X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=fa02cb83634bd078c64230e2b5b97f244a68e460;hp=453fa546366dd175a19ca23db676c9a5fd5179db;hb=792521cd3b2e337d425aadc7d8f09a2eab2eb391;hpb=4abee3b6356890888890b4907fb4c7a24bc4656e diff --git a/assignment1.mdwn b/assignment1.mdwn index 453fa546..fa02cb83 100644 --- a/assignment1.mdwn +++ b/assignment1.mdwn @@ -17,8 +17,8 @@ Booleans Recall our definitions of true and false. -> **true** defined to be `\t \f. t` -> **false** defined to be `\t \f. f` +> **true** is defined to be `\t \f. t` +> **false** is defined to be `\t \f. f` In Racket, these can be defined like this: @@ -40,9 +40,7 @@ evaluates to 10.
• Define an `and` operator. -
• Define an `xor` operator. - -If you haven't seen this term before, here's a truth table: +
• 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 @@ -75,7 +73,7 @@ Pairs Recall our definitions of ordered pairs. -> the pair **(**x**,**y**)** is defined as `\f. f x y` +> the pair **(**x**,**y**)** is defined to be `\f. f x y` To extract the first element of a pair p, you write: @@ -93,13 +91,11 @@ 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 +If you're puzzled 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.) +is a package that takes a function for operating on its elements *as an +argument*, and returns *the result of* operating on its elements with that +function. In other words, the pair is a higher-order function. (Consider the similarities between this definition of a pair and a generalized quantifier.) If you like, you can disguise what's going on like this: @@ -114,19 +110,17 @@ instead of: (p get-first) -However, the latter is still what's going on under the hood. +However, the latter is still what's going on under the hood. (Remark: `(lifted-f ((make-pair 10) 20))` stands to `(((make-pair 10) 20) f)` as `(((make-pair 10) 20) f)` stands to `((f 10) 20)`.)
-
1. Define a `swap` function that reverses the elements of a pair. - -Expected behavior: +
2. 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. +Write out the definition of `swap` in Racket.
3. Define a `dup` function that duplicates its argument to form a pair