X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=exercises%2F_assignment6.mdwn;h=b6a00dedd31771e23b6cfc49627b9ca4b87d8f28;hp=0f654f25daa146fb0dc4953bf9a861ebd77e47fa;hb=35de8baadf52a3f6488fbd0463cdc331a4ea02e3;hpb=ff5b3f5a76fb744b332bc5d0fb3ef5632ce02879

diff --git a/exercises/_assignment6.mdwn b/exercises/_assignment6.mdwn
index 0f654f25..b6a00ded 100644
--- a/exercises/_assignment6.mdwn
+++ b/exercises/_assignment6.mdwn
@@ -134,8 +134,9 @@ piece, which we can think of as a function from a type to a type.
 Call this type function M, and let P, Q, R, and S be variables over types.
 
 Recall that a monad requires a singleton function 1:P-> MP, and a
-composition operator >=>: (P->MQ) -> (Q->MR) -> (R->MS) that obey the
-following laws:
+composition operator >=>: (P->MQ) -> (Q->MR) -> (P->MR) [the type for
+the composition operator given here corrects a "type"-o from the class handout]
+that obey the following laws:
 
     1 >=> k = k
     k >=> 1 = k 
@@ -164,3 +165,24 @@ More specifically,
 Then the obvious singleton for the Option monad is \p.Just p.  Give
 (or reconstruct) the composition operator >=> we discussed in class.
 Show your composition operator obeys the monad laws.
+
+2. Do the same with crossy lists.  That is, given an arbitrary type
+'a, let the boxed type be a list of objects of type 'a.  The singleton
+is `\p.[p]`, and the composition operator is 
+
+       >=> (first:P->[Q]) (second:Q->[R]) :(P->[R]) = fun p -> [r | q <- first p, r <- second q]
+
+Sanity check: 
+
+    f p = [x, x+1]
+    s q = [x*x, x+x]
+    >=> f s 7 = [49, 14, 64, 16]
+
+3. Do the same for zippy lists.  That is, you need to find a
+composition operator such that
+
+    f p = [x, x+1]
+    s q = [x*x, x+x]
+    >=> f s 7 = [49, 64]
+
+and then prove it obeys the monad laws.