X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment2.mdwn;h=066f1b1f60b6863e8738e2604bd2d8748b53a7ed;hp=65fe479ccb1357c6711e689115b38cefb8df757b;hb=7bffcdc79c27f459cb7d451f23b4ce8e5b39b125;hpb=8aa265f15b21b2f78be32a940f8df98720387c1b diff --git a/assignment2.mdwn b/assignment2.mdwn index 65fe479c..066f1b1f 100644 --- a/assignment2.mdwn +++ b/assignment2.mdwn @@ -56,6 +56,7 @@ The `junk` in `extract-head` is what you get back if you evaluate: As we said, the predecessor and the extract-tail functions are harder to define. We'll just give you one implementation of these, so that you'll be able to test and evaluate lambda-expressions using them in Scheme or OCaml.
predecesor ≡ (\shift n. n shift (make-pair zero junk) get-second) (\pair. pair (\fst snd. make-pair (successor fst) fst))
+
 extract-tail ≡ (\shift lst. lst shift (make-pair empty junk) get-second) (\hd pair. pair (\fst snd. make-pair (make-list hd fst) fst))
The `junk` is what you get back if you evaluate: @@ -87,7 +88,7 @@ For these exercises, assume that `LIST` is the result of evaluating: should evaluate to a list containing just those of `a`, `b`, `c`, `d`, and `e` such that `f` applied to them evaluates to `true`. -
  • How would you implement map using the either the version 1 or the version 2 implementation of lists? +
  • What goes wrong when we try to apply these techniques using the version 1 or version 2 implementation of lists?
  • Our version 3 implementation of the numbers are usually called "Church numerals". If `m` is a Church numeral, then `m s z` applies the function `s` to the result of applying `s` to ... to `z`, for a total of *m* applications of `s`, where *m* is the number that `m` represents or encodes.