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(*<*)
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theory Slides1
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imports "../CpsG" "../ExtGG" "~~/src/HOL/Library/LaTeXsugar"
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begin
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notation (latex output)
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set ("_") and
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Cons ("_::/_" [66,65] 65)
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ML {*
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open Printer;
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show_question_marks_default := false;
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*}
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notation (latex output)
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Cons ("_::_" [78,77] 73) and
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vt ("valid'_state") and
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runing ("running") and
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birthtime ("last'_set") and
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If ("(\<^raw:\textrm{>if\<^raw:}> (_)/ \<^raw:\textrm{>then\<^raw:}> (_)/ \<^raw:\textrm{>else\<^raw:}> (_))" 10) and
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Prc ("'(_, _')") and
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holding ("holds") and
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waiting ("waits") and
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Th ("T") and
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Cs ("C") and
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readys ("ready") and
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depend ("RAG") and
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preced ("prec") and
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cpreced ("cprec") and
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dependents ("dependants") and
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cp ("cprec") and
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holdents ("resources") and
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original_priority ("priority") and
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DUMMY ("\<^raw:\mbox{$\_\!\_$}>")
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(*>*)
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text_raw {*
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\renewcommand{\slidecaption}{Nanjing, P.R. China, 1 August 2012}
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\newcommand{\bl}[1]{#1}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\Large Priority Inheritance Protocol \\[-3mm]
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\Large Proved Correct \\[0mm]
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\end{tabular}}
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\begin{center}
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\small Xingyuan Zhang \\
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\small \mbox{PLA University of Science and Technology} \\
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\small \mbox{Nanjing, China}
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\end{center}
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\begin{center}
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\small joint work with \\
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Christian Urban \\
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Kings College, University of London, U.K.\\
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Chunhan Wu \\
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My Ph.D. student now working for Christian\\
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\large Prioirty Inheritance Protocol (PIP)}
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\large
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\begin{itemize}
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\item Widely used in Real-Time OSs \pause
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\item One solution of \textcolor{red}{`Priority Inversion'} \pause
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\item A flawed manual correctness proof (1990)\pause
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\begin{itemize} \large
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\item {Notations with no precise definition}
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\item {Resorts to intuitions}
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\end{itemize} \pause
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\item Formal treatments using model-checking \pause
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\begin{itemize} \large
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\item {Applicable to small size system models}
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\item { Unhelpful for human understanding }
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\end{itemize} \pause
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\item Verification of PCP in PVS (2000)\pause
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\begin{itemize} \large
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\item {A related protocol}
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\item {Priority Ceiling Protocol}
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\end{itemize}
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Our Motivation}
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\large
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\begin{itemize}
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\item Undergraduate OS course in our university \pause
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\begin{itemize}
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\item {\large Experiments using instrutional OSs }
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\item {\large PINTOS (Stanford) is chosen }
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\item {\large Core project: Implementing PIP in it}
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\end{itemize} \pause
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\item Understanding is crucial for the implemention \pause
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\item Existing literature of little help \pause
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\item Some mention the complication
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\mbox{Some excerpts}}
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\begin{quote}
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``Priority inheritance is neither ef$\!$ficient nor reliable.
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Implementations are either incomplete (and unreliable)
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or surprisingly complex and intrusive.''
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\end{quote}\medskip
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\pause
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\begin{quote}
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``I observed in the kernel code (to my disgust), the Linux
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PIP implementation is a nightmare: extremely heavy weight,
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involving maintenance of a full wait-for graph, and requiring
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updates for a range of events, including priority changes and
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interruptions of wait operations.''
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\end{quote}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Our Aims}
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\large
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\begin{itemize}
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\item Formal specification at appropriate abstract level,
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convenient for:
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\begin{itemize} \large
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\item Constructing interactive proofs
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\item Clarifying the underlying ideas
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\end{itemize} \pause
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\item Theorems usable to guide implementation, critical point:
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\begin{itemize} \large
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\item Understanding the relationship with real OS code \pause
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\item Not yet formalized
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\end{itemize}
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Real-Time OSes}
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\large
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\begin{itemize}
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\item Purpose: gurantee the most urgent task to be processed in time
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\item Processes have priorities\\
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\item Resources can be locked and unlocked
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\end{itemize}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Problem}
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\Large
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\begin{center}
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\begin{tabular}{l}
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\alert{H}igh-priority process\\[4mm]
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\onslide<2->{\alert{M}edium-priority process}\\[4mm]
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\alert{L}ow-priority process\\[4mm]
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\end{tabular}
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\end{center}
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\onslide<3->{
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\begin{itemize}
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\item \alert{Priority Inversion} @{text "\<equiv>"} \alert{H $<$ L}
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\item<4> avoid indefinite priority inversion
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\end{itemize}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Priority Inversion}
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\begin{center}
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\includegraphics[scale=0.4]{PriorityInversion.png}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Mars Pathfinder Mission 1997}
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\Large
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\begin{center}
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\includegraphics[scale=0.2]{marspath1.png}
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\includegraphics[scale=0.22]{marspath3.png}
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\includegraphics[scale=0.4]{marsrover.png}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Solution}
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\Large
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\alert{Priority Inheritance Protocol (PIP):}
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\begin{center}
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\begin{tabular}{l}
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\alert{H}igh-priority process\\[4mm]
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\textcolor{gray}{Medium-priority process}\\[4mm]
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\alert{L}ow-priority process\\[21mm]
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{\normalsize (temporarily raise its priority)}
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{A Correctness ``Proof'' in 1990}
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\Large
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\begin{itemize}
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\item a paper$^\star$
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in 1990 ``proved'' the correctness of an algorithm for PIP\\[5mm]
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\end{itemize}
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\normalsize
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\begin{quote}
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\ldots{}after the thread (whose priority has been raised) completes its
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critical section and releases the lock, it ``returns to its original
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priority level''.
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\end{quote}\bigskip
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\small
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$^\star$ in IEEE Transactions on Computers
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{}
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\Large
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\begin{center}
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\begin{tabular}{l}
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\alert{H}igh-priority process 1\\[2mm]
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\alert{H}igh-priority process 2\\[8mm]
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\alert{L}ow-priority process
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\end{tabular}
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\end{center}
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\onslide<2->{
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\begin{itemize}
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\item Solution: \\Return to highest \alert{remaining} priority
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\end{itemize}}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Event Abstraction}
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\begin{itemize}\large
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\item Use Inductive Approach of L. Paulson \pause
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\item System is event-driven \pause
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\item A \alert{state} is a list of events
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\end{itemize}
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\pause
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\begin{center}
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\includegraphics[scale=0.4]{EventAbstract.png}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Events}
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\Large
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\begin{center}
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\begin{tabular}{l}
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Create \textcolor{gray}{thread priority}\\
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Exit \textcolor{gray}{thread}\\
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Set \textcolor{gray}{thread priority}\\
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Lock \textcolor{gray}{thread cs}\\
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Unlock \textcolor{gray}{thread cs}\\
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\end{tabular}
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\end{center}\medskip
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Precedences}
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\large
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\begin{center}
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\begin{tabular}{l}
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@{thm preced_def[where thread="th"]}
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\end{tabular}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{RAGs}
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\begin{center}
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\newcommand{\fnt}{\fontsize{7}{8}\selectfont}
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\begin{tikzpicture}[scale=1]
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%%\draw[step=2mm] (-3,2) grid (1,-1);
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\node (A) at (0,0) [draw, rounded corners=1mm, rectangle, very thick] {@{text "th\<^isub>0"}};
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\node (B) at (2,0) [draw, circle, very thick, inner sep=0.4mm] {@{text "cs\<^isub>1"}};
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\node (C) at (4,0.7) [draw, rounded corners=1mm, rectangle, very thick] {@{text "th\<^isub>1"}};
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\node (D) at (4,-0.7) [draw, rounded corners=1mm, rectangle, very thick] {@{text "th\<^isub>2"}};
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417 |
\node (E) at (6,-0.7) [draw, circle, very thick, inner sep=0.4mm] {@{text "cs\<^isub>2"}};
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\node (E1) at (6, 0.2) [draw, circle, very thick, inner sep=0.4mm] {@{text "cs\<^isub>3"}};
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\node (F) at (8,-0.7) [draw, rounded corners=1mm, rectangle, very thick] {@{text "th\<^isub>3"}};
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\draw [<-,line width=0.6mm] (A) to node [pos=0.54,sloped,above=-0.5mm] {\fnt{}holding} (B);
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\draw [->,line width=0.6mm] (C) to node [pos=0.4,sloped,above=-0.5mm] {\fnt{}waiting} (B);
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\draw [->,line width=0.6mm] (D) to node [pos=0.4,sloped,below=-0.5mm] {\fnt{}waiting} (B);
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\draw [<-,line width=0.6mm] (D) to node [pos=0.54,sloped,below=-0.5mm] {\fnt{}holding} (E);
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\draw [<-,line width=0.6mm] (D) to node [pos=0.54,sloped,above=-0.5mm] {\fnt{}holding} (E1);
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\draw [->,line width=0.6mm] (F) to node [pos=0.45,sloped,below=-0.5mm] {\fnt{}waiting} (E);
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\end{tikzpicture}
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\end{center}\bigskip
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\begin{center}
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\begin{minipage}{0.8\linewidth}
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\raggedleft
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@{thm cs_depend_def}
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\end{minipage}
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\end{center}\pause
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{Good Next Events}
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%%\large
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450 |
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\begin{center}
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@{thm[mode=Rule] thread_create[where thread=th]}\bigskip
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453 |
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454 |
@{thm[mode=Rule] thread_exit[where thread=th]}\bigskip
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455 |
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@{thm[mode=Rule] thread_set[where thread=th]}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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*}
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text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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467 |
\mode<presentation>{
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468 |
\begin{frame}[c]
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469 |
\frametitle{Good Next Events}
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470 |
%%\large
|
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471 |
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472 |
\begin{center}
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473 |
@{thm[mode=Rule] thread_P[where thread=th]}\bigskip
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474 |
|
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475 |
@{thm[mode=Rule] thread_V[where thread=th]}\bigskip
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476 |
\end{center}
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477 |
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478 |
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479 |
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\end{frame}}
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481 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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482 |
*}
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362
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483 |
(*<*)
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484 |
context extend_highest_gen
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485 |
begin
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486 |
(*>*)
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360
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487 |
text_raw {*
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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489 |
\mode<presentation>{
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490 |
\begin{frame}[c]
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362
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491 |
\frametitle{\mbox{\large Theorem: ``No indefinite priority inversion''}}
|
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360
|
492 |
|
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362
|
493 |
\pause
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360
|
494 |
|
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362
|
495 |
Theorem $^\star$: If th is the thread with the highest precedence in state
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|
496 |
@{text "s"}: \pause
|
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|
497 |
\begin{center}
|
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|
498 |
\textcolor{red}{@{thm highest})}
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|
499 |
\end{center}
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|
500 |
\pause
|
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|
501 |
and @{text "th"} is blocked by a thread @{text "th'"} in
|
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|
502 |
a future state @{text "s'"} (with @{text "s' = t@s"}): \pause
|
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|
503 |
\begin{center}
|
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|
504 |
\textcolor{red}{@{text "th' \<in> running (t@s)"} and @{text "th' \<noteq> th"}} \pause
|
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|
505 |
\end{center}
|
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|
506 |
\fbox{ \hspace{1em} \pause
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|
507 |
\begin{minipage}{0.95\textwidth}
|
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360
|
508 |
\begin{itemize}
|
|
362
|
509 |
\item @{text "th'"} did not hold or wait for a resource in s:
|
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|
510 |
\begin{center}
|
|
|
511 |
\textcolor{red}{@{text "\<not>detached s th'"}}
|
|
|
512 |
\end{center} \pause
|
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|
513 |
\item @{text "th'"} is running with the precedence of @{text "th"}:
|
|
|
514 |
\begin{center}
|
|
|
515 |
\textcolor{red}{@{text "cp (t@s) th' = preced th s"}}
|
|
|
516 |
\end{center}
|
|
360
|
517 |
\end{itemize}
|
|
362
|
518 |
\end{minipage}}
|
|
|
519 |
\pause
|
|
360
|
520 |
\small
|
|
|
521 |
$^\star$ modulo some further assumptions\bigskip\pause
|
|
|
522 |
It does not matter which process gets a released lock.
|
|
|
523 |
|
|
|
524 |
\end{frame}}
|
|
|
525 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
526 |
*}
|
|
|
527 |
|
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|
528 |
text_raw {*
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|
529 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
530 |
\mode<presentation>{
|
|
|
531 |
\begin{frame}[t]
|
|
|
532 |
\frametitle{Implementation}
|
|
|
533 |
|
|
362
|
534 |
s $=$ current state; @{text "s'"} $=$ next state $=$ @{text "e#s"}\bigskip\bigskip
|
|
360
|
535 |
|
|
362
|
536 |
When @{text "e"} = \alert{Create th prio}, \alert{Exit th}
|
|
360
|
537 |
|
|
|
538 |
\begin{itemize}
|
|
|
539 |
\item @{text "RAG s' = RAG s"}
|
|
364
|
540 |
\item No precedence needs to be recomputed
|
|
360
|
541 |
\end{itemize}
|
|
|
542 |
|
|
|
543 |
\end{frame}}
|
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|
544 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
545 |
*}
|
|
|
546 |
|
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|
547 |
text_raw {*
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|
548 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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|
549 |
\mode<presentation>{
|
|
|
550 |
\begin{frame}[t]
|
|
|
551 |
\frametitle{Implementation}
|
|
362
|
552 |
|
|
|
553 |
s $=$ current state; @{text "s'"} $=$ next state $=$ @{text "e#s"}\bigskip\bigskip
|
|
360
|
554 |
|
|
|
555 |
|
|
362
|
556 |
When @{text "e"} = \alert{Set th prio}
|
|
360
|
557 |
|
|
|
558 |
\begin{itemize}
|
|
|
559 |
\item @{text "RAG s' = RAG s"}
|
|
364
|
560 |
\item No precedence needs to be recomputed
|
|
360
|
561 |
\end{itemize}
|
|
|
562 |
|
|
|
563 |
\end{frame}}
|
|
|
564 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
565 |
*}
|
|
|
566 |
|
|
|
567 |
text_raw {*
|
|
|
568 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
569 |
\mode<presentation>{
|
|
|
570 |
\begin{frame}[t]
|
|
|
571 |
\frametitle{Implementation}
|
|
|
572 |
|
|
362
|
573 |
s $=$ current state; @{text "s'"} $=$ next state $=$ @{text "e#s"}\bigskip\bigskip
|
|
|
574 |
|
|
|
575 |
When @{text "e"} = \alert{Unlock th cs} where there is a thread to take over
|
|
360
|
576 |
|
|
|
577 |
\begin{itemize}
|
|
|
578 |
\item @{text "RAG s' = RAG s - {(C cs, T th), (T th', C cs)} \<union> {(C cs, T th')}"}
|
|
|
579 |
\item we have to recalculate the precedence of the direct descendants
|
|
|
580 |
\end{itemize}\bigskip
|
|
|
581 |
|
|
362
|
582 |
\pause
|
|
|
583 |
|
|
|
584 |
When @{text "e"} = \alert{Unlock th cs} where no thread takes over
|
|
360
|
585 |
|
|
|
586 |
\begin{itemize}
|
|
|
587 |
\item @{text "RAG s' = RAG s - {(C cs, T th)}"}
|
|
|
588 |
\item no recalculation of precedences
|
|
|
589 |
\end{itemize}
|
|
|
590 |
|
|
|
591 |
|
|
|
592 |
\end{frame}}
|
|
|
593 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
594 |
*}
|
|
|
595 |
|
|
|
596 |
text_raw {*
|
|
|
597 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
598 |
\mode<presentation>{
|
|
|
599 |
\begin{frame}[t]
|
|
|
600 |
\frametitle{Implementation}
|
|
|
601 |
|
|
362
|
602 |
s $=$ current state; @{text "s'"} $=$ next state $=$ @{text "e#s"}\bigskip\bigskip
|
|
|
603 |
|
|
|
604 |
When @{text "e"} = \alert{Lock th cs} where cs is not locked
|
|
360
|
605 |
|
|
|
606 |
\begin{itemize}
|
|
|
607 |
\item @{text "RAG s' = RAG s \<union> {(C cs, T th')}"}
|
|
|
608 |
\item no recalculation of precedences
|
|
|
609 |
\end{itemize}\bigskip
|
|
|
610 |
|
|
362
|
611 |
\pause
|
|
|
612 |
|
|
|
613 |
When @{text "e"} = \alert{Lock th cs} where cs is locked
|
|
360
|
614 |
|
|
|
615 |
\begin{itemize}
|
|
|
616 |
\item @{text "RAG s' = RAG s - {(T th, C cs)}"}
|
|
|
617 |
\item we have to recalculate the precedence of the descendants
|
|
|
618 |
\end{itemize}
|
|
|
619 |
|
|
|
620 |
|
|
|
621 |
\end{frame}}
|
|
|
622 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
623 |
*}
|
|
|
624 |
|
|
|
625 |
|
|
|
626 |
text_raw {*
|
|
|
627 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
628 |
\mode<presentation>{
|
|
|
629 |
\begin{frame}[c]
|
|
|
630 |
\frametitle{Conclusion}
|
|
|
631 |
|
|
362
|
632 |
\begin{itemize} \large
|
|
|
633 |
\item Aims fulfilled \medskip \pause
|
|
|
634 |
\item Alternative way \pause
|
|
363
|
635 |
\begin{itemize}
|
|
362
|
636 |
\item using Isabelle/HOL in OS code development \medskip
|
|
|
637 |
\item through the Inductive Approach
|
|
|
638 |
\end{itemize} \pause
|
|
364
|
639 |
\item Future research \pause
|
|
363
|
640 |
\begin{itemize}
|
|
362
|
641 |
\item scheduler in RT-Linux\medskip
|
|
|
642 |
\item multiprocessor case\medskip
|
|
363
|
643 |
\item other ``nails'' ? (networks, \ldots) \medskip \pause
|
|
364
|
644 |
\item Refinement to real code and relation between implementations
|
|
362
|
645 |
\end{itemize}
|
|
360
|
646 |
\end{itemize}
|
|
|
647 |
\end{frame}}
|
|
|
648 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
649 |
*}
|
|
|
650 |
|
|
363
|
651 |
text_raw {*
|
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|
652 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
653 |
\mode<presentation>{
|
|
|
654 |
\begin{frame}[c]
|
|
|
655 |
\frametitle{Questions?}
|
|
|
656 |
|
|
|
657 |
\begin{itemize} \large
|
|
|
658 |
\item Thank you for listening!
|
|
|
659 |
\end{itemize}
|
|
|
660 |
|
|
|
661 |
\end{frame}}
|
|
|
662 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
663 |
*}
|
|
|
664 |
|
|
362
|
665 |
|
|
360
|
666 |
(*<*)
|
|
|
667 |
end
|
|
362
|
668 |
end
|
|
360
|
669 |
(*>*) |