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Lectures

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Dmitry Boulytchev 2018-11-19 00:20:43 +03:00
parent 29efb45353
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34
doc/04.tex
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@ -24,25 +24,35 @@ In the concrete syntax for the constructs we add the closing keywords ``\llang{i
\]
\begin{figure}[t]
\[\trans{c}{\llang{skip}}{c}\ruleno{Skip$_{bs}$}\]
\arraycolsep=10pt
%\def\arraystretch{2.9}
\[\trans{c}{\llang{skip}}{c}\ruleno{Skip$_{bs}$}\]\vskip2mm
\[
\crule{\trans{c}{\mbox{$S_1$}}{c^\prime}}
\trule{\begin{array}{cc}
\sembr{e}\;s\ne 0 & \trans{c}{\mbox{$S_1$}}{c^\prime}
\end{array}}
{\trans{c=\inbr{s, \_, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
{\sembr{e}\;s\ne 0}\ruleno{If-True$_{bs}$}
\]
\ruleno{If-True$_{bs}$}
\]\vskip2mm
\[
\crule{\trans{c}{\mbox{$S_2$}}{c^\prime}}
\trule{\begin{array}{cc}
\sembr{e}\;s=0 & \trans{c}{\mbox{$S_1$}}{c^\prime}
\end{array}}
{\trans{c=\inbr{s, \_, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
{\sembr{e}\;s=0}\ruleno{If-False$_{bs}$}
\]
\ruleno{If-False$_{bs}$}
\]\vskip3mm
\[
\crule{\trans{c}{\llang{$S$}}{c^\prime},\;\trans{c^\prime}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
\trule{\begin{array}{ccc}
{\sembr{e}\;s\ne 0} & \trans{c}{\llang{$S$}}{c^\prime} & \trans{c^\prime}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}\\
\end{array}
}
{\trans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
{\sembr{e}\;s\ne 0}\ruleno{While-True$_{bs}$}
\]
\ruleno{While-True$_{bs}$}
\]\vskip3mm
\[
\ctrans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c}{\sembr{e}\;s=0}\ruleno{While-False$_{bs}$}
\trule{\sembr{e}\;s=0}
{\trans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c}}
\ruleno{While-False$_{bs}$}
\]
\caption{Big-step operational semantics for control flow statements}
\label{bs_stmt_cf}