diff -r 9c968d0de9a0 -r 2ce98ee39990 inferences.tex --- a/inferences.tex Sat Oct 04 12:46:04 2014 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,91 +0,0 @@ -\documentclass{article} -\usepackage{charter} -\usepackage{proof} - -\begin{document} - -\section*{Inference Rules} - -\begin{enumerate} -\item Frequently used inference rules: - -\begin{center} -\mbox{\infer{F,\Gamma \vdash F}{}}\medskip - -\mbox{\infer{\Gamma \vdash F_2} - {\Gamma \vdash F_1 \Rightarrow F_2 & \Gamma \vdash F_1}} -\hspace{10mm} -\mbox{\infer{\Gamma \vdash F_1 \Rightarrow F_2} - {F_1, \Gamma \vdash F_2}}\medskip - -\mbox{\infer{\Gamma \vdash P \;\textit{says}\; F} - {\Gamma \vdash F}} -\hspace{10mm} -\mbox{\infer[\star]{\Gamma \vdash F} - {\Gamma \vdash P \;\textit{controls}\; F & \Gamma \vdash P - \;\textit{says}\; F}}\medskip - -\mbox{\infer{\Gamma \vdash P \;\textit{says}\;F_2} - {\Gamma \vdash P \;\textit{says}\; (F_1 \Rightarrow F_2) & - \Gamma \vdash P \;\textit{says}\;F_1}}\medskip - -\mbox{\infer{\Gamma \vdash F[x := t]} - {\Gamma \vdash \forall x. F}}\medskip - -\mbox{\infer{\Gamma \vdash F_1 \wedge F_2} - {\Gamma \vdash F_1 & \Gamma \vdash F_2}} -\hspace{10mm} -\mbox{\infer{\Gamma \vdash F_1} - {\Gamma \vdash F_1 \wedge F_2}} -\hspace{10mm} -\mbox{\infer{\Gamma \vdash F_2} - {\Gamma \vdash F_1 \wedge F_2}}\medskip - -\mbox{\infer[\star]{\Gamma \vdash Q\;\textit{says}\; F}{\Gamma \vdash P\mapsto Q & - \Gamma \vdash P\;\textit{says}\; F}} -\end{center} - -\item Less frequently used inference rules: - -\begin{center} -\mbox{\infer{\Gamma \vdash slev(P) < slev(Q)} - {\Gamma \vdash slev(P) = l_1 & \Gamma \vdash slev(Q) = l_2 & - \Gamma \vdash l_1 < l_2}}\medskip - -\mbox{\infer{\Gamma \vdash slev(P) = slev(Q)} - {\Gamma \vdash slev(P) = l & \Gamma \vdash slev(Q) = l}}\medskip - -\mbox{\infer{\Gamma \vdash l_1 < l_3} - {\Gamma \vdash l_1 < l_2 & \Gamma \vdash l_2 < l_3}}\medskip - -\mbox{\infer[\star]{\Gamma \vdash P \mapsto R}{\Gamma \vdash P\mapsto Q & \Gamma - \vdash Q \mapsto R}}\medskip - - -\mbox{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_1}} -\hspace{5mm} -\mbox{\infer{\Gamma \vdash F_1 \vee F_2}{\Gamma \vdash F_2}} -\hspace{5mm} -\mbox{\infer{\Gamma \vdash F_3}{\Gamma \vdash F_1 \vee F_2 & F_1, \Gamma - \vdash F_3 & F_2, \Gamma \vdash F_3}}\medskip - -\mbox{\infer[c\;\mbox{must be a fresh variable}]{\Gamma \vdash \forall - x. F}{\Gamma \vdash F[x := c]}}\medskip - -\mbox{\infer{\Gamma \vdash \textit{true}}{}}\medskip - -\mbox{\infer[\star]{\Gamma \vdash P\;\textit{controls}\; F}{\Gamma \vdash P\mapsto Q - & \Gamma \vdash Q\;\textit{controls} F}} - - -\end{center} -\end{enumerate} - - -$\star$ derived rules -\end{document} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: t -%%% End: