[Haskell-cafe] Applicative transformers

[David Menendez]

On Wed, Feb 15, 2017 at 12:01 PM, 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.
> 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 <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>
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