Do notation for monad in function returning a different type

Question

Is there a way to write do notation for a monad in a function which the return type isn't of said monad?

I have a main function doing most of the logic of the code, supplemented by another function which does some calculations for it in the middle. The supplementary function might fail, which is why it is returning a Maybe value. I'm looking to use the do notation for the returned values in the main function. Giving a generic example:

-- does some computation to two Ints which might fail
compute :: Int -> Int -> Maybe Int

-- actual logic 
main :: Int -> Int -> Int
main x y = do
  first <- compute x y
  second <- compute (x+2) (y+2)
  third <- compute (x+4) (y+4)
  -- does some Int calculation to first, second and third

What I intend is for first, second, and third to have the actual Int values, taken out of the Maybe context, but doing the way above makes Haskell complain about not being able to match types of Maybe Int with Int.

Is there a way to do this? Or am I heading towards the wrong direction?

Pardon me if some terminology is wrongly used, I'm new to Haskell and still trying to wrap my head around everything.

EDIT

main has to return an Int, without being wrapped in Maybe, as there is another part of the code using the result of mainas Int. The results of a single compute might fail, but they should collectively pass (i.e. at least one would pass) in main, and what I'm looking for is a way to use do notation to take them out of Maybe, do some simple Int calculations to them (e.g. possibly treating any Nothing returned as 0), and return the final value as just Int.

Answer 1

Well the signature is in essence wrong. The result should be a Maybe Int:

main :: Int -> Int -> Maybe Int
main x y = do
  first <- compute x y
  second <- compute (x+2) (y+2)
  third <- compute (x+4) (y+4)
  return (first + second + third)

For example here we return (first + second + third), and the return will wrap these in a Just data constructor.

This is because your do block, implicitly uses the >>= of the Monad Maybe, which is defined as:

instance Monad Maybe where
    Nothing >>=_ = Nothing
    (Just x) >>= f = f x
    return = Just

So that means that it will indeed "unpack" values out of a Just data constructor, but in case a Nothing comes out of it, then this means that the result of the entire do block will be Nothing.

This is more or less the convenience the Monad Maybe offers: you can make computations as a chain of succesful actions, and in case one of these fails, the result will be Nothing, otherwise it will be Just result.

You can thus not at the end return an Int instead of a Maybe Int, since it is definitely possible - from the perspective of the types - that one or more computations can return a Nothing.

You can however "post" process the result of the do block, if you for example add a "default" value that will be used in case one of the computations is Nothing, like:

import Data.Maybe(fromMaybe)

main :: Int -> Int -> Int
main x y = fromMaybe 0 $ do
  first <- compute x y
  second <- compute (x+2) (y+2)
  third <- compute (x+4) (y+4)
  return (first + second + third)

Here in case the do-block thus returns a Nothing, we replace it with 0 (you can of course add another value in the fromMaybe :: a -> Maybe a -> a as a value in case the computation "fails").

If you want to return the first element in a list of Maybes that is Just, then you can use asum :: (Foldable t, Alternative f) => t (f a) -> f a, so then you can write your main like:

-- first non-failing computation

import Data.Foldable(asum)
import Data.Maybe(fromMaybe)

main :: Int -> Int -> Int
main x y = fromMaybe 0 $ asum [
    compute x y
    compute (x+2) (y+2)
    compute (x+4) (y+4)
]

Note that the asum can still contain only Nothings, so you still need to do some post-processing.

Answer 2

I have two interpretations of your question, so to answer both of them:

Sum the Maybe Int values that are Just n to get an Int

To sum Maybe Ints while throwing out Nothing values, you can use sum with Data.Maybe.catMaybes :: [Maybe a] -> [a] to throw out Nothing values from a list:

sum . catMaybes $ [compute x y, compute (x+2) (y+2), compute (x+4) (y+4)]

Get the first Maybe Int value that's Just n as an Int

To get the first non-Nothing value, you can use catMaybes combined with listToMaybe :: [a] -> Maybe a to get Just the first value if there is one or Nothing if there isn't and fromMaybe :: a -> Maybe a -> a to convert Nothing to a default value:

fromMaybe 0 . listToMaybe . catMaybes $ [compute x y, compute (x+2) (y+2), compute (x+4) (y+4)]

If you're guaranteed to have at least one succeed, use head instead:

head . catMaybes $ [compute x y, compute (x+2) (y+2), compute (x+4) (y+4)]

Answer 3

Willem's answer is basically perfect, but just to really drive the point home, let's think about what would happen if you could write something that allows you to return an int.

So you have the main function with type Int -> Int -> Int, let's assume an implementation of your compute function as follows:

compute :: Int -> Int -> Maybe Int
compute a 0 = Nothing
compute a b = Just (a `div` b)

Now this is basically a safe version of the integer division function div :: Int -> Int -> Int that returns a Nothing if the divisor is 0.

If you could write a main function as you like that returns an Int, you'd be able to write the following:

unsafe :: Int
unsafe = main 10 (-2)

This would make the second <- compute ... fail and return a Nothing but now you have to interpret your Nothing as a number which is not good. It defeats the whole purpose of using Maybe monad which captures failure safely. You can, of course, give a default value to Nothing as Willem described, but that's not always appropriate.

More generally, when you're inside a do block you should just think inside "the box" that is the monad and don't try to escape. In some cases like Maybe you might be able to do unMaybe with something like fromMaybe or maybe functions, but not in general.