http://stackoverflow.com/questions/9423622/strict-fmap-using-only-functor-not-monad seems to cover it.

On Mon, Aug 10, 2015 at 4:17 PM, Alexey Egorov <electreg@list.ru> wrote:
Hello haskellers,

I wonder why <$> and <$!> have different typeclass constraints?

(<$>) :: Functor f => (a -> b) -> f a -> f b
(<$!>) :: Monad m => (a -> b) -> m a -> m b
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