Abstraction and Refinement in Higher Order Logic

Authors:
Matt Fairtlough;Michael Mendler;Xiaochun Cheng
Affiliations:
-;-;-
Venue:
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Year:
2001

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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.