Abstraction and refinement in higher order logic

Abstract

We develop within higher order logic (HOL) a general and flexible method of abstraction and refinement, which specifically addresses the problem of handling constraints. We provide a HOL interpretation of first-order Lax Logic, which can be seen as a modal extension of deliverables. This provides a new technique for automating reasoning about behavioural constraints by allowing constraints to be associated with, but formally separated from, an abstracted model.We demonstrate a number of uses, e.g. achieving a formal separation of the logical and timing aspects of hardware design, and systematically generating timing constraints for a simple sequential device from a formal proof of its abstract behaviour. The method and proofs have been implemented in Isabelle as a definitional extension of the HOL logic which extends work by Jacobs and Melham on encoding dependent types in HOL.We assume familiarity with HOL but not detailed knowledge of circuit design.