(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
+2. Do the same with lists. That is, given an arbitrary type
+'a, let the boxed type be ['a], i.e., 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]
+ >=> (first:P->[Q]) (second:Q->[R]) :(P->[R]) = List.flatten (List.map f (g a))
-Sanity check:
+For example:
f p = [p, p+1]
s q = [q*q, q+q]
>=> 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 = [p, p+1]
- s q = [q*q, q+q]
- >=> f s 7 = [49, 16]
-
-and then prove it obeys the monad laws.