X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=1c5dc9811536796dc52ebade7c949289ef5ebe89;hp=bfaafdc0acae1d1cad18d6bfdf36c927ba2ded0a;hb=0bec426ca6b6e8672c487a1b9f0a3ef1823d267a;hpb=567ca6641f7c2f470cd0003e32efeab52ab9c9c9

diff --git a/assignment1.mdwn b/assignment1.mdwn
index bfaafdc0..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
@@ -27,6 +26,7 @@ In Racket, these can be defined like this:
 	(define false (lambda (t) (lambda (f) f)))
 
 * Define a "neg" operator that negates "true" and "false".
+
 Expected behavior: 
 
     (((neg true) 10) 20)
@@ -40,6 +40,7 @@ evaluates to 10.
 * Define an "and" operator.
 
 * Define an "xor" operator. 
+
 (If you haven't seen this term before, here's a truth table:
 
     true xor true = false
@@ -79,11 +80,11 @@ 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 (lamda (fst) (lambda (snd) fst)))
-        (define get-second (lamda (fst) (lambda (snd) snd)))
+        (define get-first (lambda (fst) (lambda (snd) fst)))
+        (define get-second (lambda (fst) (lambda (snd) snd)))
 
 Now we can write:
 
@@ -91,7 +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:
 
@@ -109,7 +110,8 @@ instead of:
 However, the latter is still what's going on under the hood.
 
 
-13. Define a "swap" function that reverses the elements of a pair.
+* Define a "swap" function that reverses the elements of a pair.
+
 Expected behavior:
 
         (define p ((make-pair 10) 20))
@@ -119,27 +121,27 @@ Expected behavior:
 Write out the definition of swap in Racket.
 
 
-14. Define a "dup" function that duplicates its argument to form a pair
+* Define a "dup" function that duplicates its argument to form a pair
 whose elements are the same.
 Expected behavior:
 
         ((dup 10) get-first) ; evaluates to 10
         ((dup 10) get-second) ; evaluates to 10
 
-15. Define a "sixteen" function that makes
+* Define a "sixteen" function that makes
 sixteen copies of its argument (and stores them in a data structure of
 your choice).
 
-16. Inspired by our definition of ordered pairs, propose a data structure capable of representing ordered tripes. That is,
+* Inspired by our definition of ordered pairs, propose a data structure capable of representing ordered tripes. That is,
 
         (((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.
 
-17. 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.
+* 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.
 
 You can help yourself to the following definition:
 
     (define add (lambda (x) (lambda (y) (+ x y))))
 
-18. [Super hard, unless you have lots of experience programming] Write a function that reverses the order of the elements in a list.
+* Write a function that reverses the order of the elements in a list. [Only attempt this problem if you're feeling frisky, it's super hard unless you have lots of experience programming.]