Added Crypto & Lambda handouts

Advanced/Lambda Calculus/parts/02 boolean.tex

@@ -0,0 +1,71 @@
+\documentclass[../main.tex]{subfiles}
+
+
+\begin{document}
+
+	\section{Boolean Algebra}
+
+	The Kestrel selects its first argument, and the Kite selects its second. This \say{choosing} behavior is awfully similar to something you may have already seen...
+
+	\vspace{1ex}
+
+	Let $T = K\phantom{I} = \lm ab . a$ \\
+	Let $F = KI = \lm ab . b$ \\
+
+	\problem{}
+	Write a function $\text{NOT}$ so that $(\text{NOT} ~ T) = F$ and $(\text{NOT}~F) = T$. \\
+	\hint{What is $(T~\heartsuit~\star)$? How about $(F~\heartsuit~\star)$?}
+
+
+	\begin{solution}
+		$\text{NOT} = \lm a . (a~F~T)$ \\
+	\end{solution}
+
+	\vfill
+
+	\problem{}
+	Write functions $\text{AND}$, $\text{OR}$, and $\text{XOR}$ that satisfy the following table.
+
+	\begin{center}
+	\begin{tabular}{|| c c || c | c | c ||}
+		\hline
+		$A$ & $B$ & $(\text{AND}~A~B)$ & $(\text{OR}~A~B)$ & $(\text{XOR}~A~B)$ \\
+		\hline\hline
+		F & F & F & F & F \\
+		\hline
+		F & T & F & T & T \\
+		\hline
+		T & F & F & T & T \\
+		\hline
+		T & T & T & T & F \\
+		\hline
+	\end{tabular}
+	\end{center}
+
+	\begin{solution}
+		There's more than one way to do this, of course, but make sure the kids understand how the solutions below work.
+		\begin{align*}
+			\text{AND} &= \lm ab . (a~b~F) = \lm ab . aba \\
+			\text{OR} &= \lm ab . (a~T~b)  = \lm ab . aab \\
+			\text{XOR} &= \lm ab . (a~ (\text{NOT}~b) ~b)
+		\end{align*}
+
+		It may be worth mentioning that OR $= \lm ab.(M~a~b)$ is also a solution.
+	\end{solution}
+
+	\problem{}
+	To complete our boolean algebra, write the boolean equality check EQ. \\
+	What inputs should it take? What outputs should it produce?
+
+	\begin{solution}
+		$\text{EQ} = \lm ab . [a~(bTF)~(bFT)] = \lm ab . [a~b~(\text{NOT}~b)]$
+
+		\vspace{1ex}
+
+		$\text{EQ} = \lm ab . [\text{NOT}~(\text{XOR}~a~b)]$
+	\end{solution}
+
+	\vfill
+	\pagebreak
+
+\end{document}