X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=9c7eaf552677f56c997890a4c2a29b8ea5340a0f;hp=560d288ebc4e7687af786a57f1eccb4a67b05fca;hb=aa7244316365eb60642e4ab70bee7cfcc427593b;hpb=8f9abe589a3b7c615b72adc6cbf57e7de1d931d3 diff --git a/assignment1.mdwn b/assignment1.mdwn index 560d288e..9c7eaf55 100644 --- a/assignment1.mdwn +++ b/assignment1.mdwn @@ -81,7 +81,7 @@ 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 (lambda (fst) (lambda (snd) fst))) @@ -93,7 +93,7 @@ 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: @@ -111,7 +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)) @@ -121,27 +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. +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.]