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Co-authored-by: Mark <mark@betalupi.com>
Co-committed-by: Mark <mark@betalupi.com>

src/Advanced/Lambda Calculus/parts/01 combinators.tex

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+\section{Combinators}
+
+\definition{}
+A \textit{free variable} in a $\lm$-expression is a variable that isn't bound to any input. \par
+For example, $b$ is a free variable in $(\lm a.a)~b$.
+
+\definition{Combinators}
+A \textit{combinator} is a lambda expression with no free variables.
+
+\vspace{1mm}
+
+Notable combinators are often named after birds.\hspace{-0.5ex}\footnotemark{} We've already met a few: \par
+The \textit{Idiot}, $I = \lm a.a$ \par
+The \textit{Mockingbird}, $M = \lm f.ff$ \par
+The \textit{Cardinal}, $C = \lm fgx.(~ f(g(x)) ~)$
+The \textit{Kestrel}, $K = \lm ab . a$
+
+
+
+\problem{}
+If we give the Kestrel two arguments, it does something interesting: \par
+It selects the first and rejects the second. \par
+Convince yourself of this fact by evaluating $(K~\heartsuit~\star)$.
+
+\vfill
+
+\problem{}<kitedef>
+Modify the Kestrel so that it selects its \textbf{second} argument and rejects the first. \par
+
+\begin{solution}
+	$\lm ab . b$.
+\end{solution}
+
+\vfill
+
+\problem{}
+We'll call the combinator from \ref{kitedef} the \textit{Kite}, $KI$. \par
+Show that we can also obtain the kite by evaluating $(K~I)$.
+
+
+\vfill
+\pagebreak