diff --git a/formalism/typed.tex b/formalism/typed.tex index de17f96..9464f1d 100644 --- a/formalism/typed.tex +++ b/formalism/typed.tex @@ -1248,6 +1248,44 @@ \subsubsection{Iterated actions} } \end{mathpar} +\subsection{Mark erasure} +\label{sec:typed-mark-erasure} +\judgbox{\ensuremath{\erase{\ZCMV}}} is a metafunction $\ZCMName \to \ZMName$ defined as follows: +% +\newcommand{\erasesToRow}[2]{\erase{#1} & = & #2} +\[\begin{array}{rcl} + \erasesToRow{\ZCCursor{\ECMV}}{\ZCCursor{\erase{\ECMV}}} \\ + \erasesToRow{(\ZCLamT{x}{\ZTMV}{\ECMV})}{\ZCLamT{x}{\ZTMV}{(\erase{\ECMV})}} \\ + \erasesToRow{(\ZCLamE{x}{\TMV}{\ZCMV})}{\ZCLamE{x}{\TMV}{(\erase{\ZCMV})}} \\ + \erasesToRow{\ZCLamAnaNonMatchedArrowT{x}{\ZTMV}{\ECMV}}{\ZCLamT{x}{\ZTMV}{(\erase{\ECMV})}} \\ + \erasesToRow{\ZCLamAnaNonMatchedArrowE{x}{\TMV}{\ZCMV}}{\ZCLamE{x}{\TMV}{(\erase{\ZCMV})}} \\ + \erasesToRow{\ZCLamInconAscT{x}{\ZTMV}{\ECMV}}{\ZCLamT{x}{\ZTMV}{(\erase{\ECMV})}} \\ + \erasesToRow{\ZCLamInconAscE{x}{\TMV}{\ZCMV}}{\ZCLamE{x}{\TMV}{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCApL{\ZCMV}{\ECMV})}{\ZCApL{(\erase{\ZCMV})}{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCApR{\ECMV}{\ZCMV})}{\ZCApR{(\erase{\ECMV})}{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCApSynNonMatchedArrowL{\ZCMV}{\ECMV})}{\ZCApL{\erase{\ZCMV}}{(\erase{\ECMV})}} \\ + \erasesToRow{(\ZCApSynNonMatchedArrowR{\ECMV}{\ZCMV})}{\ZCApR{\erase{\ECMV}}{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCLetL{x}{\ZCMV}{\ECMV})}{\ZCLetL{x}{(\erase{\ZCMV})}{(\erase{\ECMV})}} \\ + \erasesToRow{(\ZCLetR{x}{\ECMV}{\ZCMV})}{\ZCLetR{x}{(\erase{\ECMV})}{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCPlusL{\ZCMV}{\ECMV})}{\ZCPlusL{(\erase{\ZCMV})}{(\erase{\ECMV})}} \\ + \erasesToRow{(\ZCPlusR{\ECMV}{\ZCMV})}{\ZCPlusR{(\erase{\ECMV})}{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCIfC{\ZCMV}{\ECMV_1}{\ECMV_2})}{\ZCIfC{(\erase{\ZCMV})}{(\erase{\ECMV_1})}{(\erase{\ECMV_2})}} \\ + \erasesToRow{(\ZCIfL{\ECMV_1}{\ZCMV}{\ECMV_2})}{\ZCIfL{(\erase{\ECMV_1})}{(\erase{\ZCMV})}{(\erase{\ECMV_2})}} \\ + \erasesToRow{(\ZCIfL{\ECMV_1}{\ECMV_2}{\ZCMV})}{\ZCIfR{(\erase{\ECMV_1})}{(\erase{\ECMV_2})}{(\erase{\ZCMV})}} \\ + \erasesToRow{\ZCInconBrC{\ZCMV}{\ECMV_1}{\ECMV_2}}{\ZCIfC{(\erase{\ZCMV})}{(\erase{\ECMV_1})}{(\erase{\ECMV_2})}} \\ + \erasesToRow{\ZCInconBrL{\ECMV_1}{\ZCMV}{\ECMV_2}}{\ZCIfL{(\erase{\ECMV_1})}{(\erase{\ZCMV})}{(\erase{\ECMV_2})}} \\ + \erasesToRow{\ZCInconBrR{\ECMV_1}{\ECMV_2}{\ZCMV}}{\ZCIfR{(\erase{\ECMV_1})}{(\erase{\ECMV_2})}{(\erase{\ZCMV})}} \\ + \erasesToRow{\ZCPairL{\ZCMV}{\ECMV}}{\ZCPairL{\erase{\ZCMV}}{\erase{\ECMV}}} \\ + \erasesToRow{\ZCPairR{\ECMV}{\ZCMV}}{\ZCPairR{\erase{\ECMV}}{\erase{\ZCMV}}} \\ + \erasesToRow{\ZCPairAnaNonMatchedProdL{\ZCMV}{\ECMV}}{\ZCPairL{\erase{\ZCMV}}{\erase{\ECMV}}} \\ + \erasesToRow{\ZCPairAnaNonMatchedProdR{\ECMV}{\ZCMV}}{\ZCPairR{\erase{\ECMV}}{\erase{\ZCMV}}} \\ + \erasesToRow{(\ZCProjL{\ZCMV})}{\ZCProjL{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCProjLSynNonMatchedProd{\ZCMV})}{\ZCProjL{\erase{\ZCMV}}} \\ + \erasesToRow{(\ZCProjR{\ZCMV})}{\ZCProjR{(\erase{\ZCMV})}} \\ + \erasesToRow{(\ZCProjRSynNonMatchedProd{\ZCMV})}{\ZCProjR{\erase{\ZCMV}}} \\ + \erasesToRow{\ZCInconType{\ZCMV}}{\erase{\ZCMV}} \\ +\end{array}\] + \subsection{Metatheorems} \label{sec:typed-metatheorems} \begin{theorem}[name=Sensibility] \