MATHEMATICAL ENGINEERING TECHNICAL REPORTS Generator-based GG Fortress Library —Collection of GGs and Theories—

We have proposed a novel library called “GG Library” on Fortress in the previous report. The library supports easy development of correct and efficient parallel programs, allowing users to write naive generate-and-test programs easily and uniformly with generator-ofgenerators that abstract generation of nested data structures. The library has an automatic optimization mechanism by dispatching efficient implementation to a user program written with generator-of-generators based on a collection of theories. To enrich the power of GG library, we need to make collections of generator-of-generators and their theories for optimization. This report collects generator-of-generators and their theories for optimization with formal discussion, as well as their implementations in GG library.