X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2Fweek2_encodings.mdwn;h=ac92202e696a20e38663d8813b921e8c79b47f44;hp=eca15145ea0d6dfea0ffb22350904d5c6efbcf3d;hb=b93e99adfad61e703393d71f919af78a10b02101;hpb=189cf62eaea54348792dbecc9147f43fc2760e3e

diff --git a/topics/week2_encodings.mdwn b/topics/week2_encodings.mdwn
index eca15145..ac92202e 100644
--- a/topics/week2_encodings.mdwn
+++ b/topics/week2_encodings.mdwn
@@ -8,8 +8,7 @@ we've become acquainted with.
 
 ## Booleans ##
 
-We'll start with the `if ... then
-... else...` construction we saw last week:
+We'll start with the `if ... then ... else ...` construction we saw last week:
 
     if M then N else L
 
@@ -55,7 +54,7 @@ Sucess! In the same spirit, `'false` could be **K I**, which reduces to `(\y x.
                      ~~> ((\x x) L)
                      ~~> L
 
-So have seen our first major encoding in the Lambda Calculus:
+So we have seen our first major encoding in the Lambda Calculus:
 "true" is represented by **K**, and "false" is represented by **K I**.
 We'll be building up a lot of representations in the weeks to come,
 and they will all maintain the discipline that if a expression is
@@ -316,7 +315,7 @@ Now we saw above how to define `map` in terms of `fold_right`. In Kapulet syntax
 
 In our Lambda Calculus encoding, `fold_right (f, z) xs` gets translated to `xs f z`. That is, the list itself is the operator, just as we saw triples being. So we just need to know how to represent `lambda (x, zs). g x & zs`, on the one hand, and `[]` on the other, into the Lambda Calculus, and then we can also express `map`. Well, in the Lambda Calculus we're working with curried functions, and there's no infix syntax, so we'll replace the first by `lambda x zs. cons (g x) zs`. But we just defined `cons`, and the lambda is straightforward. And we also just defined `[]`. So we already have all the pieces to do this. Namely:
 
-    map (g, z) xs
+    map g xs
 
 in Kapulet syntax, turns into this in our lambda evaluator:
 
@@ -403,7 +402,7 @@ And indeed this is the Church encoding of the numbers:
 <code>3 &equiv; \f z. f (f (f z)) ;  or \f z. f<sup>3</sup> z</code>  
 <code>...</code>
 
-The encoding for `0` can also be written as `\f z. z`, which we've also proposed as the encoding for `[]` and for `false`. Don't read too much into this.
+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.
 
 Given the above, can you figure out how to define the `succ` function? We already worked through the definition of `cons`, and this is just a simplification of that, so you should be able to do it. We'll make it a homework.