Linking HOL Light to Mathematica using OpenMath

One of the most important benefits of using a theorem prover system is the absolute accuracy of the obtained result. However, solving mathematical problems often requires both deductive reasoning and algebraic computation. This issue is due to the fact that many real-life problems can be described with equations for which we cannot find easily symbolic (or closed-form) solutions and therefore we are not able to formalize them using the theorem prover. In other cases, some applications require well developed libraries and a deep knowledge of the theories to formalize simple expressions. A straightforward way to overcome these issues is the use of computer algebra systems or numerical approaches which are known to be the most efficient tools in symbolic computation. However, to preserve the soundness of the computation, the results of these systems should be formally verified. In this thesis, we present a general architecture to connect HOL Light, a higher-order logic theorem prover, to any mechanized mathematical system that supports the mathematical standard OpenMath. We implemented a prototype, called HolMatica, which links HOL Light to the computer algebra system Mathematica through OpenMath. We describe our implementation of a HOL Light translator which converts HOL Light statements into OpenMath object and vice-versa