How should lazy actx.compile interact with memoization (on the output end)?

This is a longer-shot companion issue to https://github.com/inducer/pytato/issues/164 (and https://github.com/inducer/arraycontext/issues/99).

Suppose an `actx.compile`d function evaluates something that's memoized (for the sake of argument, imagine a temperature in mirgecom). After the compiled evaluation concludes, the memoization of dependent data becomes unavailable, since we're now working on a different array (/array container) instance. It'd be nice if that weren't the case.

(This isn't immensely relevant for mirgecom, since the output of the `compile`d function will typically be fed into a time integrator, which would invalidate any memoized temperature anyhow.)

cc @kaushikcfd

Start by reading the companion issues inducer/pytato#164 and inducer/arraycontext#99, then trace actx.compile through a case where the evaluated function uses memoized data. Compare the array or array-container instances before and after compiled evaluation. Done means dependent-data memoization remains available after compilation, if that behavior is feasible.

Written by the indexing model from the issue text.