Some minor wording fixes.

[matthijs/master-project/report.git] / Chapters / Normalization.tex

diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex
index c1c6268770ceb7bfab66fff709d598b29a7cf666..6853d88d704b166eaed7ccb0b3964b2d4f284afb 100644 (file)
--- a/Chapters/Normalization.tex
+++ b/Chapters/Normalization.tex
@@ -7,7 +7,7 @@
 % will end up on a single line. The strut=no option prevents a bunch of empty
 % space at the start of the frame.
 \define[1]\example{
-  \framed[offset=1mm,align=right,strut=no]{
+  \framed[offset=1mm,align=right,strut=no,background=box,frame=off]{
     \setuptyping[option=LAM,style=sans,before=,after=]
     \typebuffer[#1]
     \setuptyping[option=none,style=\tttf]
@@ -230,10 +230,10 @@ the core language in a notation that resembles lambda calculus.
 
 Each of these transforms is meant to be applied to every (sub)expression
 in a program, for as long as it applies. Only when none of the
-expressions can be applied anymore, the program is in normal form. We
-hope to be able to prove that this form will obey all of the constraints
-defined above, but this has yet to happen (though it seems likely that
-it will).
+transformations can be applied anymore, the program is in normal form (by
+definition). We hope to be able to prove that this form will obey all of the
+constraints defined above, but this has yet to happen (though it seems likely
+that it will).
 
 Each of the transforms will be described informally first, explaining
 the need for and goal of the transform. Then, a formal definition is
@@ -684,7 +684,7 @@ arguments into normal form. The goal here is to:
 When looking at the arguments of a user-defined function, we can
 divide them into two categories:
 \startitemize
-  \item Arguments with a runtime representable type (\eg bits or vectors).
+  \item Arguments of a runtime representable type (\eg bits or vectors).
 
         These arguments can be preserved in the program, since they can
         be translated to input ports later on.  However, since we can
@@ -720,7 +720,7 @@ When looking at the arguments of a builtin function, we can divide them
 into categories: 
 
 \startitemize
-  \item Arguments with a runtime representable type.
+  \item Arguments of a runtime representable type.
         
         As we have seen with user-defined functions, these arguments can
         always be reduced to a simple variable reference, by the
@@ -729,7 +729,7 @@ into categories:
         functions can be limited to signal references, instead of
         needing to support all possible expressions.
 
-  \item Arguments with a function type.
+  \item Arguments of a function type.
         
         These arguments are functions passed to higher order builtins,
         like \lam{map} and \lam{foldl}. Since implementing these