Communication analysis and code generation for data parallel languages are naturally formulated as operations on integer sets. Principal analysis and code generation tasks require manipulation of sets of data, sets of processors, and sets of iterations. We describe a practical, executable, equational framework for analysis and optimization of High Performance Fortran based on abstract operations on sets of integers. This framework serves as the basis for the Rice dhpf compiler. We describe tradeoffs in the framework's implementation, the formulation of important analyses and optimizations using the framework, and a set-based code generation strategy that supports the framework.