Sorry for being slow getting back, I have been offline.
The answer is that the database is supposed to figure out
exactly what the SQL is supposed to do, and then come up
with a very efficient way to do that. With a Turing-complete
language it is impossible to answer detailed questions
about arbitrary code, and is difficult to answer them even
for normal code.
Sure, optimizers can speed up code. But in a normal
language they can't recognize a bad algorithm and rewrite it
with a more efficient one. But SQL routinely is optimized
to be using algorithms which are far better than any that
the developer would have thought up.
SQL could not do this if the developer had, for instance,
the freedom to write a series of nested loops with
possibly relevant side-effects and a difficult to discern
purpose.
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