Allow maths in shape constraints.

[jesnie]

Feature request

Allow maths in shape constraints.

Motivation

For example:

@check_shapes(
    "left: [left_rows, left_columns]",
    "right: [right_rows, right_columns]",
    "return: [left_rows * right_rows, left_columns + right_columns]",
)
def cartesian_product(left, right):
    ....

Proposal

The ability to do maths in shape constraints.

This is hard, because we need to be able to learn/infer the values of the variables (left_rows, left_columns, etc...), and in general we cannot work backwards solve arbitrary equations. We could solve this in a couple of ways:

1. Require the user to declare their shapes in order, so that when a shape variable is used in maths, its value is already known.
2. Check shapes lazily, and only evaluate a shape when all the required information is available.

I don't like (1), because I don't like have to impose an ordering on constraints, and because optional arguments can make it hard to predict when a variable value will actually be available. I like (2) better, but it does have the disadvantage that sometimes a shape variable value may never be known, and no check actually performed.