1 | \relax |
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2 | \ifx\hyper@anchor\@undefined |
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6 | \gdef \newlabel#1#2{\newlabelxx{#1}#2} |
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7 | \gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} |
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8 | \AtEndDocument{\let \contentsline\oldcontentsline |
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10 | \else |
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11 | \global \let \hyper@last\relax |
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12 | \fi |
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13 | |
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14 | \bibstyle{abbrv} |
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15 | \select@language{english} |
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16 | \@writefile{toc}{\select@language{english}} |
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17 | \@writefile{lof}{\select@language{english}} |
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18 | \@writefile{lot}{\select@language{english}} |
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19 | \@writefile{toc}{\contentsline {paragraph}{Abstract}{2}{section*.1}} |
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20 | \citation{Leroy09} |
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21 | \citation{Cerco10} |
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22 | \citation{SCADE} |
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23 | \citation{Fornari10} |
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24 | \citation{AbsInt} |
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25 | \citation{AbsintScade} |
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26 | \citation{W09} |
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27 | \citation{Frama-C} |
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28 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{5}{section.1}} |
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29 | \newlabel{intro-sec}{{1}{5}{Introduction\relax }{section.1}{}} |
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30 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Meaning of cost annotations}{5}{subsection.1.1}} |
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31 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Soundness and precision of cost annotations}{6}{subsection.1.2}} |
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32 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Compositionality}{6}{subsection.1.3}} |
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33 | \newlabel{comp-intro}{{1.3}{6}{Compositionality\relax }{subsection.1.3}{}} |
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34 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Direct approach to cost annotations}{6}{subsection.1.4}} |
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35 | \newlabel{direct-intro}{{1.4}{6}{Direct approach to cost annotations\relax }{subsection.1.4}{}} |
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36 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.5}Labelling approach to cost annotations}{7}{subsection.1.5}} |
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37 | \newlabel{label-intro}{{1.5}{7}{Labelling approach to cost annotations\relax }{subsection.1.5}{}} |
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38 | \newlabel{STEP1}{{1}{7}{Labelling approach to cost annotations\relax }{equation.1.1}{}} |
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39 | \citation{CIL02} |
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40 | \citation{Pottier} |
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41 | \newlabel{step2}{{2}{8}{Labelling approach to cost annotations\relax }{equation.1.2}{}} |
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42 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.6}A toy compiler}{8}{subsection.1.6}} |
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43 | \newlabel{toy-intro}{{1.6}{8}{A toy compiler\relax }{subsection.1.6}{}} |
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44 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.7}A C compiler}{8}{subsection.1.7}} |
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45 | \newlabel{Ccompiler-intro}{{1.7}{8}{A C compiler\relax }{subsection.1.7}{}} |
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46 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.8}Organisation}{9}{subsection.1.8}} |
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47 | \@writefile{toc}{\contentsline {section}{\numberline {2}A toy compiler}{9}{section.2}} |
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48 | \newlabel{toy-compiler-sec}{{2}{9}{A toy compiler\relax }{section.2}{}} |
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49 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}{\sf Imp}: language and semantics}{9}{subsection.2.1}} |
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50 | \newlabel{imp-sec}{{2.1}{9}{\imp : language and semantics\relax }{subsection.2.1}{}} |
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51 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Big-step semantics}{9}{subsection.2.2}} |
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52 | \citation{Leroy09-ln} |
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53 | \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Big-step operational semantics of ${\sf Imp}$}}{10}{table.1}} |
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54 | \newlabel{semantics-imp}{{1}{10}{Big-step operational semantics of $\imp $\relax }{table.1}{}} |
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55 | \@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Small-step operational semantics of ${\sf Imp}$ commands}}{10}{table.2}} |
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56 | \newlabel{small-step-imp}{{2}{10}{Small-step operational semantics of $\imp $ commands\relax }{table.2}{}} |
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57 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Small-step semantics}{10}{subsection.2.3}} |
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58 | \@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Operational semantics ${\sf Vm}$ programs}}{11}{table.3}} |
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59 | \newlabel{semantics-vm}{{3}{11}{Operational semantics $\vm $ programs\relax }{table.3}{}} |
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60 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.4}{\sf Vm}: language and semantics}{11}{subsection.2.4}} |
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61 | \newlabel{vm-sec}{{2.4}{11}{\vm : language and semantics\relax }{subsection.2.4}{}} |
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62 | \newlabel{unicity-height-prop}{{2}{11}{\vm : language and semantics\relax }{theorem.2}{}} |
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63 | \citation{Leroy09-ln} |
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64 | \citation{MP67} |
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65 | \@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Conditions for well-formed code}}{12}{table.4}} |
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66 | \newlabel{well-formed-instr}{{4}{12}{Conditions for well-formed code\relax }{table.4}{}} |
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67 | \@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Compilation from ${\sf Imp}$ to ${\sf Vm}$}}{12}{table.5}} |
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68 | \newlabel{compil-imp-vm}{{5}{12}{Compilation from $\imp $ to $\vm $\relax }{table.5}{}} |
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69 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Compilation from ${\sf Imp}$ to ${\sf Vm}$}{12}{subsection.2.5}} |
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70 | \newlabel{compil-imp-vm-sec}{{2.5}{12}{Compilation from $\imp $ to $\vm $\relax }{subsection.2.5}{}} |
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71 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Soundness of compilation for the big-step semantics}{12}{subsection.2.6}} |
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72 | \newlabel{soundness-big-step-prop}{{3}{12}{Soundness of compilation for the big-step semantics\relax }{theorem.3}{}} |
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73 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Soundness of compilation for the small-step semantics}{12}{subsection.2.7}} |
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74 | \citation{Larus05} |
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75 | \newlabel{soundness-small-step}{{4}{13}{Soundness of compilation for the small-step semantics\relax }{theorem.4}{}} |
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76 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.8}Compiled code is well-formed}{13}{subsection.2.8}} |
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77 | \newlabel{well-formed-prop}{{5}{13}{Compiled code is well-formed\relax }{theorem.5}{}} |
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78 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.9}${\sf Mips}$: language and semantics}{13}{subsection.2.9}} |
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79 | \newlabel{mips-sec}{{2.9}{13}{$\mips $: language and semantics\relax }{subsection.2.9}{}} |
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80 | \@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Operational semantics ${\sf Mips}$ programs}}{14}{table.6}} |
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81 | \newlabel{semantics-mips}{{6}{14}{Operational semantics $\mips $ programs\relax }{table.6}{}} |
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82 | \@writefile{toc}{\contentsline {subsection}{\numberline {2.10}Compilation from ${\sf Vm}$ to ${\sf Mips}$}{14}{subsection.2.10}} |
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83 | \newlabel{compil-vm-mips-sec}{{2.10}{14}{Compilation from $\vm $ to $\mips $\relax }{subsection.2.10}{}} |
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84 | \newlabel{p-function}{{3}{14}{Compilation from $\vm $ to $\mips $\relax }{equation.2.3}{}} |
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85 | \newlabel{d-function}{{4}{14}{Compilation from $\vm $ to $\mips $\relax }{equation.2.4}{}} |
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86 | \newlabel{simulation-vm-mips}{{6}{14}{Compilation from $\vm $ to $\mips $\relax }{theorem.6}{}} |
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87 | \@writefile{toc}{\contentsline {section}{\numberline {3}Direct approach for the toy compiler}{14}{section.3}} |
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88 | \newlabel{toy-direct-sec}{{3}{14}{Direct approach for the toy compiler\relax }{section.3}{}} |
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89 | \@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Compilation from ${\sf Vm}$ to ${\sf Mips}$}}{15}{table.7}} |
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90 | \newlabel{compil-vm-mips}{{7}{15}{Compilation from $\vm $ to $\mips $\relax }{table.7}{}} |
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91 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}${\sf Mips}$ and ${\sf Vm}$ cost annotations}{15}{subsection.3.1}} |
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92 | \@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Upper bounds on the cost of ${\sf Vm}$ instructions}}{16}{table.8}} |
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93 | \newlabel{cost-approx-instr}{{8}{16}{Upper bounds on the cost of $\vm $ instructions\relax }{table.8}{}} |
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94 | \newlabel{annot-vm-mips}{{7}{16}{$\mips $ and $\vm $ cost annotations\relax }{theorem.7}{}} |
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95 | \newlabel{labelled-simulation-vm-mips}{{8}{16}{$\mips $ and $\vm $ cost annotations\relax }{theorem.8}{}} |
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96 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}${\sf Imp}$ cost annotation}{16}{subsection.3.2}} |
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97 | \newlabel{imp-cost-annotation}{{3.2}{16}{$\imp $ cost annotation\relax }{subsection.3.2}{}} |
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98 | \citation{Leroy09-ln} |
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99 | \@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Annotation for ${\sf Imp}$ programs}}{17}{table.9}} |
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100 | \newlabel{annotation-imp}{{9}{17}{Annotation for $\imp $ programs\relax }{table.9}{}} |
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101 | \newlabel{annot-imp-vm}{{9}{17}{$\imp $ cost annotation\relax }{theorem.9}{}} |
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102 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Composition}{17}{subsection.3.3}} |
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103 | \newlabel{annot-composition}{{10}{17}{Composition\relax }{theorem.10}{}} |
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104 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.4}${\sf Coq}$ development}{18}{subsection.3.4}} |
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105 | \newlabel{coq-development-sec}{{3.4}{18}{$\coq $ development\relax }{subsection.3.4}{}} |
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106 | \@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Limitations of the direct approach}{18}{subsection.3.5}} |
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107 | \newlabel{limitations-direct-sec}{{3.5}{18}{Limitations of the direct approach\relax }{subsection.3.5}{}} |
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108 | \@writefile{toc}{\contentsline {section}{\numberline {4}Labelling approach for the toy compiler}{18}{section.4}} |
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109 | \newlabel{label-toy-sec}{{4}{18}{Labelling approach for the toy compiler\relax }{section.4}{}} |
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110 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Labelled ${\sf Imp}$}{18}{subsection.4.1}} |
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111 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Labelled ${\sf Vm}$}{19}{subsection.4.2}} |
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112 | \newlabel{labelled-sim-imp-vm}{{11}{19}{Labelled $\vm $\relax }{theorem.11}{}} |
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113 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Labelled ${\sf Mips}$}{20}{subsection.4.3}} |
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114 | \newlabel{sim-vm-mips-prop}{{13}{20}{Labelled $\mips $\relax }{theorem.13}{}} |
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115 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Labellings and instrumentations}{20}{subsection.4.4}} |
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116 | \newlabel{lab-instr-erasure-imp}{{14}{20}{Labellings and instrumentations\relax }{theorem.14}{}} |
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117 | \newlabel{labelling-def}{{15}{20}{Labellings and instrumentations\relax }{theorem.15}{}} |
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118 | \newlabel{global-commutation-prop}{{16}{20}{Labellings and instrumentations\relax }{theorem.16}{}} |
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119 | \newlabel{instrument-to-label-prop}{{17}{21}{Labellings and instrumentations\relax }{theorem.17}{}} |
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120 | \@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Sound and precise labellings}{21}{subsection.4.5}} |
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121 | \newlabel{sound-label-sec}{{4.5}{21}{Sound and precise labellings\relax }{subsection.4.5}{}} |
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122 | \newlabel{sound-label-prop}{{20}{21}{Sound and precise labellings\relax }{theorem.20}{}} |
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123 | \newlabel{precise-label-prop}{{22}{21}{Sound and precise labellings\relax }{theorem.22}{}} |
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124 | \newlabel{lab-sound}{{23}{21}{Sound and precise labellings\relax }{theorem.23}{}} |
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125 | \@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Two labellings for the ${\sf Imp}$ language}}{22}{table.10}} |
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126 | \newlabel{labelling}{{10}{22}{Two labellings for the $\imp $ language\relax }{table.10}{}} |
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127 | \newlabel{ann-correct}{{25}{22}{Sound and precise labellings\relax }{theorem.25}{}} |
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128 | \citation{CIL02} |
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129 | \citation{Leroy09} |
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130 | \@writefile{toc}{\contentsline {section}{\numberline {5}A ${\sf C}$ compiler}{23}{section.5}} |
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131 | \newlabel{C-compiler-sec}{{5}{23}{A $\C $ compiler\relax }{section.5}{}} |
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132 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}${\sf Clight}$}{23}{subsection.5.1}} |
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133 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}${\sf Cminor}$}{23}{subsection.5.2}} |
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134 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf Clight}$ to ${\sf Cminor}$.}{23}{section*.3}} |
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135 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}${\sf RTLAbs}$}{23}{subsection.5.3}} |
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136 | \newlabel{syntax-clight}{{5.1}{24}{$\Clight $\relax }{subsection.5.1}{}} |
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137 | \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Syntax of the ${\sf Clight}$ language}}{24}{figure.1}} |
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138 | \newlabel{syntax-cminor}{{5.2}{25}{$\Cminor $\relax }{subsection.5.2}{}} |
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139 | \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Syntax of the ${\sf Cminor}$ language}}{25}{figure.2}} |
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140 | \@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Syntax of the ${\sf RTLAbs}$ language}}{26}{table.11}} |
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141 | \newlabel{RTLAbs:syntax}{{11}{26}{Syntax of the $\RTLAbs $ language\relax }{table.11}{}} |
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142 | \@writefile{toc}{\contentsline {paragraph}{Syntax.}{26}{section*.4}} |
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143 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf Cminor}$ to ${\sf RTLAbs}$.}{26}{section*.5}} |
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144 | \@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Syntax of the ${\sf RTL}$ language}}{27}{table.12}} |
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145 | \newlabel{RTL:syntax}{{12}{27}{Syntax of the $\RTL $ language\relax }{table.12}{}} |
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146 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.4}${\sf RTL}$}{27}{subsection.5.4}} |
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147 | \@writefile{toc}{\contentsline {paragraph}{Syntax.}{27}{section*.6}} |
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148 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf RTLAbs}$ to ${\sf RTL}$.}{27}{section*.7}} |
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149 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.5}${\sf ERTL}$}{27}{subsection.5.5}} |
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150 | \@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Syntax of the ${\sf ERTL}$ language}}{28}{table.13}} |
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151 | \newlabel{ERTL:syntax}{{13}{28}{Syntax of the $\ERTL $ language\relax }{table.13}{}} |
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152 | \@writefile{toc}{\contentsline {paragraph}{Syntax.}{28}{section*.8}} |
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153 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf RTL}$ to ${\sf ERTL}$.}{28}{section*.9}} |
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154 | \@writefile{toc}{\contentsline {paragraph}{Optimizations.}{28}{section*.10}} |
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155 | \@writefile{lot}{\contentsline {table}{\numberline {14}{\ignorespaces Syntax of the ${\sf LTL}$ language}}{29}{table.14}} |
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156 | \newlabel{LTL:syntax}{{14}{29}{Syntax of the $\LTL $ language\relax }{table.14}{}} |
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157 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.6}${\sf LTL}$}{29}{subsection.5.6}} |
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158 | \@writefile{toc}{\contentsline {paragraph}{Syntax.}{29}{section*.11}} |
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159 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf ERTL}$ to ${\sf LTL}$.}{29}{section*.12}} |
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160 | \@writefile{toc}{\contentsline {paragraph}{Optimizations.}{29}{section*.13}} |
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161 | \@writefile{lot}{\contentsline {table}{\numberline {15}{\ignorespaces Syntax of the ${\sf LIN}$ language}}{30}{table.15}} |
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162 | \newlabel{LIN:syntax}{{15}{30}{Syntax of the $\LIN $ language\relax }{table.15}{}} |
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163 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.7}${\sf LIN}$}{30}{subsection.5.7}} |
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164 | \@writefile{toc}{\contentsline {paragraph}{Syntax.}{30}{section*.14}} |
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165 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf LTL}$ to ${\sf LIN}$.}{30}{section*.15}} |
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166 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.8}${\sf Mips}$}{30}{subsection.5.8}} |
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167 | \@writefile{toc}{\contentsline {paragraph}{Translation of ${\sf LIN}$ to ${\sf Mips}$.}{30}{section*.16}} |
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168 | \@writefile{lot}{\contentsline {table}{\numberline {16}{\ignorespaces Syntax of the ${\sf Mips}$ language}}{31}{table.16}} |
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169 | \newlabel{mips:syntax}{{16}{31}{Syntax of the $\mips $ language\relax }{table.16}{}} |
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170 | \@writefile{lot}{\contentsline {table}{\numberline {17}{\ignorespaces Building the annotation of a ${\sf Clight}$ program in the labelling approach}}{31}{table.17}} |
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171 | \newlabel{annot-clight-summary}{{17}{31}{Building the annotation of a $\Clight $ program in the labelling approach\relax }{table.17}{}} |
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172 | \@writefile{toc}{\contentsline {section}{\numberline {6}Labelling approach for the ${\sf C}$ compiler}{31}{section.6}} |
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173 | \newlabel{C-label-sec}{{6}{31}{Labelling approach for the $\C $ compiler\relax }{section.6}{}} |
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174 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Labelled ${\sf Clight}$ and labelled ${\sf Cminor}$}{31}{subsection.6.1}} |
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175 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Labels in ${\sf RTLAbs}$ and the back-end languages}{32}{subsection.6.2}} |
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176 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Labelling of the source language}{32}{subsection.6.3}} |
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177 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.1}Sequential instructions}{32}{subsubsection.6.3.1}} |
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178 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.2}Ternary expressions}{32}{subsubsection.6.3.2}} |
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179 | \@writefile{toc}{\contentsline {paragraph}{Related cases.}{33}{section*.17}} |
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180 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.3}Conditionals}{33}{subsubsection.6.3.3}} |
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181 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.4}Loops}{33}{subsubsection.6.3.4}} |
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182 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.5}Program Labels and Gotos}{34}{subsubsection.6.3.5}} |
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183 | \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.6}Function calls}{34}{subsubsection.6.3.6}} |
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184 | \newlabel{fun-call-sec}{{6.3.6}{34}{Function calls\relax }{subsubsection.6.3.6}{}} |
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185 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.4}Verifications on the object code}{35}{subsection.6.4}} |
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186 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.5}Building the cost annotation}{35}{subsection.6.5}} |
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187 | \citation{Cerco10} |
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188 | \bibcite{AbsInt}{1} |
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189 | \bibcite{Cerco10}{2} |
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190 | \bibcite{SCADE}{3} |
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191 | \bibcite{Frama-C}{4} |
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192 | \bibcite{AbsintScade}{5} |
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193 | \bibcite{Fornari10}{6} |
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194 | \bibcite{Larus05}{7} |
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195 | \@writefile{toc}{\contentsline {subsection}{\numberline {6.6}Testing}{36}{subsection.6.6}} |
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196 | \@writefile{toc}{\contentsline {section}{\numberline {7}Conclusion and future work}{36}{section.7}} |
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197 | \newlabel{conclusion-sec}{{7}{36}{Conclusion and future work\relax }{section.7}{}} |
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198 | \bibcite{Leroy09}{8} |
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199 | \bibcite{Leroy09-ln}{9} |
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200 | \bibcite{MP67}{10} |
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201 | \bibcite{CIL02}{11} |
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202 | \bibcite{Pottier}{12} |
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203 | \bibcite{W09}{13} |
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204 | \@writefile{toc}{\contentsline {section}{\numberline {A}Assessment of the deliverable within the $CerCo$ project}{38}{appendix.A}} |
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205 | \@writefile{toc}{\contentsline {section}{\numberline {B}Proofs}{40}{appendix.B}} |
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206 | \newlabel{paper-proofs}{{B}{40}{Proofs\relax }{appendix.B}{}} |
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207 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.1}Notation}{40}{subsection.B.1}} |
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208 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.2}Proof of proposition \ref {soundness-small-step}}{40}{subsection.B.2}} |
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209 | \newlabel{access-lemma}{{26}{40}{Proof of proposition \ref {soundness-small-step}\relax }{theorem.26}{}} |
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210 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.3}Proof of proposition \ref {labelled-simulation-vm-mips}}{41}{subsection.B.3}} |
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211 | \newlabel{step1}{{7}{41}{Proof of proposition \ref {labelled-simulation-vm-mips}\relax }{equation.B.7}{}} |
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212 | \@writefile{toc}{\contentsline {paragraph}{The memory realisation.}{41}{section*.19}} |
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213 | \@writefile{toc}{\contentsline {paragraph}{The inequation.}{41}{section*.20}} |
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214 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.4}Proof of proposition \ref {annot-composition}}{41}{subsection.B.4}} |
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215 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.5}Proof of proposition \ref {labelled-sim-imp-vm}}{42}{subsection.B.5}} |
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216 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.6}Proof of proposition \ref {sim-vm-mips-prop}}{42}{subsection.B.6}} |
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217 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.7}Proof of proposition \ref {lab-instr-erasure-imp}}{42}{subsection.B.7}} |
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218 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.8}Proof of proposition \ref {global-commutation-prop}}{42}{subsection.B.8}} |
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219 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.9}Proof of proposition \ref {instrument-to-label-prop}}{42}{subsection.B.9}} |
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220 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.10}Proof of proposition \ref {sound-label-prop}}{43}{subsection.B.10}} |
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221 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.11}Proof of proposition \ref {precise-label-prop}}{43}{subsection.B.11}} |
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222 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.12}Proof of proposition \ref {lab-sound}}{43}{subsection.B.12}} |
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223 | \newlabel{precise-lemma}{{29}{43}{Proof of proposition \ref {lab-sound}\relax }{theorem.29}{}} |
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224 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.13}Proof of proposition \ref {ann-correct}}{43}{subsection.B.13}} |
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