Re: [Python-ideas] Predicate Sets

20 Jan 2014

      Although a cute point, I'm not too concerned about the Russell's Paradox
issue.  The obvious implementation will get a "RuntimeError: maximum
recursion depth exceeded" in that case.  But then, no predicate is
guaranteed to halt, so that's not really special to the russellset.

On the other hand, even though I think the idea of a 'predicateset' is cute
mathematically, I'm not really sure what it actually gets you, even in
readability.

I am perfectly happy spelling this:

  mypset = predicateset(somefunc)
  if x in mypset: ...

As:

  if somefunc(x): ...

Even for the set operators, set comprehensions seem pretty much equally
elegant:

  such_that = {1, 2, 3} & mypset  # Looks nice, I agree

But then, this looks pretty nice also:

  such_that = {x for x in {1, 2, 3} if somefunc(x)}

OK, sure the predicateset version might save a few characters, but not all
that many.

If you want to combine predicate sets that's really just like combining
predicates.  It *does* sort of remind me that I'd like some standard HOFs
as builtins or in the standard library (probably in functools).  But still,
where you might write:

  in_both_sets = mypset & mypset2

It's not bad to write a small support module:

  # combinators.py
  def allP(*fns):
      return lambda x: all(f(x) for f in fns)

  def anyP(*fns):
      return lambda x: any(f(x) for f in fns)

Then express the intersection as:

  in_both_pred = allP(somefunc, somefunc2)
...
From there, you can just use the predicate 'in_both_pred' as above.
 Similarly for union, define:
in_either_pred = anyP(somefunc, somefunc2)

On Mon, Jan 20, 2014 at 11:05 AM, Georg Brandl  wrote:
...
Am 20.01.2014 08:56, schrieb Andrew Barnert:
...
From: Daniel da Silva  Sent: Sunday, January
19,
2014 3:41 PM
...
Overview: Sets in mathematics can be defined by a list of elements
without
repetitions, and alternatively by a predicate (function) that determines
inclusion.
The whole point of modern set theory is that sets cannot be defined by a
predicate alone; only by a predicate _and a set to apply it over_. Which
we
already have in set comprehensions.
And your suggestion has the exact same problem that naive set theory had:
...
...
...
myset = predicateset(lambda s: s.startswith('a'))
'xyz' in myset
False
...
...
...
russellset = predicateset(lambda s: s not in s)
russellset in russelset
Presumably this should cause the computer to scream "DOES NOT COMPUTE!"
and
blow up...
I think it will just raise a NameError...
SCNR,
Georg
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Re: [Python-ideas] Predicate Sets

David Mertz