This came up as I was trying to define a sphere manifold type which can
have distinct metric structures put on it, here is how I have to do it in
Julia:
abstract Manifold
abstract Metric
immutable Metric1 <: Metric
end
immutable Metric2 <: Metric
end
immutable Sphere{T<:Metric} <: Manifold
dim::int
end
metric(M::Sphere{Metric1}, x1, x2) = ...
metric(M::Sphere{Metric2}, x1, x2) = ...
As you can see, I have to define a whole other type tree just so my metric
function can distinguish between sphere manifolds depending on what metric
structure I want it to have. It would be both simpler and make more sense
conceptually to attach the metric to the manifold itself when I instantiate
it. Of course you might say I should just define two functions metric1 and
metric2, but this doesn't really make sense either because these metrics do
not cut across multiple manifolds, and thus there would be no way to take
advantage of the multiple dispatch functionality.
