python-peps/pep-0218.txt

PEP: 218
Title: Adding a Built-In Set Object Type
Version: $Revision$
Author: gvwilson@ddj.com (Greg Wilson)
Status: Draft
Type: Standards Track
Python-Version: 2.2
Created: 31-Jul-2000
Post-History: 


Introduction

    This PEP proposes adding a Set module to the standard Python
    library, and to then make sets a built-in Python type if that
    module is widely used.  After explaining why sets are desirable,
    and why the common idiom of using dictionaries in their place is
    inadequate, we describe how we intend built-in sets to work, and
    then how the preliminary Set module will behave.  The penultimate
    section discusses the mutability (or otherwise) of sets and set
    elements, and the solution which the Set module will implement.
    The last section then looks at alternatives that were considered,
    but discarded.


Rationale

    Sets are a fundamental mathematical structure, and are very
    commonly used in algorithm specifications.  They are much less
    frequently used in implementations, even when they are the "right"
    structure.  Programmers frequently use lists instead, even when
    the ordering information in lists is irrelevant, and by-value
    lookups are frequent.  (Most medium-sized C programs contain a
    depressing number of start-to-end searches through malloc'd
    vectors to determine whether particular items are present or
    not...)

    Programmers are often told that they can implement sets as
    dictionaries with "don't care" values.  Items can be added to
    these "sets" by assigning the "don't care" value to them;
    membership can be tested using "dict.has_key"; and items can be
    deleted using "del".  However, the other main operations on sets
    (union, intersection, and difference) are not directly supported
    by this representation, since their meaning is ambiguous for
    dictionaries containing key/value pairs.


Long-Term Proposal

    The long-term goal of this PEP is to add a built-in set type to
    Python.  This type will be an unordered collection of unique
    values, just as a dictionary is an unordered collection of
    key/value pairs.  Constant sets will be represented using the
    usual mathematical notation, so that "{1, 2, 3}" will be a set of
    three integers.

    In order to avoid ambiguity, the empty set will be written "{-}",
    rather than "{}" (which is already used to represent empty
    dictionaries).  We feel that this notation is as reasonable as the
    use of "(3,)" to represent single-element tuples; a more radical
    strategy is discussed in the "Alternatives" section, and more
    readable than the earlier proposal "{,}".

    Iteration and comprehension will be implemented in the obvious
    ways, so that:

        for x in S:

    will step through the elements of S in arbitrary order, while:

        {x**2 for x in S} 

    will produce a set containing the squares of all elements in S,
    Membership will be tested using "in" and "not in", and basic set
    operations will be implemented by a mixture of overloaded
    operators:

        |               union
        &               intersection
        ^               symmetric difference
        -               asymmetric difference

    and methods:

        S.add(x)        Add "x" to the set.

        S.update(s)     Add all elements of sequence "s" to the set.

        S.remove(x)     Remove "x" from the set.  If "x" is not
                        present, this method raises a LookupError
                        exception.

        S.discard(x)    Remove "x" from the set if it is present, or
                        do nothing if it is not.

        S.pop()         Remove and return an arbitrary element,
                        raising a LookupError if the element is not
                        present.

        S.clear()       Remove all elements from this set.

    and one new built-in conversion function:

        set(x)          Create a set containing the elements of the
                        collection "x".

    Notes:

    1. We propose using the bitwise operators "|&" for intersection
       and union.  While "+" for union would be intuitive, "*" for
       intersection is not (very few of the people asked guessed what
       it did correctly).

    2. We considered using "+" to add elements to a set, rather than
       "add".  However, Guido van Rossum pointed out that "+" is
       symmetric for other built-in types (although "*" is not).  Use
       of "add" will also avoid confusion between that operation and
       set union.

    3. Sets raise "LookupError" exceptions, rather than "KeyError" or
       "ValueError", because set elements are neither keys nor values.


Open Issues for the Long-Term Proposal

    Earlier drafts of PEP 218 had only a single set type, but the
    sets.py implementation in Python 2.3 has two, Set and
    ImmutableSet.  The long-term proposal has a single built-in
    conversion function, set(iterable); how should instances of a
    built-in immutable set type be created?  Possibilities include a
    second immutable_set() built-in, or perhaps the set() function
    could take an additional argument,
    e.g. set(iterable, immutable=True)?

    The PEP proposes {1,2,3} as the set notation and {-} for the empty
    set.  Would there be different syntax for an immutable and a
    mutable set?  Perhaps the built-in syntax would only be for
    mutable sets, and an immutable set would be created from a mutable
    set using the appropriate built-in function,
    e.g. immutable_set({1,2,3}).


Short-Term Proposal

    In order to determine whether there is enough demand for sets to
    justify making them a built-in type, and to give users a chance to
    try out the semantics we propose for sets, our short-term proposal
    is to add a "Set" class to the standard Python library.  This
    class will have the operators and methods described above; it will
    also have named methods corresponding to all of the operations: a
    "union" method for "|", and a "union_update" method for "|=", and
    so on.

    This class will use a dictionary internally to contain set values.
    To avoid having to duplicate values (e.g. for iteration through
    the set), the class will rely on the iterators added in Python
    2.2.

    Tim Peters believes that the class's constructor should take a
    single sequence as an argument, and populate the set with that
    sequence's elements.  His argument is that in most cases,
    programmers will be creating sets from pre-existing sequences, so
    that this case should be the common one.  However, this would
    require users to remember an extra set of parentheses when
    initializing a set with known values:

    >>> Set((1, 2, 3, 4))       # case 1

    On the other hand, feedback from a small number of novice Python
    users (all of whom were very experienced with other languages)
    indicates that people will find a "parenthesis-free" syntax more
    natural:

    >>> Set(1, 2, 3, 4)         # case 2

    On the other, other hand, if Python does adopt a dictionary-like
    notation for sets in the future, then case 2 will become
    redundant.  We have therefore adopted the first strategy, in which
    the initializer takes a single iterable argument.


Mutability

    The most difficult question to resolve in this proposal was
    whether sets ought to be able to contain mutable elements.  A
    dictionary's keys must be immutable in order to support fast,
    reliable lookup.  While it would be easy to require set elements
    to be immutable, this would preclude sets of sets (which are
    widely used in graph algorithms and other applications).

    There are two classes implemented in the "sets" module.  Instances
    of the Set class can be modified by the addition or removal of
    elements, and the ImmutableSet class is "frozen", with an
    unchangeable collection of elements.  Therefore, an ImmutableSet
    may be used as a dictionary key or as a set element, but cannot be
    updated.  Both types of set require that their elements are
    immutable, hashable objects.


Alternatives

    An alternative to the notation "{-}" for the empty set would be to
    re-define "{}" to be the empty collection, rather than the empty
    dictionary.  Operations which made this object non-empty would
    silently convert it to either a dictionary or a set; it would then
    retain that type for the rest of its existence.  This idea was
    rejected because of its potential impact on existing Python
    programs.  A similar proposal to modify "dict.keys" and
    "dict.values" to return sets, rather than lists, was rejected for
    the same reasons.


Copyright

    This document has been placed in the Public Domain.



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