CODEWITHSUNDEEP
haskellmonadstransformation
user6023611
user6023611

Reputation:

What is difference between those two monad transformers?

I'm familiar with monads, e.g. Reader, Error, and State. Transformers, however, are very new to me, hence this question.

Intuitively, I can tell there is a difference between the following two monad transformers, but I can't quite pinpoint what it is...

ReaderT Env (ErrorT String (StateT Integer Identity)) a

ReaderT Env (StateT Integer (ErrorT String Identity)) a

What makes these two monad transformers different?

Upvotes: 4

Views: 85

Answers (2)

chi
chi

Reputation: 116139

ReaderT Env (ErrorT String (StateT Integer Identity)) a
ReaderT Env (StateT Integer (ErrorT String Identity)) a

Briefly put, in the first errors only depend on the Env input, while the second allows errors to depend on both Env and the Integer state.

Upvotes: 1

leftaroundabout
leftaroundabout

Reputation: 120711

To simplify, compare only the relevant part (which isn't trivially the same):

MaybeT (StateT Integer Identity) a
StateT Integer (MaybeT Identity) a

We know that (ignoring the newtype abstractions)

type MaybeT m a = m (Maybe a)
type StateT s m a = s -> m (a, s)

Hence, the two transformer stack come out to be

MaybeT (Λb. Integer -> (b, Integer)) a
    ≡ Integer -> (Maybe a, Integer)

and

StateT Integer (Λb. Maybe b) a
    ≡ Integer -> Maybe (a, Integer)

So, these aren't exactly the same, the difference being that the latter only yields the state-integer inside of the Maybe. This means, if the MaybeT is down in the stack then the computation must immediately terminate as soon as you get a Nothing, whereas if the MaybeT is used on top then the State can still keep on going.

This is even more drastic with IO: once you get an exception, you can't possibly continue – exceptions can only be caught in IO itself. This is one reason why there can be no IOT transformer.

Upvotes: 5

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