Overloading vs. Overriding in Julia - operator-overloading

Question

I am not familiar with Julia but I feel like I noticed it allows you to define functions multiple times with different signatures, such as this:
FK5Coords{e}(ra::T, dec::T) where {e,T<:AbstractFloat} = FK5Coords{e, T}(ra, dec)
FK5Coords{e}(ra::Real, dec::Real) where {e} =
FK5Coords{e}(promote(float(ra), float(dec))...)
To me it looks like this allows you to call FK5Coords with two different signatures.
So I'm wondering (a) if that is true, if Julia allows overloading functions like this, and (b) if Julia allows something like super in a function, which seems like it would conflict with overloading. And (c), what an example snippet of Julia code looks like that shows (1) overloading in one example, and (2) overriding in the other.
The reason I'm asking is because I am wondering how Julia solves the problem of having both super and function overloading, because both require defining the function again and it seems you would have to flag it with some metadata or something to say "in this case I am overriding" or "in this case I am overloading".
Note: If that was not an example of overloading, then (from Wikipedia) this was what I was imagining Julia supported (along these lines):
// volume of a cylinder
double volume(const double r, const int h)
{
return 3.1415926*r*r*static_cast<double>(h);
}
// volume of a cuboid
long volume(const long l, const int b, const int h)
{
return l*b*h;
}

Answer 1

So I'm wondering (a) if that is true, if Julia allows overloading functions like this
Julia allows you to write different versions of the same function (different "methods" for the function) that differ in the type/number of arguments. That's pretty similar to overloading, except that overloading usually means the function to be called is decided based on the compile-time type of the arguments, whereas in Julia it's decided based on the run-time type of the arguments. This is commonly called dynamic dispatch. See this C++ example to see what overloading lacks and dispatch gives you.
(b) if Julia allows something like super in a function, which seems like it would conflict with overloading
The reason I'm asking is because I am wondering how Julia solves the problem of having both super and function overloading, because both require defining the function again and it seems you would have to flag it with some metadata or something to say "in this case I am overriding" or "in this case I am overloading".
I'm not sure why you think overloading will conflict with super. In C++, overriding involves having the exact same argument numbers and types, whereas overloading requires having either the number or the type of arguments be different. Compilers are smart enough to easily distinguish between those two cases, and AFAICT C++ can have a super method despite having both overloading and overriding, except that it also has multiple inheritance. I believe (with my limited C++ knowledge) that multiple inheritance is the reason C++ doesn't have a super method call, not overloading.
Anyway, if you peel back behind the Object-oriented curtain and look into method signatures, you'll see that all overriding is really a particular type of overloading: Dog::run(int dist, int dir) can override Animal::run(int dist, int dir) (assume Dog inherits from Animal), but that's equivalent to overloading a run(Animal a, int dist, int dir) function with a run(Dog d, int dist, int dir) definition. (If run was a virtual function, this would be dynamic dispatch instead of overloading, but that's a separate discussion.)
In Julia we do this explicitly, so the definitions would be run(d::Dog, dist::Int, dir::Int) and run(a::Animal, dist::Int, dir::Int). However, in Julia, you can only inherit from abstract types, so here the supertype Animal would be an abstract type, so you can't really call the second method with an Animal instance - the second method definition is really a shorthand way of saying "call this method for any instance of some concrete subtype of Animal, unless that subtype has its own separate method definition" (which Dog does, in this case). I'm not aware of any easy way of calling the second method run(Animal... from the first run(Dog..., which would be the equivalent of a super call.
(You can also 'override' a method from another module with import, but if it has completely the same parameters and parameter types, you'd probably be committing type piracy, which is usually a bad idea. I'm not aware of any way of getting back the original method after this type of overriding. "Overloading" (using dispatch) by defining and using your own types is much more common anyway.)
(c), what an example snippet of Julia code looks like that shows (1) overloading in one example, and (2) overriding in the other.
The first code snippet you posted is an example of using dispatch (which is what Julia uses instead of overloading). For another example, let's first define our base type and function:
abstract type Vehicle end
function move(v::Vehicle, dist::Float64)
println("Moving by $dist meters")
end
Now we can create another method of this function for dispatch ("overload" it) this way:
function move(v::Vehicle, dist::LightYears)
println("Blazing across $dist light years")
end
We can do an object-oriented style "override" too (though at the language level this is just seen as another method for dispatch):
struct Car <: Vehicle
model::String
end
function move(c::Car, dist::Float64)
println("$model is moving $dist meters")
end
This is the equivalent of overriding Vehicle.move(float dist) in derived class as Car.move(float dist).
And just for the heck of it, the volume function from the question:
# volume of a cylinder
volume(r::Float64, h::Int) = π*r*r*h
volume(l::Int, b::Int, h::Int) = l*b*h;
Now the correct volume method to call will be decided based on the number (and type) of arguments passed (and the return type is automatically inferred by the compiler, Float64 for the first method and Int for the second one).