Thanks for this detailed criticism, it’s quite useful.
My understanding is that for functions with more than a few arguments, it is expected in Julia that only a small subset of the possibly thousands of combinations will be covered. Thousands, because with multiple dispatch you dispatch on the types of all the arguments. The binary operator “*” in Julia has 364 methods, and that just takes two arguments. So you define the ones that are useful.
Sure, that is an absolutely sensible design decision. But for other cases completeness is vital. Consider for instance the trivial case of the map function over lists (constructed by :: and []), often abbreviated as * :
f * [ ] = [ ]
f * a::as = (f a)::(f * as)
Even if that is a nearly trivial case, it is easy to see that one could forget the first case, as all the interesting bits happen elsewhere. Now imagine, I would want to have a lazy reversal of lists, that I store as an alternative until I need to deconstruct it. I write that x~xs, meaning "x added to the end of xs".
Now I have to expand my map function as follows (because map does not care about ordering):
f * a~as = (f a) ~ (f * as)
If I miss that case (or method on Julia's case) my extension of the datatype is plain wrong.
My understanding is that for functions with more than a few arguments, it is expected in Julia that only a small subset of the possibly thousands of combinations will be covered. Thousands, because with multiple dispatch you dispatch on the types of all the arguments. The binary operator “*” in Julia has 364 methods, and that just takes two arguments. So you define the ones that are useful.