\sisac}, which is under development at TU Graz. The present state of {\sisac{}} happens to provide the {\em first} occasion for authoring by a non-member of the {\sisac}-developer team. So this challenge involves alpha-testing of the underlying \emph{CTP-based programming language}, because error messages are still not user-friendly and need frequent contact with {\sisac}-developers.
1.26 So the practical outcome of this thesis is twofold:
1.27 -
1.28 -(1) interactive course material hopefully useful in education within the SPSC Lab and within STEOP, the introductory orientation phase at TUG, as a preview for students in Telematics on later application of math knowledge introduced in the first semester and
1.29 -
1.30 -(2) a detailed description of technicalities in programming implemented as an interactive Isabelle/Isar theory, providing future programmers with guidelines and \sisac-developers with feedback in usability of the CTP-based program language.
1.31 +\begin{enumerate}
1.32 +\item Interactive course material hopefully useful in education within the SPSC Lab and within STEOP, the introductory orientation phase at TUG, as a preview for students in Telematics on later application of math knowledge introduced in the first semester and
1.33 +\item A detailed description of technicalities in programming implemented as an interactive Isabelle/Isar theory, providing future programmers with guidelines and {\sisac}-developers with feedback in usability of the CTP-based program language.
1.34 +\end{enumerate}
1.35 \end{abstract}\clearpage
1.36
1.37 +%----------// T O C \\----------%
1.38
1.39 \pagenumbering{Roman}
1.40 +This thesis is structured into a generell part describing the math fundamentals, a practical part including the work on \cal{ISAC} and finally the management part overviewing the work process.
1.41 \tableofcontents
1.42 \clearpage
1.43 \pagenumbering{arabic}
1.44 -
1.45 -\setcounter{page}{5}
1.46 -
1.47 -This thesis is structured into a generell part describing the math fundamentals, a practical part including the work on \cal{ISAC} and finally the management part overviewing the work process.
1.48 +\setcounter{page}{6}
1.49
1.50 %----------// PART-1 \\----------%
1.51
1.52 \part{Project Fundamentals}
1.53
1.54 \section{Introduction}
1.55 -
1.56 The motivation to this thesis mainly takes it source from the feeling of understanding difficult signal processing tasks and the will to help others to get this feeling to.
1.57 \par Signal Processing requieres a huge range of mathematic knowledge as well as a feeling for simplification and number tricks but even though this fact, the operations themself are no higher ones. The main task is to understand. Aside this description we think of the classic math ideas and techniques, consisting of predefined formulas, notations and forumularsations we learn.
1.58 -\par Mathematics mechanized in Computer Theorem Provers \emph{(CTP)} has (almost) a problem with traditional mathematical notations (predicate calculus) for axioms, definitions, lemmas, theorems as a computer programm or script is not able to interpret every greek or latin letter and every greek, latin or whatever calculations symbol. Also if we would be able to handle thehse symbols we would have a problem to interpret them correctly. In different problems, symbols and letters have different meanings and ask for different ways to get through. Exclusive from the input, also the output can be a problem. We are familar with a specified notations and style taught in university but a computer programm has no knowledge of the form probved by a professor and the maschines themselve also have not yet the possibilities to print every symbol (correct) Recent developments provide proofs in a humand readable format but according to the fact that there is no mony for good working formel editors yet, the style is one thing we have to live with.
1.59 +\par Mathematics mechanized in Computer Theorem Provers (\emph{CTP}) has (almost) a problem with traditional mathematical notations (predicate calculus) for axioms, definitions, lemmas, theorems as a computer programm or script is not able to interpret every greek or latin letter and every greek, latin or whatever calculations symbol. Also if we would be able to handle thehse symbols we would have a problem to interpret them correctly. In different problems, symbols and letters have different meanings and ask for different ways to get through. Exclusive from the input, also the output can be a problem. We are familar with a specified notations and style taught in university but a computer programm has no knowledge of the form probved by a professor and the maschines themselve also have not yet the possibilities to print every symbol (correct) Recent developments provide proofs in a humand readable format but according to the fact that there is no mony for good working formel editors yet, the style is one thing we have to live with.
1.60 \par This thesis tries to \empg{connect} these two worlds and is one of the first guidelines to implement problem classes in {\sisac}. For others see related works. %--01--
1.61 -The major challenge of the practical part, of this thesis, is, that "`connecting the two worlds"' involves programming in a CTP-based programming language which is in a very early state of prototyping. There is no concrete experience data ready to hand.
1.62 +The major challenge of the practical part, of this thesis, is, that "`connecting the two worlds"' involves programming in a CTP-based programming language which is in a very early state of prototyping. There is no concrete experience data ready to grep.
1.63
1.64 \subsection{Mechanization of Mathematics}
1.65 -
1.66 -todo
1.67 -
1.68 -hughe theories of mathematics
1.69 -
1.70 -still a hugh gap between these theories and ``real applications'' e.g. in SP
1.71 -
1.72 -? academic engineering starts from physics (experimentation, measurement) and then proceeds to mathematical modelling --- mechanized math starts from mathematical models and (hopefully !) proceeds to match physics.
1.73 -
1.74 -CTP Isabelle ... survey of knowledge, links to knowledge
1.75 -
1.76 -\paragraph{\sisac}
1.77 -TODO
1.78 -
1.79 -adds an ``application'' axis (formal specifications of problems) and an ``algorithmic'' axis to the ``deductive'' axis of knowledge ... 3-dimensional universe of mathematics.
1.80 +A problem behind is the mechanization of mathematic theories in CTP-bases languages. There is still a hugh gap between these theories and this what we call an applications - in Example Signal Processing. Until we are not able to fill this gap we have to live with it but first have a look on the meaning of this statement:
1.81 +\par Mechanized math starts from mathematical models and \emph{hopefully} proceeds to match physics. Academic engineering starts from physics (experimentation, measurement) and then proceeds to mathematical modelling and formalization. The process from a physical observance to a mathematical theory is unavoidable bound of setting up a big collection of standards, rules, definition but also exceptions. These are the things making mechanization that difficult.
1.82 +\par A computer or a CTP-System builds on programms witth predefined logical ruels and does not know any mathematical trick or recipe to walk around difficult expressions. For such a system the only possibility is to work through its known definitions vulgo theories and stops if none of these fits. Specified on Signal Processing or any other application it is often possible to walk through by doing simple creases. This creases are in generell based on simple math operatiopms but the challange is to teach the machine \emph{all}\footnote{Its pride to call it \emph{all}.} of them. Unfortunataly the goal of CTP Isabelle is to reach a high level of \emph{all} but it in real it will still be a survey of knowledge which links to other knowledge and {\sisac{}} a trainer and helper but no human compensating calulator.
1.83 +\par {\sisac{}} itselfs aims to adds an \emph{application} axis (formal specifications of problems outof topics from Signal Processing, etc.) and an \emph{algorithmic} axis to the \emph{deductive} axis of physical knowledge. The result is a three-dimensional universe of mathematics.
1.84
1.85 \subsection{Goals of the Thesis}
1.86 -
1.87 -todo
1.88 -
1.89 -
1.90 -\subsection{Structure of the Thesis}
1.91 -
1.92 -todo
1.93 +Imagine a piece of software would be able to support you by understanding every problem class, upcoming in the first years attending university - wouldn't it be great?
1.94 +\par {\sisac{}} tries to do that, but the current state of the art is miles away from this goal and a single implementation of a problem is not enough to cahnge this circumstamce. Through this fact it is all the more essential to try, test, research and document the implementation of problem classes from "`real world"' applications. Responding to the abstract at the begin of this document the thesis has two folds; on the one hand certainly to provide interactiv course material for Signal Processing (which means to implement a single problem provided by the Institute of Signal Processing and Speech Communication (SPSC); follow up Calulcations), and to extract experience data respectively help the {\sisac{}}-team by setting up a detailed description of technicalities hacking {\sisac{}} on the other hand.
1.95
1.96 \section{Mechanization of Mathematics for SP Problems}
1.97 -todo
1.98
1.99 \subsection{Relevant Knowledge available in Isabelle}
1.100 todo
1.101 @@ -185,6 +163,8 @@
1.102
1.103 terms are not full simplified in traditional notations, in isac we have to simplify them complete to check weather results are compatible or not. in e.g. the solutions of an second order linear equation is an rational in isac but in tradition we keep fractions as long as possible and as long as they are 'beautiful' (1/8, 5/16,...)
1.104
1.105 +\clearpage
1.106 +
1.107 %----------// PART 2 \\----------%
1.108
1.109 \part{Implementation}