From 101b2a435c05ae480eaefaf30348e80bd2d3de5d Mon Sep 17 00:00:00 2001 From: Chris Barker Date: Mon, 27 Sep 2010 14:57:57 -0400 Subject: [PATCH] edits --- assignment3.mdwn | 45 ++++++++------------------------------------- 1 file changed, 8 insertions(+), 37 deletions(-) diff --git a/assignment3.mdwn b/assignment3.mdwn index 9039a957..775eb79e 100644 --- a/assignment3.mdwn +++ b/assignment3.mdwn @@ -65,13 +65,13 @@ same length. That is, listLenEq mylist (makeList meh (makeList meh nil))) ~~> false -4. (Still easy) Now write the same function, but don't use the length function (hint: use `leq` as a model). +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 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 3 lists are within our -reach. Give definitions for such a map and a filter. +reach. Give definitions for `map` and a `filter` for verson 1 type lists. 6. Linguists analyze natural language expressions into trees. We'll need trees in future weeks, and tree structures provide good @@ -94,16 +94,17 @@ Then we have the following representations: Limitations of this scheme include the following: there is no easy way -to label a constituent (typically a syntactic category, S or NP or VP, +to label a constituent with a syntactic category (S or NP or VP, etc.), and there is no way to represent a tree in which a mother has a single daughter. When processing a tree, you can test for whether the tree contains only a numeral (in which case the tree is leaf node) by testing for whether the length of the list is less than or equal to 1. This will -be your base case for your recursive functions that operate on trees. +be your base case for your recursive functions that operate on these +trees. -Write a function that sums the number of leaves in a tree. +#Write a function that sums the number of leaves in a tree.# Expected behavior:
@@ -127,35 +128,5 @@ count-leaves tb ~~> 6
 count-leaves tc ~~> 6
 
 
-Write a function that counts the number of leaves.
+#Write a function that counts the number of leaves.#
 
-
-
-
-[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.] - -; trees -let t1 = (makeList 1 nil) in -let t2 = (makeList 2 nil) in -let t3 = (makeList 3 nil) in -let t12 = (makeList t1 (makeList t2 nil)) in -let t23 = (makeList t2 (makeList t3 nil)) in -let ta = (makeList t1 t23) in -let tb = (makeList t12 t3) in -let tc = (makeList t1 (makeList t23 nil)) in -- 2.11.0