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Dmitry Boulytchev 2018-12-06 21:36:23 +03:00
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doc/04.tex
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@ -26,33 +26,33 @@ In the concrete syntax for the constructs we add the closing keywords ``\llang{i
\begin{figure}[t]
\arraycolsep=10pt
%\def\arraystretch{2.9}
\[\trans{c}{\llang{skip}}{c}\ruleno{Skip$_{bs}$}\]\vskip2mm
\[\trans{c}{\llang{skip}}{c}\ruleno{Skip}\]\vskip2mm
\[
\trule{\begin{array}{cc}
\sembr{e}\;s\ne 0 & \trans{c}{\mbox{$S_1$}}{c^\prime}
\sembr{e}\;\sigma\ne 0 & \trans{c}{\mbox{$S_1$}}{c^\prime}
\end{array}}
{\trans{c=\inbr{s, \_, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
\ruleno{If-True$_{bs}$}
{\trans{c=\inbr{\sigma,\, \_,\, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
\ruleno{If-True}
\]\vskip2mm
\[
\trule{\begin{array}{cc}
\sembr{e}\;s=0 & \trans{c}{\mbox{$S_1$}}{c^\prime}
\sembr{e}\;\sigma=0 & \trans{c}{\mbox{$S_1$}}{c^\prime}
\end{array}}
{\trans{c=\inbr{s, \_, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
\ruleno{If-False$_{bs}$}
{\trans{c=\inbr{\sigma,\, \_,\, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
\ruleno{If-False}
\]\vskip3mm
\[
\trule{\begin{array}{ccc}
{\sembr{e}\;s\ne 0} & \trans{c}{\llang{$S$}}{c^\prime} & \trans{c^\prime}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}\\
{\sembr{e}\;\sigma\ne 0} & \trans{c}{\llang{$S$}}{c^\prime} & \trans{c^\prime}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}\\
\end{array}
}
{\trans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
\ruleno{While-True$_{bs}$}
{\trans{c=\inbr{\sigma,\, \_,\, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
\ruleno{While-True}
\]\vskip3mm
\[
\trule{\sembr{e}\;s=0}
{\trans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c}}
\ruleno{While-False$_{bs}$}
\trule{\sembr{e}\;\sigma=0}
{\trans{c=\inbr{\sigma,\, \_,\, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c}}
\ruleno{While-False}
\]
\caption{Big-step operational semantics for control flow statements}
\label{bs_stmt_cf}