On Wed, Feb 15, 2017 at 12:01 PM, Laurent Christophe
Hi guys, the way `StateT` are implemented as `Applicative` have been buggling my mind for some time. https://hackage.haskell.org/package/transformers-0.5.2.0/ docs/src/Control.Monad.Trans.State.Lazy.html#line-201
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? https://www.haskell.org/haskellwiki/Applicative_functor#Applicative_ transfomers
StateT s m is not a composition of applicative functors. It allows two-way
communication between the state and the underlying monad m.
Like Compose m (State s), effects in m can affect how the state evolves.
Like Compose (State s) m, the state can influence what effects occur in m.
For example, StateT s Maybe will discard changes to the state if a
subcomputation returns Nothing and permits subcomputations to choose
whether to return Nothing based on the state. No applicative composition of
State s and Maybe can do both.
These limitations are implied by the underlying types:
Compose m (State s) a = m (s -> (a, s))
Compose (State s) m a = s -> (m a, s)
StateT s m a = s -> m (a, s)
--
Dave Menendez