X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=ef1c561ca349fdb54a3fb17fd1e838bbeaf20232;hp=bfaafdc0acae1d1cad18d6bfdf36c927ba2ded0a;hb=043cdafb6314cb4e7afb5c474e96064ad6ffa7cf;hpb=567ca6641f7c2f470cd0003e32efeab52ab9c9c9 diff --git a/assignment1.mdwn b/assignment1.mdwn index bfaafdc0..ef1c561c 100644 --- a/assignment1.mdwn +++ b/assignment1.mdwn @@ -27,6 +27,7 @@ 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 +41,7 @@ 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 @@ -82,8 +84,8 @@ To extract the first element of a pair p, you write: 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: @@ -109,7 +111,8 @@ 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 +122,27 @@ 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. -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.