[Python-ideas] Predicate Sets

[Terry Reedy]

On 1/19/2014 6:41 PM, Daniel da Silva wrote:
> Below is a description of a very simple but immensely useful class
> called a "predicate set". In combination with the set and list
> comprehensions they would allow another natural layer of reasoning with
> mathematical set logic in Python.

Sets defined by predicates are usually infinite and mathematical set 
logic works fine with such.

> *Overview:*
>      Sets in mathematics can be defined by a list of elements without
> repetitions, and alternatively by a predicate (function) that determines
> inclusion. A predicate set would be a set-like class that is
> instantiated with a predicate function that is called to determine ``a
> in the_predicate_set''.
>
>  >> myset = predicateset(lambda s: s.startswith('a'))
>  >> 'xyz' in myset
> False
>  >> 'abc' in myset
> True
>  >> len(myself)
> Traceback (most recent call last):
>    [...]
> TypeError

This illustrates the problem with the idea. Only containment is really 
straightforward. (I am aware that some operations could be implemented 
by defining new predicates. To combines sets with predicatesets, the 
sets would have to be represented by predicates, as done below.)

> *Example Uses:*
> # Dynamic excludes in searching
> foo_files = search_files('foo', exclude=set(['a.out', 'Makefile']))
> bar_files = search_files('bar', exclude=predicateset(lambda fname: not
> fname.endswith('~'))) # exclude *~
>
> # Use in place of a set with an ORM
> validusernames = predicateset(lambda s: re.match(s, '[a-zA-Z0-9]+'))

I think these examples are backwards. The APIs should accept functions 
either in addition to or instead of collections. It is trivial to turn a 
collection into a predicate

 >>> p = {'a', 'b', 'c'}.__contains__
 >>> p('a')
True
 >>> p('d')
False

You need realistic examples that use other operations (but not len ;-).

-- 
Terry Jan Reedy