WIP: experiment with first class dim objects

[aseyboldt]

Very much still an experiment! I'm still working on this, but thought it might be helpful to already share what I have so far...

In this version of named-dims, we use objects to represent dimensions instead of plain strings. This allows us to ensure that array axes with shared dimensions are always compatible.

A dimension variable stores the length of the dimension at runtime.
The type of the dimension provides the identity that is used to ensure tensors don't use duplicate dimensions.

# A dimension variable
>>> foo = px.dim("foo")

# We can inspect the dim type (the final .dim attribute should be hidden a little when we go further with this)
>>> foo.type.dim
BaseDim(size=None, name='foo', uuid=UUID('930aff02-e5d7-4a25-89da-486c9d5b2412'))

We can then create tensors with given dimensions:

>>> x = px.xtensor("x", dims=[foo, foo.clone_dim()])
>>> x.type.dims
(BaseDim(size=None, name='foo', uuid=UUID('930aff02-e5d7-4a25-89da-486c9d5b2412')),
 CloneDim(size=None, name=None, base=BaseDim(size=None, name='foo', uuid=UUID('930aff02-e5d7-4a25-89da-486c9d5b2412')), uuid=UUID('01ba2ef7-6d73-4082-b769-b5cb7909a16d')))

(Obvious todo: improve pretty printing!)
(Currently those are the dim.type.dim objects, I think we could just use dim.type directly to make it cleaner)

foo.clone_dim() prodvides a new dimension, that has the same shape as foo, but a different identity, so that we can build a tensor out of foo and foo.clone_dim(). Different instances of foo.clone_dim() are treated as different dimensions.

We can recover a dimension variable from an xtensor that has this dimension (because it implicitly stores the size of the dimension, and also stores the dimension type):

>>> x.dims[1].dprint();
FromTensor{dim_type=<pytensor.xtensor.type.DimType object at 0x7f3d372b3080>} [id A]
 └─ x [id B]

@OriolAbril @ricardoV94

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📚 Documentation preview 📚: https://pytensor--1517.org.readthedocs.build/en/1517/

[ricardoV94]

numpy uses int64 for shape internally so we end up doing it also