[WIP] Add basic ExtensionIndex class
Explored this a bit 2 weeks ago, so thought could open it as a WIP PR in case it might serve discussion.

For me, the main question is how "complete" we want this to be, before we consider merging it. This WIP certainly already is able to preserve the EA in the Index (not convert to objects), and basic indexing works (but only tested the basics, and not all combinations of uniques/duplicated, sorted/non-sorted ... indexes)

Closes https://github.com/pandas-dev/pandas/issues/22861
Hello @jorisvandenbossche! Thanks for updating the PR.

 - There are no PEP8 issues in the file [`pandas/core/dtypes/generic.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/core/dtypes/generic.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/base.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/core/indexes/base.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/extension.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/core/indexes/extension.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/base/__init__.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/extension/base/__init__.py) !

 - In the file [`pandas/tests/extension/base/index.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/extension/base/index.py), following                are the PEP8 issues :
> [Line 64:27](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/extension/base/index.py#L64): [E261](https://duckduckgo.com/?q=pep8%20E261) at least two spaces before inline comment
> [Line 64:28](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/extension/base/index.py#L64): [E262](https://duckduckgo.com/?q=pep8%20E262) inline comment should start with '# '


 - There are no PEP8 issues in the file [`pandas/tests/extension/decimal/test_decimal.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/extension/decimal/test_decimal.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/test_integer.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/extension/test_integer.py) !

 - There are no PEP8 issues in the file [`pandas/tests/indexes/test_extension.py`](https://github.com/jorisvandenbossche/pandas/blob/00d4a167d8738532348ee06e8b763ddcc58b0f66/pandas/tests/indexes/test_extension.py) !



##### Comment last updated on October 19, 2018 at 13:41 Hours UTC Interesting, this is less work than I expected. If I were to do `df.groupby('extension_array').sum()`, would we get back an extension index? Or do we need to update the `Index.__new__` to make an `ExtensionIndex` in that case? > Interesting, this is less work than I expected.

That might also be because I didn't yet test that much :)

> If I were to do df.groupby('extension_array').sum(), would we get back an extension index?

Indeed:

```
In [1]: df = pd.DataFrame({'key': pd.core.arrays.integer_array([1, 2, 1, 3, 2]), 'val': range(5)})

In [2]: df.groupby('key').mean()
Out[2]: 
     val
key     
1    1.0
2    2.5
3    3.0

In [3]: df.groupby('key').mean().index
Out[3]: ExtensionIndex([1, 2, 3], dtype='Int64', name='key')
```

That's the small change in `Index.__new__` to construct an ExtensionIndex, if an ExtensionArray is passed (that is not a built-in one). 
So it at least already preserves the array dtype in such cases. Ah, I completely overlooked that. Putting here a comment I already wrote a time ago, but the actual discussion can maybe go in https://github.com/pandas-dev/pandas/issues/23565

The main question here is: **which values to use for indexing?**

Currently, in this PR I tried to create the correct indexing Engine based on the values of `EA._values_for_factorize`, because that seemed a natural fit (for indexing, they need to be hashable like for factorize). 

However, in many cases, we are using `_ndarray_values` internally. And eg for IntegerArray, those two are actually different: `_values_for_factorize` is an object array (to have the NaNs), but `_ndarray_values` is the integers. This raises errors in the engine not expecting an integer array. Of course, we might need to change `_ndarray_values` for `IntegerArray` to also return object, but that also means that indexing would be quite expensive in general (using the object dtype path)

 Just thinking out loud here: For IntegerArray, one could in principle write an engine that uses `_ndarray_values`, correct? You would need to take care to mask the "missing values" (1s) in every operation, but it should be doable.

Regardless, I'm ok with a default "ExtensionIndex" (an Index with the extension `dtype` preserved) for now, with the possibility of more customizable extension index classes later. > Just thinking out loud here: For IntegerArray, one could in principle write an engine that uses _ndarray_values, correct? You would need to take care to mask the "missing values" (1s) in every operation, but it should be doable.

But that would mean writing a custom engine?

Anyway (also future wise), an engine that works with values/mask combination might be useful in general. 
But that is not for this PR :-) 

I suppose short term the easiest is to use the object dtype values for IntegerArray for all indexing related things. > But that would mean writing a custom engine?

Right, it would push more work onto the EA author (which is us for IntegerArray). Pandas would provide the hooks somewhere in `pd.Index.__new__`

```python
engine = getattr(ExtensionArray, '_index_engine', default_engine)
```

> I suppose short term the easiest is to use the object dtype values for IntegerArray for all indexing related things.


Agreed. Ensuring that `Index.dtype` is `Int64Dtype`, and not object, seems the most important thing. Then we can give speed improvements without breaking API.
 nice idea for 0.25 :> good idea, but needs a reboot. Still hoping for this feature! I'm wondering what the current thoughts on this issue are wrt to 

https://github.com/pandas-dev/pandas/issues/30001

Is it being considered a non issue or a different work around being put in place?  see #22861