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ekmett / linear

Low-dimensional linear algebra primitives for Haskell.
http://hackage.haskell.org/package/linear
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Derive instance Real a => Real (V1 a) #170

Open noughtmare opened 2 years ago

noughtmare commented 2 years ago

This works:

deriving instance Real a => Real (V1 a)

With this instance you can use realToFrac to convert any real V1 to any fractional type.

RyanGlScott commented 2 years ago

This seems like the sort of instance that V1 could have, but V{0,2,3,4} couldn't, as I'm not sure what sensible Real behavior would look like for the latter. This is a bit strange, since these types are typically meant to have the same API, but with different dimensions.

On the other hand, there are already some minor differences in the number of instances each vector type has (e.g., some have Field1 but not Field2 instances.) Perhaps this falls into the category of "minor differences" as well. If so, it would be worth mentioning that as a disclaimer in the Haddocks for the instance. A similar disclaimer would apply if you wanted to write a RealFloat instance for V1.

noughtmare commented 2 years ago

I think V0 could also have a trivial instance. And yes, if Real is added then I see no reason not to add RealFrac and RealFloat too.

RyanGlScott commented 2 years ago

I think V0 could also have a trivial instance.

What did you have in mind for an implementation of toRational? I agree that any such implementation would be trivial, but at the same time, we'd have to make an opinionated choice of which Rational to return, which gives me pause.

Taneb commented 2 years ago

I'm a -0.2 to adding these instances. They don't feel right to me, largely for the reason that @RyanGlScott said that they're not possible for larger vectors, but also it doesn't feel at all a very vector-y typeclass, which I think is an important design consideration here.

noughtmare commented 2 years ago

What did you have in mind for an implementation of toRational?

Always returning zero. I think toRational 0 = 0 should hold for any Real (It should be a "Num homomorphism", so to speak). Nevermind, this would also imply toRational 1 = 1, so I guess you're right that it is not obvious.