Various small fixes following from Bert's commentaar.

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

diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex
index cf905c3c6155003bef0419d251ebafaef4cd1e36..0700b3acb044d0f4ac7929d0fbddde318f169295 100644 (file)
--- a/Chapters/Normalization.tex
+++ b/Chapters/Normalization.tex
@@ -551,7 +551,7 @@
     \stoplambda
 
     Again, the transformation does not apply to this lambda abstraction, so we
-    look at its body. For brevity, we'll put the case statement on one line from
+    look at its body. For brevity, we'll put the case expression on one line from
     now on.
 
     \startlambda
@@ -821,7 +821,6 @@
           \stopframedtext
         }
 
-      \defref{beta-reduction}
       \subsubsection[sec:normalization:beta]{β-reduction}
         β-reduction is a well known transformation from lambda calculus, where it is
         the main reduction step. It reduces applications of lambda abstractions,
@@ -1428,7 +1427,7 @@
         \stoptrans
         \todo{Check the subscripts of this transformation}
 
-        Note that this transformation applies to case statements with any
+        Note that this transformation applies to case expressions with any
         scrutinee. If the scrutinee is a complex expression, this might result
         in duplicate hardware. An extra condition to only apply this
         transformation when the scrutinee is already simple (effectively
@@ -1481,10 +1480,10 @@
         \in{section}[sec:transformation:caseremoval].
 
       \subsubsection[sec:transformation:caseremoval]{Case removal}
-        This transform removes any case statements with a single alternative and
+        This transform removes any case expression with a single alternative and
         only wild binders.
 
-        These "useless" case statements are usually leftovers from case simplification
+        These "useless" case expressions are usually leftovers from case simplification
         on extractor case (see the previous example).
 
         \starttrans
@@ -2060,7 +2059,7 @@
         transformations will probably need updating to handle them in all
         cases.
 
-      \subsection{Normalization of stateful descriptions}
+      \subsection[sec:normalization:stateproblems]{Normalization of stateful descriptions}
         Currently, the intended normal form definition\refdef{intended
         normal form definition} offers enough freedom to describe all
         valid stateful descriptions, but is not limiting enough. It is
@@ -2079,8 +2078,6 @@
         matching, causing a state input to be unpacked multiple times or
         be unpacked and repacked only in some of the code paths.
 
-        \todo{example?}
-
         Without going into detail about the exact problems (of which
         there are probably more than have shown up so far), it seems
         unlikely that these problems can be solved entirely by just
@@ -2090,6 +2087,9 @@
         of course mean that the intended normal form definition must be
         extended as well to be more specific about how state handling
         should look like in normal form.
+        \in{Section}[sec:prototype:statelimits] already contains a
+        tight description of the limitations on the use of state
+        variables, which could be adapted into the intended normal form.
 
   \section[sec:normalization:properties]{Provable properties}
     When looking at the system of transformations outlined above, there are a