->combinatory

[lambda.git] / topics / _week3_what_is_computation.mdwn

diff --git a/topics/_week3_what_is_computation.mdwn b/topics/_week3_what_is_computation.mdwn
index 7575abc..47748a1 100644 (file)
--- a/topics/_week3_what_is_computation.mdwn
+++ b/topics/_week3_what_is_computation.mdwn
@@ -9,10 +9,10 @@ This equation can be interpreted as expressing the thought that the
 complex expression `3 + 4` evaluates to `7`.  The evaluation of the
 expression computing a sum.  There is a clear sense in which the
 expression `7` is simpler than the expression `3 + 4`: `7` is
-syntactically simple, and `3 + 4` is syntactically complex.  
+syntactically simple, and `3 + 4` is syntactically complex.
 
 Now let's take this folk notion of computation, and put some pressure
-on it.  
+on it.
 
 ##Church arithmetic##
 
@@ -64,14 +64,14 @@ But now consider multiplication:
 Is the final result simpler?  This time, the answer is not so straightfoward.
 Compare the starting expression with the final expression:
 
-        *           3             4 
+        *           3             4
         (\lrf.l(rf))(\fz.f(f(fz)))(\fz.f(f(f(fz))))
     ~~> 12
         (\fz.f(f(f(f(f(f(f(f(f(f(f(fz))))))))))))
 
 And if we choose different numbers, the result is even less clear:
 
-        *           3             6 
+        *           3             6
         (\lrf.l(rf))(\fz.f(f(fz)))(\fz.f(f(f(f(f(fz))))))
     ~~> 18
         (\fz.f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(fz))))))))))))))))))
@@ -99,7 +99,7 @@ that reduce to that term.
 
 In the arithmetic example, there is only one number that corresponds
 to the sum of 3 and 4 (namely, 7).  But there are many sums that add
-up to 7: 3+4, 4+3, 5+2, 2+5, 6+1, 1+6, etc.  
+up to 7: 3+4, 4+3, 5+2, 2+5, 6+1, 1+6, etc.
 
 So the unevaluated expression contains information that is missing
 from the evaluated value: information about *how* that value was
@@ -124,7 +124,7 @@ pathological examples where the results do not align so well:
 In this example, reduction returns the exact same lambda term.  There
 is no simplification at all.
 
-    (\x.xxx)(\x.xxx) ~~> ((\x.xxxx)(\x.xxxx)(\x.xxxx)) 
+    (\x.xxx)(\x.xxx) ~~> ((\x.xxxx)(\x.xxxx)(\x.xxxx))
 
 Even worse, in this case, the "reduced" form is longer and more
 complex by any measure.