Concerning Scalar + Vector i.e. +^ it's just a shortcut. Very useful even if
it's not good (?) from the design point of view. Also one could find useful
shortcut like .<, .<=, .>, .>= which mean compare length of vector. It's not
usual for vector algebra but probably still make sense.
What I want to ask you guys can we define a function with arbitrary number
of parameters? Actually not really arbitrary but just several possibilities
(as we have with value constructors).
For instance cross product can have 1, 2 or 3 vectors as inputs depends on
the dimension. Is it 2d, 3d or 4d case.
On Sat, Jan 24, 2009 at 3:59 PM, Luke Palmer
2009/1/24 Olex P
But you know it doesn't make too much sense because I also have to define addition Scalar + Vector (that means construct vector from scalar and add a vector), Vector + Scalar and so on. And as we are not able to overload operations in C++ like way we have to create several different operations even if their meaning is pretty close.
Well, yeah, but their meaning isn't *the same*, so we don't give them the same name.
For vectors, putting a carat (or other signifier like a dot) on the side of the operation which has the vector is relatively common practice.
Scalar +^ Vector Vector ^+^ Vector
And so on.
And also, I wonder, what are you going and adding scalars to vectors for!? (I've heard of multiplying scalars by vectors -- that's in the definition of a vector space, but adding...?)
Oh, instead of overloading a million operations that just work component-wise on vectors the way C++ guys do it, you can just define a higher-order function:
vmap :: (Vector v) => (Double -> Double) -> v -> v
Or however it works out in your situation. Then you can reserve those precious symbols for things that are actually vectory, like inner products.
Luke