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The PEAK Rules Core Framework
NOTE: This document is for people who are extending the core framework in some
way, e.g. adding custom action types to specialize method combination, or
creating new kinds of engines or conditions. It isn't intended to be user
documentation for the built-in rule facility.
.. contents:: **Table of Contents**
Overview and Terminology
The PEAK-Rules core framework provides a generic API for creating and
manipulating generic functions, with a high degree of extensibility. Almost
any concept implemented by the core can be replaced by a third-party
implementation on a function-by-function basis. In this way, an individual
library or application can provide for its specific needs, without needing to
reinvent the entire spectrum of tools.
The main concepts implemented by the core are:
Generic functions
    A function with a "dispatching" add-on, that manages a collection of
    methods, where each method has a rule to determine its applicability.
    When a generic function is invoked, a combination of the methods that
    apply to the invocation (as determined by their rules) is invoked.
Method combination
    The ability to compose a set of methods into a single function, with their
    precedence determined by the type of method and the logical implication
    relationships of their applicability rules.
Development Roadmap
The first versions will focus on developing a core framework for extensible
functions that is itself implemented using extensible functions. This
self-bootstrapping core will implement a type-tuple-caching engine using
relatively primitive operations, and will then have a method combination
system built on that. The core will thus be capable of implementing generic
functions with multiple dispatch based on positional argument types, and the
decorator APIs will be built around that.
The next phase of development will add alternative engines that are oriented
towards predicate dispatch and more sophisticated ways of specifying regular
class dispatch (e.g. being able to say things like ``isinstance(x,Foo) or
isinstance(y,Foo)``). To some extent this will be porting the expression
machinery from RuleDispatch to work on the new core, but in a lot of ways it'll
just be redone from scratch. Having type-based multiple dispatch available to
implement the framework should enable a significant reduction in the complexity
of the resulting library.
An additional phase will focus on adding new features not possible with the
RuleDispatch engine, such as "predicate functions" (a kind of dynamic macro
or rule expansion feature), "classifiers" (a way of priority-sequencing a
set of alternative criteria) and others.
Finally, specialty features such as index customization, thread-safety,
event-oriented rulesets, and such will be introduced.
Design Concepts
(Note: Criteria, signatures, and predicates are described and tested in detail
by the ``Criteria.txt`` document.)
    A criterion is a symbolic representation of a test that returns a boolean
    for a given value, for example by testing its type. The simplest criterion
    is just a class or type object, meaning that the value should be of that
    A condition expressed purely in terms of simple tests "and"ed together,
    using no "or" operations of any kind. A signature specifies what argument
    expressions are tested, and which criteria should be applied to them.
    The simplest possible signature is a tuple of criteria, with each criterion
    applied to the corresponding argument in an argument tuple. (An empty tuple
    matches any possible input.) Signatures are also described
    One or more signatures "or"ed together. (Note that this means that
    signatures are predicates, but predicates are not necessarily signatures.)
    A combination of a predicate, an action type, and a body (usually a
    function.) The existence of a rule implies the existence of one or more
    actions of the given action type and body, one for each possible signature
    that could match the predicate.
Action Type
    A factory that can produce an Action when supplied with a signature, body,
    and sequence. (Examples in ``peak.rules`` will include the ``MethodList``,
    ``MethodChain``, ``Around``, ``Before``, and ``After`` types.)
    An object representing the behavior of a single invocation of a generic
    function. Action objects may be combined (using a generic function of
    the form ``combine_actions(a1,a2)``) to create combined methods ala
    RuleDispatch. Each action comprises at least a signature and a body, but
    actions of more complex types may include other information.
Rule Set
    A collection of rules, combined with some policy information (such
    as the default action type) and optional optimization hints. A rule
    set does not directly implement dispatching. Instead, rule engines
    subscribe to rule sets, and the rule set informs them when actions are
    added and removed due to changes in the rule set's rules.
    This would almost be better named an "action set" than a "rule set",
    in that it's (virtually speaking) a collection of actions rather than
    rules. However, you do add and remove entries from it by specifying
    rules; the actions are merely implied by the rules.
    Generic functions will have a ``__rules__`` attribute that points to their
    rule set, so that the various decorators can add rules to them. You
    will probably be able to subclass the base RuleSet class or create
    alternate implementations, as might be useful for supporting persistent or
    database-stored rules. (Although you'd probably also need a custom rule
    engine for that.)
Rule Engine
    An object that manages the dispatching of a given rule set to implement
    a specific generic function. Generic functions will have an ``__engine__``
    attribute that points to their current engine. Engines will be responsible
    for doing any indexing, caching, or code generation that may be required to
    implement the resulting generic function.
    The default engine will implement simple type-based multiple dispatch with
    type-tuple caching. For simple generic functions this is likely to be
    faster than almost anything else, even C-assisted RuleDispatch. It also
    should have far less definition-time overhead than a RuleDispatch-style
    engine would.
    Engines will be pluggable, and in fact there will be a mechanism to allow
    engines to be switched at runtime when certain conditions are met. For
    example, the default engine could switch automatically to a
    RuleDispatch-like engine if a rule is added whose conditions can't be
    translated to simple type dispatching. There will also be some type of
    hint system to allow users to suggest what kind of engine implementation
    or special indexing might be appropriate for a particular function.
Method Combination
Method combination is performed using the ``combine_actions()`` API function::
    >>> from peak.rules import combine_actions
``combine_actions()`` takes two arguments: a pair of actions. They are
compared using the ``overrides()`` generic function to see if one is more
specific than the other. If so, the more specific action's ``override()``
method is called, passing in the less-specific action. If neither action
can override the other, the first action's ``merge()`` method is called,
passing in the other action.
In either case, the result of calling the ``merge()`` or ``override()`` method
is returned.
So, to define a custom action type for method combination, and it needs to
implement ``merge()`` and ``override()`` methods, and it must be comparable to
other method types via the ``overrides()`` generic function.
Signature Implication
The ``implies()`` function is used to determine the logical implication
relationship between two signatures. A signature ``s1`` implies a
signature ``s2`` if ``s2`` will always match an invocation matched by ``s1``.
(Action implication is based on signature implication; see the `Action Types`_
section below for more details.)
For the simplest signatures (tuples of types), this corresponds to a subclass
relationship between the elements of the tuples::
    >>> from peak.rules import implies
    >>> implies(int, object)
    >>> implies(object, int)
    >>> implies(int, str)
    >>> implies(int, int)
    >>> implies( (int,str), (object,object) )
    >>> implies( (object,int), (object,str) )
It's possible for a longer tuple to imply a shorter one::
    >>> implies( (int,int), (object,) )
But not the other way around::
    >>> implies( (int,), (object,object) )
And as a special case of type implication, any classic class implies both
``object`` and ``InstanceType``, but cannot imply any other new-style classes.
This special-casing is used to work around the fact that ``isinstance()`` will
say that a classic class instance is an instance of both ``object`` and
``InstanceType``, but ``issubclass()`` doesn't agree. PEAK-Rules wants to
conform with ``isinstance()`` here::
    >>> class X: pass
    >>> implies(X, object)
    >>> implies(X, type(X())) # InstanceType
Action Types
The default action type (for rules with no specified action type) is
``Method``. A ``Method`` combines a body, signature, precedence, and an
optional "chained" action that it can fall back to. All of these values
are optional, except for the body::
    >>> from peak.rules import Method, overrides
    >>> def dummy(*args, **kw):
    ... print "called with", args, kw
    >>> meth = Method.make(dummy, (object,), 1)
    >>> meth
    Method(<...dummy...>, (<type 'object'>,), 1, None)
Calling a ``Method`` invokes the wrapped body::
    >>> meth(1,2,x=3)
    called with (1, 2) {'x': 3}
One ``Method`` overrides another if and only if its signature implies the
    >>> overrides(Method.make(dummy,(int,int)), Method.make(dummy,(object,object)))
    >>> overrides(Method.make(dummy,(object,object)), Method.make(dummy,(int,int)))
When a method overrides another, you get the overriding method::
    >>> meth.override(Method.make(dummy))
    Method(<...dummy...>, (<type 'object'>,), 1, None)
Unless the overriding method's body is a function whose first parameter is
named ``next_method``, in which case a chain of methods is created via the
"tail" of a copy of the overriding method::
    >>> def overriding_fn(next_method, etc):
    ... print "calling", next_method
    ... return next_method(etc)
    >>> chain = Method.make(overriding_fn).override(Method.make(dummy))
    >>> chain
    Method(<...overriding_fn...>, (), 0, Method(<...dummy...>, (), 0, None))
The resulting chain is a callable ``Method``, and the ``next_method`` is passed
in to the first function of the chain::
    >>> chain(42)
    calling Method(<...dummy...>, (), 0, None)
    called with (42,) {}
``Around`` methods are identical to normal ``Method`` objects, except that
whenever an ``Around`` method and a regular ``Method`` are combined, the
``Around`` method overrides the regular one. This forces all the regular
methods to be further down the chain than all of the "around" methods.
    >>> from peak.rules import Around
    >>> combine_actions(Method.make(dummy), Around(overriding_fn))
    Around(<...overriding_fn...>, (), 0, Method(<...dummy...>, (), 0, None))
You will normally only want to use ``Around`` methods with functions that have
a ``next_method`` parameter, since their purpose is to wrap "around" the
calling of lower-precedence methods. If you don't do this, then the method
chain will always end at that ``Around`` instance::
    >>> combine_actions(Method.make(overriding_fn), Around(dummy))
    Around(<...dummy...>, (), 0, None)
The simplest possible action type is ``NoApplicableMethods``, meaning that
there is no applicable action. When it's overridden by another method, it
will of course get chained to the other method's tail (if appropriate).
    >>> from peak.rules import NoApplicableMethods
    >>> naf = NoApplicableMethods()
    >>> meth = Method.make(overriding_fn)
    >>> combine_actions(naf, meth)
    Method(<...overriding_fn...>, (), 0, NoApplicableMethods())
    >>> combine_actions(meth, naf)
    Method(<...overriding_fn...>, (), 0, NoApplicableMethods())
Calling a ``NoApplicableMethods`` raises it, displaying the arguments it was
called with::
    >>> naf(1,2,x="y")
    Traceback (most recent call last):
    NoApplicableMethods: ((1, 2), {'x': 'y'})
Before, After, and MethodList
``MethodList`` actions differ from normal method chain actions in a number of
* In case of ambiguity, they are ordered according to the sequence they were
  given in the underlying rule set.
* They do not need to inspect or call a ``next_method()``; the next method is
  always called automatically.
The ``Before`` and ``After`` action types are both ``MethodList`` subclasses.
``Before`` actions are invoked before their tail action, and ``After`` actions
are invoked afterward::
    >>> from peak.rules import Before, After
    >>> def primary(*args,**kw):
    ... print "primary method called"
    ... return 99
    >>> b = Before.make(dummy).override(Method.make(primary))
    >>> a = After.make(dummy).override(Method.make(primary))
    >>> b(23)
    called with (23,) {}
    primary method called
    >>> a(42)
    primary method called
    called with (42,) {}
Notice that to create a ``MethodList`` with only one method, you must use the
``make()`` classmethod. ``Method`` also has this classmethod, but it has the
same signature as the main constructor. The main constructor for
``MethodList`` has a different signature for its internal use.
The combination of before, after, primary, and around methods is as shown::
    >>> b = Before.make(dummy)
    >>> a = After.make(dummy)
    >>> p = Method.make(primary)
    >>> o = Around.make(overriding_fn)
    >>> combine_actions(b, combine_actions(a, combine_actions(p, o)))(17)
    calling Before(...dummy..., After(...dummy..., Method(...primary...)))
    called with (17,) {}
    primary method called
    called with (17,) {}
``Around`` methods take precedence over all other method types, so the around
method's tail is a ``Before`` that wraps the ``After`` that wraps the primary
Within a ``MethodList``, methods are ordered by signature implication first,
and then by definition order within groups of ambiguous signatures::
    >>> b1 = Before.make("b1", (), 1)
    >>> b2 = Before.make("b2", (), 2)
    >>> b3 = Before.make("b3", (int,), 3)
    >>> combine_actions(b2, b3).sorted()
    [((<type 'int'>,), 'b3'), ((), 'b2')]
    >>> combine_actions(b2, b1).sorted()
    [((), 'b1'), ((), 'b2')]
    >>> combine_actions(b3, combine_actions(b1,b2)).sorted()
    [((<type 'int'>,), 'b3'), ((), 'b1'), ((), 'b2')]
``After`` methods sort the opposite way::
    >>> a1 = After.make("a1", (), 1)
    >>> a2 = After.make("a2", (), 2)
    >>> a3 = After.make("a3", (int,), 3)
    >>> combine_actions(a2, a3).sorted()
    [((), 'a2'), ((<type 'int'>,), 'a3')]
    >>> combine_actions(a2, a1).sorted()
    [((), 'a2'), ((), 'a1')]
    >>> combine_actions(a3, combine_actions(a1,a2)).sorted()
    [((), 'a2'), ((), 'a1'), ((<type 'int'>,), 'a3')]
And lower-precedence duplicate bodies are automatically eliminated from the
    >>> combine_actions(a1,a1).sorted()
    [((), 'a1')]
    >>> combine_actions(b1,b1).sorted()
    [((), 'b1')]
    >>> combine_actions(b1, Before.make("b1", (int,), 1)).sorted()
    [((<type 'int'>,), 'b1')]
When you combine actions whose signatures are ambiguous (i.e. identical,
overlapping, or mutually exclusive), you end up with an ``AmbiguousMethods``
object containing the ambiguous methods::
    >>> am = combine_actions(meth, meth)
    >>> am
    AmbiguousMethods([Method(...), Method(...)])
Ambiguous methods can be overridden by an action that would override all of
the ambiguous actions::
    >>> m1 = Method.make(dummy, (int,))
    >>> combine_actions(am, m1) is m1
    >>> combine_actions(m1, am) is m1
And if appropriate, the ``AmbiguousMethods`` will end up chained to the
overriding method::
    >>> m2 = Method.make(overriding_fn, (str,))
    >>> combine_actions(am, m2)
    Method(<...overriding_fn...>, (<type 'str'>,), 0, AmbiguousMethods(...))
    >>> combine_actions(m2, am)
    Method(<...overriding_fn...>, (<type 'str'>,), 0, AmbiguousMethods(...))
Ambiguous methods override and ignore anything that would be overridden by
any of their members::
    >>> am = combine_actions(m1, m1)
    >>> combine_actions(am, meth) is am
    >>> combine_actions(meth, am) is am
But anything that overlaps just results in a bigger ``AmbiguousMethods``::
    >>> combine_actions(m2,am)
    AmbiguousMethods([Method(...), Method(...), Method(...)])
    >>> combine_actions(am,m2)
    AmbiguousMethods([Method(...), Method(...), Method(...)])
And invoking an ``AmbiguousMethods`` instance just outputs diagnostic info::
    >>> am(1,2,x="y")
    Traceback (most recent call last):
    AmbiguousMethods: ([Method(...), Method(...)], (1, 2), {'x': 'y'})
XXX decorators and how to create them: when, around, before, after
>>> from peak.rules import before, after
>>> def p(x): print x
>>> def f(): p("yo!")
Rule decorators return the function they are decorating, unless the function's
name is also the name of the generic function they're adding to::
>>> before(f)(lambda: p("before"))
<function <lambda> at ...>
>>> after(f)(lambda: p("after"))
<function <lambda> at ...>
>>> f()
Creating Custom Combinations
XXX custom combination demo from RuleDispatch (compute upcharges+tax)
Rules Management
Rules are currently implemented as 3-item tuples comprising a predicate, a
body, and an action type that will be used as a factory to create the actions
for the rule. At minimum, all a rule needs is a body, so there's a convenience
constructor (``Rule``) that allows you to create a rule with defaults. The
predicate and action type default to ``()`` and ``None`` if not specified::
    >>> from peak.rules import Rule
    >>> def dummy(): pass
    >>> r = Rule(dummy, sequence=0)
    >>> r
    Rule(<function dummy ...>, (), None, 0)
An action type of ``None`` (or any false value) means that the ruleset should
decide what action type to use. Actually, it can decide anyway, since the
rule set is always responsible for creating action objects; the rule's action
type is really just advisory to begin with.
``RuleSet`` objects hold the rules and policy information for a generic
function, including the default action type and optional optimziation hints.
Iterating over a ruleset yields its actions::
    >>> from peak.rules import RuleSet
    >>> rs = RuleSet()
    >>> list(rs)
And rules can be added and removed with the ``add()`` and ``remove()``
    >>> r = Rule(dummy, sequence=42)
    >>> rs.add(r)
    >>> list(rs)
    [Rule(<function dummy ...>, (), <...Method...>, 42)]
    >>> rs.remove(r)
    >>> list(rs)
Observers can be added with the ``subscribe()`` and ``unsubscribe()`` methods.
Observers have their ``actions_changed`` method called with an "added" set
and a "removed" set of action definitions. (An action definition is a
tuple of the form ``(actiontype, body, signature, precedence)``, and can thus
be used to create action objects.)
    >>> class DummyObserver:
    ... def actions_changed(self, added, removed):
    ... for a in added: print "Add:", a
    ... for a in removed: print "Remove:", a
    >>> do = DummyObserver()
    >>> rs.subscribe(do)
    >>> rs.add(r)
    Add: Rule(<function dummy ...>, (), <...Method...>, 42)
    >>> rs.remove(r)
    Remove: Rule(<function dummy ...>, (), <...Method...>, 42)
    >>> rs.unsubscribe(do)
When an observer is first added, it's notified of the current contents of the
``RuleSet``, if any. As a result, observers don't need to do any special case
handling for their initial setup. Everything can be handled via the normal
operation of the ``actions_changed()`` method::
    >>> rs.add(r)
    >>> rs.subscribe(do)
    Add: Rule(<function dummy ...>, (), <...Method...>, 42)
Unsubscribing, however, does not send any removal messages::
    >>> rs.unsubscribe(do)
Criteria and Logic
This section is currently just design notes to myself, hopefully to grow into
a more thorough discussion and doctests of the relevant sub-frameworks.
DNF Logic
# These 2 funcs must skip dupes and return the item alone if only 1 found
disj(*items) = Or( [i for item in items for i in disjuncts(item)] )
conj(items) = And([i for item in items for i in conjuncts(item)] )
def combinatorial(seq, *tail):
    if tail:
        return ((item,)+t for item in seq for t in combinatorial(*tail))
        return ((item,) for item in seq)
# this func would be more efficient if 'conj' were moved inside 'combinatorial'
# especially if conj were a binary operation, and the results of each nested
# loop were reduced to a unique set...
intersect(*items) = Or(
    map(conj, combinatorial(*map(disjuncts,items)))
# simplified, but still needs dupe skipping/flattening of the Or
intersect(i1, i2) = Or(
    *[conj((a,b)) for a in set(disjuncts(i1)) for b in set(disjuncts(i2))]
disjuncts(Or) = Or.items
disjuncts(Not) = map(negate, conjuncts(Not.expr))
disjuncts(*) = [*]
conjuncts(And) = And.items
conjuncts(Not) = map(negate, disjuncts(Not.expr))
conjuncts(*) = [*]
negate(And) = Or(map(negate,And.items))
negate(Or) = And(map(negate,Or.items))
negate(Not) = Not.expr
negate(Compare) = reverse comparison sense ?
negate(*) = Not(*)
Not-methods and negate() function could be eliminated by CriteriaBuilder
tracking negation during build.
implies(Or, *) iff all Or.items imply *
implies(And, *) iff any And.items imply *
implies(*, *) iff equal items [need to define for struct/struct, too!]
implies(Range, Range) by range overlap
implies(IsInstance, IsInstance) by subclass relationships/truth map
to_logic(Call) -> via function mapping for Call(Const(),...)
to_logic(Compare) -> Identity, IsInstance, Range, etc.?
to_logic(*) -> Truth(expr, mode)
dispatch_table(*, Identity, cases) -> {seed: bitmap}
  where bitmap = inclusions[seed] | (inclusions[None] - exclusions[seed])
     | (cases - known_cases)
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