Algebraic Combinators for Data Dependencies and Their Applications

The notion of Data Dependency Algebra (DDA) is an algebraic formalism that turns data dependencies into first class citizens in the program code through a dedicated Application Programming Interface (API). This forms the basis of a platform independent parallel programming model [BH09]. In this paper, we further expand the theory of DDAs by proposing algebraic combinators operating on top of DDAs as a means to declare compound DDAs of custom complexity. The purpose is to allow the programmer to combine existing DDA implementations via high-level language constructs using simple declarations. The implementation of the compound DDA is generated at compile-time yet through the API its components are readily available for the programmer after declaration. We instantiate these ideas through the case-study of a DDA-based polynomial multiplication.