Laws for ProductB are overly restrictive about barbies HOT 4 CLOSED

Thanks for bringing this up! I too saw ProductB as a stronger "applicative", but was somehow convinced that we were in need of the the uniqueness properties that follow from the laws most of the time, so adding an intermediate ApplicativeB class was not worth it.

So I went to see those places where I thought we were using this, and ended up with the exact opposite conclusion: ProductB just captures those types whose unique "applicative" instance can be generated automatically, but I don't think we are actually using the extra "uniqueness" guarantees anywhere else. This is great, I wished I had noticed it before 🙂

So, how should an ApplicativeB class look like? I don't think we can have a direct equivalent of <*> (apply) without something like impredicative-types. So without apply, this would be probably better named MonoidalB.

class FunctorB b => MonoidalB b where
  bunit :: b Unit
  bprod :: b f -> b g -> b (f `Product` g)

With laws (following Applicative programming with effects)

• Naturality of bprod:

bmap (hf ** hg) (bf `bprod` bg) = bmap hf bf `bprod` bmap hg bg
  
where
  (**) :: (forall a. f a -> f' a)
       -> (forall a. g a -> g' a)
       -> (f `Product` g) a
       -> (f' `Product` g') a
  hf ** hg (Pair fa ha) = Pair (hf fa) (hg ga)

• Left/right identity:

bmap (\(Pair _ ga) -> ga) (bunit `bprod` bg) = bg
bmap (\(Pair fa _) -> fa) (bf `bprod` bunit) = bf

• Associativity:

bmap (\(Pair fa (Pair ga ha)) -> Pair (Pair fa ga) ha) (bf `bprod` (bg `bprod` bh))  = (bf `bprod` bg) `bprod` bh

from barbies.

I think ProductB is a different kinded applicative (provided that we relax its laws). We can't define analog of <*> so have to use bprod. And buniq and bunit are equivalent:

bunit   = buniq Unit
buniq f = bmap (\_ -> f) bunit

Should we use buinq we'll have to change identity laws. This should work I think:

bmap (\(Pair _ ga) -> ga) (buniq Unit `bprod` bg) = bg
bmap (\(Pair fa _) -> fa) (bf `bprod` buniq Unit) = bf

So we already have an applicative. Its name obscures in connection to Applicative type class and maybe it should be renamed but I have no opinion on that. All in all only thing needed to add Applicative is to change documentation.

P.S. It always amazed me how much one can deduce just by looking at documentation!

from barbies.

This is now fixed on master. ProductB was renamed to ApplicativeB (also ProductBC got removed, wasn't really needed these days). I think I managed to do this without completely breaking backwards compatibility: Data.Barbie is now deprecated but should be exposing the previous API.

from barbies.

Release 2.0.0.0 includes these changes

from barbies.