fix links to v4 lists

[lambda.git] / assignment3.mdwn

diff --git a/assignment3.mdwn b/assignment3.mdwn
index c7c5be4..6f4f3f6 100644 (file)
--- 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 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
 
 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).
 
 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,
 
 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
 
 
 
      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
 work like Church numerals) made it much easier to define operations

-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 `map` and a `filter` for verson 1 type lists.
+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.

 
 #Computing with trees#
 
 
 #Computing with trees#
 


@@ -89,7 +96,7 @@ Then we have the following representations:
    (a)           (b)             (c)  
     .
    /|\            /\              /\
    (a)           (b)             (c)  
     .
    /|\            /\              /\

-  / | \          /\ 3             1/\
+  / | \          /\ 3            1 /\

   1 2  3        1  2               2 3
 
 [[1];[2];[3]]  [[[1];[2]];[3]]   [[1];[[2];[3]]]
   1 2  3        1  2               2 3
 
 [[1];[2];[3]]  [[[1];[2]];[3]]   [[1];[[2];[3]]]


@@ -111,23 +118,23 @@ trees.
 Expected behavior:
 
 <pre>
 Expected behavior:
 
 <pre>

-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

 </pre>
 
 2.   Write a function that counts the number of leaves.
 </pre>
 
 2.   Write a function that counts the number of leaves.