Added Crypto & Lambda handouts

Advanced/Lambda Calculus/parts/01 combinators.tex

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+\documentclass[../main.tex]{subfiles}
+
+
+\begin{document}
+
+	\section{Combinators}
+
+	\definition{}
+	A \textit{free variable} in a $\lm$-expression is a variable that isn't bound to any input. \\
+	For example, $b$ is a free variable in $\lm a. b$. The same is true of $\star$ in any of the previous pages.
+
+	A \textit{combinator} is a function with no free variables.
+
+	\definition{The Kestrel}
+
+	Notable combinators are often named after birds.\hspace{-0.5ex}\footnotemark{} We've already met a few: \\
+	The \textit{Idiot}, $I = \lm a.a$ \\
+	The \textit{Mockingbird}, $M = \lm f.ff$ \\
+	The \textit{Cardinal}, $C = \lm fgx.(~ f(g(x)) ~)$ \\
+
+	\footnotetext{Raymond Smullyan's \textit{To Mock a Mockingbird} is responsible for this.}
+
+	\vspace{2ex}
+
+	Another notable combinator is $K$, the \textit{Kestrel}:
+	$$
+		K = \lm ab . a
+	$$
+	\problem{}
+	What does the Kestrel do? Explain in plain English. \\
+	\hint{What is $(K~\heartsuit~\star)$?}
+
+	\vspace{2cm}
+
+	\problem{}
+	Reduce $(K~I)$ to derive the \textit{Kite}. How does the Kite compare to the Kestrel? \\
+	We'll call the Kite KI.
+
+	\begin{solution}
+		$\text{KI} = \lm ab . b$. \\
+	\end{solution}
+
+	\vfill
+	\pagebreak
+
+
+\end{document}