Relational Algebra and SQL Queries

Relational algebra is a formal query language whose operands are relations and whose operators produce new relations. It serves two roles: it is the theoretical foundation for how DBMSs process queries, and many of its ideas are directly incorporated into SQL.

Evaluating an expression yields two things:

• Result schema — determined by the schemas of the input relations and the operators applied
• Result instance — the actual set of tuples obtained by running the operations

The complete set {σ, π, ∪, ρ, −, ×} is sufficient to express every other operator; joins, intersection, and renaming can all be derived from these six primitives.