X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=exercises%2F_assignment6.mdwn;h=ebc20e064bc1ad1f7d02756ad8a015913dfaea9d;hp=50e89ac84d80e7357c0c6d1c298fed12aecbc53c;hb=b13412acbd429e1cc83669d6e881e3d9e98fbda3;hpb=b04c88ae4081976cc721ab9e9fb0b89bd5962942 diff --git a/exercises/_assignment6.mdwn b/exercises/_assignment6.mdwn index 50e89ac8..ebc20e06 100644 --- a/exercises/_assignment6.mdwn +++ b/exercises/_assignment6.mdwn @@ -134,8 +134,8 @@ 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) -> (P->MR) [type type for -the composition operator corrects a "type"-o from the class handout] +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 @@ -166,23 +166,15 @@ 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 +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 = [x, x+1] - s q = [x*x, x+x] - >=> f s 7 = [49, 14, 64, 16] + 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 = [x, x+1] - s q = [x*x, x+x] - >=> f s 7 = [49, 64] - -and then prove it obeys the monad laws.