instance (Applicative f, Semigroup f) => Semigroup (NonEmpty f a)

[wereHamster]

Would be useful to concatenate two NonEmpty Array a types together, for example. Is there a reason why it doesn't exist?

[paluh]

Is anything wrong with @wereHamster's proposition? Should I provide pull request?

[damncabbage]

I have the same question; I've written a non-typeclass version of append already for our own (internal) Prelude.

[matthewleon]

For some reason the assumption in such an implementation that pure means singleton (I'm assuming that is what your Applicative constraint is for) rubs me the wrong way. Can you prove that this always end up being law-abiding?

[wereHamster]

Maybe Applicative is not needed, I don't know anymore.

[paluh]

@matthewleon

Taking this implementation:

append ∷ ∀ a f. Semigroup (f a) ⇒ Applicative f ⇒ NonEmpty f a → NonEmpty f a → NonEmpty f a
append (NonEmpty a1 f1) (NonEmpty a2 f2) = NonEmpty a1 (f1 <> pure a2 <> f2)

We have:

 NonEmpty a1 f1 <> (NonEmpty a2 f2 <> NonEmpty a3 f3)
 -- using append
 NonEmpty a1 f1 <> NonEmpty a2 (f2 <> pure a3 <> f3)
 -- using append
 NonEmpty a1 (f1 <> pure a2 <> (f2 <> pure a3 <> f3))
 -- using associativity of f
 NonEmpty a1 ((f1 <> pure a2 <> f2) <> pure a3 <> f3)
 -- using append
 NonEmpty a1 (f1 <> pure a2 <> f2) <> NonEmpty a3 f3
 -- using append
 (NonEmpty a1 f1 <> NonEmpty a2 f2) <> NonEmpty a3 f3

So it seems that Associativity holds.

[paluh]

P.S.
But I fully understand your doubts about Applicative as it is too strong constraint in this context, because we don't really need Apply...

[paluh]

On the other hand pure without any additional operations seems to be "lawless", so I'm not sure if there is any sensible alternative...

[ahansen90]

Is there any reason we couldn't just implement this and swap it out for a weaker constraint afterwards?

[hdgarrood]

The only problem with this is that we don't know that pure will behave sensibly alongside <>, because we don't have any laws which govern their behaviour. Then again, this is a valid semigroup as proved by @paluh, and in practice this data type is probably most often used with types like Array or List which will behave sensibly, so I think adding this instance probably does make sense.

[JordanMartinez]

Closed by #50.