Do notation for monad in function returning a different type

do notation haskell
haskell bind operator
maybe monad haskell
state monad
monad laws
haskell return
haskell io monad
haskell list monad

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.

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.

A Fistful of Monads, We even saw how to map a function a -> b over other functions of type r -> a to get m a, how do you apply to it a function that takes a normal a and returns a We've already encountered do notation when we were doing I/O and there we​  In fact it is a Writer monad using the Builder type, and all you need is just the Builder monoid. Even more unfortunate, the applicative functors were introduced to Haskell's standard libraries only after monads and arrows, thus many types were instances of the Monad and Arrow classes, but not instances of Applicative.

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.

All About Monads, There are as many different type of monads as there are strategies for combining computations, but there The return function puts a value into a monad container. Here is a sample of do notation using the Maybe monad:  m a is a container holding a value of type a. The return function puts a value into a monad container. The >>= function takes the value from a monad container and passes it to a function to produce a monad container containing a new value, possibly of a different type.

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)]

Do notation considered harmful, It contains the Put monad, which in principle has nothing to do with a a new function called void that makes ignoring of return values explicit:  The first function that the Monad type class defines is return. It's the same as pure, only with a different name. Its type is (Monad m) => a -> m a. It takes a value and puts it in a minimal default context that still holds that value. In other words, it takes something and wraps it in a monad.

Haskell/do notation, result was of the type IO () , i.e. an empty value in the IO monad. This example will "return" the full name as a string inside the IO monad, which will be assigned to the variable "name" in our new function. The de-sugared version is simply a regular let expression where the in part is whatever follows from the do syntax. Returning values . The last statement in do notation is the overall result of the do block. In the previous example, the result was of the type IO (), i.e. an empty value in the IO monad.

Monad (functional programming), In functional programming, a monad is a design pattern that allows structuring programs return :: a -> M a (also called unit) which wraps any value of type a into a The do notation in haskell, for instance, allows to write monadic code blocks as function types s -> a from a common source s , is another canonical example  Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression. As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Lesson 31. Making Monads easier with do-notation, Gxz do-notation rv ymspifil working with Monad a; Xalrtsnae ltxm Monad But the use of the Monad methods >>= , >> , and return quickly becomes cumbersome. as an echo function, using >>= is often easier than doing things with do-notation. This task should be similar to the types of problems you solved in unit 4. When using do-notation and a monad like State or IO programs look very much like programs written in an imperative language as each line contains a statement that can change the simulated global state of the program and optionally binds a (local) variable that can be used by the statements later in the code block.

Comments
  • The point is that these calculations should result in a Maybe as well, or if not, you can use a return.
  • Not sure what you're referring to, compute or main? Either way, compute already returns a Maybe value, while main is intended to definitely return an Int, hence no Maybe. In other words, one of the calculations in main might fail, but at least one should pass which guarantees that main has an Int return value.
  • but the idea of a Monad Maybe is to see Maybes as "potentially failing" computations. So here you make a "chain" of potentially failing computations, and return Just result in case it succeeds, and Nothing otherwise. If you are sure compute will always return an Just _, then why does it have the signature Int -> Int -> Maybe Int?
  • Thanks, your comment that refers to it as a chain of successful actions made it clearer to me, and I realize I actually am going in the wrong direction. What I intend is not for it to be a chain of actions, but a series of computations (which any might fail, but one is guaranteed to pass), and returning the first out of the series that passed. In essence, what main is doing is abstracting away the possible failures and choosing the first that succeeds, so that a definite Int value can be used elsewhere when it calls main. Is there a way to do this?
  • @lookarpthestars: you could use asum for that, like asum [compute x y, compute (x+2) (y+2)], which will return the first Just in the list, but this is still a Maybe, since it is possible that all computations fail.
  • See: hackage.haskell.org/package/base-4.12.0.0/docs/…
  • Sweet, this comment along with the part you added after the edit gives me something to work from. Appreciate the concise answer.
  • @lookarpthestars to your first comment, no, main is not "choosing the first that succeeds". only if all three computations succeed it returns a Just (with the sum of three results). otherwise it returns Nothing. so it tries to run all of them (one after another, but all of them) and then combine all the results.