inducer / inducer/arraycontext

Repeated freezes cause repeated computation

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Descripción

(Maybe this is an `arraycontext` issue? Not sure.)

Suppose a moderately complex expression is built and evaluated. Then it is evaluated again. Repeated codegen (most likely cached, though see inducer/pytato#163) and repeated evaluation ensues. This isn't ideal. Possibly, a symbolic array, once evaluated, should hold on to its value, to avoid reevaluation. If we don't deal with this somehow, then pytato's arrays can't be meaningfully memoized (e.g. with `@memoize`/`@memoize_method` from pytools), as, sure, they memoize the expression, but the actual evaluation is done again and again.

A simple approach to this would be simply stuff the evaluated value into a hidden attribute (`_evaluated`?) on the expression nodes. I'm aware that this introduces mutation into otherwise immutable objects... but it's the cache-y kind of mutability, and it doesn't change the semantics of the object in the slightest. So I suspect it's OK.

Another possible concern is the lifetime of the evaluated value (i.e. it might outstay its welcome). I don't *think* that'll be a big concern because
- somebody held on to the symbolic value, demonstrating that there's at least potential interest in reevaluating.
- if it becomes an issue, we could make an interface to free the stored value, enabling the memory to be freed.

Generally, codegen should stop at already-evaluated notes (and treat them as `DataWrapper`s).

@MTCam is hitting this with cache retrievals upon freeze when exercising lazy evaluation for chemistry in https://github.com/illinois-ceesd/mirgecom.

cc @kaushikcfd

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