[Python-ideas] universal set object for use in set manipulation

[Georg Brandl]

Steven D'Aprano schrieb:

>> Implementation of a universal set would be pretty trivial.
> 
> You think so? I can think of a number of problems.

First, I don't think this is important enough to become a standard
Python type.  But regardless, these problems are quite easy to answer.

> (1) What elements should go into the universal set? Strings, ints, 
> floats, presidents... ?

Everything. Every possible (i.e. hashable) object is a (virtual) member
of the universal set.  You're thinking too mathematically here.  Python has
no notion of a category of elements for ordinary sets as well -- you can
put a president in a set together with integers without problems.

> (2) What is len(set.universal())?

Since it was apparently decided that len() can "lie", sys.maxsize would be
a nice value.  Otherwise, an exception.

> (3) What does set.universal() print?

'set.universal()'.

> (4) What does set.universal().clear() do?

It clears the set. Afterwards, the set is empty.

> (5) For that matter, union(), copy(), difference(), issubset(), etc?

union() is a no-op, as well as any operation that adds elements.
intersection() just returns the "other" set.
copy() just returns another instance of the universal set.
issubset() - the universal set is the subset of no other set except
the universal set.

To make difference() or remove() and pop() possible, one would have to
expand the notion to a "universal-except" set which again has a finite
number of exceptions.

> (The universal set for strings of length one is a subset of the 
> universal set for all strings.)

Again, see the comment for (1).

> I don't think there is a suitable solution for all of these issues. That 
> would mean that set.universal() can't be a real set object, it has to 
> be some sort of not-quite-a-set object that doesn't provide the entire 
> set interface.

Of course, it could not be an ordinary set object (i.e. one actually containing
references to its members) -- that would require an infinite amount of memory.
However, it *can* implement much of the set interface without a problem.

Georg

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