This grant supports research and development on "Hydra", a digital circuit design system based on stream recursion equations. Hydra supplies a solid mathematical foundation for circuit specification, derivation, simulation, analysis and layout. In the SBIR Phase I research, an experimental prototype compiler that translates a specification into an efficient simulation program was built. This research addresses several problems. First, circuit analysis algorithms are being used to produce parallel simulators both for MIMD and SIMD architectures. Second, the functional language notation of the compiler is being improved to incorporate visualization techniques, interactive graphics and functional geometry. Finally, methods for incorporating Hydra into existing sets of circuit design tools are being investigated. Phase I objectives were met quite successfully. The problem, derivation of digital designs from functional programs is important because of its promise to demonstrate how functional programming ideas fare in real world IC design. The P.I. and his associates' past work has been of high quality; they are well qualified to carry out the proposed research.