Lazy attributes

AUTHORS:

  • Nicolas Thiery (2008): Initial version

  • Nils Bruin (2013-05): Cython version

class sage.misc.lazy_attribute.lazy_attribute(f)[source]

Bases: _lazy_attribute

A lazy attribute for an object is like a usual attribute, except that, instead of being computed when the object is constructed (i.e. in __init__), it is computed on the fly the first time it is accessed.

For constant values attached to an object, lazy attributes provide a shorter syntax and automatic caching (unlike methods), while playing well with inheritance (like methods): a subclass can easily override a given attribute; you don’t need to call the super class constructor, etc.

Technically, a lazy_attribute is a non-data descriptor (see Invoking Descriptors in the Python reference manual).

EXAMPLES:

We create a class whose instances have a lazy attribute x:

sage: class A():
....:     def __init__(self):
....:         self.a=2 # just to have some data to calculate from
....:
....:     @lazy_attribute
....:     def x(self):
....:         print("calculating x in A")
....:         return self.a + 1
....:

>>> from sage.all import *
>>> class A():
...     def __init__(self):
...         self.a=Integer(2) # just to have some data to calculate from
....:
>>>     @lazy_attribute
...     def x(self):
...         print("calculating x in A")
...         return self.a + Integer(1)
....:

For an instance a of A, a.x is calculated the first time it is accessed, and then stored as a usual attribute:

sage: a = A()
sage: a.x
calculating x in A
3
sage: a.x
3

>>> from sage.all import *
>>> a = A()
>>> a.x
calculating x in A
3
>>> a.x
3

Implementation details

We redo the same example, but opening the hood to see what happens to the internal dictionary of the object:

sage: a = A()
sage: a.__dict__
{'a': 2}
sage: a.x
calculating x in A
3
sage: a.__dict__
{'a': 2, 'x': 3}
sage: a.x
3
sage: timeit('a.x') # random
625 loops, best of 3: 89.6 ns per loop

>>> from sage.all import *
>>> a = A()
>>> a.__dict__
{'a': 2}
>>> a.x
calculating x in A
3
>>> a.__dict__
{'a': 2, 'x': 3}
>>> a.x
3
>>> timeit('a.x') # random
625 loops, best of 3: 89.6 ns per loop

This shows that, after the first calculation, the attribute x becomes a usual attribute; in particular, there is no time penalty to access it.

A lazy attribute may be set as usual, even before its first access, in which case the lazy calculation is completely ignored:

sage: a = A()
sage: a.x = 4
sage: a.x
4
sage: a.__dict__
{'a': 2, 'x': 4}

>>> from sage.all import *
>>> a = A()
>>> a.x = Integer(4)
>>> a.x
4
>>> a.__dict__
{'a': 2, 'x': 4}

Class binding results in the lazy attribute itself:

sage: A.x
<sage.misc.lazy_attribute.lazy_attribute object at ...>

>>> from sage.all import *
>>> A.x
<sage.misc.lazy_attribute.lazy_attribute object at ...>

Conditional definitions

The function calculating the attribute may return NotImplemented to declare that, after all, it is not able to do it. In that case, the attribute lookup proceeds in the super class hierarchy:

sage: class B(A):
....:     @lazy_attribute
....:     def x(self):
....:         if hasattr(self, "y"):
....:             print("calculating x from y in B")
....:             return self.y
....:         else:
....:             print("y not there; B does not define x")
....:             return NotImplemented
....:
sage: b = B()
sage: b.x
y not there; B does not define x
calculating x in A
3
sage: b = B()
sage: b.y = 1
sage: b.x
calculating x from y in B
1

>>> from sage.all import *
>>> class B(A):
...     @lazy_attribute
...     def x(self):
...         if hasattr(self, "y"):
...             print("calculating x from y in B")
...             return self.y
...         else:
...             print("y not there; B does not define x")
...             return NotImplemented
....:
>>> b = B()
>>> b.x
y not there; B does not define x
calculating x in A
3
>>> b = B()
>>> b.y = Integer(1)
>>> b.x
calculating x from y in B
1

Attribute existence testing

Testing for the existence of an attribute with hasattr currently always triggers its full calculation, which may not be desirable when the calculation is expensive:

sage: a = A()
sage: hasattr(a, "x")
calculating x in A
True

>>> from sage.all import *
>>> a = A()
>>> hasattr(a, "x")
calculating x in A
True

It would be great if we could take over the control somehow, if at all possible without a special implementation of hasattr, so as to allow for something like:

sage: class A ():
....:     @lazy_attribute
....:     def x(self, existence_only=False):
....:         if existence_only:
....:             print("testing for x existence")
....:             return True
....:         else:
....:             print("calculating x in A")
....:             return 3
....:
sage: a = A()
sage: hasattr(a, "x") # todo: not implemented
testing for x existence
sage: a.x
calculating x in A
3
sage: a.x
3

>>> from sage.all import *
>>> class A ():
...     @lazy_attribute
...     def x(self, existence_only=False):
...         if existence_only:
...             print("testing for x existence")
...             return True
...         else:
...             print("calculating x in A")
...             return Integer(3)
....:
>>> a = A()
>>> hasattr(a, "x") # todo: not implemented
testing for x existence
>>> a.x
calculating x in A
3
>>> a.x
3

Here is a full featured example, with both conditional definition and existence testing:

sage: class B(A):
....:     @lazy_attribute
....:     def x(self, existence_only=False):
....:         if hasattr(self, "y"):
....:             if existence_only:
....:                 print("testing for x existence in B")
....:                 return True
....:             else:
....:                 print("calculating x from y in B")
....:                 return self.y
....:         else:
....:             print("y not there; B does not define x")
....:             return NotImplemented
....:
sage: b = B()
sage: hasattr(b, "x") # todo: not implemented
y not there; B does not define x
testing for x existence
True
sage: b.x
y not there; B does not define x
calculating x in A
3
sage: b = B()
sage: b.y = 1
sage: hasattr(b, "x") # todo: not implemented
testing for x existence in B
True
sage: b.x
calculating x from y in B
1

>>> from sage.all import *
>>> class B(A):
...     @lazy_attribute
...     def x(self, existence_only=False):
...         if hasattr(self, "y"):
...             if existence_only:
...                 print("testing for x existence in B")
...                 return True
...             else:
...                 print("calculating x from y in B")
...                 return self.y
...         else:
...             print("y not there; B does not define x")
...             return NotImplemented
....:
>>> b = B()
>>> hasattr(b, "x") # todo: not implemented
y not there; B does not define x
testing for x existence
True
>>> b.x
y not there; B does not define x
calculating x in A
3
>>> b = B()
>>> b.y = Integer(1)
>>> hasattr(b, "x") # todo: not implemented
testing for x existence in B
True
>>> b.x
calculating x from y in B
1

lazy attributes and introspection

Todo

Make the following work nicely:

sage: b.x?                # todo: not implemented
sage: b.x??               # todo: not implemented

>>> from sage.all import *
>>> b.x?                # todo: not implemented
>>> b.x??               # todo: not implemented

Right now, the first one includes the doc of this class, and the second one brings up the code of this class, both being not very useful.

Lazy attributes and Cython

This attempts to check that lazy attributes work with built-in functions like cpdef methods:

sage: class A:
....:     def __len__(x):
....:         return int(5)
....:     len = lazy_attribute(len)
....:
sage: A().len
5

>>> from sage.all import *
>>> class A:
...     def __len__(x):
...         return int(Integer(5))
...     len = lazy_attribute(len)
....:
>>> A().len
5

Since Issue #11115, extension classes derived from Parent can inherit a lazy attribute, such as element_class:

sage: cython_code = ["from sage.structure.parent cimport Parent",
....: "from sage.structure.element cimport Element",
....: "cdef class MyElement(Element): pass",
....: "cdef class MyParent(Parent):",
....: "    Element = MyElement"]
sage: cython('\n'.join(cython_code))                                            # needs sage.misc.cython
sage: P = MyParent(category=Rings())                                            # needs sage.misc.cython
sage: P.element_class    # indirect doctest                                     # needs sage.misc.cython
<class '...MyElement'>

>>> from sage.all import *
>>> cython_code = ["from sage.structure.parent cimport Parent",
... "from sage.structure.element cimport Element",
... "cdef class MyElement(Element): pass",
... "cdef class MyParent(Parent):",
... "    Element = MyElement"]
>>> cython('\n'.join(cython_code))                                            # needs sage.misc.cython
>>> P = MyParent(category=Rings())                                            # needs sage.misc.cython
>>> P.element_class    # indirect doctest                                     # needs sage.misc.cython
<class '...MyElement'>

About descriptor specifications

The specifications of descriptors (see 3.4.2.3 Invoking Descriptors in the Python reference manual) are incomplete w.r.t. inheritance, and maybe even ill-implemented. We illustrate this on a simple class hierarchy, with an instrumented descriptor:

sage: class descriptor():
....:     def __get__(self, obj, cls):
....:         print(cls)
....:         return 1
sage: class A():
....:     x = descriptor()
sage: class B(A):
....:     pass
....:

>>> from sage.all import *
>>> class descriptor():
...     def __get__(self, obj, cls):
...         print(cls)
...         return Integer(1)
>>> class A():
...     x = descriptor()
>>> class B(A):
...     pass
....:

This is fine:

sage: A.x
<class '__main__.A'>
1

>>> from sage.all import *
>>> A.x
<class '__main__.A'>
1

The behaviour for the following case is not specified (see Instance Binding) when x is not in the dictionary of B but in that of some super category:

sage: B().x
<class '__main__.B'>
1

>>> from sage.all import *
>>> B().x
<class '__main__.B'>
1

It would seem more natural (and practical!) to get A rather than B.

From the specifications for Super Binding, it would be expected to get A and not B as cls parameter:

sage: super(B, B()).x
<class '__main__.B'>
1

>>> from sage.all import *
>>> super(B, B()).x
<class '__main__.B'>
1

Due to this, the natural implementation runs into an infinite loop in the following example:

sage: class A():
....:     @lazy_attribute
....:     def unimplemented_A(self):
....:         return NotImplemented
....:     @lazy_attribute
....:     def unimplemented_AB(self):
....:         return NotImplemented
....:     @lazy_attribute
....:     def unimplemented_B_implemented_A(self):
....:         return 1
....:
sage: class B(A):
....:     @lazy_attribute
....:     def unimplemented_B(self):
....:         return NotImplemented
....:     @lazy_attribute
....:     def unimplemented_AB(self):
....:         return NotImplemented
....:     @lazy_attribute
....:     def unimplemented_B_implemented_A(self):
....:         return NotImplemented
....:
sage: class C(B):
....:     pass
....:

>>> from sage.all import *
>>> class A():
...     @lazy_attribute
...     def unimplemented_A(self):
...         return NotImplemented
...     @lazy_attribute
...     def unimplemented_AB(self):
...         return NotImplemented
...     @lazy_attribute
...     def unimplemented_B_implemented_A(self):
...         return Integer(1)
....:
>>> class B(A):
...     @lazy_attribute
...     def unimplemented_B(self):
...         return NotImplemented
...     @lazy_attribute
...     def unimplemented_AB(self):
...         return NotImplemented
...     @lazy_attribute
...     def unimplemented_B_implemented_A(self):
...         return NotImplemented
....:
>>> class C(B):
...     pass
....:

This is the simplest case where, without workaround, we get an infinite loop:

sage: hasattr(B(), "unimplemented_A") # todo: not implemented
False

>>> from sage.all import *
>>> hasattr(B(), "unimplemented_A") # todo: not implemented
False

Todo

Improve the error message:

sage: B().unimplemented_A # todo: not implemented
Traceback (most recent call last):
...
AttributeError: 'super' object has no attribute 'unimplemented_A'...

>>> from sage.all import *
>>> B().unimplemented_A # todo: not implemented
Traceback (most recent call last):
...
AttributeError: 'super' object has no attribute 'unimplemented_A'...

We now make some systematic checks:

sage: B().unimplemented_A
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_A'...
sage: B().unimplemented_B
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_B'...
sage: B().unimplemented_AB
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_AB'...
sage: B().unimplemented_B_implemented_A
1

sage: C().unimplemented_A()
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_A'...
sage: C().unimplemented_B()
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_B'...
sage: C().unimplemented_AB()
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_AB'...
sage: C().unimplemented_B_implemented_A # todo: not implemented
1

>>> from sage.all import *
>>> B().unimplemented_A
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_A'...
>>> B().unimplemented_B
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_B'...
>>> B().unimplemented_AB
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_AB'...
>>> B().unimplemented_B_implemented_A
1

>>> C().unimplemented_A()
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_A'...
>>> C().unimplemented_B()
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_B'...
>>> C().unimplemented_AB()
Traceback (most recent call last):
...
AttributeError: '...' object has no attribute 'unimplemented_AB'...
>>> C().unimplemented_B_implemented_A # todo: not implemented
1
class sage.misc.lazy_attribute.lazy_class_attribute(f)[source]

Bases: lazy_attribute

A lazy class attribute for a class is like a usual class attribute, except that, instead of being computed when the class is constructed, it is computed on the fly the first time it is accessed, either through the class itself or through one of its objects.

This is very similar to lazy_attribute except that the attribute is a class attribute. More precisely, once computed, the lazy class attribute is stored in the class rather than in the object. The lazy class attribute is only computed once for all the objects:

sage: class Cl():
....:     @lazy_class_attribute
....:     def x(cls):
....:          print("computing x")
....:          return 1
sage: Cl.x
computing x
1
sage: Cl.x
1

>>> from sage.all import *
>>> class Cl():
...     @lazy_class_attribute
...     def x(cls):
...          print("computing x")
...          return Integer(1)
>>> Cl.x
computing x
1
>>> Cl.x
1

As for a any usual class attribute it is also possible to access it from an object:

sage: b = Cl()
sage: b.x
1

>>> from sage.all import *
>>> b = Cl()
>>> b.x
1

First access from an object also properly triggers the computation:

sage: class Cl1():
....:     @lazy_class_attribute
....:     def x(cls):
....:          print("computing x")
....:          return 1
sage: Cl1().x
computing x
1
sage: Cl1().x
1

>>> from sage.all import *
>>> class Cl1():
...     @lazy_class_attribute
...     def x(cls):
...          print("computing x")
...          return Integer(1)
>>> Cl1().x
computing x
1
>>> Cl1().x
1

Warning

The behavior of lazy class attributes with respect to inheritance is not specified. It currently depends on the evaluation order:

sage: class A():
....:     @lazy_class_attribute
....:     def x(cls):
....:          print("computing x")
....:          return str(cls)
....:     @lazy_class_attribute
....:     def y(cls):
....:          print("computing y")
....:          return str(cls)
sage: class B(A):
....:     pass

sage: A.x
computing x
"<class '__main__.A'>"
sage: B.x
"<class '__main__.A'>"

sage: B.y
computing y
"<class '__main__.B'>"
sage: A.y
computing y
"<class '__main__.A'>"
sage: B.y
"<class '__main__.B'>"

>>> from sage.all import *
>>> class A():
...     @lazy_class_attribute
...     def x(cls):
...          print("computing x")
...          return str(cls)
...     @lazy_class_attribute
...     def y(cls):
...          print("computing y")
...          return str(cls)
>>> class B(A):
...     pass

>>> A.x
computing x
"<class '__main__.A'>"
>>> B.x
"<class '__main__.A'>"

>>> B.y
computing y
"<class '__main__.B'>"
>>> A.y
computing y
"<class '__main__.A'>"
>>> B.y
"<class '__main__.B'>"