Systems and methods for storing and accessing data. A query language statement may reference a plurality of data sets and a plurality of algebraic relations between the data sets may be composed from the query language statement. The algebraic relations may be used to define new data sets and to optimize access to data sets. A store of algebraic relations may be accumulated over time. Alternative collections of algebraic relations may be generated and evaluated to determine an optimized collection of algebraic relations to use in calculating and providing a requested data set. The optimization may be performed using the algebraic relations rather than retrieving underlying data sets from storage. As a result, optimization may be performed at processor speeds to minimize the amount of time required for data to be retrieved from slower storage.