generalize min and max to non-numeric types

[StefanKarpinski]

Since < is generic and applies not only to numeric types, in principle, min and max should also be, although then having negative and positive infinities as the zero-argument default is wrong.

[JeffBezanson]

We could just remove the type declarations on the arguments to min and max.

Then I propose we get rid of the definitions for max(x::Real) etc. and have 1-argument versions always mean reduction over a container.

Maybe we should also have a compiler intrinsic for min/max of two native type numbers, since that could be faster than calling libm fmax like we do now.

[StefanKarpinski]

Yes, that all seems reasonable. Also, if you apply min/max to an empty but typed container, then we can give the right min/max value for that type in some cases, but in general, it's ill-defined.

[JeffBezanson]

I just started doing that; min(int8([])) gives an Int8, but min({}) gives an error.
Interestingly I believe "" serves as a minimum string, but there is no maximal string...except RepString("\U10ffff",Inf)???

[StefanKarpinski]

Interestingly I believe "" serves as a minimum string, but there is no maximal string...except RepString("\U10ffff",Inf)???

Yes, that seems correct — RepString("\U10ffff", Inf) isn't a real string since strings have finite length. The fact that that expression does throw an error is a mistake. I think strings are a case where there's a global min but no global max.

[JeffBezanson]

Oh dear, that's because my default constructors accept any arguments and assign them to the fields, which performs conversion. Thinking about this again, I'm not sure this is right. Maybe a default constructor should only accept arguments of the field types.

[StefanKarpinski]

I kind of always thought that was a bit suspect. It's nice sometimes, but it's also kind of dangerous.

[JeffBezanson]

I can change it very easily if we want.

[StefanKarpinski]

Yeah, the only issue is that there's probably a bunch of places we'll want to insert manual convert calls then. But it's probably best to do this now rather than later.

[JeffBezanson]

As far as the original purpose of this issue, we're ready to go. I made max and min reductions require typemin(eltype(container)) to be able to give an answer for an empty container. All we have to do is change the 2-argument declarations and delete the 0-argument ones. FWIW lisp doesn't allow min and max to take zero arguments.