X-Git-Url: https://git.stderr.nl/gitweb?p=matthijs%2Fmaster-project%2Freport.git;a=blobdiff_plain;f=Chapters%2FNormalization.tex;h=03f379244e0299b787ae294c90e4db2c07eab829;hp=78b7a1d2e2352662fd759c495af3904b7fdd163b;hb=68e92ccd2b456b9ce81b0617417bc8abdaff6fa3;hpb=ee64b2e24b792c580ba5c0bfa38c5ed642800945

diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex
index 78b7a1d..03f3792 100644
--- a/Chapters/Normalization.tex
+++ b/Chapters/Normalization.tex
@@ -641,8 +641,6 @@
       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
@@ -799,8 +797,33 @@
        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.