From: jim <jim@web>
Date: Sat, 14 Feb 2015 22:01:00 +0000 (-0500)
Subject: alignment
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=3303e8c15d71c68c58c6eec5d6dc7c03e3d6d7bd

alignment
---

diff --git a/topics/week2_encodings.mdwn b/topics/week2_encodings.mdwn
index 290cd5d8..6adafda0 100644
--- a/topics/week2_encodings.mdwn
+++ b/topics/week2_encodings.mdwn
@@ -397,6 +397,8 @@ In fact, there's a way of looking at this that makes it look incredibly natural.
 
     \x. f (g x)
 
+For example, the operation that maps a number `n` to <code>n<sup>2</sup>+1</code> is the composition of the successor function and the squaring function (first we square, then we take the successor).
+
 The composition of a function `f` with itself, namely:
 
     \x. f (f x)
@@ -415,10 +417,10 @@ we are proposing to encode it as:
 
 And indeed this is the Church encoding of the numbers:
 
-<code>0 &equiv; \f z. I z &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \f z. f<sup>0</sup> z</code>  
-<code>1 &equiv; \f z. f z &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \f z. f<sup>1</sup> z</code>  
-<code>2 &equiv; \f z. f (f z) &nbsp;&nbsp;&nbsp;&nbsp;;  or \f z. f<sup>2</sup> z</code>  
-<code>3 &equiv; \f z. f (f (f z)) ;  or \f z. f<sup>3</sup> z</code>  
+<code>0 &equiv; \f z. z &nbsp;&nbsp;;  <~~> \f z. I z, or \f z. f<sup>0</sup> z</code>  
+<code>1 &equiv; \f z. f z &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \f z. f<sup>1</sup> z</code>  
+<code>2 &equiv; \f z. f (f z) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \f z. f<sup>2</sup> z</code>  
+<code>3 &equiv; \f z. f (f (f z)) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;  or \f z. f<sup>3</sup> z</code>  
 <code>...</code>
 
 The encoding for `0` is equivalent to `\f z. z`, which we've also proposed as the encoding for `[]` and for `false`. Don't read too much into this.