On Sat, Feb 23, 2008 at 8:00 AM, Harri Kiiskinen wrote:

then why does

let i = fmap (^4) [1,2,3] in shows i " "

give

"[1,16,81] "

I'll probably mess this up somewhere, but if I do, reset assured that someone else here will correct me ;) fmap (^4) [1,2,3] == [1,16,81] so shows " " of that == "[1,16,81] " (note the trailing space), obvious I hope. However, [1,16,81] >>= \i -> shows i " " operates in the list monad. I can't find the actual instance of Monad [] right now, but it will apply 'shows i " "' to each element in the first list and concat the results. Since strings are just [Char], concating them is string concatenation. And so you have "1 16 81 " (again, note the trailing space) AGL -- Adam Langley agl@imperialviolet.org http://www.imperialviolet.org

Harri Kiiskinen wrote:

fmap (^4) [1,2,3] >>= \i -> shows i " " let i = fmap (^4) [1,2,3] in shows i " "

Probably very simple, but there must be a delicate difference between these two expressions. I just don't get it.

First, let's simplify these expressions using the following equation: fmap (^4) [1,2,3] == [1,16,81] So, we have x1 = [1,16,81] >>= \i -> shows i " " x2 = let i = [1,16,81] in shows i " " Let's examine the x2 first. We can substitute i, and obtain shows [1,16,81] " " note that the whole list is passed to shows. shows then "prints" it to a string, using the notation for lists, and adds a trailing space. Note that shows is called here with type: shows :: [Integer] -> String -> String Now, we consider x1. Here >>= is invoked for the list monad, which extracts each member 1,16,81 from the list and applies shows to them separately, and concatenates all the results. In other words, we can rewrite x1 as: shows 1 " " ++ shows 16 " " ++ shows 81 " " Note that here we pass single elements to shows, and not the whole list. Indeed, here we are calling shows at a different type: shows :: Integer -> String -> String But this is fine, since shows knows how to print Integers as well as lists of them. Concluding: the monadic bind operator >>= is not function application.