Yes, this is valid, and we should probably do it.
mempty = pure mempty
mappend = liftA2 mappend
will make a valid Monoid for any Applicative instance, and
x <> y = (<>) <$> x <.> y
will make a valid Semigroup for any Apply instance. Proving this seems
a bit gross. It's probably best to go via a well-known alternative
formulation of Applicative:
class Functor f => Apply' f where
pair :: f a -> f b -> f (a, b)
instance Apply' f => Applicative' f where
pure' :: a -> f a
This formulation lets you reassociate by switching between (a, (b,c))
and ((a,b),c) rather than shifting fmaps around.
On Tue, Mar 21, 2017 at 3:53 AM, Louis Pan
Hi all,
In my Glazier GUI library, I had to use newtype wrappers to create Semigroup and Monoid instances for ReaderT.
Is there a reason why ReaderT doesn't have an instance of Semigroup and Monoid?
The reader ((->) a) is a Monoid and a Semigroup. https://hackage.haskell.org/package/base-4.9.1.0/docs/src/GHC.Base.html#line... https://hackage.haskell.org/package/base-4.9.1.0/docs/src/Data.Semigroup.htm...
Could the following be added to the transformers package? Or is it not lawful?
instance (Applicative m, Semigroup a) => Semigroup (ReaderT r m a) where f <> g = (<>) <$> f <*> g {-# INLINABLE (<>) #-}
instance (Applicative m, Monoid a) => Monoid (ReaderT r m a) where mempty = pure mempty {-# INLINABLE mempty #-}
f `mappend` g = mappend <$> f <*> g {-# INLINABLE mappend #-}
Does it make sense to extend the monoid instance to all the other transformers? Eg.
instance (Monad m, Semigroup a) => Semigroup (StateT s m a) where f <> g = (<>) <$> f <*> g {-# INLINABLE (<>) #-}
instance (Monad m, Monoid a) => Monoid (StateT s m a) where mempty = pure mempty {-# INLINABLE mempty #-}
f `mappend` g = mappend <$> f <*> g {-# INLINABLE mappend #-}
instance (Monad m, Monoid w, Semigroup a) => Semigroup (WriterT w m a) where f <> g = (<>) <$> f <*> g {-# INLINABLE (<>) #-}
instance (Monad m, Monoid w, Monoid a) => Monoid (WriterT w m a) where mempty = pure mempty {-# INLINABLE mempty #-}
f `mappend` g = mappend <$> f <*> g {-# INLINABLE mappend #-}
and also for MaybeT, IdentityT, ExceptT, etc
Regards,
Louis
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