[Haskell-cafe] Applicative transformers
will.yager at gmail.com
Wed Feb 15 18:03:38 UTC 2017
StateT mf <*> StateT mx
mf :: s -> m (a -> b, s)
mx :: s -> m (a, s)
We have (s :: s) in scope. We can apply mf to s no problem. Now what do we do with mx? We also need to give it (_ :: s). We could give it the same s we gave mf, but that would be wrong. It would ignore any state changes in mf.
So the correct option is to use the s value returned by mf. But there's no way to get it out of the monad. You could use the functor properties of m to get
fmap (\(s, f) -> fmap (\(s, a) -> (s, f a)) (mx s)) (mf s)
Which has type
m (m (s, b))
So you still need a monadic join to get the desired result.
The applicative instance doesn't really help as far as I can tell because it doesn't let you do anything to things of the form
x -> m y
Which is what StateT is made of.
> On Feb 15, 2017, at 11:01 AM, Laurent Christophe <lachrist at vub.ac.be> wrote:
> Hi guys, the way `StateT` are implemented as `Applicative` have been buggling my mind for some time.
> instance (Functor m, Monad m) => Applicative (StateT s m) where
> pure a = StateT $ \ s -> return (a, s)
> StateT mf <*> StateT mx = StateT $ \ s -> do
> (f, s') <- mf s
> (x, s'') <- mx s'
> return (f x, s'')
> Using dependant monadic computations, this implementation cannot be expressed in term of applicative.
> This explains why we cannot have `instance (Applicative m) => Applicative (State s m)`.
> However using real monadic style computations for implementing `<*>` buggles my mind.
> Moreover `liftA2 (<*>)` can be used to generically compose applicative functors so why monads are needed?
> Any inputs would be greatly appreciated!
> Haskell-Cafe mailing list
> To (un)subscribe, modify options or view archives go to:
> Only members subscribed via the mailman list are allowed to post.
-------------- next part --------------
An HTML attachment was scrubbed...
More information about the Haskell-Cafe