Instead of creating "type" classes (i.e. Types) and manually attaching them to Aesara objects (i.e. via Variable.type), we should actual use Python's built-in type/class inheritance. I'm not immediately aware of any required functionality in the current Aesara type system that wouldn't allow this.

Here's an illustration of the current situation:

import aesara.tensor as at


x = at.vector()

We created a simple Aesara vector, x; now, let's inspect its (Python) types:

>>> type(x).mro()

[aesara.tensor.var.TensorVariable,
 aesara.tensor.var._tensor_py_operators,
 aesara.gof.graph.Variable,
 aesara.gof.graph.Node,
 aesara.gof.utils.object2,
 object]

Oddly, there's also a separate Variable.type field/member/property introduced by inheriting from Variable:

>>> x.type

TensorType(float64, vector)

>>> x.type.Variable

aesara.tensor.var.TensorVariable

>>> x.type.Constant

aesara.tensor.var.TensorConstant

As we can see, this extra Type object holds information about the variable's dtype and broadcastable dimensions (i.e. the vector means x.type.broadcastable equals [False]/[True]). From the latter two properties, it's also clear that the actual Python type (i.e. TensorVariable) is directly associated with the Aesara type (i.e. TensorType) as illustrated by the value of TensorType.Variable.

This leads to the question: why doesn't TensorVariable just inherit from its x.type type/class (i.e. some TensorType)?

If anything, the mechanics behind such inheritance might seem non-standard, as it could require some form of automatic type generation for sub-classes like TensorVariable, but—even so—that's pretty straightforward to do in a __new__ class method (e.g. we already do that in symbolic-pymc).

Regarding actual code changes, it seems like we would at least need to change all the Variable.type invocations with the standard type(...) calls, and/or more direct calls to isinstance(x, TensorType) instead of things like x.type == TensorType(...).

We could also keep Variable.type and have it return type(self) just to make the initial transition easy.