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

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

Suppose an `actx.compile`d 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 `compile`d 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

先閱讀連結的配套 issue #164 和 issue #100，然後追蹤 actx.compile 如何將其輸入佔位符化。調查輸入物件身分和相依狀態是否能夠可靠地保留並識別，以用於記憶化。要算完成，需要確定一個重複使用已計算狀態的設計，但此 issue 未指定實作或驗收測試。

由索引模型根據 Issue 內容生成。