X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=1c5dc9811536796dc52ebade7c949289ef5ebe89;hp=d08685013201556158ac4ca21bdde7d7ff22da7c;hb=336e427a64c1956e15a722da848a906a149d42fd;hpb=6501d908788cd4be578ab1aa55db3e43e80f87be

diff --git a/assignment1.mdwn b/assignment1.mdwn
index d0868501..1c5dc981 100644
--- a/assignment1.mdwn
+++ b/assignment1.mdwn
@@ -1,8 +1,7 @@
 Reduction
 ---------
 
-Find "normal forms" for the following (that is, reduce them as far as it's possible to reduce 
-them):
+Find "normal forms" for the following (that is, reduce them until no more reductions are possible):
 
     1. (\x \y. y x) z
     2. (\x (x x)) z
@@ -81,7 +80,7 @@ To extract the first element of a pair p, you write:
 
         p (\fst \snd. fst)
 
-Here are some defintions in Racket:
+Here are some definitions in Racket:
 
         (define make-pair (lambda (fst) (lambda (snd) (lambda (f) ((f fst) snd)))))
         (define get-first (lambda (fst) (lambda (snd) fst)))
@@ -93,7 +92,7 @@ Now we can write:
         (p get-first)   ; will evaluate to 10
         (p get-second)  ; will evaluate to 20
 
-If you're bothered by having the pair to the left and the function that operates on it come second, think about why it's being done this way: the pair is a package that takes a function for operating on its elements as an argument, and returns the result of operating on its elemens with that function. In other words, the pair is also a function.
+If you're bothered by having the pair to the left and the function that operates on it come second, think about why it's being done this way: the pair is a package that takes a function for operating on its elements as an argument, and returns the result of operating on its elemens with that function. In other words, the pair is also a function.  (Of course, in the untyped lambda calculus, absolutely *everything* is a function: functors, arguments, abstracts, redexes, values---everything.)
 
 If you like, you can disguise what's going on like this:
 
@@ -137,7 +136,7 @@ your choice).
 
         (((make-triple M) N) P)
 
-should return an object that behaves in a reasonable way to serve as a triple. In addition to defining the make-triple function, you have to show how to extraxt elements of your triple. Write a get-first-of-triple function, that does for triples what get-first does for pairs. Also write get-second-of-triple and get-third-of-triple functions.
+should return an object that behaves in a reasonable way to serve as a triple. In addition to defining the make-triple function, you have to show how to extract elements of your triple. Write a get-first-of-triple function, that does for triples what get-first does for pairs. Also write get-second-of-triple and get-third-of-triple functions.
 
 * Write a function second-plus-third that when given to your triple, returns the result of adding the second and third members of the triple.