System and method for incremental view maintenance based on differential calculus over natural algebra of k-relations

A database system comprising:

• one or more servers communicatively coupled to each other, each server comprising a non-transitory computer-readable medium and one or more processors, wherein:
• a first subset of the one or more servers comprises a storage engine subsystem, the storage engine subsystem configured to:
• maintain original data in one or more base tables, and
• generate and store materialized views and subviews;
• a second subset of the one or more servers comprises a diff engine subsystem configured to receive and translate Natural Algebra representations of a Natural Algebra view definition into corresponding derived Natural Algebra expressions;
• a third subset of the one or more servers comprises an Optimizer configured to receive and translate derived Natural Algebra expressions into Incremental View Maintenance plans (134);
• a fourth subset of the one or more servers comprises a delta extractor subsystem configured to extract transactional changes to the original data or batches of the transactional changes in a form that can be passed as input to the Incremental View Maintenance plans in order to compute the changes to the materialized views;
• and
• a fifth subset of the one or more servers comprises a database query system configured to:
• receive database queries and transactions according to one or more supported database query languages;
• translate the database queries and transactions into the Natural Algebra;
• generate database plans based on the translated database queries and translations;
• and
• execute the database plans.