A Calculus for Collections and Aggregates

We present a calculus that should play for database query languages the same role that the lambda calculus plays for functional programming. For the semantic foundations of the calculus we introduce a new concept: monads enriched with algebraic structure. We model collection types through enriched monads and aggregate operations through enriched monad algebras. The calculus derives program equivalences that underlie a good number of the optimizations used in query languages.

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