Deductive Synthesis of Numerical Simulation Programs fromNetworks of Algebraic and Ordinary Differential Equations

Authors:
Thomas Ellman;Takahiro Murata
Affiliations:
Department of Computer Science, Hill Center for Mathematical Sciences, Rutgers University, Piscataway, New Jersey 08855. E-mail: ellman@cs.rutgers.edu, murata@cs.rutgers.edu;Department of Computer Science, Hill Center for Mathematical Sciences, Rutgers University, Piscataway, New Jersey 08855. E-mail: ellman@cs.rutgers.edu, murata@cs.rutgers.edu
Venue:
Automated Software Engineering
Year:
1998

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Abstract

Scientists and engineers face recurring problems ofconstructing, testing and modifying numerical simulationprograms. The process of coding and revising such simulators isextremely time-consuming, because they are almost always writtenin conventional programming languages. Scientists and engineerscan therefore benefit from software that facilitatesconstruction of programs for simulating physical systems. Ourresearch adapts the methodology of deductive program synthesisto the problem of constructing numerical simulation codes. Wehave focused on simulators that can be represented as secondorder functional programs composed of numerical integration androot extraction routines. We have developed a system that usesfirst order Horn logic to synthesize numerical simulators builtfrom these components. Our approach is based on two ideas:first, we axiomatize only the relationship between integrationand differentiation. We neither attempt nor require a completeaxiomatization of mathematical analysis. Second, our systemuses a representation in which functions are reified as objects.Function objects are encoded as lambda expressions. Ourknowledge base includes an axiomatization of term equality inthe lambda calculus. It also includes axioms defining thesemantics of numerical integration and root extraction routines.We use depth bounded SLD resolution to construct proofs andsynthesize programs. Our system has successfully constructednumerical simulators for computational design of jet enginenozzles and sailing yachts, among others. Our resultsdemonstrate that deductive synthesis techniques can be used toconstruct numerical simulation programs for realisticapplications.