ANN: intervalset Was: Set type for datetime intervals

[Random832]

On Tue, Apr 5, 2016, at 04:11, Nagy László Zsolt wrote:
>  But there is still need to check begin <= end. But maybe
> you are right: if we suppose that nobody will try to use an interval
> where end < begin then we can use plain tuples. But then the user *must*
> make sure not to use invalid intervals.

The IntervalSet constructor and add method could switch them or throw an
exception. But I'm not saying to use plain tuples. I'm saying to make
Interval a "dumb" object, which *only* supports being constructed and
added to a set, rather than putting a bunch of set-like operations on
it.

> It is blurred by design. There is an interpretation where an interval
> between [0..4] equals to a set of intervals ([0..2],[2..4]).

No, because 2.5 is in one and not the other. Floats are orderable with
ints, so it's not reasonable to say "this is an int intervalset so no
floats are contained in it". But that's another discussion.

But why would you want to use [0..4] directly instead of ([0..4])?

> Actually,
> you can ask: "is an element within the interval?" The same question can
> be asked for an Interval set. So the same type of value can be
> "contained" within an interval and also witin an interval set. In the
> current implementation, if you try to create a set with these two
> intervals [0..2] and [2..4], then they are unified into a single element
> on purpose: to make sure that there is only a single official
> representation of it. E.g. ([0..2],[2..4]) is not a valid set, only
> ([0..4]) is.

Uh, exactly. I don't understand why any of this makes it useful to have
these operations on interval objects.

> By definition, a set is given with its elements, e.g. for any possible
> item, you can tell if it is part of the set or not. So if
> ([0..2],[2..4]) and ([0..4]) have exactly the same elements (by the
> given definition), then they are not just equal: they are the same set.
> The same reasoning is used in math when they say: there cannot be
> multiple empty sets. There exists a single empty set. It happens that we
> can only represent a finite number of elements in any set on a computer.
> I wanted to have a well defined single way to represent any given set.

What? *I* am the one who wants a well defined single way to represent a
given set. *You* are the one who wants to make [0..4] a set-like object
that is different from ([0..4]) and doesn't quite support the same
operations.

> I can also see your point. From another point a view, a set and a set of
> sets is not the same type.

I'm saying an interval is _not_ a set. It is merely part of the way of
describing the set. Just like the word "of" isn't a set just because
"the set of all even numbers" is a set.

You could consider "the set of [dates|numbers|etc] in a single interval"
to be a type of set, certainly. But there's no reason to have such a set
_not_ fully support set operations even when those operations will not
return a set of a single interval.

> However, I do not share this view, because if
> we start thinking this way, then operations like the one below does not
> make sense:
> 
> [0..4]) - (1..2] == [0..1] | [2..4]
> 
> If you make a strinct distinction between intervals and interval sets,
> then the above equation does not make sense, because you cannot remove
> an element from a set that is not an "element" of it. The above equation
> makes sense only if the "intervalset" is a general representation of
> possible values, and the "interval" type is a special representation of
> (the same) possible values.

I don't understand why you want to let the user use the "interval" type
for purposes other than adding to an intervalset in the first place
Nothing you've posted has explained this.

> It is clear when you ask the question: "is 3
> in the interval?" and you can also ask "is 3 in the interval set?"
> - so
> the value of the same type can be contained in the interval and also in
> the interval set. Maybe the naming is bad, and it should be named
> "Intervals" instead of IntervalSet?