Why dynamic classes?
The short answer:
Multiple inheritance is a powerful tool for constructing new classes by combining preexisting building blocks.
There is a combinatorial explosion in the number of potentially useful classes that can be produced this way.
The implementation of standard mathematical constructions calls for producing such combinations automatically.
Dynamic classes, i.e. classes created on the fly by the Python interpreter, are a natural mean to achieve this.
The long answer:
Say we want to construct a new class
permutations in a given set \(S\) (in Sage, \(S\) will be modelled by a
parent, but we won’t discuss this point here). First, we have to
choose a data structure for the permutations, typically among the
Stored by cycle type
Stored by code
Stored in list notation - C arrays of short ints (for small permutations) - python lists of ints (for huge permutations) - …
Stored by reduced word
Stored as a function
Luckily, the Sage library provides (or will provide) classes implementing each of those data structures. Those classes all share a common interface (or possibly a common abstract base class). So we can just derive our class from the chosen one:
class MyPermutation(PermutationCycleType): ...
Then we may want to further choose a specific memory behavior (unique representation, copy-on-write) which (hopefully) can again be achieved by inheritance:
class MyPermutation(UniqueRepresentation, PermutationCycleType): ...
Finally, we may want to endow the permutations in \(S\) with further operations coming from the (algebraic) structure of \(S\):
or just monoid operations (for a subset of permutations not stable by inverse)
poset operations (for left/right/Bruhat order)
word operations (searching for substrings, patterns, …)
Or any combination thereof. Now, our class typically looks like:
class MyPermutation(UniqueRepresentation, PermutationCycleType, PosetElement, GroupElement): ...
Note the combinatorial explosion in the potential number of classes which can be created this way.
In practice, such classes will be used in mathematical constructions like:
SymmetricGroup(5).subset(... TODO: find a good example in the context above ...)
In such a construction, the structure of the result, and therefore the operations on its elements can only be determined at execution time. Let us take another standard construction:
A = cartesian_product( B, C )
Depending on the structure of \(B\) and \(C\), and possibly on further options passed down by the user, \(A\) may be:
an enumerated set
Or any combination thereof.
Hardcoding classes for all potential combinations would be at best tedious. Furthermore, this would require a cumbersome mechanism to lookup the appropriate class depending on the desired combination.
Instead, one may use the ability of Python to create new classes dynamically:
type("class name", tuple of base classes, dictionary of methods)
This paradigm is powerful, but there are some technicalities to address. The purpose of this library is to standardize its use within Sage, and in particular to ensure that the constructed classes are reused whenever possible (unique representation), and can be pickled.
Combining dynamic classes and Cython classes
Cython classes cannot inherit from a dynamic class (there might be
some partial support for this in the future). On the other hand, such
an inheritance can be partially emulated using
sage.categories.examples.semigroups_cython for an example.
- class sage.structure.dynamic_class.DynamicClasscallMetaclass¶
- class sage.structure.dynamic_class.DynamicInheritComparisonClasscallMetaclass¶
- class sage.structure.dynamic_class.DynamicInheritComparisonMetaclass¶
- class sage.structure.dynamic_class.DynamicMetaclass¶
A metaclass implementing an appropriate reduce-by-construction method
- class sage.structure.dynamic_class.TestClass¶
A class used for checking that introspection works
- sage.structure.dynamic_class.dynamic_class(name, bases, cls=None, reduction=None, doccls=None, prepend_cls_bases=True, cache=True)¶
name– a string
bases– a tuple of classes
cls– a class or
reduction– a tuple or
doccls– a class or
prepend_cls_bases– a boolean (default:
cache– a boolean or
Constructs dynamically a new class
name, and bases
clsis provided, then its methods will be inserted into
C, and its bases will be prepended to
The module, documentation and source instrospection is taken from
basesif both are
basesshould be non empty if
cls` is ``None).
The constructed class can safely be pickled (assuming the arguments themselves can).
False, the result is cached, ensuring unique representation of dynamic classes.
sage.structure.dynamic_classfor a discussion of the dynamic classes paradigm, and its relevance to Sage.
To setup the stage, we create a class Foo with some methods, cached methods, and lazy attributes, and a class Bar:
sage: from sage.misc.lazy_attribute import lazy_attribute sage: from sage.misc.cachefunc import cached_function sage: from sage.structure.dynamic_class import dynamic_class sage: class Foo(object): ....: "The Foo class" ....: def __init__(self, x): ....: self._x = x ....: @cached_method ....: def f(self): ....: return self._x^2 ....: def g(self): ....: return self._x^2 ....: @lazy_attribute ....: def x(self): ....: return self._x sage: class Bar: ....: def bar(self): ....: return self._x^2
We now create a class FooBar which is a copy of Foo, except that it also inherits from Bar:
sage: FooBar = dynamic_class("FooBar", (Bar,), Foo) sage: x = FooBar(3) sage: x.f() 9 sage: x.f() is x.f() True sage: x.x 3 sage: x.bar() 9 sage: FooBar.__name__ 'FooBar' sage: FooBar.__module__ '__main__' sage: Foo.__bases__ (<type 'object'>,) sage: FooBar.__bases__ # py2 (<type 'object'>, <class __main__.Bar at ...>) sage: FooBar.__bases__ # py3 (<class '__main__.Bar'>,) sage: Foo.mro() [<class '__main__.Foo'>, <type 'object'>] sage: FooBar.mro() # py2 [<class '__main__.FooBar'>, <type 'object'>, <class __main__.Bar at ...>] sage: FooBar.mro() # py3 [<class '__main__.FooBar'>, <class '__main__.Bar'>, <class 'object'>]
If all the base classes have a zero
__dictoffset__, the dynamic class also has a zero
__dictoffset__. This means that the instances of the class don’t have a
__dict__(see trac ticket #23435):
sage: dyn = dynamic_class("dyn", (Integer,)) sage: dyn.__dictoffset__ 0
Dynamic classes are pickled by construction. Namely, upon unpickling, the class will be reconstructed by recalling dynamic_class with the same arguments:
sage: type(FooBar).__reduce__(FooBar) # py2 (<function dynamic_class at ...>, ('FooBar', (<class __main__.Bar at ...>,), <class '__main__.Foo'>, None, None)) sage: type(FooBar).__reduce__(FooBar) # py3 (<function dynamic_class at ...>, ('FooBar', (<class '__main__.Bar'>,), <class '__main__.Foo'>, None, None))
Technically, this is achieved by using a metaclass, since the Python pickling protocol for classes is to pickle by name:
sage: type(FooBar) <class 'sage.structure.dynamic_class.DynamicMetaclass'>
The following (meaningless) example illustrates how to customize the result of the reduction:
sage: BarFoo = dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (3,))) sage: type(BarFoo).__reduce__(BarFoo) (<type 'str'>, (3,)) sage: loads(dumps(BarFoo)) '3'
By default, the built class is cached:
sage: dynamic_class("FooBar", (Bar,), Foo) is FooBar True sage: dynamic_class("FooBar", (Bar,), Foo, cache=True) is FooBar True
and the result depends on the reduction:
sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (3,))) is BarFoo True sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (2,))) is BarFoo False
cache=False, a new class is created each time:
sage: FooBar1 = dynamic_class("FooBar", (Bar,), Foo, cache=False); FooBar1 <class '__main__.FooBar'> sage: FooBar2 = dynamic_class("FooBar", (Bar,), Foo, cache=False); FooBar2 <class '__main__.FooBar'> sage: FooBar1 is FooBar False sage: FooBar2 is FooBar1 False
cache="ignore_reduction", the class does not depend on the reduction:
sage: BarFoo = dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (3,)), cache="ignore_reduction") sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (2,)), cache="ignore_reduction") is BarFoo True
In particular, the reduction used is that provided upon creating the first class:
sage: dynamic_class("BarFoo", (Foo,), Bar, reduction = (str, (2,)), cache="ignore_reduction")._reduction (<type 'str'>, (3,))
The behaviour upon creating several dynamic classes from the same data but with different values for
cacheoption is currently left unspecified. In other words, for a given application, it is recommended to consistently use the same value for that option.
- sage.structure.dynamic_class.dynamic_class_internal(name, bases, cls=None, reduction=None, doccls=None, prepend_cls_bases=True)¶
See sage.structure.dynamic_class.dynamic_class? for indirect doctests.