Why does list ask about __len__?

See the Rationale section from PEP 424 that introduced __length_hint__ and offers insight on the motivation:

Being able to pre-allocate lists based on the expected size, as estimated by __length_hint__ , can be a significant optimization. CPython has been observed to run some code faster than PyPy, purely because of this optimization being present.

In addition to that, the documentation for object.__length_hint__ verifies the fact that this is purely an optimization feature:

Called to implement operator.length_hint(). Should return an estimated length for the object (which may be greater or less than the actual length). The length must be an integer >= 0. This method is purely an optimization and is never required for correctness.

So __length_hint__ is here because it can result in some nice optimizations.

PyObject_LengthHint, first tries to get a value from object.__len__ (if it is defined) and then tries to see if object.__length_hint__ is available. If neither is there, it returns a default value of 8 for lists.

listextend, which is called from list_init as Eli stated in his answer, was modified according to this PEP to offer this optimization for anything that defines either a __len__ or a __length_hint__.

list isn't the only one that benefits from this, of course, bytes objects do:

>>> bytes(Foo())
len
getitem 0
...
b'\x00\x01\x04\t\x10\x19'

so do bytearray objects but, only when you extend them:

>>> bytearray().extend(Foo())
len
getitem 0
...

and tuple objects which create an intermediary sequence to populate themselves:

>>> tuple(Foo())
len
getitem 0
...
(0, 1, 4, 9, 16, 25)

---

If anybody is wandering why exactly 'iter' is printed before 'len' in class Bar and not after as happens with class Foo:

This is because if the object in hand defines an __iter__ Python will first call it to get the iterator, thereby running the print('iter') too. The same doesn't happen if it falls back to using __getitem__.

list is a list object constructor that will allocate an initial slice of memory for its contents. The list constructor attempts to figure out a good size for that initial slice of memory by checking the length hint or the length of any object passed into the constructor . See the call to PyObject_LengthHint in the Python source here. This place is called from the list constructor -- list_init

If your object has no __len__ or __length_hint__, that's OK -- a default value of 8 is used; it just may be less efficient due to reallocations.