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

[inducer]

This is a longer-shot companion issue to https://github.com/inducer/pytato/issues/164 (and #100):

Suppose an actx.compiled function is passed an array container (for the sake of argument, imagine a mirgecom ConservedVars) that somehow holds on to already-computed, dependent state that is the subsequently used in the compiled function. Right now, any such association is destroyed when "placeholderizing" the inputs. It'd be nice to instead realize that something we're about to (re)compute has already been computed and just use it instead.

A few (substantial) challenges:

• Unless we retain the object identity of the data passed in as a placeholder, we have no way of finding the existing state.
• Even if we can find it, we can't really reliably generate an identifier for it.

cc @kaushikcfd @MTCam