Describe types, values, rough semantics
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slides.tex
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slides.tex
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@ -25,6 +25,10 @@
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\newcommand{\actions}{\mathbb{A}}
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\newcommand{\commands}{\mathbb{C}}
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\newcommand{\askip}{\operatorname{skip}}
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\newcommand{\stores}{\operatorname{Store}}
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\newcommand{\states}{\operatorname{State}}
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\newcommand{\traces}{\operatorname{Trace}}
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\newcommand{\state}[2]{\langle{} #1, #2 \rangle{}}
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\newcommand*\oldmacro{}%
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\let\oldmacro\insertshorttitle%
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@ -163,6 +167,59 @@
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\end{columns}
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\end{frame}
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\begin{frame}{Types, rough semantics}
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\hspace*{-1em}\textbf{Types \& values}
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\begin{columns}[c]
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\column{0.6\textwidth}
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\begin{itemize}
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\item $\values\,:=\,\relset \cup \set{a, \ldots, z}^\ast$
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\item Types: Int, String, Undef, $\emptyset$, $\Omega$
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\item Undef: error type
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\end{itemize}
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\column{0.4\textwidth}
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\begin{center}
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\begin{tikzpicture}{c}
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\node (E) at (0, 0) {$\emptyset$};
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\node (I) at (-1.5, 1) {Int};
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\node (S) at (0, 1) {String};
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\node (U) at (1.5, 1) {Undef};
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\node (T) at (0, 2) {$\Omega$};
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\draw[->] (E) -- (I);
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\draw[->] (E) -- (S);
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\draw[->] (E) -- (U);
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\draw[<-] (T) -- (I);
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\draw[<-] (T) -- (S);
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\draw[<-] (T) -- (U);
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\end{tikzpicture}
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\end{center}
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\end{columns}
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\vspace{1em}
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\hspace*{-1em}\textbf{Semantics}
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\begin{columns}[c]
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\column{.5\textwidth}
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\begin{itemize}
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\item Type-dependant $+$:
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\begin{itemize}
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\item $+_{String}$: concatenation
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\item $+_{Int}$: usual $+$
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\item $+_{Str, Int}$: yields Undef
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\end{itemize}
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\end{itemize}
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\column{.5\textwidth}
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\begin{align*}
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\stores &:= \vars \to \values & \rho \\
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\states &:= \commands \times \stores & \state{C}{\rho} \\
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\traces &:= \states^\ast
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\end{align*}
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\end{columns}
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\end{frame}
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\section{Abstract interpretation}
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\begin{frame}{AbsInt hot path extraction}
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