Metadata-Version: 2.1
Name: zc.relation
Version: 1.1.post2
Summary: Index intransitive and transitive n-ary relationships.
Home-page: https://github.com/zopefoundation/zc.relation
Author: Gary Poster
Author-email: gary@zope.com
License: ZPL 2.1
Description: ================
        Relation Catalog
        ================
        
        .. contents::
        
        Overview
        ========
        
        The relation catalog can be used to optimize intransitive and transitive
        searches for N-ary relations of finite, preset dimensions.
        
        For example, you can index simple two-way relations, like employee to
        supervisor; RDF-style triples of subject-predicate-object; and more complex
        relations such as subject-predicate-object with context and state.  These
        can be searched with variable definitions of transitive behavior.
        
        The catalog can be used in the ZODB or standalone. It is a generic, relatively
        policy-free tool.
        
        It is expected to be used usually as an engine for more specialized and
        constrained tools and APIs. Three such tools are zc.relationship containers,
        plone.relations containers, and zc.vault. The documents in the package,
        including this one, describe other possible uses.
        
        History
        =======
        
        This is a refactoring of the ZODB-only parts of the zc.relationship package.
        Specifically, the zc.relation catalog is largely equivalent to the
        zc.relationship index. The index in the zc.relationship 2.x line is an
        almost-completely backwards-compatible wrapper of the zc.relation catalog.
        zc.relationship will continue to be maintained, though active development is
        expected to go into zc.relation.
        
        Many of the ideas come from discussions with and code from Casey Duncan, Tres
        Seaver, Ken Manheimer, and more.
        
        Setting Up a Relation Catalog
        =============================
        
        In this section, we will be introducing the following ideas.
        
        - Relations are objects with indexed values.
        
        - You add value indexes to relation catalogs to be able to search.  Values
          can be identified to the catalog with callables or interface elements. The
          indexed value must be specified to the catalog as a single value or a
          collection.
        
        - Relations and their values are stored in the catalog as tokens: unique
          identifiers that you can resolve back to the original value. Integers are the
          most efficient tokens, but others can work fine too.
        
        - Token type determines the BTree module needed.
        
        - You must define your own functions for tokenizing and resolving tokens. These
          functions are registered with the catalog for the relations and for each of
          their value indexes.
        
        - Relations are indexed with ``index``.
        
        We will use a simple two way relation as our example here. A brief introduction
        to a more complex RDF-style subject-predicate-object set up can be found later
        in the document.
        
        Creating the Catalog
        --------------------
        
        Imagine a two way relation from one value to another.  Let's say that we
        are modeling a relation of people to their supervisors: an employee may
        have a single supervisor.  For this first example, the relation between
        employee and supervisor will be intrinsic: the employee has a pointer to
        the supervisor, and the employee object itself represents the relation.
        
        Let's say further, for simplicity, that employee names are unique and
        can be used to represent employees.  We can use names as our "tokens".
        
        Tokens are similar to the primary key in a relational database. A token is a
        way to identify an object. It must sort reliably and you must be able to write
        a callable that reliably resolves to the object given the right context. In
        Zope 3, intids (zope.app.intid) and keyreferences (zope.app.keyreference) are
        good examples of reasonable tokens.
        
        As we'll see below, you provide a way to convert objects to tokens, and resolve
        tokens to objects, for the relations, and for each value index individually.
        They can be the all the same functions or completely different, depending on
        your needs.
        
        For speed, integers make the best tokens; followed by other
        immutables like strings; followed by non-persistent objects; followed by
        persistent objects.  The choice also determines a choice of BTree module, as
        we'll see below.
        
        Here is our toy ``Employee`` example class.  Again, we will use the employee
        name as the tokens.
        
            >>> employees = {} # we'll use this to resolve the "name" tokens
            >>> from functools import total_ordering
            >>> @total_ordering
            ... class Employee(object):
            ...     def __init__(self, name, supervisor=None):
            ...         if name in employees:
            ...             raise ValueError('employee with same name already exists')
            ...         self.name = name # expect this to be readonly
            ...         self.supervisor = supervisor
            ...         employees[name] = self
            ...     # the next parts just make the tests prettier
            ...     def __repr__(self):
            ...         return '<Employee instance "' + self.name + '">'
            ...     def __lt__(self, other):
            ...         return self.name < other.name
            ...     def __eq__(self, other):
            ...         return self is other
            ...     def __hash__(self):
            ...         ''' Dummy method needed because we defined __eq__
            ...         '''
            ...         return 1
            ...
        
        So, we need to define how to turn employees into their tokens.  We call the
        tokenization a "dump" function. Conversely, the function to resolve tokens into
        objects is called a "load".
        
        Functions to dump relations and values get several arguments. The first
        argument is the object to be tokenized. Next, because it helps sometimes to
        provide context, is the catalog. The last argument is a dictionary that will be
        shared for a given search. The dictionary can be ignored, or used as a cache
        for optimizations (for instance, to stash a utility that you looked up).
        
        For this example, our function is trivial: we said the token would be
        the employee's name.
        
            >>> def dumpEmployees(emp, catalog, cache):
            ...     return emp.name
            ...
        
        If you store the relation catalog persistently (e.g., in the ZODB) be aware
        that the callables you provide must be picklable--a module-level function,
        for instance.
        
        We also need a way to turn tokens into employees, or "load".
        
        The "load" functions get the token to be resolved; the catalog, for
        context; and a dict cache, for optimizations of subsequent calls.
        
        You might have noticed in our ``Employee.__init__`` that we keep a mapping
        of name to object in the ``employees`` global dict (defined right above
        the class definition).  We'll use that for resolving the tokens.
        
            >>> def loadEmployees(token, catalog, cache):
            ...     return employees[token]
            ...
        
        Now we know enough to get started with a catalog.  We'll instantiate it
        by specifying how to tokenize relations, and what kind of BTree modules
        should be used to hold the tokens.
        
        How do you pick BTree modules?
        
        - If the tokens are 32-bit ints, choose ``BTrees.family32.II``,
          ``BTrees.family32.IF`` or ``BTrees.family32.IO``.
        
        - If the tokens are 64 bit ints, choose ``BTrees.family64.II``,
          ``BTrees.family64.IF`` or ``BTrees.family64.IO``.
        
        - If they are anything else, choose ``BTrees.family32.OI``,
          ``BTrees.family64.OI``, or ``BTrees.family32.OO`` (or
          ``BTrees.family64.OO``--they are the same).
        
        Within these rules, the choice is somewhat arbitrary unless you plan to merge
        these results with that of another source that is using a particular BTree
        module. BTree set operations only work within the same module, so you must
        match module to module. The catalog defaults to IF trees, because that's what
        standard zope catalogs use. That's as reasonable a choice as any, and will
        potentially come in handy if your tokens are in fact the same as those used by
        the zope catalog and you want to do some set operations.
        
        In this example, our tokens are strings, so we want OO or an OI variant.  We'll
        choose BTrees.family32.OI, arbitrarily.
        
            >>> import zc.relation.catalog
            >>> import BTrees
            >>> catalog = zc.relation.catalog.Catalog(dumpEmployees, loadEmployees,
            ...                                       btree=BTrees.family32.OI)
        
        [#verifyObjectICatalog]_
        
        .. [#verifyObjectICatalog] The catalog provides ICatalog.
        
            >>> from zope.interface.verify import verifyObject
            >>> import zc.relation.interfaces
            >>> verifyObject(zc.relation.interfaces.ICatalog, catalog)
            True
        
        [#legacy]_
        
        
        .. [#legacy] Old instances of zc.relationship indexes, which in the newest
            version subclass a zc.relation Catalog, used to have a dict in an
            internal data structure.  We specify that here so that the code that
            converts the dict to an OOBTree can have a chance to run.
        
            >>> catalog._attrs = dict(catalog._attrs)
        
        Look! A relation catalog! We can't do very
        much searching with it so far though, because the catalog doesn't have any
        indexes.
        
        In this example, the relation itself represents the employee, so we won't need
        to index that separately.
        
        But we do need a way to tell the catalog how to find the other end of the
        relation, the supervisor. You can specify this to the catalog with an attribute
        or method specified from ``zope.interface Interface``, or with a callable.
        We'll use a callable for now. The callable will receive the indexed relation
        and the catalog for context.
        
            >>> def supervisor(emp, catalog):
            ...     return emp.supervisor # None or another employee
            ...
        
        We'll also need to specify how to tokenize (dump and load) those values. In
        this case, we're able to use the same functions as the relations themselves.
        However, do note that we can specify a completely different way to dump and
        load for each "value index," or relation element.
        
        We could also specify the name to call the index, but it will default to the
        ``__name__`` of the function (or interface element), which will work just fine
        for us now.
        
        Now we can add the "supervisor" value index.
        
            >>> catalog.addValueIndex(supervisor, dumpEmployees, loadEmployees,
            ...                       btree=BTrees.family32.OI)
        
        Now we have an index [#addValueIndexExceptions]_.
        
        .. [#addValueIndexExceptions] Adding a value index can generate several
            exceptions.
        
            You must supply both of dump and load or neither.
        
            >>> catalog.addValueIndex(supervisor, dumpEmployees, None,
            ...                       btree=BTrees.family32.OI, name='supervisor2')
            Traceback (most recent call last):
            ...
            ValueError: either both of 'dump' and 'load' must be None, or neither
        
            In this example, even if we fix it, we'll get an error, because we have
            already indexed the supervisor function.
        
            >>> catalog.addValueIndex(supervisor, dumpEmployees, loadEmployees,
            ...                       btree=BTrees.family32.OI, name='supervisor2')
            ... # doctest: +ELLIPSIS
            Traceback (most recent call last):
            ...
            ValueError: ('element already indexed', <function supervisor at ...>)
        
            You also can't add a different function under the same name.
        
            >>> def supervisor2(emp, catalog):
            ...     return emp.supervisor # None or another employee
            ...
            >>> catalog.addValueIndex(supervisor2, dumpEmployees, loadEmployees,
            ...                       btree=BTrees.family32.OI, name='supervisor')
            ... # doctest: +ELLIPSIS
            Traceback (most recent call last):
            ...
            ValueError: ('name already used', 'supervisor')
        
            Finally, if your function does not have a ``__name__`` and you do not
            provide one, you may not add an index.
        
            >>> class Supervisor3(object):
            ...     __name__ = None
            ...     def __call__(klass, emp, catalog):
            ...         return emp.supervisor
            ...
            >>> supervisor3 = Supervisor3()
            >>> supervisor3.__name__
            >>> catalog.addValueIndex(supervisor3, dumpEmployees, loadEmployees,
            ...                       btree=BTrees.family32.OI)
            ... # doctest: +ELLIPSIS
            Traceback (most recent call last):
            ...
            ValueError: no name specified
        
            >>> [info['name'] for info in catalog.iterValueIndexInfo()]
            ['supervisor']
        
        Adding Relations
        ----------------
        
        Now let's create a few employees.  All but one will have supervisors.
        If you recall our toy ``Employee`` class, the first argument to the
        constructor is the employee name (and therefore the token), and the
        optional second argument is the supervisor.
        
            >>> a = Employee('Alice')
            >>> b = Employee('Betty', a)
            >>> c = Employee('Chuck', a)
            >>> d = Employee('Diane', b)
            >>> e = Employee('Edgar', b)
            >>> f = Employee('Frank', c)
            >>> g = Employee('Galyn', c)
            >>> h = Employee('Howie', d)
        
        Here is a diagram of the hierarchy.
        
        ::
        
                        Alice
                     __/     \__
                Betty           Chuck
                /   \           /   \
            Diane   Edgar   Frank   Galyn
              |
            Howie
        
        Let's tell the catalog about the relations, using the ``index`` method.
        
            >>> for emp in (a,b,c,d,e,f,g,h):
            ...     catalog.index(emp)
            ...
        
        We've now created the relation catalog and added relations to it. We're ready
        to search!
        
        Searching
        =========
        
        In this section, we will introduce the following ideas.
        
        - Queries to the relation catalog are formed with dicts.
        
        - Query keys are the names of the indexes you want to search, or, for the
          special case of precise relations, the ``zc.relation.RELATION`` constant.
        
        - Query values are the tokens of the results you want to match; or ``None``,
          indicating relations that have ``None`` as a value (or an empty collection,
          if it is a multiple). Search values can use
          ``zc.relation.catalog.any(args)`` or ``zc.relation.catalog.Any(args)`` to
          specify multiple (non-``None``) results to match for a given key.
        
        - The index has a variety of methods to help you work with tokens.
          ``tokenizeQuery`` is typically the most used, though others are available.
        
        - To find relations that match a query, use ``findRelations`` or
          ``findRelationTokens``.
        
        - To find values that match a query, use ``findValues`` or ``findValueTokens``.
        
        - You search transitively by using a query factory. The
          ``zc.relation.queryfactory.TransposingTransitive`` is a good common case
          factory that lets you walk up and down a hierarchy. A query factory can be
          passed in as an argument to search methods as a ``queryFactory``, or
          installed as a default behavior using ``addDefaultQueryFactory``.
        
        - To find how a query is related, use ``findRelationChains`` or
          ``findRelationTokenChains``.
        
        - To find out if a query is related, use ``canFind``.
        
        - Circular transitive relations are handled to prevent infinite loops. They
          are identified in ``findRelationChains`` and ``findRelationTokenChains`` with
          a ``zc.relation.interfaces.ICircularRelationPath`` marker interface.
        
        - search methods share the following arguments:
        
          * ``maxDepth``, limiting the transitive depth for searches;
        
          * ``filter``, allowing code to filter transitive paths;
        
          * ``targetQuery``, allowing a query to filter transitive paths on the basis
            of the endpoint;
        
          * ``targetFilter``, allowing code to filter transitive paths on the basis of
            the endpoint; and
        
          * ``queryFactory``, mentioned above.
        
        - You can set up search indexes to speed up specific transitive searches.
        
        Queries, ``findRelations``, and special query values
        ----------------------------------------------------
        
        So who works for Alice?  That means we want to get the relations--the
        employees--with a ``supervisor`` of Alice.
        
        The heart of a question to the catalog is a query.  A query is spelled
        as a dictionary.  The main idea is simply that keys in a dictionary
        specify index names, and the values specify the constraints.
        
        The values in a query are always expressed with tokens.  The catalog has
        several helpers to make this less onerous, but for now let's take
        advantage of the fact that our tokens are easily comprehensible.
        
            >>> sorted(catalog.findRelations({'supervisor': 'Alice'}))
            [<Employee instance "Betty">, <Employee instance "Chuck">]
        
        Alice is the direct (intransitive) boss of Betty and Chuck.
        
        What if you want to ask "who doesn't report to anyone?"  Then you want to
        ask for a relation in which the supervisor is None.
        
            >>> list(catalog.findRelations({'supervisor': None}))
            [<Employee instance "Alice">]
        
        Alice is the only employee who doesn't report to anyone.
        
        What if you want to ask "who reports to Diane or Chuck?"  Then you use the
        zc.relation ``Any`` class or ``any`` function to pass the multiple values.
        
            >>> sorted(catalog.findRelations(
            ...     {'supervisor': zc.relation.catalog.any('Diane', 'Chuck')}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Employee instance "Frank">, <Employee instance "Galyn">,
             <Employee instance "Howie">]
        
        Frank, Galyn, and Howie each report to either Diane or Chuck. [#any]_
        
        .. [#any] ``Any`` can be compared.
        
            >>> zc.relation.catalog.any('foo', 'bar', 'baz')
            <zc.relation.catalog.Any instance ('bar', 'baz', 'foo')>
            >>> (zc.relation.catalog.any('foo', 'bar', 'baz') ==
            ...  zc.relation.catalog.any('bar', 'foo', 'baz'))
            True
            >>> (zc.relation.catalog.any('foo', 'bar', 'baz') !=
            ...  zc.relation.catalog.any('bar', 'foo', 'baz'))
            False
            >>> (zc.relation.catalog.any('foo', 'bar', 'baz') ==
            ...  zc.relation.catalog.any('foo', 'baz'))
            False
            >>> (zc.relation.catalog.any('foo', 'bar', 'baz') !=
            ...  zc.relation.catalog.any('foo', 'baz'))
            True
        
        
        
        ``findValues`` and the ``RELATION`` query key
        ---------------------------------------------
        
        So how do we find who an employee's supervisor is?  Well, in this case,
        look at the attribute on the employee!  If you can use an attribute that
        will usually be a win in the ZODB.
        
            >>> h.supervisor
            <Employee instance "Diane">
        
        Again, as we mentioned at the start of this first example, the knowledge
        of a supervisor is "intrinsic" to the employee instance.  It is
        possible, and even easy, to ask the catalog this kind of question, but
        the catalog syntax is more geared to "extrinsic" relations, such as the
        one from the supervisor to the employee: the connection between a
        supervisor object and its employees is extrinsic to the supervisor, so
        you actually might want a catalog to find it!
        
        However, we will explore the syntax very briefly, because it introduces an
        important pair of search methods, and because it is a stepping stone
        to our first transitive search.
        
        So, o relation catalog, who is Howie's supervisor?
        
        To ask this question we want to get the indexed values off of the relations:
        ``findValues``. In its simplest form, the arguments are the index name of the
        values you want, and a query to find the relations that have the desired
        values.
        
        What about the query? Above, we noted that the keys in a query are the names of
        the indexes to search. However, in this case, we don't want to search one or
        more indexes for matching relations, as usual, but actually specify a relation:
        Howie.
        
        We do not have a value index name: we are looking for a relation. The query
        key, then, should be the constant ``zc.relation.RELATION``. For our current
        example, that would mean the query is ``{zc.relation.RELATION: 'Howie'}``.
        
            >>> import zc.relation
            >>> list(catalog.findValues(
            ...     'supervisor', {zc.relation.RELATION: 'Howie'}))[0]
            <Employee instance "Diane">
        
        Congratulations, you just found an obfuscated and comparitively
        inefficient way to write ``howie.supervisor``! [#intrinsic_search]_
        
        .. [#intrinsic_search] Here's the same with token results.
        
            >>> list(catalog.findValueTokens('supervisor',
            ...                              {zc.relation.RELATION: 'Howie'}))
            ['Diane']
        
            While we're down here in the footnotes, I'll mention that you can
            search for relations that haven't been indexed.
        
            >>> list(catalog.findRelationTokens({zc.relation.RELATION: 'Ygritte'}))
            []
            >>> list(catalog.findRelations({zc.relation.RELATION: 'Ygritte'}))
            []
        
        [#findValuesExceptions]_
        
        
        .. [#findValuesExceptions] If you use ``findValues`` or ``findValueTokens`` and
            try to specify a value name that is not indexed, you get a ValueError.
        
            >>> catalog.findValues('foo')
            Traceback (most recent call last):
            ...
            ValueError: ('name not indexed', 'foo')
        
        
        Slightly more usefully, you can use other query keys along with
        zc.relation.RELATION. This asks, "Of Betty, Alice, and Frank, who are
        supervised by Alice?"
        
            >>> sorted(catalog.findRelations(
            ...     {zc.relation.RELATION: zc.relation.catalog.any(
            ...         'Betty', 'Alice', 'Frank'),
            ...      'supervisor': 'Alice'}))
            [<Employee instance "Betty">]
        
        Only Betty is.
        
        Tokens
        ------
        
        As mentioned above, the catalog provides several helpers to work with tokens.
        The most frequently used is ``tokenizeQuery``, which takes a query with object
        values and converts them to tokens using the "dump" functions registered for
        the relations and indexed values. Here are alternate spellings of some of the
        queries we've encountered above.
        
            >>> catalog.tokenizeQuery({'supervisor': a})
            {'supervisor': 'Alice'}
            >>> catalog.tokenizeQuery({'supervisor': None})
            {'supervisor': None}
            >>> import pprint
            >>> result = catalog.tokenizeQuery(
            ...     {zc.relation.RELATION: zc.relation.catalog.any(a, b, f),
            ...     'supervisor': a}) # doctest: +NORMALIZE_WHITESPACE
            >>> pprint.pprint(result)
            {None: <zc.relation.catalog.Any instance ('Alice', 'Betty', 'Frank')>,
             'supervisor': 'Alice'}
        
        (If you are wondering about that ``None`` in the last result, yes,
        ``zc.relation.RELATION`` is just readability sugar for ``None``.)
        
        So, here's a real search using ``tokenizeQuery``.  We'll make an alias for
        ``catalog.tokenizeQuery`` just to shorten things up a bit.
        
            >>> query = catalog.tokenizeQuery
            >>> sorted(catalog.findRelations(query(
            ...     {zc.relation.RELATION: zc.relation.catalog.any(a, b, f),
            ...      'supervisor': a})))
            [<Employee instance "Betty">]
        
        The catalog always has parallel search methods, one for finding objects, as
        seen above, and one for finding tokens (the only exception is ``canFind``,
        described below). Finding tokens can be much more efficient, especially if the
        result from the relation catalog is just one step along the path of finding
        your desired result. But finding objects is simpler for some common cases.
        Here's a quick example of some queries above, getting tokens rather than
        objects.
        
        You can also spell a query in ``tokenizeQuery`` with keyword arguments. This
        won't work if your key is ``zc.relation.RELATION``, but otherwise it can
        improve readability. We'll see some examples of this below as well.
        
            >>> sorted(catalog.findRelationTokens(query(supervisor=a)))
            ['Betty', 'Chuck']
        
            >>> sorted(catalog.findRelationTokens({'supervisor': None}))
            ['Alice']
        
            >>> sorted(catalog.findRelationTokens(
            ...     query(supervisor=zc.relation.catalog.any(c, d))))
            ['Frank', 'Galyn', 'Howie']
        
            >>> sorted(catalog.findRelationTokens(
            ...     query({zc.relation.RELATION: zc.relation.catalog.any(a, b, f),
            ...            'supervisor': a})))
            ['Betty']
        
        The catalog provides several other methods just for working with tokens.
        
        - ``resolveQuery``: the inverse of ``tokenizeQuery``, converting a
          tokenizedquery to a query with objects.
        
        - ``tokenizeValues``: returns an iterable of tokens for the values of the given
          index name.
        
        - ``resolveValueTokens``: returns an iterable of values for the tokens of the
          given index name.
        
        - ``tokenizeRelation``: returns a token for the given relation.
        
        - ``resolveRelationToken``: returns a relation for the given token.
        
        - ``tokenizeRelations``: returns an iterable of tokens for the relations given.
        
        - ``resolveRelationTokens``: returns an iterable of relations for the tokens
          given.
        
        These methods are lesser used, and described in more technical documents in
        this package.
        
        Transitive Searching, Query Factories, and ``maxDepth``
        -------------------------------------------------------
        
        So, we've seen a lot of one-level, intransitive searching. What about
        transitive searching? Well, you need to tell the catalog how to walk the tree.
        In simple (and very common) cases like this, the
        ``zc.relation.queryfactory.TransposingTransitive`` will do the trick.
        
        A transitive query factory is just a callable that the catalog uses to
        ask "I got this query, and here are the results I found. I'm supposed to
        walk another step transitively, so what query should I search for next?"
        Writing a factory is more complex than we want to talk about right now,
        but using the ``TransposingTransitiveQueryFactory`` is easy. You just tell
        it the two query names it should transpose for walking in either
        direction.
        
        For instance, here we just want to tell the factory to transpose the two keys
        we've used, ``zc.relation.RELATION`` and 'supervisor'. Let's make a factory,
        use it in a query for a couple of transitive searches, and then, if you want,
        you can read through a footnote to talk through what is happening.
        
        Here's the factory.
        
            >>> import zc.relation.queryfactory
            >>> factory = zc.relation.queryfactory.TransposingTransitive(
            ...     zc.relation.RELATION, 'supervisor')
        
        Now ``factory`` is just a callable.  Let's let it help answer a couple of
        questions.
        
        Who are all of Howie's supervisors transitively (this looks up in the
        diagram)?
        
            >>> list(catalog.findValues('supervisor', {zc.relation.RELATION: 'Howie'},
            ...      queryFactory=factory))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Employee instance "Diane">, <Employee instance "Betty">,
             <Employee instance "Alice">]
        
        Who are all of the people Betty supervises transitively, breadth first (this
        looks down in the diagram)?
        
            >>> people = list(catalog.findRelations(
            ...     {'supervisor': 'Betty'}, queryFactory=factory))
            >>> sorted(people[:2])
            [<Employee instance "Diane">, <Employee instance "Edgar">]
            >>> people[2]
            <Employee instance "Howie">
        
        Yup, that looks right.  So how did that work?  If you care, read this
        footnote. [#I_care]_
        
        This transitive factory is really the only transitive factory you would
        want for this particular catalog, so it probably is safe to wire it in
        as a default.  You can add multiple query factories to match different
        queries using ``addDefaultQueryFactory``.
        
            >>> catalog.addDefaultQueryFactory(factory)
        
        Now all searches are transitive by default.
        
            >>> list(catalog.findValues('supervisor', {zc.relation.RELATION: 'Howie'}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Employee instance "Diane">, <Employee instance "Betty">,
             <Employee instance "Alice">]
            >>> people = list(catalog.findRelations({'supervisor': 'Betty'}))
            >>> sorted(people[:2])
            [<Employee instance "Diane">, <Employee instance "Edgar">]
            >>> people[2]
            <Employee instance "Howie">
        
        We can force a non-transitive search, or a specific search depth, with
        ``maxDepth`` [#needs_a_transitive_queries_factory]_.
        
        
        .. [#needs_a_transitive_queries_factory] A search with a ``maxDepth`` > 1 but
            no ``queryFactory`` raises an error.
        
            >>> catalog.removeDefaultQueryFactory(factory)
            >>> catalog.findRelationTokens({'supervisor': 'Diane'}, maxDepth=3)
            Traceback (most recent call last):
            ...
            ValueError: if maxDepth not in (None, 1), queryFactory must be available
        
            >>> catalog.addDefaultQueryFactory(factory)
        
            >>> list(catalog.findValues(
            ...     'supervisor', {zc.relation.RELATION: 'Howie'}, maxDepth=1))
            [<Employee instance "Diane">]
            >>> sorted(catalog.findRelations({'supervisor': 'Betty'}, maxDepth=1))
            [<Employee instance "Diane">, <Employee instance "Edgar">]
        
        [#maxDepthExceptions]_
        
        
        .. [#maxDepthExceptions] ``maxDepth`` must be None or a positive integer, or
            else you'll get a value error.
        
            >>> catalog.findRelations({'supervisor': 'Betty'}, maxDepth=0)
            Traceback (most recent call last):
            ...
            ValueError: maxDepth must be None or a positive integer
        
            >>> catalog.findRelations({'supervisor': 'Betty'}, maxDepth=-1)
            Traceback (most recent call last):
            ...
            ValueError: maxDepth must be None or a positive integer
        
        We'll introduce some other available search
        arguments later in this document and in other documents.  It's important
        to note that *all search methods share the same arguments as
        ``findRelations``*.  ``findValues`` and ``findValueTokens`` only add the
        initial argument of specifying the desired value.
        
        We've looked at two search methods so far: the ``findValues`` and
        ``findRelations`` methods help you ask what is related.  But what if you
        want to know *how* things are transitively related?
        
        ``findRelationChains`` and ``targetQuery``
        ------------------------------------------
        
        Another search method, ``findRelationChains``, helps you discover how
        things are transitively related.
        
        The method name says "find relation chains".  But what is a "relation
        chain"?  In this API, it is a transitive path of relations.  For
        instance, what's the chain of command above Howie?  ``findRelationChains``
        will return each unique path.
        
            >>> list(catalog.findRelationChains({zc.relation.RELATION: 'Howie'}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [(<Employee instance "Howie">,),
             (<Employee instance "Howie">, <Employee instance "Diane">),
             (<Employee instance "Howie">, <Employee instance "Diane">,
              <Employee instance "Betty">),
             (<Employee instance "Howie">, <Employee instance "Diane">,
             <Employee instance "Betty">, <Employee instance "Alice">)]
        
        Look at that result carefully.  Notice that the result is an iterable of
        tuples.  Each tuple is a unique chain, which may be a part of a
        subsequent chain.  In this case, the last chain is the longest and the
        most comprehensive.
        
        What if we wanted to see all the paths from Alice?  That will be one
        chain for each supervised employee, because it shows all possible paths.
        
            >>> sorted(catalog.findRelationChains(
            ...     {'supervisor': 'Alice'}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [(<Employee instance "Betty">,),
             (<Employee instance "Betty">, <Employee instance "Diane">),
             (<Employee instance "Betty">, <Employee instance "Diane">,
              <Employee instance "Howie">),
             (<Employee instance "Betty">, <Employee instance "Edgar">),
             (<Employee instance "Chuck">,),
             (<Employee instance "Chuck">, <Employee instance "Frank">),
             (<Employee instance "Chuck">, <Employee instance "Galyn">)]
        
        That's all the paths--all the chains--from Alice.  We sorted the results,
        but normally they would be breadth first.
        
        But what if we wanted to just find the paths from one query result to
        another query result--say, we wanted to know the chain of command from Alice
        down to Howie?  Then we can specify a ``targetQuery`` that specifies the
        characteristics of our desired end point (or points).
        
            >>> list(catalog.findRelationChains(
            ...     {'supervisor': 'Alice'},
            ...     targetQuery={zc.relation.RELATION: 'Howie'}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [(<Employee instance "Betty">, <Employee instance "Diane">,
              <Employee instance "Howie">)]
        
        So, Betty supervises Diane, who supervises Howie.
        
        Note that ``targetQuery`` now joins ``maxDepth`` in our collection of shared
        search arguments that we have introduced.
        
        ``filter`` and ``targetFilter``
        -------------------------------
        
        We can take a quick look now at the last of the two shared search arguments:
        ``filter`` and ``targetFilter``.  These two are similar in that they both are
        callables that can approve or reject given relations in a search based on
        whatever logic you can code.  They differ in that ``filter`` stops any further
        transitive searches from the relation, while ``targetFilter`` merely omits the
        given result but allows further search from it.  Like ``targetQuery``, then,
        ``targetFilter`` is good when you want to specify the other end of a path.
        
        As an example, let's say we only want to return female employees.
        
            >>> female_employees = ('Alice', 'Betty', 'Diane', 'Galyn')
            >>> def female_filter(relchain, query, catalog, cache):
            ...     return relchain[-1] in female_employees
            ...
        
        Here are all the female employees supervised by Alice transitively, using
        ``targetFilter``.
        
            >>> list(catalog.findRelations({'supervisor': 'Alice'},
            ...                            targetFilter=female_filter))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Employee instance "Betty">, <Employee instance "Diane">,
             <Employee instance "Galyn">]
        
        Here are all the female employees supervised by Chuck.
        
            >>> list(catalog.findRelations({'supervisor': 'Chuck'},
            ...                            targetFilter=female_filter))
            [<Employee instance "Galyn">]
        
        The same method used as a filter will only return females directly
        supervised by other females--not Galyn, in this case.
        
            >>> list(catalog.findRelations({'supervisor': 'Alice'},
            ...                            filter=female_filter))
            [<Employee instance "Betty">, <Employee instance "Diane">]
        
        These can be combined with one another, and with the other search
        arguments [#filter]_.
        
        .. [#filter] For instance:
        
            >>> list(catalog.findRelationTokens(
            ...     {'supervisor': 'Alice'}, targetFilter=female_filter,
            ...     targetQuery={zc.relation.RELATION: 'Galyn'}))
            ['Galyn']
            >>> list(catalog.findRelationTokens(
            ...     {'supervisor': 'Alice'}, targetFilter=female_filter,
            ...     targetQuery={zc.relation.RELATION: 'Not known'}))
            []
            >>> arbitrary = ['Alice', 'Chuck', 'Betty', 'Galyn']
            >>> def arbitrary_filter(relchain, query, catalog, cache):
            ...     return relchain[-1] in arbitrary
            >>> list(catalog.findRelationTokens({'supervisor': 'Alice'},
            ...                                 filter=arbitrary_filter,
            ...                                 targetFilter=female_filter))
            ['Betty', 'Galyn']
        
        Search indexes
        --------------
        
        Without setting up any additional indexes, the transitive behavior of
        the ``findRelations`` and ``findValues`` methods essentially relies on the
        brute force searches of ``findRelationChains``.  Results are iterables
        that are gradually computed.  For instance, let's repeat the question
        "Whom does Betty supervise?".  Notice that ``res`` first populates a list
        with three members, but then does not populate a second list.  The
        iterator has been exhausted.
        
            >>> res = catalog.findRelationTokens({'supervisor': 'Betty'})
            >>> unindexed = sorted(res)
            >>> len(unindexed)
            3
            >>> len(list(res)) # iterator is exhausted
            0
        
        The brute force of this approach can be sufficient in many cases, but
        sometimes speed for these searches is critical.  In these cases, you can
        add a "search index".  A search index speeds up the result of one or
        more precise searches by indexing the results.  Search indexes can
        affect the results of searches with a ``queryFactory`` in ``findRelations``,
        ``findValues``, and the soon-to-be-introduced ``canFind``, but they do not
        affect ``findRelationChains``.
        
        The zc.relation package currently includes two kinds of search indexes, one for
        indexing transitive membership searches in a hierarchy and one for intransitive
        searches explored in tokens.rst in this package, which can optimize frequent
        searches on complex queries or can effectively change the meaning of an
        intransitive search. Other search index implementations and approaches may be
        added in the future.
        
        Here's a very brief example of adding a search index for the transitive
        searches seen above that specify a 'supervisor'.
        
            >>> import zc.relation.searchindex
            >>> catalog.addSearchIndex(
            ...     zc.relation.searchindex.TransposingTransitiveMembership(
            ...         'supervisor', zc.relation.RELATION))
        
        The ``zc.relation.RELATION`` describes how to walk back up the chain. Search
        indexes are explained in reasonable detail in searchindex.rst.
        
        Now that we have added the index, we can search again.  The result this
        time is already computed, so, at least when you ask for tokens, it
        is repeatable.
        
            >>> res = catalog.findRelationTokens({'supervisor': 'Betty'})
            >>> len(list(res))
            3
            >>> len(list(res))
            3
            >>> sorted(res) == unindexed
            True
        
        Note that the breadth-first sorting is lost when an index is used [#updates]_.
        
        .. [#updates] The scenario we are looking at in this document shows a case
            in which special logic in the search index needs to address updates.
            For example, if we move Howie from Diane
        
            ::
        
                         Alice
                      __/     \__
                 Betty           Chuck
                 /   \           /   \
             Diane   Edgar   Frank   Galyn
               |
             Howie
        
            to Galyn
        
            ::
        
                         Alice
                      __/     \__
                 Betty           Chuck
                 /   \           /   \
             Diane   Edgar   Frank   Galyn
                                       |
                                     Howie
        
            then the search index is correct both for the new location and the old.
        
            >>> h.supervisor = g
            >>> catalog.index(h)
            >>> list(catalog.findRelationTokens({'supervisor': 'Diane'}))
            []
            >>> list(catalog.findRelationTokens({'supervisor': 'Betty'}))
            ['Diane', 'Edgar']
            >>> list(catalog.findRelationTokens({'supervisor': 'Chuck'}))
            ['Frank', 'Galyn', 'Howie']
            >>> list(catalog.findRelationTokens({'supervisor': 'Galyn'}))
            ['Howie']
            >>> h.supervisor = d
            >>> catalog.index(h) # move him back
            >>> list(catalog.findRelationTokens({'supervisor': 'Galyn'}))
            []
            >>> list(catalog.findRelationTokens({'supervisor': 'Diane'}))
            ['Howie']
        
        Transitive cycles (and updating and removing relations)
        -------------------------------------------------------
        
        The transitive searches and the provided search indexes can handle
        cycles.  Cycles are less likely in the current example than some others,
        but we can stretch the case a bit: imagine a "king in disguise", in
        which someone at the top works lower in the hierarchy.  Perhaps Alice
        works for Zane, who works for Betty, who works for Alice.  Artificial,
        but easy enough to draw::
        
                    ______
                   /      \
                  /     Zane
                 /        |
                /       Alice
               /     __/     \__
              / Betty__         Chuck
              \-/  /   \         /   \
                 Diane Edgar Frank   Galyn
                  |
                Howie
        
        Easy to create too.
        
            >>> z = Employee('Zane', b)
            >>> a.supervisor = z
        
        Now we have a cycle.  Of course, we have not yet told the catalog about it.
        ``index`` can be used both to reindex Alice and index Zane.
        
            >>> catalog.index(a)
            >>> catalog.index(z)
        
        Now, if we ask who works for Betty, we get the entire tree.  (We'll ask
        for tokens, just so that the result is smaller to look at.) [#same_set]_
        
        .. [#same_set] The result of the query for Betty, Alice, and Zane are all the
            same.
        
            >>> res1 = catalog.findRelationTokens({'supervisor': 'Betty'})
            >>> res2 = catalog.findRelationTokens({'supervisor': 'Alice'})
            >>> res3 = catalog.findRelationTokens({'supervisor': 'Zane'})
            >>> list(res1) == list(res2) == list(res3)
            True
        
            The cycle doesn't pollute the index outside of the cycle.
        
            >>> res = catalog.findRelationTokens({'supervisor': 'Diane'})
            >>> list(res)
            ['Howie']
            >>> list(res) # it isn't lazy, it is precalculated
            ['Howie']
        
            >>> sorted(catalog.findRelationTokens({'supervisor': 'Betty'}))
            ... # doctest: +NORMALIZE_WHITESPACE
            ['Alice', 'Betty', 'Chuck', 'Diane', 'Edgar', 'Frank', 'Galyn', 'Howie',
             'Zane']
        
        If we ask for the supervisors of Frank, it will include Betty.
        
            >>> list(catalog.findValueTokens(
            ...     'supervisor', {zc.relation.RELATION: 'Frank'}))
            ['Chuck', 'Alice', 'Zane', 'Betty']
        
        Paths returned by ``findRelationChains`` are marked with special interfaces,
        and special metadata, to show the chain.
        
            >>> res = list(catalog.findRelationChains({zc.relation.RELATION: 'Frank'}))
            >>> len(res)
            5
            >>> import zc.relation.interfaces
            >>> [zc.relation.interfaces.ICircularRelationPath.providedBy(r)
            ...  for r in res]
            [False, False, False, False, True]
        
        Here's the last chain:
        
            >>> res[-1] # doctest: +NORMALIZE_WHITESPACE
            cycle(<Employee instance "Frank">, <Employee instance "Chuck">,
                  <Employee instance "Alice">, <Employee instance "Zane">,
                  <Employee instance "Betty">)
        
        The chain's 'cycled' attribute has a list of queries that create a cycle.
        If you run the query, or queries, you see where the cycle would
        restart--where the path would have started to overlap.  Sometimes the query
        results will include multiple cycles, and some paths that are not cycles.
        In this case, there's only a single cycled query, which results in a single
        cycled relation.
        
            >>> len(res[4].cycled)
            1
        
            >>> list(catalog.findRelations(res[4].cycled[0], maxDepth=1))
            [<Employee instance "Alice">]
        
        To remove this craziness [#reverse_lookup]_, we can unindex Zane, and change
        and reindex Alice.
        
        .. [#reverse_lookup] If you want to, look what happens when you go the
            other way:
        
            >>> res = list(catalog.findRelationChains({'supervisor': 'Zane'}))
            >>> def sortEqualLenByName(one):
            ...     return len(one), one
            ...
            >>> res.sort(key=sortEqualLenByName)  # normalizes for test stability
            >>> from __future__ import print_function
            >>> print(res) # doctest: +NORMALIZE_WHITESPACE
            [(<Employee instance "Alice">,),
             (<Employee instance "Alice">, <Employee instance "Betty">),
             (<Employee instance "Alice">, <Employee instance "Chuck">),
             (<Employee instance "Alice">, <Employee instance "Betty">,
              <Employee instance "Diane">),
             (<Employee instance "Alice">, <Employee instance "Betty">,
              <Employee instance "Edgar">),
             cycle(<Employee instance "Alice">, <Employee instance "Betty">,
                   <Employee instance "Zane">),
             (<Employee instance "Alice">, <Employee instance "Chuck">,
              <Employee instance "Frank">),
             (<Employee instance "Alice">, <Employee instance "Chuck">,
              <Employee instance "Galyn">),
             (<Employee instance "Alice">, <Employee instance "Betty">,
              <Employee instance "Diane">, <Employee instance "Howie">)]
        
            >>> [zc.relation.interfaces.ICircularRelationPath.providedBy(r)
            ...  for r in res]
            [False, False, False, False, False, True, False, False, False]
            >>> len(res[5].cycled)
            1
            >>> list(catalog.findRelations(res[5].cycled[0], maxDepth=1))
            [<Employee instance "Alice">]
        
            >>> a.supervisor = None
            >>> catalog.index(a)
        
            >>> list(catalog.findValueTokens(
            ...     'supervisor', {zc.relation.RELATION: 'Frank'}))
            ['Chuck', 'Alice']
        
            >>> catalog.unindex(z)
        
            >>> sorted(catalog.findRelationTokens({'supervisor': 'Betty'}))
            ['Diane', 'Edgar', 'Howie']
        
        ``canFind``
        -----------
        
        We're to the last search method: ``canFind``.  We've gotten values and
        relations, but what if you simply want to know if there is any
        connection at all?  For instance, is Alice a supervisor of Howie? Is
        Chuck?  To answer these questions, you can use the ``canFind`` method
        combined with the ``targetQuery`` search argument.
        
        The ``canFind`` method takes the same arguments as findRelations.  However,
        it simply returns a boolean about whether the search has any results.  This
        is a convenience that also allows some extra optimizations.
        
        Does Betty supervise anyone?
        
            >>> catalog.canFind({'supervisor': 'Betty'})
            True
        
        What about Howie?
        
            >>> catalog.canFind({'supervisor': 'Howie'})
            False
        
        What about...Zane (no longer an employee)?
        
            >>> catalog.canFind({'supervisor': 'Zane'})
            False
        
        If we want to know if Alice or Chuck supervise Howie, then we want to specify
        characteristics of two points on a path.  To ask a question about the other
        end of a path, use ``targetQuery``.
        
        Is Alice a supervisor of Howie?
        
            >>> catalog.canFind({'supervisor': 'Alice'},
            ...                 targetQuery={zc.relation.RELATION: 'Howie'})
            True
        
        Is Chuck a supervisor of Howie?
        
            >>> catalog.canFind({'supervisor': 'Chuck'},
            ...                 targetQuery={zc.relation.RELATION: 'Howie'})
            False
        
        Is Howie Alice's employee?
        
            >>> catalog.canFind({zc.relation.RELATION: 'Howie'},
            ...                 targetQuery={'supervisor': 'Alice'})
            True
        
        Is Howie Chuck's employee?
        
            >>> catalog.canFind({zc.relation.RELATION: 'Howie'},
            ...                 targetQuery={'supervisor': 'Chuck'})
            False
        
        (Note that, if your relations describe a hierarchy, searching up a hierarchy is
        usually more efficient than searching down, so the second pair of questions is
        generally preferable to the first in that case.)
        
        Working with More Complex Relations
        ===================================
        
        So far, our examples have used a simple relation, in which the indexed object
        is one end of the relation, and the indexed value on the object is the other.
        This example has let us look at all of the basic zc.relation catalog
        functionality.
        
        As mentioned in the introduction, though, the catalog supports, and was
        designed for, more complex relations.  This section will quickly examine a
        few examples of other uses.
        
        In this section, we will see several examples of ideas mentioned above but not
        yet demonstrated.
        
        - We can use interface attributes (values or callables) to define value
          indexes.
        
        - Using interface attributes will cause an attempt to adapt the relation if it
          does not already provide the interface.
        
        - We can use the ``multiple`` argument when defining a value index to indicate
          that the indexed value is a collection.
        
        - We can use the ``name`` argument when defining a value index to specify the
          name to be used in queries, rather than relying on the name of the interface
          attribute or callable.
        
        - The ``family`` argument in instantiating the catalog lets you change the
          default btree family for relations and value indexes from
          ``BTrees.family32.IF`` to ``BTrees.family64.IF``.
        
        Extrinsic Two-Way Relations
        ---------------------------
        
        A simple variation of our current story is this: what if the indexed relation
        were between two other objects--that is, what if the relation were extrinsic to
        both participants?
        
        Let's imagine we have relations that show biological parentage. We'll want a
        "Person" and a "Parentage" relation. We'll define an interface for
        ``IParentage`` so we can see how using an interface to define a value index
        works.
        
            >>> class Person(object):
            ...     def __init__(self, name):
            ...         self.name = name
            ...     def __repr__(self):
            ...         return '<Person %r>' % (self.name,)
            ...
            >>> import zope.interface
            >>> class IParentage(zope.interface.Interface):
            ...     child = zope.interface.Attribute('the child')
            ...     parents = zope.interface.Attribute('the parents')
            ...
            >>> @zope.interface.implementer(IParentage)
            ... class Parentage(object):
            ...
            ...     def __init__(self, child, parent1, parent2):
            ...         self.child = child
            ...         self.parents = (parent1, parent2)
            ...
        
        Now we'll define the dumpers and loaders and then the catalog.  Notice that
        we are relying on a pattern: the dump must be called before the load.
        
            >>> _people = {}
            >>> _relations = {}
            >>> def dumpPeople(obj, catalog, cache):
            ...     if _people.setdefault(obj.name, obj) is not obj:
            ...         raise ValueError('we are assuming names are unique')
            ...     return obj.name
            ...
            >>> def loadPeople(token, catalog, cache):
            ...     return _people[token]
            ...
            >>> def dumpRelations(obj, catalog, cache):
            ...     if _relations.setdefault(id(obj), obj) is not obj:
            ...         raise ValueError('huh?')
            ...     return id(obj)
            ...
            >>> def loadRelations(token, catalog, cache):
            ...     return _relations[token]
            ...
            >>> catalog = zc.relation.catalog.Catalog(dumpRelations, loadRelations, family=BTrees.family64)
            >>> catalog.addValueIndex(IParentage['child'], dumpPeople, loadPeople,
            ...                       btree=BTrees.family32.OO)
            >>> catalog.addValueIndex(IParentage['parents'], dumpPeople, loadPeople,
            ...                       btree=BTrees.family32.OO, multiple=True,
            ...                       name='parent')
            >>> catalog.addDefaultQueryFactory(
            ...     zc.relation.queryfactory.TransposingTransitive(
            ...         'child', 'parent'))
        
        Now we have a catalog fully set up.  Let's add some relations.
        
            >>> a = Person('Alice')
            >>> b = Person('Betty')
            >>> c = Person('Charles')
            >>> d = Person('Donald')
            >>> e = Person('Eugenia')
            >>> f = Person('Fred')
            >>> g = Person('Gertrude')
            >>> h = Person('Harry')
            >>> i = Person('Iphigenia')
            >>> j = Person('Jacob')
            >>> k = Person('Karyn')
            >>> l = Person('Lee')
        
            >>> r1 = Parentage(child=j, parent1=k, parent2=l)
            >>> r2 = Parentage(child=g, parent1=i, parent2=j)
            >>> r3 = Parentage(child=f, parent1=g, parent2=h)
            >>> r4 = Parentage(child=e, parent1=g, parent2=h)
            >>> r5 = Parentage(child=b, parent1=e, parent2=d)
            >>> r6 = Parentage(child=a, parent1=e, parent2=c)
        
        Here's that in one of our hierarchy diagrams.
        
        ::
        
            Karyn   Lee
                 \ /
                Jacob   Iphigenia
                     \ /
                    Gertrude    Harry
                            \  /
                         /-------\
                     Fred        Eugenia
                       Donald   /     \    Charles
                             \ /       \  /
                            Betty      Alice
        
        Now we can index the relations, and ask some questions.
        
            >>> for r in (r1, r2, r3, r4, r5, r6):
            ...     catalog.index(r)
            >>> query = catalog.tokenizeQuery
            >>> sorted(catalog.findValueTokens(
            ...     'parent', query(child=a), maxDepth=1))
            ['Charles', 'Eugenia']
            >>> sorted(catalog.findValueTokens('parent', query(child=g)))
            ['Iphigenia', 'Jacob', 'Karyn', 'Lee']
            >>> sorted(catalog.findValueTokens(
            ...     'child', query(parent=h), maxDepth=1))
            ['Eugenia', 'Fred']
            >>> sorted(catalog.findValueTokens('child', query(parent=h)))
            ['Alice', 'Betty', 'Eugenia', 'Fred']
            >>> catalog.canFind(query(parent=h), targetQuery=query(child=d))
            False
            >>> catalog.canFind(query(parent=l), targetQuery=query(child=b))
            True
        
        Multi-Way Relations
        -------------------
        
        The previous example quickly showed how to set the catalog up for a completely
        extrinsic two-way relation.  The same pattern can be extended for N-way
        relations.  For example, consider a four way relation in the form of
        SUBJECTS PREDICATE OBJECTS [in CONTEXT].  For instance, we might
        want to say "(joe,) SELLS (doughnuts, coffee) in corner_store", where "(joe,)"
        is the collection of subjects, "SELLS" is the predicate, "(doughnuts, coffee)"
        is the collection of objects, and "corner_store" is the optional context.
        
        For this last example, we'll integrate two components we haven't seen examples
        of here before: the ZODB and adaptation.
        
        Our example ZODB approach uses OIDs as the tokens. this might be OK in some
        cases, if you will never support multiple databases and you don't need an
        abstraction layer so that a different object can have the same identifier.
        
            >>> import persistent
            >>> import struct
            >>> class Demo(persistent.Persistent):
            ...     def __init__(self, name):
            ...         self.name = name
            ...     def __repr__(self):
            ...         return '<Demo instance %r>' % (self.name,)
            ...
            >>> class IRelation(zope.interface.Interface):
            ...     subjects = zope.interface.Attribute('subjects')
            ...     predicate = zope.interface.Attribute('predicate')
            ...     objects = zope.interface.Attribute('objects')
            ...
            >>> class IContextual(zope.interface.Interface):
            ...     def getContext():
            ...         'return context'
            ...     def setContext(value):
            ...         'set context'
            ...
            >>> @zope.interface.implementer(IContextual)
            ... class Contextual(object):
            ...
            ...     _context = None
            ...     def getContext(self):
            ...         return self._context
            ...     def setContext(self, value):
            ...         self._context = value
            ...
            >>> @zope.interface.implementer(IRelation)
            ... class Relation(persistent.Persistent):
            ...
            ...     def __init__(self, subjects, predicate, objects):
            ...         self.subjects = subjects
            ...         self.predicate = predicate
            ...         self.objects = objects
            ...         self._contextual = Contextual()
            ...
            ...     def __conform__(self, iface):
            ...         if iface is IContextual:
            ...             return self._contextual
            ...
        
        (When using zope.component, the ``__conform__`` would normally be unnecessary;
        however, this package does not depend on zope.component.)
        
            >>> def dumpPersistent(obj, catalog, cache):
            ...     if obj._p_jar is None:
            ...         catalog._p_jar.add(obj) # assumes something else places it
            ...     return struct.unpack('<q', obj._p_oid)[0]
            ...
            >>> def loadPersistent(token, catalog, cache):
            ...     return catalog._p_jar.get(struct.pack('<q', token))
            ...
        
            >>> from ZODB.tests.util import DB
            >>> db = DB()
            >>> conn = db.open()
            >>> root = conn.root()
            >>> catalog = root['catalog'] = zc.relation.catalog.Catalog(
            ...     dumpPersistent, loadPersistent, family=BTrees.family64)
            >>> catalog.addValueIndex(IRelation['subjects'],
            ...     dumpPersistent, loadPersistent, multiple=True, name='subject')
            >>> catalog.addValueIndex(IRelation['objects'],
            ...     dumpPersistent, loadPersistent, multiple=True, name='object')
            >>> catalog.addValueIndex(IRelation['predicate'], btree=BTrees.family32.OO)
            >>> catalog.addValueIndex(IContextual['getContext'],
            ...     dumpPersistent, loadPersistent, name='context')
            >>> import transaction
            >>> transaction.commit()
        
        The ``dumpPersistent`` and ``loadPersistent`` is a bit of a toy, as warned
        above. Also, while our predicate will be stored as a string, some programmers
        may prefer to have a dump in such a case verify that the string has been
        explicitly registered in some way, to prevent typos. Obviously, we are not
        bothering with this for our example.
        
        We make some objects, and then we make some relations with those objects and
        index them.
        
            >>> joe = root['joe'] = Demo('joe')
            >>> sara = root['sara'] = Demo('sara')
            >>> jack = root['jack'] = Demo('jack')
            >>> ann = root['ann'] = Demo('ann')
            >>> doughnuts = root['doughnuts'] = Demo('doughnuts')
            >>> coffee = root['coffee'] = Demo('coffee')
            >>> muffins = root['muffins'] = Demo('muffins')
            >>> cookies = root['cookies'] = Demo('cookies')
            >>> newspaper = root['newspaper'] = Demo('newspaper')
            >>> corner_store = root['corner_store'] = Demo('corner_store')
            >>> bistro = root['bistro'] = Demo('bistro')
            >>> bakery = root['bakery'] = Demo('bakery')
        
            >>> SELLS = 'SELLS'
            >>> BUYS = 'BUYS'
            >>> OBSERVES = 'OBSERVES'
        
            >>> rel1 = root['rel1'] = Relation((joe,), SELLS, (doughnuts, coffee))
            >>> IContextual(rel1).setContext(corner_store)
            >>> rel2 = root['rel2'] = Relation((sara, jack), SELLS,
            ...                                (muffins, doughnuts, cookies))
            >>> IContextual(rel2).setContext(bakery)
            >>> rel3 = root['rel3'] = Relation((ann,), BUYS, (doughnuts,))
            >>> rel4 = root['rel4'] = Relation((sara,), BUYS, (bistro,))
        
            >>> for r in (rel1, rel2, rel3, rel4):
            ...     catalog.index(r)
            ...
        
        Now we can ask a simple question.  Where do they sell doughnuts?
        
            >>> query = catalog.tokenizeQuery
            >>> sorted(catalog.findValues(
            ...     'context',
            ...     (query(predicate=SELLS, object=doughnuts))),
            ...     key=lambda ob: ob.name)
            [<Demo instance 'bakery'>, <Demo instance 'corner_store'>]
        
        Hopefully these examples give you further ideas on how you can use this tool.
        
        Additional Functionality
        ========================
        
        This section introduces peripheral functionality.  We will learn the following.
        
        - Listeners can be registered in the catalog.  They are alerted when a relation
          is added, modified, or removed; and when the catalog is cleared and copied
          (see below).
        
        - The ``clear`` method clears the relations in the catalog.
        
        - The ``copy`` method makes a copy of the current catalog by copying internal
          data structures, rather than reindexing the relations, which can be a
          significant optimization opportunity.  This copies value indexes and search
          indexes; and gives listeners an opportunity to specify what, if anything,
          should be included in the new copy.
        
        - The ``ignoreSearchIndex`` argument to the five pertinent search methods
          causes the search to ignore search indexes, even if there is an appropriate
          one.
        
        - ``findRelationTokens()`` (without arguments) returns the BTree set of all
          relation tokens in the catalog.
        
        - ``findValueTokens(INDEX_NAME)`` (where "INDEX_NAME" should be replaced with
          an index name) returns the BTree set of all value tokens in the catalog for
          the given index name.
        
        Listeners
        ---------
        
        A variety of potential clients may want to be alerted when the catalog changes.
        zc.relation does not depend on zope.event, so listeners may be registered for
        various changes.  Let's make a quick demo listener.  The ``additions`` and
        ``removals`` arguments are dictionaries of {value name: iterable of added or
        removed value tokens}.
        
            >>> def pchange(d):
            ...     pprint.pprint(dict(
            ...         (k, v is not None and sorted(set(v)) or v) for k, v in d.items()))
            >>> @zope.interface.implementer(zc.relation.interfaces.IListener)
            ... class DemoListener(persistent.Persistent):
            ...
            ...     def relationAdded(self, token, catalog, additions):
            ...         print('a relation (token %r) was added to %r '
            ...                'with these values:' % (token, catalog))
            ...         pchange(additions)
            ...     def relationModified(self, token, catalog, additions, removals):
            ...         print('a relation (token %r) in %r was modified '
            ...                'with these additions:' % (token, catalog))
            ...         pchange(additions)
            ...         print('and these removals:')
            ...         pchange(removals)
            ...     def relationRemoved(self, token, catalog, removals):
            ...         print('a relation (token %r) was removed from %r '
            ...                'with these values:' % (token, catalog))
            ...         pchange(removals)
            ...     def sourceCleared(self, catalog):
            ...         print('catalog %r had all relations unindexed' % (catalog,))
            ...     def sourceAdded(self, catalog):
            ...         print('now listening to catalog %r' % (catalog,))
            ...     def sourceRemoved(self, catalog):
            ...         print('no longer listening to catalog %r' % (catalog,))
            ...     def sourceCopied(self, original, copy):
            ...         print('catalog %r made a copy %r' % (catalog, copy))
            ...         copy.addListener(self)
            ...
        
        Listeners can be installed multiple times.
        
        Listeners can be added as persistent weak references, so that, if they are
        deleted elsewhere, a ZODB pack will not consider the reference in the catalog
        to be something preventing garbage collection.
        
        We'll install one of these demo listeners into our new catalog as a
        normal reference, the default behavior.  Then we'll show some example messages
        sent to the demo listener.
        
            >>> listener = DemoListener()
            >>> catalog.addListener(listener) # doctest: +ELLIPSIS
            now listening to catalog <zc.relation.catalog.Catalog object at ...>
            >>> rel5 = root['rel5'] = Relation((ann,), OBSERVES, (newspaper,))
            >>> catalog.index(rel5) # doctest: +ELLIPSIS
            a relation (token ...) was added to <...Catalog...> with these values:
            {'context': None,
             'object': [...],
             'predicate': ['OBSERVES'],
             'subject': [...]}
            >>> rel5.subjects = (jack,)
            >>> IContextual(rel5).setContext(bistro)
            >>> catalog.index(rel5) # doctest: +ELLIPSIS
            a relation (token ...) in ...Catalog... was modified with these additions:
            {'context': [...], 'subject': [...]}
            and these removals:
            {'subject': [...]}
            >>> catalog.unindex(rel5) # doctest: +ELLIPSIS
            a relation (token ...) was removed from <...Catalog...> with these values:
            {'context': [...],
             'object': [...],
             'predicate': ['OBSERVES'],
             'subject': [...]}
        
            >>> catalog.removeListener(listener) # doctest: +ELLIPSIS
            no longer listening to catalog <...Catalog...>
            >>> catalog.index(rel5) # doctest: +ELLIPSIS
        
        The only two methods not shown by those examples are ``sourceCleared`` and
        ``sourceCopied``.  We'll get to those very soon below.
        
        The ``clear`` Method
        --------------------
        
        The ``clear`` method simply indexes all relations from a catalog.  Installed
        listeners have ``sourceCleared`` called.
        
            >>> len(catalog)
            5
        
            >>> catalog.addListener(listener) # doctest: +ELLIPSIS
            now listening to catalog <zc.relation.catalog.Catalog object at ...>
        
            >>> catalog.clear() # doctest: +ELLIPSIS
            catalog <...Catalog...> had all relations unindexed
        
            >>> len(catalog)
            0
            >>> sorted(catalog.findValues(
            ...     'context',
            ...     (query(predicate=SELLS, object=doughnuts))),
            ...     key=lambda ob: ob.name)
            []
        
        The ``copy`` Method
        -------------------
        
        Sometimes you may want to copy a relation catalog.  One way of doing this is
        to create a new catalog, set it up like the current one, and then reindex
        all the same relations.  This is unnecessarily slow for programmer and
        computer.  The ``copy`` method makes a new catalog with the same corpus of
        indexed relations by copying internal data structures.
        
        Search indexes are requested to make new copies of themselves for the new
        catalog; and listeners are given an opportunity to react as desired to the new
        copy, including installing themselves, and/or another object of their choosing
        as a listener.
        
        Let's make a copy of a populated index with a search index and a listener.
        Notice in our listener that ``sourceCopied`` adds itself as a listener to the
        new copy. This is done at the very end of the ``copy`` process.
        
            >>> for r in (rel1, rel2, rel3, rel4, rel5):
            ...     catalog.index(r)
            ... # doctest: +ELLIPSIS
            a relation ... was added...
            a relation ... was added...
            a relation ... was added...
            a relation ... was added...
            a relation ... was added...
            >>> BEGAT = 'BEGAT'
            >>> rel6 = root['rel6'] = Relation((jack, ann), BEGAT, (sara,))
            >>> henry = root['henry'] = Demo('henry')
            >>> rel7 = root['rel7'] = Relation((sara, joe), BEGAT, (henry,))
            >>> catalog.index(rel6) # doctest: +ELLIPSIS
            a relation (token ...) was added to <...Catalog...> with these values:
            {'context': None,
             'object': [...],
             'predicate': ['BEGAT'],
             'subject': [..., ...]}
            >>> catalog.index(rel7) # doctest: +ELLIPSIS
            a relation (token ...) was added to <...Catalog...> with these values:
            {'context': None,
             'object': [...],
             'predicate': ['BEGAT'],
             'subject': [..., ...]}
            >>> catalog.addDefaultQueryFactory(
            ...     zc.relation.queryfactory.TransposingTransitive(
            ...         'subject', 'object', {'predicate': BEGAT}))
            ...
            >>> list(catalog.findValues(
            ...     'object', query(subject=jack, predicate=BEGAT)))
            [<Demo instance 'sara'>, <Demo instance 'henry'>]
            >>> catalog.addSearchIndex(
            ...     zc.relation.searchindex.TransposingTransitiveMembership(
            ...         'subject', 'object', static={'predicate': BEGAT}))
            >>> sorted(
            ...     catalog.findValues(
            ...         'object', query(subject=jack, predicate=BEGAT)),
            ...     key=lambda o: o.name)
            [<Demo instance 'henry'>, <Demo instance 'sara'>]
        
            >>> newcat = root['newcat'] = catalog.copy() # doctest: +ELLIPSIS
            catalog <...Catalog...> made a copy <...Catalog...>
            now listening to catalog <...Catalog...>
            >>> transaction.commit()
        
        Now the copy has its own copies of internal data structures and of the
        searchindex.  For example, let's modify the relations and add a new one to the
        copy.
        
            >>> mary = root['mary'] = Demo('mary')
            >>> buffy = root['buffy'] = Demo('buffy')
            >>> zack = root['zack'] = Demo('zack')
            >>> rel7.objects += (mary,)
            >>> rel8 = root['rel8'] = Relation((henry, buffy), BEGAT, (zack,))
            >>> newcat.index(rel7) # doctest: +ELLIPSIS
            a relation (token ...) in ...Catalog... was modified with these additions:
            {'object': [...]}
            and these removals:
            {}
            >>> newcat.index(rel8) # doctest: +ELLIPSIS
            a relation (token ...) was added to ...Catalog... with these values:
            {'context': None,
             'object': [...],
             'predicate': ['BEGAT'],
             'subject': [..., ...]}
            >>> len(newcat)
            8
            >>> sorted(
            ...     newcat.findValues(
            ...         'object', query(subject=jack, predicate=BEGAT)),
            ...     key=lambda o: o.name) # doctest: +NORMALIZE_WHITESPACE
            [<Demo instance 'henry'>, <Demo instance 'mary'>, <Demo instance 'sara'>,
             <Demo instance 'zack'>]
            >>> sorted(
            ...     newcat.findValues(
            ...         'object', query(subject=sara)),
            ...     key=lambda o: o.name) # doctest: +NORMALIZE_WHITESPACE
            [<Demo instance 'bistro'>, <Demo instance 'cookies'>,
            <Demo instance 'doughnuts'>, <Demo instance 'henry'>,
            <Demo instance 'mary'>, <Demo instance 'muffins'>]
        
        The original catalog is not modified.
        
            >>> len(catalog)
            7
            >>> sorted(
            ...     catalog.findValues(
            ...         'object', query(subject=jack, predicate=BEGAT)),
            ...     key=lambda o: o.name)
            [<Demo instance 'henry'>, <Demo instance 'sara'>]
            >>> sorted(
            ...     catalog.findValues(
            ...         'object', query(subject=sara)),
            ...     key=lambda o: o.name) # doctest: +NORMALIZE_WHITESPACE
            [<Demo instance 'bistro'>, <Demo instance 'cookies'>,
             <Demo instance 'doughnuts'>, <Demo instance 'henry'>,
             <Demo instance 'muffins'>]
        
        The ``ignoreSearchIndex`` argument
        ----------------------------------
        
        The five methods that can use search indexes, ``findValues``,
        ``findValueTokens``, ``findRelations``, ``findRelationTokens``, and
        ``canFind``, can be explicitly requested to ignore any pertinent search index
        using the ``ignoreSearchIndex`` argument.
        
        We can see this easily with the token-related methods: the search index result
        will be a BTree set, while without the search index the result will be a
        generator.
        
            >>> res1 = newcat.findValueTokens(
            ...     'object', query(subject=jack, predicate=BEGAT))
            >>> res1 # doctest: +ELLIPSIS
            LFSet([..., ..., ..., ...])
            >>> res2 = newcat.findValueTokens(
            ...     'object', query(subject=jack, predicate=BEGAT),
            ...     ignoreSearchIndex=True)
            >>> res2 # doctest: +ELLIPSIS
            <generator object ... at 0x...>
            >>> sorted(res2) == list(res1)
            True
        
            >>> res1 = newcat.findRelationTokens(
            ...     query(subject=jack, predicate=BEGAT))
            >>> res1 # doctest: +ELLIPSIS
            LFSet([..., ..., ...])
            >>> res2 = newcat.findRelationTokens(
            ...     query(subject=jack, predicate=BEGAT), ignoreSearchIndex=True)
            >>> res2 # doctest: +ELLIPSIS
            <generator object ... at 0x...>
            >>> sorted(res2) == list(res1)
            True
        
        We can see that the other methods take the argument, but the results look the
        same as usual.
        
            >>> res = newcat.findValues(
            ...     'object', query(subject=jack, predicate=BEGAT),
            ...     ignoreSearchIndex=True)
            >>> res # doctest: +ELLIPSIS
            <generator object ... at 0x...>
            >>> list(res) == list(newcat.resolveValueTokens(newcat.findValueTokens(
            ...     'object', query(subject=jack, predicate=BEGAT),
            ...     ignoreSearchIndex=True), 'object'))
            True
        
            >>> res = newcat.findRelations(
            ...     query(subject=jack, predicate=BEGAT),
            ...     ignoreSearchIndex=True)
            >>> res # doctest: +ELLIPSIS
            <generator object ... at 0x...>
            >>> list(res) == list(newcat.resolveRelationTokens(
            ...     newcat.findRelationTokens(
            ...         query(subject=jack, predicate=BEGAT),
            ...         ignoreSearchIndex=True)))
            True
        
            >>> newcat.canFind(
            ...     query(subject=jack, predicate=BEGAT), ignoreSearchIndex=True)
            True
        
        ``findRelationTokens()``
        ------------------------
        
        If you call ``findRelationTokens`` without any arguments, you will get the
        BTree set of all relation tokens in the catalog.  This can be handy for tests
        and for advanced uses of the catalog.
        
            >>> newcat.findRelationTokens() # doctest: +ELLIPSIS
            <BTrees.LFBTree.LFTreeSet object at ...>
            >>> len(newcat.findRelationTokens())
            8
            >>> set(newcat.resolveRelationTokens(newcat.findRelationTokens())) == set(
            ...     (rel1, rel2, rel3, rel4, rel5, rel6, rel7, rel8))
            True
        
        ``findValueTokens(INDEX_NAME)``
        -------------------------------
        
        If you call ``findValueTokens`` with only an index name, you will get the BTree
        structure of all tokens for that value in the index. This can be handy for
        tests and for advanced uses of the catalog.
        
            >>> newcat.findValueTokens('predicate') # doctest: +ELLIPSIS
            <BTrees.OOBTree.OOBTree object at ...>
            >>> list(newcat.findValueTokens('predicate'))
            ['BEGAT', 'BUYS', 'OBSERVES', 'SELLS']
        
        Conclusion
        ==========
        
        Review
        ------
        
        That brings us to the end of our introductory examples.  Let's review, and
        then look at where you can go from here.
        
        * Relations are objects with indexed values.
        
        * The relation catalog indexes relations. The relations can be one-way,
          two-way, three-way, or N-way, as long as you tell the catalog to index the
          different values.
        
        * Creating a catalog:
        
            - Relations and their values are stored in the catalog as tokens: unique
              identifiers that you can resolve back to the original value. Integers are
              the most efficient tokens, but others can work fine too.
        
            - Token type determines the BTree module needed.
        
                - If the tokens are 32-bit ints, choose ``BTrees.family32.II``,
                  ``BTrees.family32.IF`` or ``BTrees.family32.IO``.
        
                - If the tokens are 64 bit ints, choose ``BTrees.family64.II``,
                  ``BTrees.family64.IF`` or ``BTrees.family64.IO``.
        
                - If they are anything else, choose ``BTrees.family32.OI``,
                  ``BTrees.family64.OI``, or ``BTrees.family32.OO`` (or
                  BTrees.family64.OO--they are the same).
        
              Within these rules, the choice is somewhat arbitrary unless you plan to
              merge these results with that of another source that is using a
              particular BTree module. BTree set operations only work within the same
              module, so you must match module to module.
        
            - The ``family`` argument in instantiating the catalog lets you change the
              default btree family for relations and value indexes from
              ``BTrees.family32.IF`` to ``BTrees.family64.IF``.
        
            - You must define your own functions for tokenizing and resolving tokens.
              These functions are registered with the catalog for the relations and for
              each of their value indexes.
        
            - You add value indexes to relation catalogs to be able to search.  Values
              can be identified to the catalog with callables or interface elements.
        
                - Using interface attributes will cause an attempt to adapt the
                  relation if it does not already provide the interface.
        
                - We can use the ``multiple`` argument when defining a value index to
                  indicate that the indexed value is a collection.  This defaults to
                  False.
        
                - We can use the ``name`` argument when defining a value index to
                  specify the name to be used in queries, rather than relying on the
                  name of the interface attribute or callable.
        
            - You can set up search indexes to speed up specific searches, usually
              transitive.
        
            - Listeners can be registered in the catalog. They are alerted when a
              relation is added, modified, or removed; and when the catalog is cleared
              and copied.
        
        * Catalog Management:
        
            - Relations are indexed with ``index(relation)``, and removed from the
              catalog with ``unindex(relation)``. ``index_doc(relation_token,
              relation)`` and ``unindex_doc(relation_token)`` also work.
        
            - The ``clear`` method clears the relations in the catalog.
        
            - The ``copy`` method makes a copy of the current catalog by copying
              internal data structures, rather than reindexing the relations, which can
              be a significant optimization opportunity. This copies value indexes and
              search indexes; and gives listeners an opportunity to specify what, if
              anything, should be included in the new copy.
        
        * Searching a catalog:
        
            - Queries to the relation catalog are formed with dicts.
        
            - Query keys are the names of the indexes you want to search, or, for the
              special case of precise relations, the ``zc.relation.RELATION`` constant.
        
            - Query values are the tokens of the results you want to match; or
              ``None``, indicating relations that have ``None`` as a value (or an empty
              collection, if it is a multiple). Search values can use
              ``zc.relation.catalog.any(args)`` or ``zc.relation.catalog.Any(args)`` to
              specify multiple (non-``None``) results to match for a given key.
        
            - The index has a variety of methods to help you work with tokens.
              ``tokenizeQuery`` is typically the most used, though others are
              available.
        
            - To find relations that match a query, use ``findRelations`` or
              ``findRelationTokens``.  Calling ``findRelationTokens`` without any
              arguments returns the BTree set of all relation tokens in the catalog.
        
            - To find values that match a query, use ``findValues`` or
              ``findValueTokens``.  Calling ``findValueTokens`` with only the name
              of a value index returns the BTree set of all tokens in the catalog for
              that value index.
        
            - You search transitively by using a query factory. The
              ``zc.relation.queryfactory.TransposingTransitive`` is a good common case
              factory that lets you walk up and down a hierarchy. A query factory can
              be passed in as an argument to search methods as a ``queryFactory``, or
              installed as a default behavior using ``addDefaultQueryFactory``.
        
            - To find how a query is related, use ``findRelationChains`` or
              ``findRelationTokenChains``.
        
            - To find out if a query is related, use ``canFind``.
        
            - Circular transitive relations are handled to prevent infinite loops. They
              are identified in ``findRelationChains`` and ``findRelationTokenChains``
              with a ``zc.relation.interfaces.ICircularRelationPath`` marker interface.
        
            - search methods share the following arguments:
        
              * ``maxDepth``, limiting the transitive depth for searches;
        
              * ``filter``, allowing code to filter transitive paths;
        
              * ``targetQuery``, allowing a query to filter transitive paths on the
                basis of the endpoint;
        
              * ``targetFilter``, allowing code to filter transitive paths on the basis
                of the endpoint; and
        
              * ``queryFactory``, mentioned above.
        
              In addition, the ``ignoreSearchIndex`` argument to ``findRelations``,
              ``findRelationTokens``, ``findValues``, ``findValueTokens``, and
              ``canFind`` causes the search to ignore search indexes, even if there is
              an appropriate one.
        
        Next Steps
        ----------
        
        If you want to read more, next steps depend on how you like to learn.  Here
        are some of the other documents in the zc.relation package.
        
        :optimization.rst:
            Best practices for optimizing your use of the relation catalog.
        
        :searchindex.rst:
            Queries factories and search indexes: from basics to nitty gritty details.
        
        :tokens.rst:
            This document explores the details of tokens.  All God's chillun
            love tokens, at least if God's chillun are writing non-toy apps
            using zc.relation.  It includes discussion of the token helpers that
            the catalog provides, how to use zope.app.intid-like registries with
            zc.relation, how to use tokens to "join" query results reasonably
            efficiently, and how to index joins.  It also is unnecessarily
            mind-blowing because of the examples used.
        
        :interfaces.py:
            The contract, for nuts and bolts.
        
        Finally, the truly die-hard might also be interested in the timeit
        directory, which holds scripts used to test assumptions and learn.
        
        .. ......... ..
        .. FOOTNOTES ..
        .. ......... ..
        
        .. [#I_care] OK, you care about how that query factory worked, so
            we will look into it a bit.  Let's talk through two steps of the
            transitive search in the second question.  The catalog initially
            performs the initial intransitive search requested: find relations
            for which Betty is the supervisor.  That's Diane and Edgar.
        
            Now, for each of the results, the catalog asks the query factory for
            next steps.  Let's take Diane.  The catalog says to the factory,
            "Given this query for relations where Betty is supervisor, I got
            this result of Diane.  Do you have any other queries I should try to
            look further?".  The factory also gets the catalog instance so it
            can use it to answer the question if it needs to.
        
            OK, the next part is where your brain hurts.  Hang on.
        
            In our case, the factory sees that the query was for supervisor. Its
            other key, the one it transposes with, is ``zc.relation.RELATION``. *The
            factory gets the transposing key's result for the current token.* So, for
            us, a key of ``zc.relation.RELATION`` is actually a no-op: the result *is*
            the current token, Diane. Then, the factory has its answer: replace the old
            value of supervisor in the query, Betty, with the result, Diane. The next
            transitive query should be {'supervisor', 'Diane'}. Ta-da.
        
        
        ======================================================
        Tokens and Joins: zc.relation Catalog Extended Example
        ======================================================
        
        Introduction and Set Up
        =======================
        
        This document assumes you have read the introductory README.rst and want
        to learn a bit more by example. In it, we will explore a more
        complicated set of relations that demonstrates most of the aspects of
        working with tokens.  In particular, we will look at joins, which will
        also give us a chance to look more in depth at query factories and
        search indexes, and introduce the idea of listeners. It will not explain
        the basics that the README already addressed.
        
        Imagine we are indexing security assertions in a system.  In this
        system, users may have roles within an organization.  Each organization
        may have multiple child organizations and may have a single parent
        organization.  A user with a role in a parent organization will have the
        same role in all transitively connected child relations.
        
        We have two kinds of relations, then.  One kind of relation will model
        the hierarchy of organizations.  We'll do it with an intrinsic relation
        of organizations to their children: that reflects the fact that parent
        organizations choose and are comprised of their children; children do
        not choose their parents.
        
        The other relation will model the (multiple) roles a (single) user has
        in a (single) organization.  This relation will be entirely extrinsic.
        
        We could create two catalogs, one for each type.  Or we could put them
        both in the same catalog.  Initially, we'll go with the single-catalog
        approach for our examples.  This single catalog, then, will be indexing
        a heterogeneous collection of relations.
        
        Let's define the two relations with interfaces.  We'll include one
        accessor, getOrganization, largely to show how to handle methods.
        
            >>> import zope.interface
            >>> class IOrganization(zope.interface.Interface):
            ...     title = zope.interface.Attribute('the title')
            ...     parts = zope.interface.Attribute(
            ...         'the organizations that make up this one')
            ...
            >>> class IRoles(zope.interface.Interface):
            ...     def getOrganization():
            ...         'return the organization in which this relation operates'
            ...     principal_id = zope.interface.Attribute(
            ...         'the pricipal id whose roles this relation lists')
            ...     role_ids = zope.interface.Attribute(
            ...         'the role ids that the principal explicitly has in the '
            ...         'organization.  The principal may have other roles via '
            ...         'roles in parent organizations.')
            ...
        
        Now we can create some classes.  In the README example, the setup was a bit
        of a toy.  This time we will be just a bit more practical.  We'll also expect
        to be operating within the ZODB, with a root and transactions. [#ZODB]_
        
        .. [#ZODB] Here we will set up a ZODB instance for us to use.
        
            >>> from ZODB.tests.util import DB
            >>> db = DB()
            >>> conn = db.open()
            >>> root = conn.root()
        
        Here's how we will dump and load our relations: use a "registry"
        object, similar to an intid utility. [#faux_intid]_
        
        .. [#faux_intid] Here's a simple persistent keyreference.  Notice that it is
            not persistent itself: this is important for conflict resolution to be
            able to work (which we don't show here, but we're trying to lean more
            towards real usage for this example).
        
            >>> from functools import total_ordering
            >>> @total_ordering
            ... class Reference(object): # see zope.app.keyreference
            ...     def __init__(self, obj):
            ...         self.object = obj
            ...     def _get_sorting_key(self):
            ...         # this doesn't work during conflict resolution.  See
            ...         # zope.app.keyreference.persistent, 3.5 release, for current
            ...         # best practice.
            ...         if self.object._p_jar is None:
            ...             raise ValueError(
            ...                 'can only compare when both objects have connections')
            ...         return self.object._p_oid or ''
            ...     def __lt__(self, other):
            ...         # this doesn't work during conflict resolution.  See
            ...         # zope.app.keyreference.persistent, 3.5 release, for current
            ...         # best practice.
            ...         if not isinstance(other, Reference):
            ...             raise ValueError('can only compare with Reference objects')
            ...         return self._get_sorting_key() < other._get_sorting_key()
            ...     def __eq__(self, other):
            ...         # this doesn't work during conflict resolution.  See
            ...         # zope.app.keyreference.persistent, 3.5 release, for current
            ...         # best practice.
            ...         if not isinstance(other, Reference):
            ...             raise ValueError('can only compare with Reference objects')
            ...         return self._get_sorting_key() == other._get_sorting_key()
        
            Here's a simple integer identifier tool.
        
            >>> import persistent
            >>> import BTrees
            >>> import six
            >>> class Registry(persistent.Persistent): # see zope.app.intid
            ...     def __init__(self, family=BTrees.family32):
            ...         self.family = family
            ...         self.ids = self.family.IO.BTree()
            ...         self.refs = self.family.OI.BTree()
            ...     def getId(self, obj):
            ...         if not isinstance(obj, persistent.Persistent):
            ...             raise ValueError('not a persistent object', obj)
            ...         if obj._p_jar is None:
            ...             self._p_jar.add(obj)
            ...         ref = Reference(obj)
            ...         id = self.refs.get(ref)
            ...         if id is None:
            ...             # naive for conflict resolution; see zope.app.intid
            ...             if self.ids:
            ...                 id = self.ids.maxKey() + 1
            ...             else:
            ...                  id = self.family.minint
            ...             self.ids[id] = ref
            ...             self.refs[ref] = id
            ...         return id
            ...     def __contains__(self, obj):
            ...         if (not isinstance(obj, persistent.Persistent) or
            ...             obj._p_oid is None):
            ...             return False
            ...         return Reference(obj) in self.refs
            ...     def getObject(self, id, default=None):
            ...         res = self.ids.get(id, None)
            ...         if res is None:
            ...             return default
            ...         else:
            ...             return res.object
            ...     def remove(self, r):
            ...         if isinstance(r, six.integer_types):
            ...             self.refs.pop(self.ids.pop(r))
            ...         elif (not isinstance(r, persistent.Persistent) or
            ...               r._p_oid is None):
            ...             raise LookupError(r)
            ...         else:
            ...             self.ids.pop(self.refs.pop(Reference(r)))
            ...
            >>> registry = root['registry'] = Registry()
        
            >>> import transaction
            >>> transaction.commit()
        
        In this implementation of the "dump" method, we use the cache just to
        show you how you might use it.  It probably is overkill for this job,
        and maybe even a speed loss, but you can see the idea.
        
            >>> def dump(obj, catalog, cache):
            ...     reg = cache.get('registry')
            ...     if reg is None:
            ...         reg = cache['registry'] = catalog._p_jar.root()['registry']
            ...     return reg.getId(obj)
            ...
            >>> def load(token, catalog, cache):
            ...     reg = cache.get('registry')
            ...     if reg is None:
            ...         reg = cache['registry'] = catalog._p_jar.root()['registry']
            ...     return reg.getObject(token)
            ...
        
        Now we can create a relation catalog to hold these items.
        
            >>> import zc.relation.catalog
            >>> catalog = root['catalog'] = zc.relation.catalog.Catalog(dump, load)
            >>> transaction.commit()
        
        Now we set up our indexes.  We'll start with just the organizations, and
        set up the catalog with them. This part will be similar to the example
        in README.rst, but will introduce more discussions of optimizations and
        tokens.  Then we'll add in the part about roles, and explore queries and
        token-based "joins".
        
        Organizations
        =============
        
        The organization will hold a set of organizations.  This is actually not
        inherently easy in the ZODB because this means that we need to compare
        or hash persistent objects, which does not work reliably over time and
        across machines out-of-the-box.  To side-step the issue for this example,
        and still do something a bit interesting and real-world, we'll use the
        registry tokens introduced above.  This will also give us a chance to
        talk a bit more about optimizations and tokens.  (If you would like
        to sanely and transparently hold a set of persistent objects, try the
        zc.set package XXX not yet.)
        
            >>> import BTrees
            >>> import persistent
            >>> @zope.interface.implementer(IOrganization)
            ... @total_ordering
            ... class Organization(persistent.Persistent):
            ...
            ...     def __init__(self, title):
            ...         self.title = title
            ...         self.parts = BTrees.family32.IF.TreeSet()
            ...     # the next parts just make the tests prettier
            ...     def __repr__(self):
            ...         return '<Organization instance "' + self.title + '">'
            ...     def __lt__(self, other):
            ...         # pukes if other doesn't have name
            ...         return self.title < other.title
            ...     def __eq__(self, other):
            ...         return self is other
            ...     def __hash__(self):
            ...         return 1  # dummy
            ...
        
        OK, now we know how organizations will work.  Now we can add the `parts`
        index to the catalog.  This will do a few new things from how we added
        indexes in the README.
        
        
            >>> catalog.addValueIndex(IOrganization['parts'], multiple=True,
            ...                       name="part")
        
        So, what's different from the README examples?
        
        First, we are using an interface element to define the value to be indexed.
        It provides an interface to which objects will be adapted, a default name
        for the index, and information as to whether the attribute should be used
        directly or called.
        
        Second, we are not specifying a dump or load.  They are None.  This
        means that the indexed value can already be treated as a token.  This
        can allow a very significant optimization for reindexing if the indexed
        value is a large collection using the same BTree family as the
        index--which leads us to the next difference.
        
        Third, we are specifying that `multiple=True`.  This means that the value
        on a given relation that provides or can be adapted to IOrganization will
        have a collection of `parts`.  These will always be regarded as a set,
        whether the actual colection is a BTrees set or the keys of a BTree.
        
        Last, we are specifying a name to be used for queries.  I find that queries
        read more easily when the query keys are singular, so I often rename plurals.
        
        As in the README, We can add another simple transposing transitive query
        factory, switching between 'part' and `None`.
        
            >>> import zc.relation.queryfactory
            >>> factory1 = zc.relation.queryfactory.TransposingTransitive(
            ...     'part', None)
            >>> catalog.addDefaultQueryFactory(factory1)
        
        Let's add a couple of search indexes in too, of the hierarchy looking up...
        
            >>> import zc.relation.searchindex
            >>> catalog.addSearchIndex(
            ...     zc.relation.searchindex.TransposingTransitiveMembership(
            ...         'part', None))
        
        ...and down.
        
            >>> catalog.addSearchIndex(
            ...     zc.relation.searchindex.TransposingTransitiveMembership(
            ...         None, 'part'))
        
        PLEASE NOTE: the search index looking up is not a good idea practically.  The
        index is designed for looking down [#verifyObjectTransitive]_.
        
        .. [#verifyObjectTransitive] The TransposingTransitiveMembership indexes
            provide ISearchIndex.
        
            >>> from zope.interface.verify import verifyObject
            >>> import zc.relation.interfaces
            >>> index = list(catalog.iterSearchIndexes())[0]
            >>> verifyObject(zc.relation.interfaces.ISearchIndex, index)
            True
        
        Let's create and add a few organizations.
        
        We'll make a structure like this [#silliness]_::
        
                 Ynod Corp Mangement                 Zookd Corp Management
                  /      |      \                       /      |      \
           Ynod Devs  Ynod SAs  Ynod Admins  Zookd Admins   Zookd SAs  Zookd Devs
             /      \              \                 /                /         \
         Y3L4 Proj  Bet Proj      Ynod Zookd Task Force      Zookd hOgnmd     Zookd Nbd
        
        Here's the Python.
        
        
            >>> orgs = root['organizations'] = BTrees.family32.OO.BTree()
            >>> for nm, parts in (
            ...     ('Y3L4 Proj', ()),
            ...     ('Bet Proj', ()),
            ...     ('Ynod Zookd Task Force', ()),
            ...     ('Zookd hOgnmd', ()),
            ...     ('Zookd Nbd', ()),
            ...     ('Ynod Devs', ('Y3L4 Proj', 'Bet Proj')),
            ...     ('Ynod SAs', ()),
            ...     ('Ynod Admins', ('Ynod Zookd Task Force',)),
            ...     ('Zookd Admins', ('Ynod Zookd Task Force',)),
            ...     ('Zookd SAs', ()),
            ...     ('Zookd Devs', ('Zookd hOgnmd', 'Zookd Nbd')),
            ...     ('Ynod Corp Management', ('Ynod Devs', 'Ynod SAs', 'Ynod Admins')),
            ...     ('Zookd Corp Management', ('Zookd Devs', 'Zookd SAs',
            ...                                'Zookd Admins'))):
            ...     org = Organization(nm)
            ...     for part in parts:
            ...         ignore = org.parts.insert(registry.getId(orgs[part]))
            ...     orgs[nm] = org
            ...     catalog.index(org)
            ...
        
        Now the catalog knows about the relations.
        
            >>> len(catalog)
            13
            >>> root['dummy'] = Organization('Foo')
            >>> root['dummy'] in catalog
            False
            >>> orgs['Y3L4 Proj'] in catalog
            True
        
        Also, now we can search.  To do this, we can use some of the token methods that
        the catalog provides.  The most commonly used is `tokenizeQuery`.  It takes a
        query with values that are not tokenized and converts them to values that are
        tokenized.
        
            >>> Ynod_SAs_id = registry.getId(orgs['Ynod SAs'])
            >>> catalog.tokenizeQuery({None: orgs['Ynod SAs']}) == {
            ...     None: Ynod_SAs_id}
            True
            >>> Zookd_SAs_id = registry.getId(orgs['Zookd SAs'])
            >>> Zookd_Devs_id = registry.getId(orgs['Zookd Devs'])
            >>> catalog.tokenizeQuery(
            ...     {None: zc.relation.catalog.any(
            ...         orgs['Zookd SAs'], orgs['Zookd Devs'])}) == {
            ...     None: zc.relation.catalog.any(Zookd_SAs_id, Zookd_Devs_id)}
            True
        
        Of course, right now doing this with 'part' alone is kind of silly, since it
        does not change within the relation catalog (because we said that dump and
        load were `None`, as discussed above).
        
            >>> catalog.tokenizeQuery({'part': Ynod_SAs_id}) == {
            ...     'part': Ynod_SAs_id}
            True
            >>> catalog.tokenizeQuery(
            ...     {'part': zc.relation.catalog.any(Zookd_SAs_id, Zookd_Devs_id)}
            ...     ) == {'part': zc.relation.catalog.any(Zookd_SAs_id, Zookd_Devs_id)}
            True
        
        The `tokenizeQuery` method is so common that we're going to assign it to
        a variable in our example. Then we'll do a search or two.
        
        So...find the relations that Ynod Devs supervise.
        
            >>> t = catalog.tokenizeQuery
            >>> res = list(catalog.findRelationTokens(t({None: orgs['Ynod Devs']})))
        
        OK...we used `findRelationTokens`, as opposed to `findRelations`, so res
        is a couple of numbers now.  How do we convert them back?
        `resolveRelationTokens` will do the trick.
        
            >>> len(res)
            3
            >>> sorted(catalog.resolveRelationTokens(res))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Organization instance "Bet Proj">, <Organization instance "Y3L4 Proj">,
             <Organization instance "Ynod Devs">]
        
        `resolveQuery` is the mirror image of `tokenizeQuery`: it converts
        tokenized queries to queries with "loaded" values.
        
            >>> original = {'part': zc.relation.catalog.any(
            ...                 Zookd_SAs_id, Zookd_Devs_id),
            ...             None: orgs['Zookd Devs']}
            >>> tokenized = catalog.tokenizeQuery(original)
            >>> original == catalog.resolveQuery(tokenized)
            True
        
            >>> original = {None: zc.relation.catalog.any(
            ...                 orgs['Zookd SAs'], orgs['Zookd Devs']),
            ...             'part': Zookd_Devs_id}
            >>> tokenized = catalog.tokenizeQuery(original)
            >>> original == catalog.resolveQuery(tokenized)
            True
        
        Likewise, `tokenizeRelations` is the mirror image of `resolveRelationTokens`.
        
            >>> sorted(catalog.tokenizeRelations(
            ...     [orgs["Bet Proj"], orgs["Y3L4 Proj"]])) == sorted(
            ...     registry.getId(o) for o in
            ...     [orgs["Bet Proj"], orgs["Y3L4 Proj"]])
            True
        
        The other token-related methods are as follows
        [#show_remaining_token_methods]_:
        
        .. [#show_remaining_token_methods] For what it's worth, here are some small
            examples of the remaining token-related methods.
        
            These two are the singular versions of `tokenizeRelations` and
            `resolveRelationTokens`.
        
            `tokenizeRelation` returns a token for the given relation.
        
            >>> catalog.tokenizeRelation(orgs['Zookd Corp Management']) == (
            ...     registry.getId(orgs['Zookd Corp Management']))
            True
        
            `resolveRelationToken` returns a relation for the given token.
        
            >>> catalog.resolveRelationToken(registry.getId(
            ...     orgs['Zookd Corp Management'])) is orgs['Zookd Corp Management']
            True
        
            The "values" ones are a bit lame to show now, since the only value
            we have right now is not tokenized but used straight up.  But here
            goes, showing some fascinating no-ops.
        
            `tokenizeValues`, returns an iterable of tokens for the values of
            the given index name.
        
            >>> list(catalog.tokenizeValues((1,2,3), 'part'))
            [1, 2, 3]
        
            `resolveValueTokens` returns an iterable of values for the tokens of
            the given index name.
        
            >>> list(catalog.resolveValueTokens((1,2,3), 'part'))
            [1, 2, 3]
        
        
        - `tokenizeValues`, which returns an iterable of tokens for the values
          of the given index name;
        - `resolveValueTokens`, which returns an iterable of values for the tokens of
          the given index name;
        - `tokenizeRelation`, which returns a token for the given relation; and
        - `resolveRelationToken`, which returns a relation for the given token.
        
        Why do we bother with these tokens, instead of hiding them away and
        making the API prettier?  By exposing them, we enable efficient joining,
        and efficient use in other contexts.  For instance, if you use the same
        intid utility to tokenize in other catalogs, our results can be merged
        with the results of other catalogs.  Similarly, you can use the results
        of queries to other catalogs--or even "joins" from earlier results of
        querying this catalog--as query values here.  We'll explore this in the
        next section.
        
        Roles
        =====
        
        We have set up the Organization relations.  Now let's set up the roles, and
        actually be able to answer the questions that we described at the beginning
        of the document.
        
        In our Roles object, roles and principals will simply be strings--ids, if
        this were a real system.  The organization will be a direct object reference.
        
            >>> @zope.interface.implementer(IRoles)
            ... @total_ordering
            ... class Roles(persistent.Persistent):
            ...
            ...     def __init__(self, principal_id, role_ids, organization):
            ...         self.principal_id = principal_id
            ...         self.role_ids = BTrees.family32.OI.TreeSet(role_ids)
            ...         self._organization = organization
            ...     def getOrganization(self):
            ...         return self._organization
            ...     # the rest is for prettier/easier tests
            ...     def __repr__(self):
            ...         return "<Roles instance (%s has %s in %s)>" % (
            ...             self.principal_id, ', '.join(self.role_ids),
            ...             self._organization.title)
            ...     def __lt__(self, other):
            ...         _self = (
            ...             self.principal_id,
            ...             tuple(self.role_ids),
            ...             self._organization.title,
            ...         )
            ...         _other = (
            ...             other.principal_id,
            ...             tuple(other.role_ids),
            ...             other._organization.title,
            ...         )
            ...         return _self <_other
            ...     def __eq__(self, other):
            ...         return self is other
            ...     def __hash__(self):
            ...         return 1  # dummy
            ...
        
        Now let's add add the value indexes to the relation catalog.
        
            >>> catalog.addValueIndex(IRoles['principal_id'], btree=BTrees.family32.OI)
            >>> catalog.addValueIndex(IRoles['role_ids'], btree=BTrees.family32.OI,
            ...                       multiple=True, name='role_id')
            >>> catalog.addValueIndex(IRoles['getOrganization'], dump, load,
            ...                       name='organization')
        
        Those are some slightly new variations of what we've seen in `addValueIndex`
        before, but all mixing and matching on the same ingredients.
        
        As a reminder, here is our organization structure::
        
                 Ynod Corp Mangement                 Zookd Corp Management
                  /      |      \                       /      |      \
           Ynod Devs  Ynod SAs  Ynod Admins  Zookd Admins   Zookd SAs  Zookd Devs
             /      \              \                 /                /         \
         Y3L4 Proj  Bet Proj      Ynod Zookd Task Force      Zookd hOgnmd     Zookd Nbd
        
        Now let's create and add some roles.
        
            >>> principal_ids = [
            ...     'abe', 'bran', 'cathy', 'david', 'edgar', 'frank', 'gertrude',
            ...     'harriet', 'ignas', 'jacob', 'karyn', 'lettie', 'molly', 'nancy',
            ...     'ophelia', 'pat']
            >>> role_ids = ['user manager', 'writer', 'reviewer', 'publisher']
            >>> get_role = dict((v[0], v) for v in role_ids).__getitem__
            >>> roles = root['roles'] = BTrees.family32.IO.BTree()
            >>> next = 0
            >>> for prin, org, role_ids in (
            ...     ('abe', orgs['Zookd Corp Management'], 'uwrp'),
            ...     ('bran', orgs['Ynod Corp Management'], 'uwrp'),
            ...     ('cathy', orgs['Ynod Devs'], 'w'),
            ...     ('cathy', orgs['Y3L4 Proj'], 'r'),
            ...     ('david', orgs['Bet Proj'], 'wrp'),
            ...     ('edgar', orgs['Ynod Devs'], 'up'),
            ...     ('frank', orgs['Ynod SAs'], 'uwrp'),
            ...     ('frank', orgs['Ynod Admins'], 'w'),
            ...     ('gertrude', orgs['Ynod Zookd Task Force'], 'uwrp'),
            ...     ('harriet', orgs['Ynod Zookd Task Force'], 'w'),
            ...     ('harriet', orgs['Ynod Admins'], 'r'),
            ...     ('ignas', orgs['Zookd Admins'], 'r'),
            ...     ('ignas', orgs['Zookd Corp Management'], 'w'),
            ...     ('karyn', orgs['Zookd Corp Management'], 'uwrp'),
            ...     ('karyn', orgs['Ynod Corp Management'], 'uwrp'),
            ...     ('lettie', orgs['Zookd Corp Management'], 'u'),
            ...     ('lettie', orgs['Ynod Zookd Task Force'], 'w'),
            ...     ('lettie', orgs['Zookd SAs'], 'w'),
            ...     ('molly', orgs['Zookd SAs'], 'uwrp'),
            ...     ('nancy', orgs['Zookd Devs'], 'wrp'),
            ...     ('nancy', orgs['Zookd hOgnmd'], 'u'),
            ...     ('ophelia', orgs['Zookd Corp Management'], 'w'),
            ...     ('ophelia', orgs['Zookd Devs'], 'r'),
            ...     ('ophelia', orgs['Zookd Nbd'], 'p'),
            ...     ('pat', orgs['Zookd Nbd'], 'wrp')):
            ...     assert prin in principal_ids
            ...     role_ids = [get_role(l) for l in role_ids]
            ...     role = roles[next] = Roles(prin, role_ids, org)
            ...     role.key = next
            ...     next += 1
            ...     catalog.index(role)
            ...
        
        Now we can begin to do searches [#real_value_tokens]_.
        
        
        .. [#real_value_tokens] We can also show the values token methods more
            sanely now.
        
            >>> original = sorted((orgs['Zookd Devs'], orgs['Ynod SAs']))
            >>> tokens = list(catalog.tokenizeValues(original, 'organization'))
            >>> original == sorted(catalog.resolveValueTokens(tokens, 'organization'))
            True
        
        What are all the role settings for ophelia?
        
            >>> sorted(catalog.findRelations({'principal_id': 'ophelia'}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Roles instance (ophelia has publisher in Zookd Nbd)>,
             <Roles instance (ophelia has reviewer in Zookd Devs)>,
             <Roles instance (ophelia has writer in Zookd Corp Management)>]
        
        That answer does not need to be transitive: we're done.
        
        Next question.  Where does ophelia have the 'writer' role?
        
            >>> list(catalog.findValues(
            ...     'organization', {'principal_id': 'ophelia',
            ...                        'role_id': 'writer'}))
            [<Organization instance "Zookd Corp Management">]
        
        Well, that's correct intransitively.  Do we need a transitive queries
        factory?  No! This is a great chance to look at the token join we talked
        about in the previous section.  This should actually be a two-step
        operation: find all of the organizations in which ophelia has writer,
        and then find all of the transitive parts to that organization.
        
            >>> sorted(catalog.findRelations({None: zc.relation.catalog.Any(
            ...     catalog.findValueTokens('organization',
            ...                             {'principal_id': 'ophelia',
            ...                              'role_id': 'writer'}))}))
            ... # doctest: +NORMALIZE_WHITESPACE
            [<Organization instance "Ynod Zookd Task Force">,
             <Organization instance "Zookd Admins">,
             <Organization instance "Zookd Corp Management">,
             <Organization instance "Zookd Devs">,
             <Organization instance "Zookd Nbd">,
             <Organization instance "Zookd SAs">,
             <Organization instance "Zookd hOgnmd">]
        
        That's more like it.
        
        Next question.  What users have roles in the 'Zookd Devs' organization?
        Intransitively, that's pretty easy.
        
            >>> sorted(catalog.findValueTokens(
            ...     'principal_id', t({'organization': orgs['Zookd Devs']})))
            ['nancy', 'ophelia']
        
        Transitively, we should do another join.
        
            >>> org_id = registry.getId(orgs['Zookd Devs'])
            >>> sorted(catalog.findValueTokens(
            ...     'principal_id', {
            ...         'organization': zc.relation.catalog.any(
            ...             org_id, *catalog.findRelationTokens({'part': org_id}))}))
            ['abe', 'ignas', 'karyn', 'lettie', 'nancy', 'ophelia']
        
        That's a little awkward, but it does the trick.
        
        Last question, and the kind of question that started the entire example.
         What roles does ophelia have in the "Zookd Nbd" organization?
        
            >>> list(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'ophelia'})))
            ['publisher']
        
        Intransitively, that's correct.  But, transitively, ophelia also has
        reviewer and writer, and that's the answer we want to be able to get quickly.
        
        We could ask the question a different way, then, again leveraging a join.
        We'll set it up as a function, because we will want to use it a little later
        without repeating the code.
        
            >>> def getRolesInOrganization(principal_id, org):
            ...     org_id = registry.getId(org)
            ...     return sorted(catalog.findValueTokens(
            ...         'role_id', {
            ...             'organization': zc.relation.catalog.any(
            ...                 org_id,
            ...                 *catalog.findRelationTokens({'part': org_id})),
            ...             'principal_id': principal_id}))
            ...
            >>> getRolesInOrganization('ophelia', orgs['Zookd Nbd'])
            ['publisher', 'reviewer', 'writer']
        
        As you can see, then, working with tokens makes interesting joins possible,
        as long as the tokens are the same across the two queries.
        
        We have examined tokens methods and token techniques like joins.  The example
        story we have told can let us get into a few more advanced topics, such as
        query factory joins and search indexes that can increase their read speed.
        
        Query Factory Joins
        ===================
        
        We can build a query factory that makes the join automatic.  A query
        factory is a callable that takes two arguments: a query (the one that
        starts the search) and the catalog.  The factory either returns None,
        indicating that the query factory cannot be used for this query, or it
        returns another callable that takes a chain of relations.  The last
        token in the relation chain is the most recent.  The output of this
        inner callable is expected to be an iterable of
        BTrees.family32.OO.Bucket queries to search further from the given chain
        of relations.
        
        Here's a flawed approach to this problem.
        
            >>> def flawed_factory(query, catalog):
            ...     if (len(query) == 2 and
            ...         'organization' in query and
            ...         'principal_id' in query):
            ...         def getQueries(relchain):
            ...             if not relchain:
            ...                 yield query
            ...                 return
            ...             current = catalog.getValueTokens(
            ...                 'organization', relchain[-1])
            ...             if current:
            ...                 organizations = catalog.getRelationTokens(
            ...                     {'part': zc.relation.catalog.Any(current)})
            ...                 if organizations:
            ...                     res = BTrees.family32.OO.Bucket(query)
            ...                     res['organization'] = zc.relation.catalog.Any(
            ...                         organizations)
            ...                     yield res
            ...         return getQueries
            ...
        
        That works for our current example.
        
            >>> sorted(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'ophelia'}),
            ...     queryFactory=flawed_factory))
            ['publisher', 'reviewer', 'writer']
        
        However, it won't work for other similar queries.
        
            >>> getRolesInOrganization('abe', orgs['Zookd Nbd'])
            ['publisher', 'reviewer', 'user manager', 'writer']
            >>> sorted(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'}),
            ...     queryFactory=flawed_factory))
            []
        
        oops.
        
        The flawed_factory is actually a useful pattern for more typical relation
        traversal.  It goes from relation to relation to relation, and ophelia has
        connected relations all the way to the top.  However, abe only has them at
        the top, so nothing is traversed.
        
        Instead, we can make a query factory that modifies the initial query.
        
            >>> def factory2(query, catalog):
            ...     if (len(query) == 2 and
            ...         'organization' in query and
            ...         'principal_id' in query):
            ...         def getQueries(relchain):
            ...             if not relchain:
            ...                 res = BTrees.family32.OO.Bucket(query)
            ...                 org_id = query['organization']
            ...                 if org_id is not None:
            ...                     res['organization'] = zc.relation.catalog.any(
            ...                         org_id,
            ...                         *catalog.findRelationTokens({'part': org_id}))
            ...                 yield res
            ...         return getQueries
            ...
        
            >>> sorted(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'ophelia'}),
            ...     queryFactory=factory2))
            ['publisher', 'reviewer', 'writer']
        
            >>> sorted(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'}),
            ...     queryFactory=factory2))
            ['publisher', 'reviewer', 'user manager', 'writer']
        
        A difference between this and the other approach is that it is essentially
        intransitive: this query factory modifies the initial query, and then does
        not give further queries.  The catalog currently always stops calling the
        query factory if the queries do not return any results, so an approach like
        the flawed_factory simply won't work for this kind of problem.
        
        We could add this query factory as another default.
        
            >>> catalog.addDefaultQueryFactory(factory2)
        
            >>> sorted(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'ophelia'})))
            ['publisher', 'reviewer', 'writer']
        
            >>> sorted(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'})))
            ['publisher', 'reviewer', 'user manager', 'writer']
        
        The previously installed query factory is still available.
        
            >>> list(catalog.iterDefaultQueryFactories()) == [factory1, factory2]
            True
        
            >>> list(catalog.findRelations(
            ...     {'part': registry.getId(orgs['Y3L4 Proj'])}))
            ...     # doctest: +NORMALIZE_WHITESPACE
            [<Organization instance "Ynod Devs">,
             <Organization instance "Ynod Corp Management">]
        
            >>> sorted(catalog.findRelations(
            ...     {None: registry.getId(orgs['Ynod Corp Management'])}))
            ...     # doctest: +NORMALIZE_WHITESPACE
            [<Organization instance "Bet Proj">, <Organization instance "Y3L4 Proj">,
             <Organization instance "Ynod Admins">,
             <Organization instance "Ynod Corp Management">,
             <Organization instance "Ynod Devs">, <Organization instance "Ynod SAs">,
             <Organization instance "Ynod Zookd Task Force">]
        
        Search Index for Query Factory Joins
        ====================================
        
        Now that we have written a query factory that encapsulates the join, we can
        use a search index that speeds it up.  We've only used transitive search
        indexes so far.  Now we will add an intransitive search index.
        
        The intransitive search index generally just needs the search value
        names it should be indexing, optionally the result name (defaulting to
        relations), and optionally the query factory to be used.
        
        We need to use two additional options because of the odd join trick we're
        doing.  We need to specify what organization and principal_id values need
        to be changed when an object is indexed, and we need to indicate that we
        should update when organization, principal_id, *or* parts changes.
        
        `getValueTokens` specifies the values that need to be indexed.  It gets
        the index, the name for the tokens desired, the token, the catalog that
        generated the token change (it may not be the same as the index's
        catalog, the source dictionary that contains a dictionary of the values
        that will be used for tokens if you do not override them, a dict of the
        added values for this token (keys are value names), a dict of the
        removed values for this token, and whether the token has been removed.
        The method can return None, which will leave the index to its default
        behavior that should work if no query factory is used; or an iterable of
        values.
        
            >>> def getValueTokens(index, name, token, catalog, source,
            ...                    additions, removals, removed):
            ...     if name == 'organization':
            ...         orgs = source.get('organization')
            ...         if not removed or not orgs:
            ...             orgs = index.catalog.getValueTokens(
            ...                 'organization', token)
            ...             if not orgs:
            ...                 orgs = [token]
            ...                 orgs.extend(removals.get('part', ()))
            ...         orgs = set(orgs)
            ...         orgs.update(index.catalog.findValueTokens(
            ...             'part',
            ...             {None: zc.relation.catalog.Any(
            ...                 t for t in orgs if t is not None)}))
            ...         return orgs
            ...     elif name == 'principal_id':
            ...         # we only want custom behavior if this is an organization
            ...         if 'principal_id' in source or index.catalog.getValueTokens(
            ...             'principal_id', token):
            ...             return ''
            ...         orgs = set((token,))
            ...         orgs.update(index.catalog.findRelationTokens(
            ...             {'part': token}))
            ...         return set(index.catalog.findValueTokens(
            ...             'principal_id', {
            ...                 'organization': zc.relation.catalog.Any(orgs)}))
            ...
        
            >>> index = zc.relation.searchindex.Intransitive(
            ...     ('organization', 'principal_id'), 'role_id', factory2,
            ...     getValueTokens,
            ...     ('organization', 'principal_id', 'part', 'role_id'),
            ...     unlimitedDepth=True)
            >>> catalog.addSearchIndex(index)
        
            >>> res = catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'ophelia'}))
            >>> list(res)
            ['publisher', 'reviewer', 'writer']
            >>> list(res)
            ['publisher', 'reviewer', 'writer']
        
            >>> res = catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'}))
            >>> list(res)
            ['publisher', 'reviewer', 'user manager', 'writer']
            >>> list(res)
            ['publisher', 'reviewer', 'user manager', 'writer']
        
        [#verifyObjectIntransitive]_
        
        .. [#verifyObjectIntransitive] The Intransitive search index provides
            ISearchIndex and IListener.
        
            >>> from zope.interface.verify import verifyObject
            >>> import zc.relation.interfaces
            >>> verifyObject(zc.relation.interfaces.ISearchIndex, index)
            True
            >>> verifyObject(zc.relation.interfaces.IListener, index)
            True
        
        Now we can change and remove relations--both organizations and roles--and
        have the index maintain correct state.  Given the current state of
        organizations--
        
        ::
        
                 Ynod Corp Mangement                 Zookd Corp Management
                  /      |      \                       /      |      \
           Ynod Devs  Ynod SAs  Ynod Admins  Zookd Admins   Zookd SAs  Zookd Devs
             /      \              \                 /                /         \
         Y3L4 Proj  Bet Proj      Ynod Zookd Task Force      Zookd hOgnmd     Zookd Nbd
        
        --first we will move Ynod Devs to beneath Zookd Devs, and back out.  This will
        briefly give abe full privileges to Y3L4 Proj., among others.
        
            >>> list(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Y3L4 Proj'],
            ...                   'principal_id': 'abe'})))
            []
            >>> orgs['Zookd Devs'].parts.insert(registry.getId(orgs['Ynod Devs']))
            1
            >>> catalog.index(orgs['Zookd Devs'])
            >>> res = catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Y3L4 Proj'],
            ...                   'principal_id': 'abe'}))
            >>> list(res)
            ['publisher', 'reviewer', 'user manager', 'writer']
            >>> list(res)
            ['publisher', 'reviewer', 'user manager', 'writer']
            >>> orgs['Zookd Devs'].parts.remove(registry.getId(orgs['Ynod Devs']))
            >>> catalog.index(orgs['Zookd Devs'])
            >>> list(catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Y3L4 Proj'],
            ...                   'principal_id': 'abe'})))
            []
        
        As another example, we will change the roles abe has, and see that it is
        propagated down to Zookd Nbd.
        
            >>> rels = list(catalog.findRelations(t(
            ...     {'principal_id': 'abe',
            ...      'organization': orgs['Zookd Corp Management']})))
            >>> len(rels)
            1
            >>> rels[0].role_ids.remove('reviewer')
            >>> catalog.index(rels[0])
        
            >>> res = catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'}))
            >>> list(res)
            ['publisher', 'user manager', 'writer']
            >>> list(res)
            ['publisher', 'user manager', 'writer']
        
        Note that search index order matters.  In our case, our intransitive search
        index is relying on our transitive index, so the transitive index needs to
        come first.  You want transitive relation indexes before name.  Right now,
        you are in charge of this order: it will be difficult to come up with a
        reliable algorithm for guessing this.
        
        Listeners, Catalog Administration, and Joining Across Relation Catalogs
        =======================================================================
        
        We've done all of our examples so far with a single catalog that indexes
        both kinds of relations.  What if we want to have two catalogs with
        homogenous collections of relations?  That can feel cleaner, but it also
        introduces some new wrinkles.
        
        Let's use our current catalog for organizations, removing the extra
        information; and create a new one for roles.
        
            >>> role_catalog = root['role_catalog'] = catalog.copy()
            >>> transaction.commit()
            >>> org_catalog = catalog
            >>> del catalog
        
        We'll need a slightly different query factory and a slightly different
        search index `getValueTokens` function.  We'll write those, then modify the
        configuration of our two catalogs for the new world.
        
        The transitive factory we write here is for the role catalog.  It needs
        access to the organzation catalog.  We could do this a variety of
        ways--relying on a utility, or finding the catalog from context.  We will
        make the role_catalog have a .org_catalog attribute, and rely on that.
        
            >>> role_catalog.org_catalog = org_catalog
            >>> def factory3(query, catalog):
            ...     if (len(query) == 2 and
            ...         'organization' in query and
            ...         'principal_id' in query):
            ...         def getQueries(relchain):
            ...             if not relchain:
            ...                 res = BTrees.family32.OO.Bucket(query)
            ...                 org_id = query['organization']
            ...                 if org_id is not None:
            ...                     res['organization'] = zc.relation.catalog.any(
            ...                         org_id,
            ...                         *catalog.org_catalog.findRelationTokens(
            ...                             {'part': org_id}))
            ...                 yield res
            ...         return getQueries
            ...
        
            >>> def getValueTokens2(index, name, token, catalog, source,
            ...                    additions, removals, removed):
            ...     is_role_catalog = catalog is index.catalog # role_catalog
            ...     if name == 'organization':
            ...         if is_role_catalog:
            ...             orgs = set(source.get('organization') or
            ...                        index.catalog.getValueTokens(
            ...                         'organization', token) or ())
            ...         else:
            ...             orgs = set((token,))
            ...             orgs.update(removals.get('part', ()))
            ...         orgs.update(index.catalog.org_catalog.findValueTokens(
            ...             'part',
            ...             {None: zc.relation.catalog.Any(
            ...                 t for t in orgs if t is not None)}))
            ...         return orgs
            ...     elif name == 'principal_id':
            ...         # we only want custom behavior if this is an organization
            ...         if not is_role_catalog:
            ...             orgs = set((token,))
            ...             orgs.update(index.catalog.org_catalog.findRelationTokens(
            ...                 {'part': token}))
            ...             return set(index.catalog.findValueTokens(
            ...                 'principal_id', {
            ...                     'organization': zc.relation.catalog.Any(orgs)}))
            ...     return ''
        
        If you are following along in the code and comparing to the originals, you may
        see that this approach is a bit cleaner than the one when the relations were
        in the same catalog.
        
        Now we will fix up the the organization catalog [#compare_copy]_.
        
        .. [#compare_copy] Before we modify them, let's look at the copy we made.
            The copy should currently behave identically to the original.
        
            >>> len(org_catalog)
            38
            >>> len(role_catalog)
            38
            >>> indexed = list(org_catalog)
            >>> len(indexed)
            38
            >>> orgs['Zookd Devs'] in indexed
            True
            >>> for r in indexed:
            ...     if r not in role_catalog:
            ...         print('bad')
            ...         break
            ... else:
            ...     print('good')
            ...
            good
            >>> org_names = set(dir(org_catalog))
            >>> role_names = set(dir(role_catalog))
            >>> sorted(org_names - role_names)
            []
            >>> sorted(role_names - org_names)
            ['org_catalog']
        
            >>> def checkYnodDevsParts(catalog):
            ...     res = sorted(catalog.findRelations(t({None: orgs['Ynod Devs']})))
            ...     if res != [
            ...         orgs["Bet Proj"], orgs["Y3L4 Proj"], orgs["Ynod Devs"]]:
            ...         print("bad", res)
            ...
            >>> checkYnodDevsParts(org_catalog)
            >>> checkYnodDevsParts(role_catalog)
        
            >>> def checkOpheliaRoles(catalog):
            ...     res = sorted(catalog.findRelations({'principal_id': 'ophelia'}))
            ...     if repr(res) != (
            ...         "[<Roles instance (ophelia has publisher in Zookd Nbd)>, " +
            ...         "<Roles instance (ophelia has reviewer in Zookd Devs)>, " +
            ...         "<Roles instance (ophelia has writer in " +
            ...         "Zookd Corp Management)>]"):
            ...         print("bad", res)
            ...
            >>> checkOpheliaRoles(org_catalog)
            >>> checkOpheliaRoles(role_catalog)
        
            >>> def checkOpheliaWriterOrganizations(catalog):
            ...     res = sorted(catalog.findRelations({None: zc.relation.catalog.Any(
            ...         catalog.findValueTokens(
            ...             'organization', {'principal_id': 'ophelia',
            ...                              'role_id': 'writer'}))}))
            ...     if repr(res) != (
            ...         '[<Organization instance "Ynod Zookd Task Force">, ' +
            ...         '<Organization instance "Zookd Admins">, ' +
            ...         '<Organization instance "Zookd Corp Management">, ' +
            ...         '<Organization instance "Zookd Devs">, ' +
            ...         '<Organization instance "Zookd Nbd">, ' +
            ...         '<Organization instance "Zookd SAs">, ' +
            ...         '<Organization instance "Zookd hOgnmd">]'):
            ...         print("bad", res)
            ...
            >>> checkOpheliaWriterOrganizations(org_catalog)
            >>> checkOpheliaWriterOrganizations(role_catalog)
        
            >>> def checkPrincipalsWithRolesInZookdDevs(catalog):
            ...     org_id = registry.getId(orgs['Zookd Devs'])
            ...     res = sorted(catalog.findValueTokens(
            ...         'principal_id',
            ...         {'organization': zc.relation.catalog.any(
            ...             org_id, *catalog.findRelationTokens({'part': org_id}))}))
            ...     if res != ['abe', 'ignas', 'karyn', 'lettie', 'nancy', 'ophelia']:
            ...         print("bad", res)
            ...
            >>> checkPrincipalsWithRolesInZookdDevs(org_catalog)
            >>> checkPrincipalsWithRolesInZookdDevs(role_catalog)
        
            >>> def checkOpheliaRolesInZookdNbd(catalog):
            ...     res = sorted(catalog.findValueTokens(
            ...         'role_id', {
            ...             'organization': registry.getId(orgs['Zookd Nbd']),
            ...             'principal_id': 'ophelia'}))
            ...     if res != ['publisher', 'reviewer', 'writer']:
            ...         print("bad", res)
            ...
            >>> checkOpheliaRolesInZookdNbd(org_catalog)
            >>> checkOpheliaRolesInZookdNbd(role_catalog)
        
            >>> def checkAbeRolesInZookdNbd(catalog):
            ...     res = sorted(catalog.findValueTokens(
            ...         'role_id', {
            ...             'organization': registry.getId(orgs['Zookd Nbd']),
            ...             'principal_id': 'abe'}))
            ...     if res != ['publisher', 'user manager', 'writer']:
            ...         print("bad", res)
            ...
            >>> checkAbeRolesInZookdNbd(org_catalog)
            >>> checkAbeRolesInZookdNbd(role_catalog)
            >>> org_catalog.removeDefaultQueryFactory(None) # doctest: +ELLIPSIS
            Traceback (most recent call last):
            ...
            LookupError: ('factory not found', None)
        
            >>> org_catalog.removeValueIndex('organization')
            >>> org_catalog.removeValueIndex('role_id')
            >>> org_catalog.removeValueIndex('principal_id')
            >>> org_catalog.removeDefaultQueryFactory(factory2)
            >>> org_catalog.removeSearchIndex(index)
            >>> org_catalog.clear()
            >>> len(org_catalog)
            0
            >>> for v in orgs.values():
            ...     org_catalog.index(v)
        
        This also shows using the `removeDefaultQueryFactory` and `removeSearchIndex`
        methods [#removeDefaultQueryFactoryExceptions]_.
        
        .. [#removeDefaultQueryFactoryExceptions] You get errors by removing query
            factories that are not registered.
        
            >>> org_catalog.removeDefaultQueryFactory(factory2) # doctest: +ELLIPSIS
            Traceback (most recent call last):
            ...
            LookupError: ('factory not found', <function factory2 at ...>)
        
        Now we will set up the role catalog [#copy_unchanged]_.
        
        
        .. [#copy_unchanged] Changes to one copy should not affect the other.  That
            means the role_catalog should still work as before.
        
            >>> len(org_catalog)
            13
            >>> len(list(org_catalog))
            13
        
            >>> len(role_catalog)
            38
            >>> indexed = list(role_catalog)
            >>> len(indexed)
            38
            >>> orgs['Zookd Devs'] in indexed
            True
            >>> orgs['Zookd Devs'] in role_catalog
            True
        
            >>> checkYnodDevsParts(role_catalog)
            >>> checkOpheliaRoles(role_catalog)
            >>> checkOpheliaWriterOrganizations(role_catalog)
            >>> checkPrincipalsWithRolesInZookdDevs(role_catalog)
            >>> checkOpheliaRolesInZookdNbd(role_catalog)
            >>> checkAbeRolesInZookdNbd(role_catalog)
        
            >>> role_catalog.removeValueIndex('part')
            >>> for ix in list(role_catalog.iterSearchIndexes()):
            ...     role_catalog.removeSearchIndex(ix)
            ...
            >>> role_catalog.removeDefaultQueryFactory(factory1)
            >>> role_catalog.removeDefaultQueryFactory(factory2)
            >>> role_catalog.addDefaultQueryFactory(factory3)
            >>> root['index2'] = index2 = zc.relation.searchindex.Intransitive(
            ...     ('organization', 'principal_id'), 'role_id', factory3,
            ...     getValueTokens2,
            ...     ('organization', 'principal_id', 'part', 'role_id'),
            ...     unlimitedDepth=True)
            >>> role_catalog.addSearchIndex(index2)
        
        The new role_catalog index needs to be updated from the org_catalog.
        We'll set that up using listeners, a new concept.
        
            >>> org_catalog.addListener(index2)
            >>> list(org_catalog.iterListeners()) == [index2]
            True
        
        Now the role_catalog should be able to answer the same questions as the old
        single catalog approach.
        
            >>> t = role_catalog.tokenizeQuery
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'})))
            ['publisher', 'user manager', 'writer']
        
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'ophelia'})))
            ['publisher', 'reviewer', 'writer']
        
        We can also make changes to both catalogs and the search indexes are
        maintained.
        
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Y3L4 Proj'],
            ...                   'principal_id': 'abe'})))
            []
            >>> orgs['Zookd Devs'].parts.insert(registry.getId(orgs['Ynod Devs']))
            1
            >>> org_catalog.index(orgs['Zookd Devs'])
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Y3L4 Proj'],
            ...                   'principal_id': 'abe'})))
            ['publisher', 'user manager', 'writer']
            >>> orgs['Zookd Devs'].parts.remove(registry.getId(orgs['Ynod Devs']))
            >>> org_catalog.index(orgs['Zookd Devs'])
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Y3L4 Proj'],
            ...                   'principal_id': 'abe'})))
            []
        
            >>> rels = list(role_catalog.findRelations(t(
            ...     {'principal_id': 'abe',
            ...      'organization': orgs['Zookd Corp Management']})))
            >>> len(rels)
            1
            >>> rels[0].role_ids.insert('reviewer')
            1
            >>> role_catalog.index(rels[0])
        
            >>> res = role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd Nbd'],
            ...                   'principal_id': 'abe'}))
            >>> list(res)
            ['publisher', 'reviewer', 'user manager', 'writer']
        
        Here we add a new organization.
        
            >>> orgs['Zookd hOnc'] = org = Organization('Zookd hOnc')
            >>> orgs['Zookd Devs'].parts.insert(registry.getId(org))
            1
            >>> org_catalog.index(orgs['Zookd hOnc'])
            >>> org_catalog.index(orgs['Zookd Devs'])
        
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd hOnc'],
            ...                   'principal_id': 'abe'})))
            ['publisher', 'reviewer', 'user manager', 'writer']
        
            >>> list(role_catalog.findValueTokens(
            ...     'role_id', t({'organization': orgs['Zookd hOnc'],
            ...                   'principal_id': 'ophelia'})))
            ['reviewer', 'writer']
        
        Now we'll remove it.
        
            >>> orgs['Zookd Devs'].parts.remove(registry.getId(org))
            >>> org_catalog.index(orgs['Zookd Devs'])
            >>> org_catalog.unindex(orgs['Zookd hOnc'])
        
        TODO make sure that intransitive copy looks the way we expect
        
        [#administrivia]_
        
        .. [#administrivia]
        
            You can add listeners multiple times.
        
            >>> org_catalog.addListener(index2)
            >>> list(org_catalog.iterListeners()) == [index2, index2]
            True
        
            Now we will remove the listeners, to show we can.
        
            >>> org_catalog.removeListener(index2)
            >>> org_catalog.removeListener(index2)
            >>> org_catalog.removeListener(index2)
            ... # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
            Traceback (most recent call last):
            ...
            LookupError: ('listener not found',
                          <zc.relation.searchindex.Intransitive object at ...>)
            >>> org_catalog.removeListener(None)
            ... # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
            Traceback (most recent call last):
            ...
            LookupError: ('listener not found', None)
        
            Here's the same for removing a search index we don't have
        
            >>> org_catalog.removeSearchIndex(index2)
            ... # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
            Traceback (most recent call last):
            ...
            LookupError: ('index not found',
                          <zc.relation.searchindex.Intransitive object at ...>)
        
        .. ......... ..
        .. Footnotes ..
        .. ......... ..
        
        
        .. [#silliness] In "2001: A Space Odyssey", many people believe the name HAL
            was chosen because it was ROT25 of IBM....  I cheat a bit sometimes and
            use ROT1 because the result sounds better.
        
        
        =================================================================
        Working with Search Indexes: zc.relation Catalog Extended Example
        =================================================================
        
        Introduction
        ============
        
        This document assumes you have read the README.rst document, and want to learn
        a bit more by example. In it, we will explore a set of relations that
        demonstrates most of the aspects of working with search indexes and listeners.
        It will not explain the topics that the other documents already addressed. It
        also describes an advanced use case.
        
        As we have seen in the other documents, the relation catalog supports
        search indexes.  These can return the results of any search, as desired.
        Of course, the intent is that you supply an index that optimizes the
        particular searches it claims.
        
        The searchindex module supplies a few search indexes, optimizing
        specified transitive and intransitive searches.  We have seen them working
        in other documents.  We will examine them more in depth in this document.
        
        Search indexes update themselves by receiving messages via a "listener"
        interface.  We will also look at how this works.
        
        The example described in this file examines a use case similar to that in
        the zc.revision or zc.vault packages: a relation describes a graph of
        other objects.  Therefore, this is our first concrete example of purely
        extrinsic relations.
        
        Let's build the example story a bit.  Imagine we have a graph, often a
        hierarchy, of tokens--integers.  Relations specify that a given integer
        token relates to other integer tokens, with a containment denotation or
        other meaning.
        
        The integers may also have relations that specify that they represent an
        object or objects.
        
        This allows us to have a graph of objects in which changing one part of the
        graph does not require changing the rest.  zc.revision and zc.vault thus
        are able to model graphs that can have multiple revisions efficiently and
        with quite a bit of metadata to support merges.
        
        Let's imagine a simple hierarchy.  The relation has a `token` attribute
        and a `children` attribute; children point to tokens. Relations will
        identify themselves with ids.
        
            >>> import BTrees
            >>> relations = BTrees.family64.IO.BTree()
            >>> relations[99] = None # just to give us a start
        
            >>> class Relation(object):
            ...     def __init__(self, token, children=()):
            ...         self.token = token
            ...         self.children = BTrees.family64.IF.TreeSet(children)
            ...         self.id = relations.maxKey() + 1
            ...         relations[self.id] = self
            ...
        
            >>> def token(rel, self):
            ...     return rel.token
            ...
            >>> def children(rel, self):
            ...     return rel.children
            ...
            >>> def dumpRelation(obj, index, cache):
            ...     return obj.id
            ...
            >>> def loadRelation(token, index, cache):
            ...     return relations[token]
            ...
        
        The standard TransposingTransitiveQueriesFactory will be able to handle this
        quite well, so we'll use that for our index.
        
            >>> import zc.relation.queryfactory
            >>> factory = zc.relation.queryfactory.TransposingTransitive(
            ...     'token', 'children')
            >>> import zc.relation.catalog
            >>> catalog = zc.relation.catalog.Catalog(
            ...     dumpRelation, loadRelation, BTrees.family64.IO, BTrees.family64)
            >>> catalog.addValueIndex(token)
            >>> catalog.addValueIndex(children, multiple=True)
            >>> catalog.addDefaultQueryFactory(factory)
        
        Now let's quickly create a hierarchy and index it.
        
            >>> for token, children in (
            ...     (0, (1, 2)), (1, (3, 4)), (2, (10, 11, 12)), (3, (5, 6)),
            ...     (4, (13, 14)), (5, (7, 8, 9)), (6, (15, 16)), (7, (17, 18, 19)),
            ...     (8, (20, 21, 22)), (9, (23, 24)), (10, (25, 26)),
            ...     (11, (27, 28, 29, 30, 31, 32))):
            ...     catalog.index(Relation(token, children))
            ...
        
        [#queryFactory]_ That hierarchy is arbitrary.  Here's what we have, in terms of tokens
        pointing to children::
        
                                          _____________0_____________
                                         /                           \
                                ________1_______                ______2____________
                               /                \              /          |        \
                        ______3_____            _4_          10       ____11_____   12
                       /            \          /   \         / \     / /  |  \ \ \
               _______5_______       6       13     14     25  26  27 28 29 30 31 32
              /       |       \     / \
            _7_      _8_       9   15 16
           / | \    / | \     / \
         17 18 19  20 21 22  23 24
        
        Twelve relations, with tokens 0 through 11, and a total of 33 tokens,
        including children.  The ids for the 12 relations are 100 through 111,
        corresponding with the tokens of 0 through 11.
        
        Without a transitive search index, we can get all transitive results.
        The results are iterators.
        
            >>> res = catalog.findRelationTokens({'token': 0})
            >>> import six
            >>> next_attr = '__next__' if six.PY3 else 'next'
            >>> getattr(res, next_attr) is None
            False
            >>> getattr(res, '__len__', None) is None
            True
            >>> sorted(res)
            [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111]
            >>> list(res)
            []
        
            >>> res = catalog.findValueTokens('children', {'token': 0})
            >>> sorted(res) == list(range(1, 33))
            True
            >>> list(res)
            []
        
        [#findValuesUnindexed]_ `canFind` also can work transitively, and will
        use transitive search indexes, as we'll see below.
        
            >>> catalog.canFind({'token': 1}, targetQuery={'children': 23})
            True
            >>> catalog.canFind({'token': 2}, targetQuery={'children': 23})
            False
            >>> catalog.canFind({'children': 23}, targetQuery={'token': 1})
            True
            >>> catalog.canFind({'children': 23}, targetQuery={'token': 2})
            False
        
        `findRelationTokenChains` won't change, but we'll include it in the
        discussion and examples to show that.
        
            >>> res = catalog.findRelationTokenChains({'token': 2})
            >>> chains = list(res)
            >>> len(chains)
            3
            >>> len(list(res))
            0
        
        Transitive Search Indexes
        =========================
        
        Now we can add a couple of transitive search index.  We'll talk about
        them a bit first.
        
        There is currently one variety of transitive index, which indexes
        relation and value searches for the transposing transitive query
        factory.
        
        The index can only be used under certain conditions.
        
            - The search is not a request for a relation chain.
        
            - It does not specify a maximum depth.
        
            - Filters are not used.
        
        If it is a value search, then specific value indexes cannot be used if a
        target filter or target query are used, but the basic relation index can
        still be used in that case.
        
        The usage of the search indexes is largely transparent: set them up, and
        the relation catalog will use them for the same API calls that used more
        brute force previously.  The only difference from external uses is that
        results that use an index will usually be a BTree structure, rather than
        an iterator.
        
        When you add a transitive index for a relation, you must specify the
        transitive name (or names) of the query, and the same for the reverse.
        That's all we'll do now.
        
            >>> import zc.relation.searchindex
            >>> catalog.addSearchIndex(
            ...     zc.relation.searchindex.TransposingTransitiveMembership(
            ...         'token', 'children', names=('children',)))
        
        Now we should have a search index installed.
        
        Notice that we went from parent (token) to child: this index is primarily
        designed for helping transitive membership searches in a hierarchy. Using it to
        index parents would incur a lot of write expense for not much win.
        
        There's just a bit more you can specify here: static fields for a query
        to do a bit of filtering.  We don't need any of that for this example.
        
        Now how does the catalog use this index for searches?  Three basic ways,
        depending on the kind of search, relations, values, or `canFind`.
        Before we start looking into the internals, let's verify that we're getting
        what we expect: correct answers, and not iterators, but BTree structures.
        
            >>> res = catalog.findRelationTokens({'token': 0})
            >>> list(res)
            [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111]
            >>> list(res)
            [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111]
        
            >>> res = catalog.findValueTokens('children', {'token': 0})
            >>> list(res) == list(range(1, 33))
            True
            >>> list(res) == list(range(1, 33))
            True
        
            >>> catalog.canFind({'token': 1}, targetQuery={'children': 23})
            True
            >>> catalog.canFind({'token': 2}, targetQuery={'children': 23})
            False
        
        [#findValuesIndexed]_ Note that the last two `canFind` examples from
        when we went through these examples without an index do not use the
        index, so we don't show them here: they look the wrong direction for
        this index.
        
        So how do these results happen?
        
        The first, `findRelationTokens`, and the last, `canFind`, are the most
        straightforward.  The index finds all relations that match the given
        query, intransitively. Then for each relation, it looks up the indexed
        transitive results for that token.  The end result is the union of all
        indexed results found from the intransitive search.  `canFind` simply
        casts the result into a boolean.
        
        `findValueTokens` is the same story as above with only one more step.  After
        the union of relations is calculated, the method returns the union of the
        sets of the requested value for all found relations.
        
        It will maintain itself when relations are reindexed.
        
            >>> rel = list(catalog.findRelations({'token': 11}))[0]
            >>> for t in (27, 28, 29, 30, 31):
            ...     rel.children.remove(t)
            ...
            >>> catalog.index(rel)
        
            >>> catalog.findValueTokens('children', {'token': 0})
            ... # doctest: +NORMALIZE_WHITESPACE
            LFSet([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
                   20, 21, 22, 23, 24, 25, 26, 32])
            >>> catalog.findValueTokens('children', {'token': 2})
            LFSet([10, 11, 12, 25, 26, 32])
            >>> catalog.findValueTokens('children', {'token': 11})
            LFSet([32])
        
            >>> rel.children.remove(32)
            >>> catalog.index(rel)
        
            >>> catalog.findValueTokens('children', {'token': 0})
            ... # doctest: +NORMALIZE_WHITESPACE
            LFSet([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
                   20, 21, 22, 23, 24, 25, 26])
            >>> catalog.findValueTokens('children', {'token': 2})
            LFSet([10, 11, 12, 25, 26])
            >>> catalog.findValueTokens('children', {'token': 11})
            LFSet([])
        
            >>> rel.children.insert(27)
            1
            >>> catalog.index(rel)
        
            >>> catalog.findValueTokens('children', {'token': 0})
            ... # doctest: +NORMALIZE_WHITESPACE
            LFSet([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
                   20, 21, 22, 23, 24, 25, 26, 27])
            >>> catalog.findValueTokens('children', {'token': 2})
            LFSet([10, 11, 12, 25, 26, 27])
            >>> catalog.findValueTokens('children', {'token': 11})
            LFSet([27])
        
        When the index is copied, the search index is copied.
        
            >>> new = catalog.copy()
            >>> res = list(new.iterSearchIndexes())
            >>> len(res)
            1
            >>> new_index = res[0]
            >>> res = list(catalog.iterSearchIndexes())
            >>> len(res)
            1
            >>> old_index = res[0]
            >>> new_index is old_index
            False
            >>> old_index.index is new_index.index
            False
            >>> list(old_index.index.keys()) == list(new_index.index.keys())
            True
            >>> from __future__ import print_function
            >>> for key, value in old_index.index.items():
            ...     v = new_index.index[key]
            ...     if v is value or list(v) != list(value):
            ...         print('oops', key, value, v)
            ...         break
            ... else:
            ...     print('good')
            ...
            good
            >>> old_index.names is not new_index.names
            True
            >>> list(old_index.names) == list(new_index.names)
            True
            >>> for name, old_ix in old_index.names.items():
            ...     new_ix = new_index.names[name]
            ...     if new_ix is old_ix or list(new_ix.keys()) != list(old_ix.keys()):
            ...         print('oops')
            ...         break
            ...     for key, value in old_ix.items():
            ...         v = new_ix[key]
            ...         if v is value or list(v) != list(value):
            ...             print('oops', name, key, value, v)
            ...             break
            ...     else:
            ...         continue
            ...     break
            ... else:
            ...     print('good')
            ...
            good
        
        Helpers
        =======
        
        When writing search indexes and query factories, you often want complete
        access to relation catalog data.  We've seen a number of these tools already:
        
        - `getRelationModuleTools` gets a dictionary of the BTree tools needed to
          work with relations.
        
            >>> sorted(catalog.getRelationModuleTools().keys())
            ... # doctest: +NORMALIZE_WHITESPACE
            ['BTree', 'Bucket', 'Set', 'TreeSet', 'difference', 'dump',
             'intersection', 'load', 'multiunion', 'union']
        
            'multiunion' is only there if the BTree is an I* or L* module.
            Use the zc.relation.catalog.multiunion helper function to do the
            best union you can for a given set of tools.
        
        - `getValueModuleTools` does the same for indexed values.
        
            >>> tools = set(('BTree', 'Bucket', 'Set', 'TreeSet', 'difference',
            ...              'dump', 'intersection', 'load', 'multiunion', 'union'))
            >>> tools.difference(catalog.getValueModuleTools('children').keys()) == set()
            True
        
            >>> tools.difference(catalog.getValueModuleTools('token').keys()) == set()
            True
        
        - `getRelationTokens` can return all of the tokens in the catalog.
        
            >>> len(catalog.getRelationTokens()) == len(catalog)
            True
        
            This also happens to be equivalent to `findRelationTokens` with an empty
            query.
        
            >>> catalog.getRelationTokens() is catalog.findRelationTokens({})
            True
        
            It also can return all the tokens that match a given query, or None if
            there are no matches.
        
            >>> catalog.getRelationTokens({'token': 0}) # doctest: +ELLIPSIS
            <BTrees.LOBTree.LOTreeSet object at ...>
            >>> list(catalog.getRelationTokens({'token': 0}))
            [100]
        
            This also happens to be equivalent to `findRelationTokens` with a query,
            a maxDepth of 1, and no other arguments.
        
            >>> catalog.findRelationTokens({'token': 0}, maxDepth=1) is (
            ...     catalog.getRelationTokens({'token': 0}))
            True
        
            Except that if there are no matches, `findRelationTokens` returns an empty
            set (so it *always* returns an iterable).
        
            >>> catalog.findRelationTokens({'token': 50}, maxDepth=1)
            LOSet([])
            >>> print(catalog.getRelationTokens({'token': 50}))
            None
        
        - `getValueTokens` can return all of the tokens for a given value name in
            the catalog.
        
            >>> list(catalog.getValueTokens('token')) == list(range(12))
            True
        
            This is identical to catalog.findValueTokens with a name only (or with
            an empty query, and a maxDepth of 1).
        
            >>> list(catalog.findValueTokens('token')) == list(range(12))
            True
            >>> catalog.findValueTokens('token') is catalog.getValueTokens('token')
            True
        
            It can also return the values for a given token.
        
            >>> list(catalog.getValueTokens('children', 100))
            [1, 2]
        
            This is identical to catalog.findValueTokens with a name and a query of
            {None: token}.
        
            >>> list(catalog.findValueTokens('children', {None: 100}))
            [1, 2]
            >>> catalog.getValueTokens('children', 100) is (
            ...     catalog.findValueTokens('children', {None: 100}))
            True
        
            Except that if there are no matches, `findValueTokens` returns an empty
            set (so it *always* returns an iterable); while getValueTokens will
            return None if the relation has no values (or the relation is unknown).
        
            >>> catalog.findValueTokens('children', {None: 50}, maxDepth=1)
            LFSet([])
            >>> print(catalog.getValueTokens('children', 50))
            None
        
            >>> rel.children.remove(27)
            >>> catalog.index(rel)
            >>> catalog.findValueTokens('children', {None: rel.id}, maxDepth=1)
            LFSet([])
            >>> print(catalog.getValueTokens('children', rel.id))
            None
        
        - `yieldRelationTokenChains` is a search workhorse for searches that use a
            query factory.  TODO: describe.
        
        .. ......... ..
        .. Footnotes ..
        .. ......... ..
        
        .. [#queryFactory] The query factory knows when it is not needed--not only
            when neither of its names are used, but also when both of its names are
            used.
        
            >>> list(catalog.findRelationTokens({'token': 0, 'children': 1}))
            [100]
        
        .. [#findValuesUnindexed] When values are the same as their tokens,
            `findValues` returns the same result as `findValueTokens`.  Here
            we see this without indexes.
        
            >>> list(catalog.findValueTokens('children', {'token': 0})) == list(
            ...     catalog.findValues('children', {'token': 0}))
            True
        
        .. [#findValuesIndexed] Again, when values are the same as their tokens,
            `findValues` returns the same result as `findValueTokens`.  Here
            we see this with indexes.
        
            >>> list(catalog.findValueTokens('children', {'token': 0})) == list(
            ...     catalog.findValues('children', {'token': 0}))
            True
        
        
        Optimizing Relation Catalog Use
        ===============================
        
        There are several best practices and optimization opportunities in regards to
        the catalog.
        
        - Use integer-keyed BTree sets when possible.  They can use the BTrees'
          `multiunion` for a speed boost.  Integers' __cmp__ is reliable, and in C.
        
        - Never use persistent objects as keys.  They will cause a database load every
          time you need to look at them, they take up memory and object caches, and
          they (as of this writing) disable conflict resolution.  Intids (or similar)
          are your best bet for representing objects, and some other immutable such as
          strings are the next-best bet, and zope.app.keyreferences (or similar) are
          after that.
        
        - Use multiple-token values in your queries when possible, especially in your
          transitive query factories.
        
        - Use the cache when you are loading and dumping tokens, and in your
          transitive query factories.
        
        - When possible, don't load or dump tokens (the values themselves may be used
          as tokens).  This is especially important when you have multiple tokens:
          store them in a BTree structure in the same module as the zc.relation module
          for the value.
        
        For some operations, particularly with hundreds or thousands of members in a
        single relation value, some of these optimizations can speed up some
        common-case reindexing work by around 100 times.
        
        The easiest (and perhaps least useful) optimization is that all dump
        calls and all load calls generated by a single operation share a cache
        dictionary per call type (dump/load), per indexed relation value.
        Therefore, for instance, we could stash an intids utility, so that we
        only had to do a utility lookup once, and thereafter it was only a
        single dictionary lookup. This is what the default `generateToken` and
        `resolveToken` functions in zc.relationship's index.py do: look at them
        for an example.
        
        A further optimization is to not load or dump tokens at all, but use values
        that may be tokens.  This will be particularly useful if the tokens have
        __cmp__ (or equivalent) in C, such as built-in types like ints.  To specify
        this behavior, you create an index with the 'load' and 'dump' values for the
        indexed attribute descriptions explicitly set to None.
        
        
            >>> import zope.interface
            >>> class IRelation(zope.interface.Interface):
            ...     subjects = zope.interface.Attribute(
            ...         'The sources of the relation; the subject of the sentence')
            ...     relationtype = zope.interface.Attribute(
            ...         '''unicode: the single relation type of this relation;
            ...         usually contains the verb of the sentence.''')
            ...     objects = zope.interface.Attribute(
            ...         '''the targets of the relation; usually a direct or
            ...         indirect object in the sentence''')
            ...
        
            >>> import BTrees
            >>> relations = BTrees.family32.IO.BTree()
            >>> relations[99] = None # just to give us a start
        
            >>> @zope.interface.implementer(IRelation)
            ... class Relation(object):
            ...
            ...     def __init__(self, subjects, relationtype, objects):
            ...         self.subjects = subjects
            ...         assert relationtype in relTypes
            ...         self.relationtype = relationtype
            ...         self.objects = objects
            ...         self.id = relations.maxKey() + 1
            ...         relations[self.id] = self
            ...     def __repr__(self):
            ...         return '<%r %s %r>' % (
            ...             self.subjects, self.relationtype, self.objects)
        
            >>> def token(rel, self):
            ...     return rel.token
            ...
            >>> def children(rel, self):
            ...     return rel.children
            ...
            >>> def dumpRelation(obj, index, cache):
            ...     return obj.id
            ...
            >>> def loadRelation(token, index, cache):
            ...     return relations[token]
            ...
        
            >>> relTypes = ['has the role of']
            >>> def relTypeDump(obj, index, cache):
            ...     assert obj in relTypes, 'unknown relationtype'
            ...     return obj
            ...
            >>> def relTypeLoad(token, index, cache):
            ...     assert token in relTypes, 'unknown relationtype'
            ...     return token
            ...
        
            >>> import zc.relation.catalog
            >>> catalog = zc.relation.catalog.Catalog(
            ...     dumpRelation, loadRelation)
            >>> catalog.addValueIndex(IRelation['subjects'], multiple=True)
            >>> catalog.addValueIndex(
            ...     IRelation['relationtype'], relTypeDump, relTypeLoad,
            ...     BTrees.family32.OI, name='reltype')
            >>> catalog.addValueIndex(IRelation['objects'], multiple=True)
            >>> import zc.relation.queryfactory
            >>> factory = zc.relation.queryfactory.TransposingTransitive(
            ...     'subjects', 'objects')
            >>> catalog.addDefaultQueryFactory(factory)
        
            >>> rel = Relation((1,), 'has the role of', (2,))
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 1}))
            [2]
        
        If you have single relations that relate hundreds or thousands of
        objects, it can be a huge win if the value is a 'multiple' of the same
        type as the stored BTree for the given attribute.  The default BTree
        family for attributes is IFBTree; IOBTree is also a good choice, and may
        be preferrable for some applications.
        
            >>> catalog.unindex(rel)
            >>> rel = Relation(
            ...     BTrees.family32.IF.TreeSet((1,)), 'has the role of',
            ...     BTrees.family32.IF.TreeSet())
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 1}))
            []
            >>> list(catalog.findValueTokens('subjects', {'objects': None}))
            [1]
        
        Reindexing is where some of the big improvements can happen.  The following
        gyrations exercise the optimization code.
        
            >>> rel.objects.insert(2)
            1
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 1}))
            [2]
            >>> rel.subjects = BTrees.family32.IF.TreeSet((3,4,5))
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 3}))
            [2]
        
            >>> rel.subjects.insert(6)
            1
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 6}))
            [2]
        
            >>> rel.subjects.update(range(100, 200))
            100
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 100}))
            [2]
        
            >>> rel.subjects = BTrees.family32.IF.TreeSet((3,4,5,6))
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 3}))
            [2]
        
            >>> rel.subjects = BTrees.family32.IF.TreeSet(())
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 3}))
            []
        
            >>> rel.subjects = BTrees.family32.IF.TreeSet((3,4,5))
            >>> catalog.index(rel)
            >>> list(catalog.findValueTokens('objects', {'subjects': 3}))
            [2]
        
        tokenizeValues and resolveValueTokens work correctly without loaders and
        dumpers--that is, they do nothing.
        
            >>> catalog.tokenizeValues((3,4,5), 'subjects')
            (3, 4, 5)
            >>> catalog.resolveValueTokens((3,4,5), 'subjects')
            (3, 4, 5)
        
        
        =======
        Changes
        =======
        
        
        1.1.post2 (2018-06-18)
        ======================
        
        - Another attempt to fix PyPI page by using correct expected metadata syntax.
        
        
        1.1.post1 (2018-06-18)
        ======================
        
        - Fix PyPI page by using correct ReST syntax.
        
        
        1.1 (2018-06-15)
        ================
        
        - Add support for Python 3.5 and 3.6.
        
        
        1.0 (2008-04-23)
        ================
        
        This is the initial release of the zc.relation package.  However, it
        represents a refactoring of another package, zc.relationship.  This
        package contains only a modified version of the relation(ship) index,
        now called a catalog. The refactored version of zc.relationship index
        relies on (subclasses) this catalog. zc.relationship also maintains a
        backwards-compatible subclass.
        
        This package only relies on the ZODB, zope.interface, and zope.testing
        software, and can be used inside or outside of a standard ZODB database.
        The software does have to be there, though (the package relies heavily
        on the ZODB BTrees package).
        
        If you would like to switch a legacy zc.relationship index to a
        zc.relation catalog, try this trick in your generations script.
        Assuming the old index is ``old``, the following line should create
        a new zc.relation catalog with your legacy data:
        
            >>> new = old.copy(zc.relation.Catalog)
        
        Why is the same basic data structure called a catalog now?  Because we
        exposed the ability to mutate the data structure, and what you are really
        adding and removing are indexes.  It didn't make sense to put an index in
        an index, but it does make sense to put an index in a catalog.  Thus, a
        name change was born.
        
        The catalog in this package has several incompatibilities from the earlier
        zc.relationship index, and many new features.  The zc.relationship package
        maintains a backwards-compatible subclass.  The following discussion
        compares the zc.relation catalog with the zc.relationship 1.x index.
        
        Incompatibilities with zc.relationship 1.x index
        ------------------------------------------------
        
        The two big changes are that method names now refer to ``Relation`` rather
        than ``Relationship``; and the catalog is instantiated slightly differently
        from the index.  A few other changes are worth your attention.  The
        following list attempts to highlight all incompatibilities.
        
        :Big incompatibilities:
        
            - ``findRelationshipTokenSet`` and ``findValueTokenSet`` are renamed, with
              some slightly different semantics, as ``getRelationTokens`` and
              ``getValueTokens``.  The exact same result as
              ``findRelationTokenSet(query)`` can be obtained with
              ``findRelationTokens(query, 1)`` (where 1 is maxDepth).  The same
              result as ``findValueTokenSet(reltoken, name)`` can be obtained with
              ``findValueTokens(name, {zc.relation.RELATION: reltoken}, 1)``.
        
            - ``findRelations`` replaces ``findRelatonships``.  The new method will use
              the defaultTransitiveQueriesFactory if it is set and maxDepth is not 1.
              It shares the call signature of ``findRelationChains``.
        
            - ``isLinked`` is now ``canFind``.
        
            - The catalog instantiation arguments have changed from the old index.
        
              * ``load`` and ``dump`` (formerly ``loadRel`` and ``dumpRel``,
                respectively) are now required arguments for instantiation.
        
              * The only other optional arguments are ``btree`` (was ``relFamily``) and
                ``family``. You now specify what elements to index with
                ``addValueIndex``
        
              * Note also that ``addValueIndex`` defaults to no load and dump function,
                unlike the old instantiation options.
        
            - query factories are different.  See ``IQueryFactory`` in the interfaces.
        
              * they first get (query, catalog, cache) and then return a getQueries
                callable that gets relchains and yields queries; OR None if they
                don't match.
        
              * They must also handle an empty relchain.  Typically this should
                return the original query, but may also be used to mutate the
                original query.
        
              * They are no longer thought of as transitive query factories, but as
                general query mutators.
        
        :Medium:
        
            - The catalog no longer inherits from
              zope.app.container.contained.Contained.
        
            - The index requires ZODB 3.8 or higher.
        
        :Small:
        
            - ``deactivateSets`` is no longer an instantiation option (it was broken
              because of a ZODB bug anyway, as had been described in the
              documentation).
        
        Changes and new features
        ------------------------
        
        - The catalog now offers the ability to index certain
          searches.  The indexes must be explicitly instantiated and registered
          you want to optimize. This can be used when searching for values, when
          searching for relations, or when determining if two objects are
          linked.  It cannot be used for relation chains. Requesting an index
          has the usual trade-offs of greater storage space and slower write
          speed for faster search speed.  Registering a search index is done
          after instantiation time; you can iteratate over the current settings
          used, and remove them.  (The code path expects to support legacy
          zc.relationship index instances for all of these APIs.)
        
        - You can now specify new values after the catalog has been created, iterate
          over the settings used, and remove values.
        
        - The catalog has a copy method, to quickly make new copies without actually
          having to reindex the relations.
        
        - query arguments can now specify multiple values for a given name by
          using zc.relation.catalog.any(1, 2, 3, 4) or
          zc.relation.catalog.Any((1, 2, 3, 4)).
        
        - The catalog supports specifying indexed values by passing callables rather
          than interface elements (which are also still supported).
        
        - ``findRelations`` and new method ``findRelationTokens`` can find
          relations transitively and intransitively.  ``findRelationTokens``
          when used intransitively repeats the legacy zc.relationship index
          behavior of ``findRelationTokenSet``.
          (``findRelationTokenSet`` remains in the API, not deprecated, a companion
          to ``findValueTokenSet``.)
        
        - in findValues and findValueTokens, ``query`` argument is now optional.  If
          the query evaluates to False in a boolean context, all values, or value
          tokens, are returned.  Value tokens are explicitly returned using the
          underlying BTree storage.  This can then be used directly for other BTree
          operations.
        
        - Completely new docs.  Unfortunately, still really not good enough.
        
        - The package has drastically reduced direct dependecies from zc.relationship:
          it is now more clearly a ZODB tool, with no other Zope dependencies than
          zope.testing and zope.interface.
        
        - Listeners allow objects to listen to messages from the catalog (which can
          be used directly or, for instance, to fire off events).
        
        - You can search for relations, using a key of zc.relation.RELATION...which is
          really an alias for None. Sorry. But hey, use the constant! I think it is
          more readable.
        
        - tokenizeQuery (and resolveQuery) now accept keyword arguments as an
          alternative to a normal dict query.  This can make constructing the query
          a bit more attractive (i.e., ``query = catalog.tokenizeQuery;
          res = catalog.findValues('object', query(subject=joe, predicate=OWNS))``).
        
Keywords: zope zope3 relation
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 2
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: Implementation :: CPython
Classifier: License :: OSI Approved :: Zope Public License
Provides-Extra: test
