An interpretation of Noden in HOL

Abstract

We describe the use of the HOL system to corroborate the logical consistency of Noden, an integrated HDL and proof system. The Noden logic is interpreted by representing terms of the logic (which are terms of the Noden HDL) as logical statements in the HOL logic. We describe the datatypes representing types and values, and sample the representation of built-in operations, functions and macros as HOL function specifications. An interpretation of Noden truth-valued statements is presented as a translation of these to HOL sequents, and the representation of Noden proof operations as HOL conversions. Results of the work are summarised, including exposed errors and ambiguities of the Noden logic and implementation. We conclude that this approach to providing assurance of soundness and consistency of a less secure proof system is not only useful, but is a practical method of prototyping and an aid to specifying such a system.