Add missing parenthesis.

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

diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex
index 03f379244e0299b787ae294c90e4db2c07eab829..f9a10157970ad68d646a6d5948f697f516af8f23 100644 (file)
--- a/Chapters/Normalization.tex
+++ b/Chapters/Normalization.tex
@@ -28,11 +28,7 @@
   core can describe expressions that do not have a direct hardware
   interpretation.
 
-  \todo{Describe core properties not supported in \VHDL, and describe how the
-  \VHDL we want to generate should look like.}
-
   \section{Normal form}
-    \todo{Refresh or refer to distinct hardware per application principle}
     The transformations described here have a well-defined goal: To bring the
     program in a well-defined form that is directly translatable to hardware,
     while fully preserving the semantics of the program. We refer to this form as
@@ -629,9 +625,11 @@
 
       In particular, we define no particular order of transformations. Since
       transformation order should not influence the resulting normal form,
-      \todo{This is not really true, but would like it to be...} this leaves
-      the implementation free to choose any application order that results in
-      an efficient implementation.
+      this leaves the implementation free to choose any application order that
+      results in an efficient implementation. Unfortunately this is not
+      entirely true for the current set of transformations. See
+      \in{section}[sec:normalization:non-determinism] for a discussion of this
+      problem.
 
       When applying a single transformation, we try to apply it to every (sub)expression
       in a function, not just the top level function body. This allows us to
@@ -798,6 +796,7 @@
        normal form.
 
         \placeintermezzo{}{
+          \defref{substitution notation}
           \startframedtext[width=8cm,background=box,frame=no]
           \startalignment[center]
             {\tfa Substitution notation}
@@ -890,7 +889,8 @@
         This transformation is not needed to get an expression into intended
         normal form (since these bindings are part of the intended normal
         form), but makes the resulting \small{VHDL} a lot shorter.
-        
+       
+        \refdef{substitution notation}
         \starttrans
         letrec
           a0 = E0
@@ -1647,7 +1647,7 @@
         
         This propagation makes higher order values become applied (in
         particular both of the alternatives of the case now have a
-        representable type. Completely applied top level functions (like the
+        representable type). Completely applied top level functions (like the
         first alternative) are now no longer invalid (they fall under
         \in{item}[item:completeapp] above). (Completely) applied lambda
         abstractions can be removed by β-abstraction. For our example,
@@ -1822,6 +1822,7 @@
         solves (part of) the polymorphism, higher order values and
         unrepresentable literals in an expression.
 
+        \refdef{substitution notation}
         \starttrans
         letrec 
           a0 = E0
@@ -1944,7 +1945,6 @@
 
         \todo{Examples. Perhaps reference the previous sections}
 
-
   \section{Unsolved problems}
     The above system of transformations has been implemented in the prototype
     and seems to work well to compile simple and more complex examples of
@@ -2013,7 +2013,7 @@
         let y = (a * b) in y + y
         \stoplambda
 
-      \subsection{Non-determinism}
+      \subsection[sec:normalization:non-determinism]{Non-determinism}
         As an example, again consider the following expression:
 
         \startlambda