On: Julia Computing raises $24M Series A

[StefanKarpinski]

Technical enforcement would be nice, but it's a hard design problem and my point is that even with that, you still need the cultural aspect. Time and time again, we see that culture trumps technology for these kinds of things. In this case, the proof is in the pudding: in Julia there is no technical enforcement of consistency, but semantic meaning of generic functions is broadly respected and generic code works. It would be nice to add some kind of protocols that support enforcement, but it's (apparently) not necessary and it's a hard design problem.

> For example, the language does not let you overload + for a non-commutative operation

It does allow it? I'm not even sure how one would disallow non-commutative operations. How would you know if a definition is commutative?

[enriquto → StefanKarpinski]

(Now I realize that you are one of the designers of Julia, I feel deeply honored by your answers. I really love your job with the language!)

> how one would disallow non-commutative operations. How would you know if a definition is commutative?

I don't think that this is possible without solving the halting problem. But in practice, you can do that by documenting this enforcement and making it unfeasible to overload a commutative operator with non-commutative code. For example, the callers of the overloaded commutative operator can and do assume commutativity to optimize compilation; as in, you fill a matrix with "f(i+j)" and it may only evaluate the upper-half of the matrix (this is even more interesting for the associative case). I think that Mathematica does a similar thing, I recall several symbols for operators to be overloaded assuming certain symmetries. As another example, in C++ you must overload "<" with something that is an order relation, otherwise the sort function fails. Being more fancy, a test option of the interpreter may run each call of the operator in a random order, etc.

Also, related to Mathematica, using juxtaposition for product is very natural to mathematicians. It is indeed hard point of friction when moving from Mathematica to Maple or Matlab.