Implementing Virtual Substitution in Keymaerax
نویسنده
چکیده
Virtual Substitution is an existential quantifier elimination method for statements of First Order Logic over the Reals (FOLR) satisfying certain constraints. Although not a comprehensive QE tool, it’s relative simplicity and efficiency compared to other QE techniques make it a useful method. Moreover, Virtual Substitution can be very useful for proving results about CPS models that involve polynomials with low degree. In this paper, we discuss a partial implementation of Virtual Substitution in KeymaeraX based on certain assumptions we make about the input formula. Although not a complete implementation of Virtual Substitution, the implementation is designed to apply virtual substitution to FOLR statements made up of existential quantifiers and comparison formulas involving linear polynomials. In addition, the implementation can apply virtual substitution to certain FOLR statements containing quadratics.
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