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Window functions and relational algebra

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I'm just discovering the power of window functions.  Is there any
mathematical formalism for them, similar to relational algebra?


It would seem to me that window functions aren't expressable in pure
relational algebra, but that a well defined extension to it would be
possible to express them; at least for those of us so inclinded, being
able to think in terms of an alegbra would make reasoning about them
much more powerful.


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