From 887b6de1d6b6b890cd4a1b1a24a61bf72244a0fe Mon Sep 17 00:00:00 2001
From: mark <mark@betalupi.com>
Date: Tue, 17 Oct 2023 11:45:33 -0700
Subject: [PATCH] Minor edits

---
 Advanced/Lambda Calculus/parts/00 intro.tex | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/Advanced/Lambda Calculus/parts/00 intro.tex b/Advanced/Lambda Calculus/parts/00 intro.tex
index 9ce3324..97a1dcf 100755
--- a/Advanced/Lambda Calculus/parts/00 intro.tex	
+++ b/Advanced/Lambda Calculus/parts/00 intro.tex	
@@ -149,13 +149,18 @@ The first \say{pure} functions we'll define are $I$ and $M$:
 \end{itemize}
 
 Note that $I$ and $M$ don't have a meaning on their own. They are not formal functions. \par
-Rather, it's notation that says \say{write $\lm x.x$ whenever you see $I$.}
+Rather, they are abbreviations that say \say{write $\lm x.x$ whenever you see $I$.}
 
 
 
 
 \problem{}
-Reduce the following expressions.
+Reduce the following expressions. \par
+\hint{
+	Of course, your final result will be a function. \\
+	Functions are the only objects we have!
+}
+
 \begin{itemize}[itemsep=2mm]
 	\item $I~I$
 	\item $(I~I)~I$
@@ -167,7 +172,7 @@ Reduce the following expressions.
 \vfill
 
 In lambda calculus, functions are left-associative: \par
-$(f~g~h)$ is equivalent to $((f~g)~h)$, not $(f~(g~h))$
+$(f~g~h)$ means $((f~g)~h)$, not $(f~(g~h))$
 
 As usual, we use parentheses to group terms if we want to override this order: $(f~(g~h)) \neq ((f~g)~h)$ \par
 In this handout, all types of parentheses ( $(), [~],$ etc ) are equivalent.
@@ -254,6 +259,7 @@ Evaluate $(C~a~b~x)$ for arbitary expressions $a$ and $b$. \par
 \problem{}
 Using the definition of $C$ above, evaluate $C~M~I~\star$ \par
 Then, evaluate $C~I~M~I$ \par
+\note[Note]{$\star$ represents an arbitrary expression. Treat it like an unknown variable.}
 
 \vfill