Use η/β-expansion instead of η/β-abstraction.

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

diff --git a/Chapters/Prototype.tex b/Chapters/Prototype.tex
index b391d4fcbc6951c2c86af451b805cec8187aae28..101594bf2a9b4aaacbd210c1242fd968ed0f2fa7 100644 (file)
--- a/Chapters/Prototype.tex
+++ b/Chapters/Prototype.tex
@@ -73,7 +73,7 @@
     Haskell an obvious choice.
 
   \section[sec:prototype:output]{Output format}
-    The second important question is: What will be our output format?
+    The second important question is: what will be our output format?
     This output format should at least allow for programming the
     hardware design into a field-programmable gate array (\small{FPGA}).
     The choice of output format is thus limited by what hardware
@@ -379,7 +379,7 @@
       func arg
       \stoplambda
       This is function application. Each application consists of two
-      parts: The function part and the argument part. Applications are used
+      parts: the function part and the argument part. Applications are used
       for normal function \quote{calls}, but also for applying type
       abstractions and data constructors.
 
@@ -516,12 +516,12 @@
       
       A case expression evaluates its scrutinee, which should have an
       algebraic datatype, into weak head normal form (\small{WHNF}) and
-      (optionally) binds it to \lam{bndr}. Every alternative lists a
-      single constructor (\lam{C0 ... Cn}). Based on the actual
-      constructor of the scrutinee, the corresponding alternative is
-      chosen. The binders in the chosen alternative (\lam{bndr0,0 ....
-      bndr0,m} are bound to the actual arguments to the constructor in
-      the scrutinee.
+      (optionally) binds it to \lam{bndr}. If bndr is wild, \refdef{wild
+      binders} it is left out.  Every alternative lists a single constructor
+      (\lam{C0 ... Cn}). Based on the actual constructor of the scrutinee, the
+      corresponding alternative is chosen. The binders in the chosen
+      alternative (\lam{bndr0,0 ....  bndr0,m} are bound to the actual
+      arguments to the constructor in the scrutinee.
 
       This is best illustrated with an example. Assume
       there is an algebraic datatype declared as follows\footnote{This
@@ -884,7 +884,7 @@
       Word} and \hs{Word} types by pattern matching and by using the explicit
       the \hs{State constructor}.
 
-      This explicit conversion makes the \VHDL\ generation easier: Whenever we
+      This explicit conversion makes the \VHDL\ generation easier: whenever we
       remove (unpack) the \hs{State} type, this means we are accessing the
       current state (\eg, accessing the register output). Whenever we are a
       adding (packing) the \hs{State} type, we are producing a new value for
@@ -1246,7 +1246,7 @@
       function.
 
       Fortunately, the \lam{accs'} variable (and any other substate) has a
-      property that we can easily check: It has a \lam{State} type
+      property that we can easily check: it has a \lam{State} type
       annotation. This means that whenever \VHDL\ is generated for a tuple
       (or other algebraic type), we can simply leave out all elements that
       have a \lam{State} type. This will leave just the parts of the state
@@ -1303,7 +1303,7 @@
       \stoplambda
               
       When we would really leave out the crossed out parts, we get a slightly
-      weird program: There is a variable \lam{s} which has no value, and there
+      weird program: there is a variable \lam{s} which has no value, and there
       is a variable \lam{s'} that is never used. Together, these two will form
       the state process of the function. \lam{s} contains the "current" state,
       \lam{s'} is assigned the "next" state. So, at the end of each clock