\begin{frame} \frametitle{Combinatory Logic (CL)} \small \begin{block}{} \begin{center} \( \begin{array}{lcl} \rule[1ex]{0ex}{2ex} Ap(Ap(Ap (S,x),y),z) & \to & Ap(Ap(x,z), Ap(y,z))\\ Ap(Ap(K,x),y)&\to& x\\ Ap (I,x)&\to& x \rule[-2ex]{0ex}{2ex} \end{array}\) \end{center} \end{block} \onslide<2-> \begin{block}{CL in \alert<2>{infix notation}} \begin{center} \(\begin{array}{lcl} \rule[1ex]{0ex}{2ex} (((S\cdot x)\cdot y)\cdot z) &\to&((x\cdot z)\cdot(y\cdot z))\\ ((K\cdot x)\cdot y) & \to& x\\ (I\cdot x)& \to& x \rule[-2ex]{0ex}{2ex} \end{array}\) \end{center} \end{block} \onslide<3-> \begin{block}{CL in \alert<3>{standard notation}} \begin{center} \(\begin{array}{lcl} \rule[1ex]{0ex}{2ex} Sxyz &\to&xz(yz)\\ Kxy &\to &x\\ Ix &\to &x \rule[-2ex]{0ex}{2ex} \end{array}\) \end{center} \end{block} \end{frame}