Why sequence requires monad if applicative would suffice?

Question

The signature of sequence is

sequence :: Monad m => t (m a) -> m (t a)

But we can implement it as

sequence = traverse id

requiring m to be just Applicative . If monads are applicatives then why bother having this constraint on type level?

Answer 1

There are many functions in Haskell that are equivalent but distinct because Applicative (resp. Functor ) didn't use to be a superclass of Monad . For example:

• return vs. pure

• ap vs. <*>

• liftM vs. liftA vs. fmap

• liftM2 , liftM3 , &c. vs. liftA2 , liftA3 , &c.

• mapM / forM vs. traverse / for

• mapM_ / forM_ vs. traverse_ / for_

• sequence vs. sequenceA

• mzero & mplus (from MonadPlus ) vs. empty & <|> (from Alternative )

The old functions with their original Monad signatures are still present, but in new code, since the Applicative–Monad Proposal (AMP) was implemented, you can always use the Applicative versions because they're slightly more general—that is, you can always replace return with pure , but not vice versa.