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-Reduction
----------
-
-Find "normal forms" for the following (that is, reduce them as far as it's possible to reduce 
-them):
-
-    1. (\x \y. y x) z
-    2. (\x (x x)) z
-    3. (\x (\x x)) z
-    4. (\x (\z x)) z
-    5. (\x (x (\y y))) (\z (z z))
-    6. (\x (x x)) (\x (x x))
-    7. (\x (x x x)) (\x (x x x))
-
-
-Booleans
---------
-
-Recall our definitions of true and false.
-
-	"true" defined to be `\t \f. t`
-	"false" defined to be `\t \f. f`
-
-In Racket, these can be defined like this:
-
-	(define true (lambda (t) (lambda (f) t)))
-	(define false (lambda (t) (lambda (f) f)))
-
-* Define a "neg" operator that negates "true" and "false".
-
-Expected behavior: 
-
-    (((neg true) 10) 20)
-
-evaluates to 20, and 
-
-    (((neg false) 10) 20)
-
-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
-    true xor false = true
-    false xor true = true
-    false xor false = false
-
-)
-
-* Inspired by our definition of boolean values, propose a data structure
-capable of representing one of the two values "black" or "white". 
-If we have
-one of those values, call it a black-or-white-value, we should be able to
-write:
-
-      	the-black-or-white-value if-black if-white
-
-(where if-black and if-white are anything), and get back one of if-black or
-if-white, depending on which of the black-or-white values we started with. Give
-a definition for each of "black" and "white". (Do it in both lambda calculus
-and also in Racket.)
-
-* Now propose a data structure capable of representing one of the three values
-"red" "green" or "blue," based on the same model. (Do it in both lambda
-calculus and also in Racket.)
-
-
-
-Pairs
------
-
-Recall our definitions of ordered pairs.
-
-        the pair (x,y) is defined as `\f. f x y`
-
-To extract the first element of a pair p, you write:
-
-        p (\fst \snd. fst)
-
-Here are some defintions in Racket:
-
-        (define make-pair (lambda (fst) (lambda (snd) (lambda (f) ((f fst) snd)))))
-        (define get-first (lambda (fst) (lambda (snd) fst)))
-        (define get-second (lambda (fst) (lambda (snd) snd)))
-
-Now we can write:
-
-        (define p ((make-pair 10) 20))
-        (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 like, you can disguise what's going on like this:
-
-        (define lifted-get-first (lambda (p) (p get-first)))
-        (define lifted-get-second (lambda (p) (p get-second)))
-
-Now you can write:
-
-        (lifted-get-first p)
-
-instead of:
-
-        (p get-first)
-
-However, the latter is still what's going on under the hood.
-
-
-* Define a "swap" function that reverses the elements of a pair.
-
-Expected behavior:
-
-        (define p ((make-pair 10) 20))
-        ((p swap) get-first) ; evaluates to 20
-        ((p swap) get-second) ; evaluates to 10
-
-Write out the definition of swap in Racket.
-
-
-* 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
-
-* Define a "sixteen" function that makes
-sixteen copies of its argument (and stores them in a data structure of
-your choice).
-
-* 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.
-
-* 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))))
-
-* [Only attempt this if you're feeling frisky, it's super hard unless you have lots of experience programming] Write a function that reverses the order of the elements in a list.