From d541a6500e8d82e1a8862924dca00c360d482c6a Mon Sep 17 00:00:00 2001 From: barker Date: Mon, 13 Sep 2010 09:37:06 -0400 Subject: [PATCH] --- assignment1.mdwn | 34 ++++++++++++++++------------------ 1 file changed, 16 insertions(+), 18 deletions(-) diff --git a/assignment1.mdwn b/assignment1.mdwn index 313db956..9be95780 100644 --- a/assignment1.mdwn +++ b/assignment1.mdwn @@ -74,28 +74,32 @@ Here are some defintions in Racket: (define get-second (lamda (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 seco\ -nd, think about why it's being done this way: the pair is a package that takes a function for op\ -erating 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. 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. 13. 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 @@ -106,30 +110,24 @@ Write out the definition of swap in Racket. 14. 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 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 representin\ -g 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 de\ -fining 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. +16. Inspired by our definition of ordered pairs, propose a data structure capable of representing ordered tripes. That is, -> I expect some to come back with the lovely -> (\f. f first second third) -> and others, schooled in a certain mathematical perversion, to come back -> with: -> (\f. f first (\g. g second third)) + (((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 add\ -ing the second and third members of the triple. +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. 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. -- 2.11.0