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,
-reasonable map and filter functions for version 3 lists are within our
+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#
(a) (b) (c)
.
/|\ /\ /\
- / | \ /\ 3 1/\
+ / | \ /\ 3 1 /\
1 2 3 1 2 2 3
[[1];[2];[3]] [[[1];[2]];[3]] [[1];[[2];[3]]]
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.#
+2. Write a function that counts the number of leaves.