Professionalize Test Suite

[kclowes]

What feature should we add?

It's unclear where to add tests, so this issue will involve moving them around in a way that makes sense and provides a baseline for new tests to be added. We'd also like to add the ability to test against different backends. Testing against different backends may make sense to split out into its own issue.

[fselmo]

I think you addressed this but just to clarify at least part of it. We should try to see if there is a way to run the same tests against different backends in order to DRY the code and avoid missing some tests for some backends. I think it may make sense to have some backend-specific tests but we should see what we can combine along the way.