Procedurally transform subquery into join

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Is there a generalized procedure or algorithm for transforming a SQL subquery into a join, or vice versa? That is, is there a set of typographic operations that can be applied to a syntactically correct SQL query statement containing a subquery that results in a functionally equivalent statement without a subquery? If so, what are they (i.e., what's the algorithm), and in what cases do they not apply?

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