Make "hashable" a glossary entry and clarify docs on __cmp__, __eq__ and __hash__.

I hope the concept of hashability is better understandable now.
Thanks to Tim Hatch for pointing out the flaws here.

Doc/c-api/concrete.rst

@@ -2231,8 +2231,8 @@ Dictionary Objects
 .. cfunction:: int PyDict_SetItem(PyObject *p, PyObject *key, PyObject *val)
 
    Insert *value* into the dictionary *p* with a key of *key*.  *key* must be
-   hashable; if it isn't, :exc:`TypeError` will be raised. Return ``0`` on success
-   or ``-1`` on failure.
+   :term:`hashable`; if it isn't, :exc:`TypeError` will be raised. Return ``0``
+   on success or ``-1`` on failure.
 
 
 .. cfunction:: int PyDict_SetItemString(PyObject *p, const char *key, PyObject *val)

Doc/glossary.rst

@@ -153,6 +153,20 @@ Glossary
       in the past to create a "free-threaded" interpreter (one which locks
       shared data at a much finer granularity), but performance suffered in the
       common single-processor case.
+
+   hashable
+      An object is *hashable* if it has a hash value that never changes during
+      its lifetime (it needs a :meth:`__hash__` method), and can be compared to
+      other objects (it needs an :meth:`__eq__` or :meth:`__cmp__` method).
+      Hashable objects that compare equal must have the same hash value.
+
+      Hashability makes an object usable as a dictionary key and a set member,
+      because these data structures use the hash value internally.
+
+      All of Python's immutable built-in objects are hashable, while all mutable
+      containers (such as lists or dictionaries) are not.  Objects that are
+      instances of user-defined classes are hashable by default; they all
+      compare unequal, and their hash value is their :func:`id`.
     
    IDLE
       An Integrated Development Environment for Python.  IDLE is a basic editor

Doc/library/datetime.rst

@@ -262,7 +262,7 @@ compared to an object of a different type, :exc:`TypeError` is raised unless the
 comparison is ``==`` or ``!=``.  The latter cases return :const:`False` or
 :const:`True`, respectively.
 
-:class:`timedelta` objects are hashable (usable as dictionary keys), support
+:class:`timedelta` objects are :term:`hashable` (usable as dictionary keys), support
 efficient pickling, and in Boolean contexts, a :class:`timedelta` object is
 considered to be true if and only if it isn't equal to ``timedelta(0)``.
 

Doc/library/difflib.rst

@@ -20,7 +20,7 @@ diffs. For comparing directories and files, see also, the :mod:`filecmp` module.
 .. class:: SequenceMatcher
 
    This is a flexible class for comparing pairs of sequences of any type, so long
-   as the sequence elements are hashable.  The basic algorithm predates, and is a
+   as the sequence elements are :term:`hashable`.  The basic algorithm predates, and is a
    little fancier than, an algorithm published in the late 1980's by Ratcliff and
    Obershelp under the hyperbolic name "gestalt pattern matching."  The idea is to
    find the longest contiguous matching subsequence that contains no "junk"
@@ -313,7 +313,7 @@ The :class:`SequenceMatcher` class has this constructor:
    on blanks or hard tabs.
 
    The optional arguments *a* and *b* are sequences to be compared; both default to
-   empty strings.  The elements of both sequences must be hashable.
+   empty strings.  The elements of both sequences must be :term:`hashable`.
 
 :class:`SequenceMatcher` objects have the following methods:
 

Doc/library/random.rst

@@ -60,7 +60,7 @@ Bookkeeping functions:
 .. function:: seed([x])
 
    Initialize the basic random number generator. Optional argument *x* can be any
-   hashable object. If *x* is omitted or ``None``, current system time is used;
+   :term:`hashable` object. If *x* is omitted or ``None``, current system time is used;
    current system time is also used to initialize the generator when the module is
    first imported.  If randomness sources are provided by the operating system,
    they are used instead of the system time (see the :func:`os.urandom` function
@@ -165,7 +165,7 @@ Functions for sequences:
    (the sample) to be partitioned into grand prize and second place winners (the
    subslices).
 
-   Members of the population need not be hashable or unique.  If the population
+   Members of the population need not be :term:`hashable` or unique.  If the population
    contains repeats, then each occurrence is a possible selection in the sample.
 
    To choose a sample from a range of integers, use an :func:`xrange` object as an

Doc/library/stdtypes.rst

@@ -1419,7 +1419,7 @@ Set Types --- :class:`set`, :class:`frozenset`
 
 .. index:: object: set
 
-A :dfn:`set` object is an unordered collection of distinct hashable objects.
+A :dfn:`set` object is an unordered collection of distinct :term:`hashable` objects.
 Common uses include membership testing, removing duplicates from a sequence, and
 computing mathematical operations such as intersection, union, difference, and
 symmetric difference.
@@ -1438,7 +1438,7 @@ There are currently two builtin set types, :class:`set` and :class:`frozenset`.
 The :class:`set` type is mutable --- the contents can be changed using methods
 like :meth:`add` and :meth:`remove`.  Since it is mutable, it has no hash value
 and cannot be used as either a dictionary key or as an element of another set.
-The :class:`frozenset` type is immutable and hashable --- its contents cannot be
+The :class:`frozenset` type is immutable and :term:`hashable` --- its contents cannot be
 altered after it is created; it can therefore be used as a dictionary key or as
 an element of another set.
 
@@ -1538,8 +1538,7 @@ or ``a>b``. Accordingly, sets do not implement the :meth:`__cmp__` method.
 Since sets only define partial ordering (subset relationships), the output of
 the :meth:`list.sort` method is undefined for lists of sets.
 
-Set elements are like dictionary keys; they need to define both :meth:`__hash__`
-and :meth:`__eq__` methods.
+Set elements, like dictionary keys, must be :term:`hashable`.
 
 Binary operations that mix :class:`set` instances with :class:`frozenset` return
 the type of the first operand.  For example: ``frozenset('ab') | set('bc')``
@@ -1619,21 +1618,20 @@ Mapping Types --- :class:`dict`
    statement: del
    builtin: len
 
-A :dfn:`mapping` object maps immutable values to arbitrary objects.  Mappings
-are mutable objects.  There is currently only one standard mapping type, the
-:dfn:`dictionary`.
-(For other containers see the built in :class:`list`,
-:class:`set`, and :class:`tuple` classes, and the :mod:`collections`
-module.)
+A :dfn:`mapping` object maps :term:`hashable` values to arbitrary objects.
+Mappings are mutable objects.  There is currently only one standard mapping
+type, the :dfn:`dictionary`.  (For other containers see the built in
+:class:`list`, :class:`set`, and :class:`tuple` classes, and the
+:mod:`collections` module.)
 
-A dictionary's keys are *almost* arbitrary values.  Only
-values containing lists, dictionaries or other mutable types (that are compared
-by value rather than by object identity) may not be used as keys. Numeric types
-used for keys obey the normal rules for numeric comparison: if two numbers
-compare equal (such as ``1`` and ``1.0``) then they can be used interchangeably
-to index the same dictionary entry. (Note however, that since computers
-store floating-point numbers as approximations it is usually unwise to
-use them as dictionary keys.)
+A dictionary's keys are *almost* arbitrary values.  Values that are not
+:term:`hashable`, that is, values containing lists, dictionaries or other
+mutable types (that are compared by value rather than by object identity) may
+not be used as keys.  Numeric types used for keys obey the normal rules for
+numeric comparison: if two numbers compare equal (such as ``1`` and ``1.0``)
+then they can be used interchangeably to index the same dictionary entry.  (Note
+however, that since computers store floating-point numbers as approximations it
+is usually unwise to use them as dictionary keys.)
 
 Dictionaries can be created by placing a comma-separated list of ``key: value``
 pairs within braces, for example: ``{'jack': 4098, 'sjoerd': 4127}`` or ``{4098:

Doc/library/weakref.rst

@@ -87,7 +87,7 @@ Extension types can easily be made to support weak references; see
    but cannot be propagated; they are handled in exactly the same way as exceptions
    raised from an object's :meth:`__del__` method.
 
-   Weak references are hashable if the *object* is hashable.  They will maintain
+   Weak references are :term:`hashable` if the *object* is hashable.  They will maintain
    their hash value even after the *object* was deleted.  If :func:`hash` is called
    the first time only after the *object* was deleted, the call will raise
    :exc:`TypeError`.
@@ -108,7 +108,7 @@ Extension types can easily be made to support weak references; see
    the proxy in most contexts instead of requiring the explicit dereferencing used
    with weak reference objects.  The returned object will have a type of either
    ``ProxyType`` or ``CallableProxyType``, depending on whether *object* is
-   callable.  Proxy objects are not hashable regardless of the referent; this
+   callable.  Proxy objects are not :term:`hashable` regardless of the referent; this
    avoids a number of problems related to their fundamentally mutable nature, and
    prevent their use as dictionary keys.  *callback* is the same as the parameter
    of the same name to the :func:`ref` function.

Doc/reference/datamodel.rst

@@ -409,9 +409,10 @@ Set types
    Frozen sets
       .. index:: object: frozenset
 
-      These represent an immutable set. They are created by the built-in
-      :func:`frozenset` constructor. As a frozenset is immutable and hashable, it can
-      be used again as an element of another set, or as a dictionary key.
+      These represent an immutable set.  They are created by the built-in
+      :func:`frozenset` constructor.  As a frozenset is immutable and
+      :term:`hashable`, it can be used again as an element of another set, or as
+      a dictionary key.
 
    .. % Set types
 
@@ -1315,6 +1316,9 @@ Basic customization
 
    .. versionadded:: 2.1
 
+   .. index::
+      single: comparisons
+
    These are the so-called "rich comparison" methods, and are called for comparison
    operators in preference to :meth:`__cmp__` below. The correspondence between
    operator symbols and method names is as follows: ``x<y`` calls ``x.__lt__(y)``,
@@ -1329,14 +1333,16 @@ Basic customization
    context (e.g., in the condition of an ``if`` statement), Python will call
    :func:`bool` on the value to determine if the result is true or false.
 
-   There are no implied relationships among the comparison operators. The truth of
-   ``x==y`` does not imply that ``x!=y`` is false.  Accordingly, when defining
-   :meth:`__eq__`, one should also define :meth:`__ne__` so that the operators will
-   behave as expected.
+   There are no implied relationships among the comparison operators. The truth
+   of ``x==y`` does not imply that ``x!=y`` is false.  Accordingly, when
+   defining :meth:`__eq__`, one should also define :meth:`__ne__` so that the
+   operators will behave as expected.  See the paragraph on :meth:`__hash__` for
+   some important notes on creating :term:`hashable` objects which support
+   custom comparison operations and are usable as dictionary keys.
 
-   There are no reflected (swapped-argument) versions of these methods (to be used
-   when the left argument does not support the operation but the right argument
-   does); rather, :meth:`__lt__` and :meth:`__gt__` are each other's reflection,
+   There are no swapped-argument versions of these methods (to be used when the
+   left argument does not support the operation but the right argument does);
+   rather, :meth:`__lt__` and :meth:`__gt__` are each other's reflection,
    :meth:`__le__` and :meth:`__ge__` are each other's reflection, and
    :meth:`__eq__` and :meth:`__ne__` are their own reflection.
 
@@ -1349,14 +1355,15 @@ Basic customization
       builtin: cmp
       single: comparisons
 
-   Called by comparison operations if rich comparison (see above) is not defined.
-   Should return a negative integer if ``self < other``, zero if ``self == other``,
-   a positive integer if ``self > other``.  If no :meth:`__cmp__`, :meth:`__eq__`
-   or :meth:`__ne__` operation is defined, class instances are compared by object
-   identity ("address").  See also the description of :meth:`__hash__` for some
-   important notes on creating objects which support custom comparison operations
-   and are usable as dictionary keys. (Note: the restriction that exceptions are
-   not propagated by :meth:`__cmp__` has been removed since Python 1.5.)
+   Called by comparison operations if rich comparison (see above) is not
+   defined.  Should return a negative integer if ``self < other``, zero if
+   ``self == other``, a positive integer if ``self > other``.  If no
+   :meth:`__cmp__`, :meth:`__eq__` or :meth:`__ne__` operation is defined, class
+   instances are compared by object identity ("address").  See also the
+   description of :meth:`__hash__` for some important notes on creating
+   :term:`hashable` objects which support custom comparison operations and are
+   usable as dictionary keys. (Note: the restriction that exceptions are not
+   propagated by :meth:`__cmp__` has been removed since Python 1.5.)
 
 
 .. method:: object.__rcmp__(self, other)
@@ -1371,25 +1378,29 @@ Basic customization
       object: dictionary
       builtin: hash
 
-   Called for the key object for dictionary  operations, and by the built-in
-   function :func:`hash`.  Should return a 32-bit integer usable as a hash value
+   Called for the key object for dictionary operations, and by the built-in
+   function :func:`hash`.  Should return an integer usable as a hash value
    for dictionary operations.  The only required property is that objects which
    compare equal have the same hash value; it is advised to somehow mix together
    (e.g., using exclusive or) the hash values for the components of the object that
-   also play a part in comparison of objects.  If a class does not define a
-   :meth:`__cmp__` method it should not define a :meth:`__hash__` operation either;
-   if it defines :meth:`__cmp__` or :meth:`__eq__` but not :meth:`__hash__`, its
-   instances will not be usable as dictionary keys.  If a class defines mutable
-   objects and implements a :meth:`__cmp__` or :meth:`__eq__` method, it should not
-   implement :meth:`__hash__`, since the dictionary implementation requires that a
-   key's hash value is immutable (if the object's hash value changes, it will be in
-   the wrong hash bucket).
+   also play a part in comparison of objects.
+
+   If a class does not define a :meth:`__cmp__` or :meth:`__eq__` method it
+   should not define a :meth:`__hash__` operation either; if it defines
+   :meth:`__cmp__` or :meth:`__eq__` but not :meth:`__hash__`, its instances
+   will not be usable as dictionary keys.  If a class defines mutable objects
+   and implements a :meth:`__cmp__` or :meth:`__eq__` method, it should not
+   implement :meth:`__hash__`, since the dictionary implementation requires that
+   a key's hash value is immutable (if the object's hash value changes, it will
+   be in the wrong hash bucket).
+
+   User-defined classes have :meth:`__cmp__` and :meth:`__hash__` methods
+   by default; with them, all objects compare unequal and ``x.__hash__()``
+   returns ``id(x)``.
 
    .. versionchanged:: 2.5
-      :meth:`__hash__` may now also return a long integer object; the 32-bit integer
-      is then derived from the hash of that object.
-
-   .. index:: single: __cmp__() (object method)
+      :meth:`__hash__` may now also return a long integer object; the 32-bit
+      integer is then derived from the hash of that object.
 
 
 .. method:: object.__nonzero__(self)

Doc/reference/expressions.rst

@@ -276,7 +276,7 @@ the corresponding datum.
 .. index:: pair: immutable; object
 
 Restrictions on the types of the key values are listed earlier in section
-:ref:`types`.  (To summarize, the key type should be hashable, which excludes
+:ref:`types`.  (To summarize, the key type should be :term:`hashable`, which excludes
 all mutable objects.)  Clashes between duplicate keys are not detected; the last
 datum (textually rightmost in the display) stored for a given key value
 prevails.