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45 lines
1.9 KiB
TeX
45 lines
1.9 KiB
TeX
\documentclass[../generics]{subfiles}
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\begin{document}
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\chapter{Derived Requirements Summary}\label{derived summary}
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\index{$\vdash$}
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\IndexStep{GenSig}
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\IndexStep{ReqSig}
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\IndexStep{AssocType}
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\IndexStep{Conf}
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\IndexStep{Equiv}
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\IndexStep{Same}
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\IndexStep{Member}
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\IndexStep{Concrete}
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\begin{gather*}
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\vdash\ConfReq{T}{P}\tag{\textsc{GenSig}}\\
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\vdash\ConfReq{T}{C}\\
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\vdash\ConfReq{T}{AnyObject}\\
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\vdash\FormalReq{T == U}\\[\medskipamount]
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\ConfReq{T}{P}\vdash\texttt{T.A}\tag{\textsc{AssocType}}\\
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\ConfReq{T}{P}\vdash\texttt{T.[P]A}\\
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\ConfReq{T}{P}\vdash\FormalReq{T.[P]A == T.A}\\[\medskipamount]
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\vdash\ConfReq{Self.U}{Q}_\texttt{P}\tag{\textsc{ReqSig}}\\
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\vdash\ConfReq{Self.U}{C}_\texttt{P}\\
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\vdash\ConfReq{Self.U}{AnyObject}_\texttt{P}\\
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\vdash\FormalReq{Self.U == Self.V}_\texttt{P}\\[\medskipamount]
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\ConfReq{T}{P},\,\ConfReq{Self.U}{Q}\vdash\ConfReq{T.U}{Q}\tag{\textsc{Conf}}\\
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\ConfReq{T}{P},\,\ConfReq{Self.U}{C}\vdash\ConfReq{T.U}{C}\\
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\ConfReq{T}{P},\,\ConfReq{Self.U}{AnyObject}\vdash\ConfReq{T.U}{AnyObject}\\
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\ConfReq{T}{P},\,\FormalReq{Self.U == Self.V}\vdash\FormalReq{T.U == T.V}\\[\medskipamount]
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\texttt{T}\vdash\FormalReq{T == T}\tag{\textsc{Equiv}}\\
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\FormalReq{T == U}\vdash\FormalReq{U == T}\\
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\FormalReq{T == U},\,\FormalReq{U == V}\vdash\FormalReq{T == V}\\[\medskipamount]
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\ConfReq{U}{P},\,\FormalReq{T == U}\vdash\ConfReq{T}{P}\tag{\textsc{Same}}\\
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\ConfReq{U}{C},\,\FormalReq{T == U}\vdash\ConfReq{T}{C}\\
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\ConfReq{U}{AnyObject},\,\FormalReq{T == U}\vdash\ConfReq{T}{AnyObject}\\[\medskipamount]
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\ConfReq{U}{P},\,\FormalReq{T == U}\vdash\FormalReq{T.A == U.A}\tag{\textsc{Member}}\\
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\ConfReq{U}{P},\,\FormalReq{T == U}\vdash\FormalReq{T.[P]A == U.[P]A}\\[\medskipamount]
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\FormalReq{T == U}\vdash\FormalReq{G<T> == G<U>}\qquad\mbox{(arbitrary type constructor \texttt{G<>})}\tag{\textsc{Concrete}}\\
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\FormalReq{G<T> == G<U>}\vdash\FormalReq{T == U}\qquad\mbox{(arbitrary type constructor \texttt{G<>})}
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\end{gather*}
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\end{document} |