I am learning about the Writer Monad on the book Learn You A Haskell.
this is the piece of code:
import Control.Monad.Writer
logNumber :: Int -> Writer [String] Int
logNumber num = writer (num, ["Got number: " ++ show num])
multWithLog :: Writer [String] Int
multWithLog = do
a <- logNumber 3
b <- logNumber 5
return (a * b)
When running multWithLog, this is the result:
*Main> runWriter multWithLog
(15,["Got number: 3","Got number: 5"])
On this lines:
a <- logNumber 3
b <- logNumber 5
It is easy to see that a = 3 and b = 5, since both of them are being multiplied on the return function.
What I don't understand is why those values are 3 and 5. Shouldn't a and b be the values that contain inside the Writer Monad? In this case tuples?
For example, with this was with the Maybe Monad, a and bwould be 3 and 5:
do
a <- Just 3
b <- Just 5
return (a * b)
In this case it makes sense to me, since a and b receive the content inside Just. But with the initial example, a and b only receive part of the value.
It is easy to see that a = 3 and b = 5, since both of them are being multiplied on the return function. What I don't understand is why those values are 3 and 5. Shouldn't a and b be the values that contain inside the Writer Monad? In this case tuples?
No. I think the simplest way to answer this is to just implement the Writer type and study its Monad class instance:
newtype Writer w a = Writer { runWriter :: (a, w) }
instance Functor (Writer w) where
fmap f (Writer (a, w)) = Writer (f a, w)
instance Monoid w => Applicative (Writer w) where
pure a = Writer (a, mempty)
Writer (f, w) <*> Writer (a, w') = Writer (f a, w <> w')
instance Monoid w => Monad (Writer w) where
return = pure
Writer (a, w) >>= f = let (b, w') = runWriter (f a)
in Writer (b, w <> w')
tell :: w -> Writer w ()
tell w = Writer ((), w)
As you can see in the instance method for >>=, the function f is applied to the a value, not the whole tuple. The syntax a <- logNumber 3 is desugared using >>=, so the value that's bound to a will be the first element of the tuple that Writer wraps around.