X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment3.mdwn;h=6f4f3f64f2bdda0ca0a12729271ef413e3a8eeee;hp=e91eeee58765ddf36d5f331b42de2d8e6ee84c5e;hb=fcaf8b03257c825dcacad9882a695560273f5812;hpb=4b32ef1b335f61cabb654b2e5c91ba3611b42650 diff --git a/assignment3.mdwn b/assignment3.mdwn index e91eeee5..6f4f3f64 100644 --- a/assignment3.mdwn +++ b/assignment3.mdwn @@ -36,7 +36,8 @@ let isZero = \n. n (\x. false) true in let succ = \n s z. s (n s z) in let mult = \m n s. m (n s) in let length = Y (\length l. isNil l 0 (succ (length (tail l)))) in -let pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil))) in +let pred = \n. isZero n 0 (length (tail (n (\p. makeList meh p) nil))) +in let leq = \m n. isZero(n pred m) in let eq = \m n. and (leq m n)(leq n m) in @@ -57,21 +58,27 @@ greater than 2 (it does't provide enough resources for the JavaScript interpreter; web pages are not supposed to be that computationally intensive). -3. (Easy) Write a function `listLenEq` that returns true just in case two lists have the +3. (Easy) Write a function `listLenEq` that returns true just in case +two lists have the same length. That is, - listLenEq mylist (makeList meh (makeList meh (makeList meh nil))) ~~> true + listLenEq mylist (makeList meh (makeList meh (makeList meh nil))) + ~~> true listLenEq mylist (makeList meh (makeList meh nil))) ~~> false -4. (Still easy) Now write the same function, but don't use the length function. +4. (Still easy) Now write the same function, but don't use the length +function. -5. In assignment 2, we discovered that version 3-type lists (the ones that +5. In assignment 2, we discovered that version 3-type lists (the ones +that work like Church numerals) made it much easier to define operations -like `map` and `filter`. But now that we have recursion in our toolbox, +like `map` and `filter`. But now that we have recursion in our +toolbox, reasonable map and filter functions for version 1 lists are within our -reach. Give definitions for `map` and a `filter` for verson 1 type lists. +reach. Give definitions for `map` and a `filter` for verson 1 type +lists. #Computing with trees#