From: Matthijs Kooijman <matthijs@stdin.nl>
Date: Tue, 1 Dec 2009 19:53:35 +0000 (+0100)
Subject: Rename example function app2 to twice.
X-Git-Tag: final-thesis~124
X-Git-Url: https://git.stderr.nl/gitweb?p=matthijs%2Fmaster-project%2Freport.git;a=commitdiff_plain;h=bff5a598be513f497ad61d29b7c7584f94d2b993;hp=feee31da167a3c0505d2683d3e81e2597743f1a6

Rename example function app2 to twice.

app2 would get the 2 in subscript, which might be confusing.
---

diff --git a/Chapters/Normalization.tex b/Chapters/Normalization.tex
index e2f3a96..fbad0ea 100644
--- a/Chapters/Normalization.tex
+++ b/Chapters/Normalization.tex
@@ -1788,17 +1788,17 @@
         expression shows an example:
 
         \startlambda
-        app2 :: (Word -> Word) -> Word -> Word
-        app2 = λf.λa.f (f a)
+        twice :: (Word -> Word) -> Word -> Word
+        twice = λf.λa.f (f a)
 
         main = λa.app (λx. x + x) a
         \stoplambda
 
-        This example shows a function \lam{app2} that takes a function as a
+        This example shows a function \lam{twice} that takes a function as a
         first argument and applies that function twice to the second argument.
         Again, we've made the function monomorphic for clarity, even though
         this function would be a lot more useful if it was polymorphic. The
-        function \lam{main} uses \lam{app2} to apply a lambda epression twice.
+        function \lam{main} uses \lam{twice} to apply a lambda epression twice.
 
         When faced with a user defined function, a body is available for that
         function. This means we could create a specialized version of the
@@ -1808,23 +1808,23 @@
         Applying this transformation to the example gives:
 
         \startlambda
-        app2' :: Word -> Word
-        app2' = λb.(λf.λa.f (f a)) (λx. x + x) b
+        twice' :: Word -> Word
+        twice' = λb.(λf.λa.f (f a)) (λx. x + x) b
 
         main = λa.app' a
         \stoplambda
 
         The \lam{main} function is now in normal form, since the only higher
         order value there is the top level lambda expression. The new
-        \lam{app2'} function is a bit complex, but the entire original body of
-        the original \lam{app2} function is wrapped in a lambda abstraction
+        \lam{twice'} function is a bit complex, but the entire original body of
+        the original \lam{twice} function is wrapped in a lambda abstraction
         and applied to the argument we've specialized for (\lam{λx. x + x})
         and the other arguments. This complex expression can fortunately be
         effectively reduced by repeatedly applying β-reduction: 
 
         \startlambda
-        app2' :: Word -> Word
-        app2' = λb.(b + b) + (b + b)
+        twice' :: Word -> Word
+        twice' = λb.(b + b) + (b + b)
         \stoplambda
 
         This example also shows that the resulting normal form might not be as