Sven Panne wrote:
Regarding Functor/Applicative: The obvious instances for e.g. a 2-dimensional
vertex are:
data Vertex2 a = Vertex2 a a
instance Functor Vertex2 where
fmap f (Vertex2 x y) = Vertex2 (f x) (f y)
instance Applicative Vertex2 where
pure a = Vertex2 a a
Vertex2 f g <*> Vertex2 x y = Vertex2 (f x) (g y)
They fulfill all required laws, but are these the only possible instances? If
not, are they at least the most "canonical" ones in a given sense? And
finally: Does somebody have a real-world example where the Applicative
instance is useful? Usages of the Functor instance are much more obvious for
me.
I'd say those are the right instances. Some obvious uses (perhaps more
useful for Vector2 than Vertex2, but still) are:
liftA2 (+) (Vertex2 1 3) (Vertex2 4 5) == Vertex2 5 8
pure 0 == Vertex2 0 0
The latter being a useful shorthand to get a vertex for the origin.
Also, if you define Foldable:
foldl1 (+) . liftA2 (*) v w == dotProduct v w
The useful thing being that that definition of dotProduct is the same
for 2-, 3- and 4- dimensional things, and for vertexes and vectors. So
possible additions to your type-class list are Foldable and maybe
Traversable (no harm, although I'd have to reach further for an example
for this). I guess the tricky decision might be whether to provide a
Num instance (again, probably more suitable for Vector2)?
instance Num a => Num (Vertex2 a) where
(+) = liftA2 (+)
(-) = liftA2 (-)
(*) = liftA2 (*)
abs = fmap abs
signum = fmap signum
negate = fmap negate
fromInteger = pure . fromInteger
Even if you don't want to define Num, note how easy having the
Applicative instance makes defining some of the operators :-)
Thanks,
Neil.
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