Very good write!
I also wrote a bit earlier on monotonic functions: on how to utilize the fact we have a monotonic function, to cover for a missing index:

Monotonic functions, SQL and MySQL

Regards

However, the point of SQL (as we have been told for the decades) is that you give the idea, we handle the details, and this proposal is to make this statement more true.

Rewriting the conditions, though, may be not easy as it seems. Say, col1 / y = z is not the same as col1 = z * y (due to the rounding errors). This requires extra handling too.

And what about functions that are piecewise monotonic? Like get all records of Jan 1st of any year? This is not so easy to rewrite as a sargable condition.

So having these things handled automatically in Drizzle would be very nice :)

Finally, I’d just say that perhaps the reason that many RDBMS have yet to implement such optimizations is because in many (all?) cases where a monotonic function might be inlined within the optimizer into a sargable parameter, the SQL statement can be rewritten in such a way as to manually perform the translation.

Simple example would be rewriting this MySQLish SQL SELECT statement (assume an index on t1(date_col)):

SELECT * FROM t1 WHERE TO_DAYS(date_col) > TO_DAYS(NOW()) – 8;

to

SELECT * FROM t1 WHERE date_col > NOW() – INTERVAL 8 DAY;

Cheers, and nice blog! :)

-jay