In the following sections, we will be using a number of functions and
notations, which we will define here.
- \todo{Define substitution (notation)}
-
\subsubsection{Concepts}
A \emph{global variable} is any variable (binder) that is bound at the
top level of a program, or an external module. A \emph{local variable} is any
optimizations, but they are required to get our program into intended
normal form.
+ \placeintermezzo{}{
+ \startframedtext[width=8cm,background=box,frame=no]
+ \startalignment[center]
+ {\tfa Substitution notation}
+ \stopalignment
+ \blank[medium]
+
+ In some of the transformations in this chapter, we need to perform
+ substitution on an expression. Substitution means replacing every
+ occurence of some expression (usually a variable reference) with
+ another expression.
+
+ There have been a lot of different notations used in literature for
+ specifying substitution. The notation that will be used in this report
+ is the following:
+
+ \startlambda
+ E[A=>B]
+ \stoplambda
+
+ This means expression \lam{E} with all occurences of \lam{A} replaced
+ with \lam{B}.
+ \stopframedtext
+ }
+
+ \defref{beta-reduction}
\subsubsection[sec:normalization:beta]{β-reduction}
- \defref{beta-reduction}
β-reduction is a well known transformation from lambda calculus, where it is
the main reduction step. It reduces applications of lambda abstractions,
removing both the lambda abstraction and the application.