Deductive synthesis of numerical simulation programs from networks of algebraic and ordinary differential equations

Computational science and engineering design can benefit from software tools that facilitate construction of programs for simulating physical systems. Our research adapts the methodology of deductive program synthesis to the problem of synthesizing numerical simulation codes. We have focused on simulators that can be represented as second-order functional programs composed of numerical integration and root-extraction routines. Synthesis of second-order programs appears to present a problem for deductive systems that operate in first order logic. We present a recursive synthesis algorithm that overcomes this difficulty for a class of program synthesis problems. Our system has successfully constructed numerical simulators for computational design of jet-engine nozzles and sailing yachts, among others.