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SQL is a dialect of a relational algebra. It assumes a relational model. It is used to query relations.

"Even the query language of SQL is loosely based on a relational algebra, though the operands in SQL (tables) are not exactly relations and several useful theorems about the relational algebra do not hold in the SQL counterpart (arguably to the detriment of optimisers and/or users). The SQL table model is a bag (multiset), rather than a set."

from: https://en.wikipedia.org/wiki/Relational_algebra#Implementat...

I remember how this suprised me a lot after thinking that SQL and SQL databases are based on relations, thinking "how can two equal rows co-exist in a relation". SQL needs things like "hidden identifiers / row keys" and so on to be squeezed into being "relational".

I'd argue from practical experience that an SQL which universally enforced set-relations would introduce significant implementation overhead: DISTINCT on large relations is v. expensive!

I believe it would also add complexity on net for users, as they would have to re-introduce those "hidden identifiers / row keys" in the not-uncommon cases where bag semantics are desired.

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