I could not believe it in julia Version 0.6.0 (2017-06-19 13:05 UTC) I got julia> max(Set([1]), Set([2])) Set([2]) julia> max(Set([2]), Set([1])) Set([1]) julia> min(Set([1]), Set([2])) Set([1]) julia> min(Set([2]), Set([1])) Set([2]) Now, Set{T} where T does not have a canonical total order but a…

Item 1. is valid for partial and total orders. Item 2. is the distinctive definition of total orders. Everything you say about isless and isequal is true. They need to be aware of eachother. So Item 2. is always true for total orders. For only partial orders, isless should not be defined, so Item…

Just out of interest, what result should you expect when taking the max of two sets? The relevant code appears to be <( l::Set, r::Set) = (length(l) < length(r)) && (l <= r) <=(l::Set, r::Set) = issubset(l, r) and since max will return the second argument if < is false, it’s returning the second …

Thanks for your interest. I would expect max(s1,s2) == union(s1,s2) and min(s1,s2) = intersect(s1,s2) for sets s1 and s2. Actually max and min are not the correct names, if the order is partial, it should be upperbound or supremum resp. lowerbound or infimum instead, which would be the correct ter…

[image] klacru: I would expect max(s1,s2) == union(s1,s2) and min(s1,s2) = intersect(s1,s2) for sets s1 and s2. This would turn max at least into an O(n) operation with no short-circuiting.

That is correct, union(s1,s2) and intersect(s1,s2) on sets are more expensive than s1 < s2 on sets in general. If length(s1) < length(s2) or if both are IntSet, the effort is comparable. I would never trade performance for usability of results.

What does the code example show? The wit of my original post was max(a,b) != max(b,a), even if a != b. That means max applied to sets is not commutative.

My code was intended to show how one can define equality and not get obviously-commutative results from max (though I would argue that the results do show commutativity). I guess my point is this: julia> Set([1]) < Set([2]) false julia> Set([2]) < Set([1]) false julia> Set([2]) == Set([1]) false …

I do not agree with your arguments. What I wanted to explain, that the current implementation of max is not ok for types, which implement a partial order (by defining <). The implementation max(x,y) = ifelse(y < x, x, y) makes max commutative only for totally ordered types (which are implementing i…

I found some comments about it. Since sort uses isless, I would agree with @klacru ’s suggestion to do the same with max/maximum.

I’d agree as well. Thanks for the discussion.

Changing the definitions of min and max to use isless seems reasonable, although for non-floating-point types < and isless should be identical, so arguably the real bug here is that they differ for sets. The fact that < and <= are defined for sets is quite old and probably not a great idea – we have…

max(x::T, y::T) and min must be commutative!

Internals & Design

jpiitula August 2, 2017, 6:42pm 15

The name join is already used for other purposes, without a corresponding meet, whereas supremum and infimum, sup and inf, lub and glb seem quite free (or if used in packages, perhaps mean more or less the same as proposed here).

Extend the domain of maximum and minimum to include empty collection?

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max(x::T, y::T) and min must be commutative!

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