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

Comece lendo as issues relacionadas inducer/pytato#164 e inducer/arraycontext#99 e, em seguida, acompanhe actx.compile em um caso em que a função avaliada usa memoized data. Compare as instâncias de array ou array-container antes e depois da avaliação compilada. Considera-se concluído quando a memoização de dados dependentes continuar disponível após a compilação, se esse comportamento for viável.

Escrita pelo modelo de indexação a partir do texto da issue.