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A research paper introduces MQuery, a formal mathematical framework for MongoDB's aggregation pipeline, addressing the lack of rigorous specification in JSON document databases. The formalization proves MongoDB's aggregation framework is at least as expressive as relational algebra, while also supporting nested relational algebra and linear recursion. The mathematical foundation enables safe query optimization through algebraic rewriting rules, including filter anticipation, unnesting postponement, and join optimization. The paper addresses current ambiguities in MongoDB semantics, such as loose equality violations and path polysemy issues.

Towards a Standard for JSON Document Databases