Lambda edits

Advanced/Lambda Calculus/parts/00 intro.tex

@@ -6,11 +6,9 @@ Consider the following statement:
 $$
 	I = \lm a . a
 $$
-
 This tells us that $I$ is a function that takes its input, $a$, to itself. We'll call this the \textit{identity function}.
 
 To apply functions, put them next to their inputs. We'll omit the usual parentheses to save space.
-
 $$
 (I~\star) =
 (\lm \tzm{b}a. a)~\tzmr{a}\star =
@@ -26,13 +24,10 @@ $$
 		(a.center) to (b.center);
 \end{tikzpicture}
 $$
-
 Functions are left-associative: If $A$ and $B$ are functions, $(A~B~\star)$ is equivalent to $((A~B)~\star)$.
 As usual, we'll use parentheses to group terms if we want to override this order: $(A~(B~\star)) \neq (A~B~\star)$ \par
 In this handout, all types of parentheses ( $(), [~],$ etc ) are equivalent.
 
-\vfill
-
 \generic{$\beta$-Reduction:}
 
 $\beta$-reduction is a fancy name for \say{simplifying an expression.} We've already done it once above.
@@ -61,12 +56,8 @@ $$
 			(c.center) to (d.center);
 	\end{tikzpicture}
 $$
-
 We cannot reduce this any further, so we stop. Our expression is now in \textit{$\beta$-normal form}.
 
-\vfill
-\pagebreak
-
 \problem{}
 Reduce the following expressions:
 \begin{itemize}