A -Semi-Ring-Based Query Algebra for Incremental View Maintenance and Query Compilation

Explore an algebraic approach to incremental view maintenance in database systems. Delve into the construction of a ring of databases, extended to form a powerful aggregate query calculus with a polynomial normal form. Learn how this calculus, closed under a universal difference operator, enables the expression of delta queries and their higher-order derivatives. Discover a multi-layered incremental view maintenance scheme that simplifies the process of keeping views fresh upon updates. Examine how this method can eliminate expensive query operators like joins and aggregate sums from incremental view maintenance programs. Investigate the resulting query language built on avalanche (semi)rings, which algebraizes range-restriction and guarantees finite query results without explicit selection operations. Understand how this algebraic language, behaving like a polynomial ring of relations, facilitates easy manipulation and serves as a natural internal representation for query processors and compilers.