X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment3.mdwn;h=6f4f3f64f2bdda0ca0a12729271ef413e3a8eeee;hp=c4ea316287a62ceb9de2af825b31d6a53877470f;hb=fcaf8b03257c825dcacad9882a695560273f5812;hpb=e4ea387ecb1a2dcb069060afccbe8ac1e70f7061 diff --git a/assignment3.mdwn b/assignment3.mdwn index c4ea3162..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# @@ -111,23 +118,23 @@ trees. Expected behavior:
```-let t1 = (make-list 1 nil) in
-let t2 = (make-list 2 nil) in
-let t3 = (make-list 3 nil) in
-let t12 = (make-list t1 (make-list t2 nil)) in
-let t23 = (make-list t2 (make-list t3 nil)) in
-let ta = (make-list t1 t23) in
-let tb = (make-list t12 t3) in
-let tc = (make-list t1 (make-list t23 nil)) in
-
-count-leaves t1 ~~> 1
-count-leaves t2 ~~> 2
-count-leaves t3 ~~> 3
-count-leaves t12 ~~> 3
-count-leaves t23 ~~> 5
-count-leaves ta ~~> 6
-count-leaves tb ~~> 6
-count-leaves tc ~~> 6
+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
+
+sum-leaves t1 ~~> 1
+sum-leaves t2 ~~> 2
+sum-leaves t3 ~~> 3
+sum-leaves t12 ~~> 3
+sum-leaves t23 ~~> 5
+sum-leaves ta ~~> 6
+sum-leaves tb ~~> 6
+sum-leaves tc ~~> 6
```
2. Write a function that counts the number of leaves.