Scientists and engineers face recurring problems of constructing, testing and modifying numerical simulation programs. The process of coding and revising such simulators is extremely time-consuming, because they are almost always written in conventional programming languages. Scientists and engineers can therefore benefit from software that facilitates construction of programs for simulating physical systems. Our research adapts the methodology of deductive program synthesis to the problem of constructing 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. We have developed a system that uses first order Horn logic to synthesize numerical simulators built from these components. Our approach is based on two ideas: First, we axiomatize only the relationship between integration and differentiation. We neither attempt nor require a complete axiomatization of mat..
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