\begin{frame} \small \begin{example}[Combinatory Logic] \smallskip \begin{tabular}{l@{\qquad}lr} \alert<1>{signature} & \alert<1>{$\m{S}$ ~ $\m{K}$ ~ $\m{I}$} ~ (constants) \quad \onslide<2-> \alert<2>{$\cdot$} ~ (application, binary, infix) \\ \onslide<3-> \\ \alert<3>{terms} & \GREEN{$\m{S}$ \quad $((\m{K} \cdot \m{I}) \cdot \m{I}) \cdot \m{S}$ \quad $(x \cdot z) \cdot (y \cdot z)$} \\ \onslide<4-> \\ \alert<4>{rewrite rules} & \GREEN{$\begin{array}[t]{r@{~}c@{~}l@{\qquad\qquad}r@{~}c@{~}l} \m{I} \cdot x & \to & x \\[.5ex] (\m{K} \cdot x) \cdot y & \to & x \\[.5ex] ((\m{S} \cdot x) \cdot y) \cdot z & \to & (x \cdot z) \cdot (y \cdot z) \end{array}$} \\ \onslide<5-> \\ \alert<5-7>{rewriting} & \GREEN{$\begin{array}[t]{@{}r@{~}c@{~}l} \alert<6>{((\m{S} \cdot \m{K}) \cdot \m{K}) \cdot x} & \onslide<6->{\to} & \onslide<6->{\alert<7>{(\m{K} \cdot x) \cdot (\m{K} \cdot x)}} \\ & \onslide<7->{\to} & \onslide<7->{x} \end{array}$} \\ \onslide<8-> \\ inventor & \href{http://en.wikipedia.org/wiki/Moses_Schoenfinkel}% {\alert<8>{Moses Sch\"onfinkel}} (1924) & \makebox[0mm][l]{\smash{\includegraphics[height=9ex]{../graphics/moses.jpg}}} \end{tabular} \end{example} \end{frame}