* 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
Here are some defintions 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:
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))
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.
-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.
+* [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.