X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment3.mdwn;h=f93afd6110ce1e32550d37639f6f7ac7f3a77bc4;hp=d00dba0b2cbbfa44a6adc84668e145aa6e96a7b6;hb=b059b718b62f3b4beffb3bd7fbe66af01069f9c9;hpb=97cbee46cb35e1eb7aa5ea5f8b1af3583f5b7522;ds=sidebyside diff --git a/assignment3.mdwn b/assignment3.mdwn index d00dba0b..f93afd61 100644 --- a/assignment3.mdwn +++ b/assignment3.mdwn @@ -4,92 +4,94 @@ Assignment 3 Once again, the lambda evaluator will make working through this assignment much faster and more secure. -*Writing recursive functions on version 1 style lists* +##Writing recursive functions on version 1 style lists## Recall that version 1 style lists are constructed like this: - - -do eta-reductions too - - - - - -
+2. Using the `length` function as a model, and using the predecessor +function, write a function that computes factorials. (Recall that n!, +the factorial of n, is n times the factorial of n-1.) + +Warning: my browser isn't able to compute factorials of numbers +greater than 2 (it does't provide enough resources for the JavaScript +interpreter; web pages are not supposed to be that computationally +intensive). + + +3. 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 nil))) ~~> false + +4. Now write the same function, but don't use the length function (hint: use `leq` as a model). + +##Trees## + +Since we'll be working with linguistic objects, let's approximate +trees as follows: a tree is a version 1 list +a Church number is a tree, and +if A and B are trees, then (make-pair A B) is a tree. + + + + +[The following should be correct, but won't run in my browser: + +let factorial = Y (\fac n. isZero n 1 (mult n (fac (predecessor n)))) in + ++let reverse = + Y (\rev l. isNil l nil + (isNil (tail l) l + (makeList (head (rev (tail l))) + (rev (makeList (head l) + (rev (tail (rev (tail l))))))))) in + +reverse (makeList 1 (makeList 2 (makeList 3 nil)))- + +It may require more resources than my browser is willing to devote to +JavaScript.] +