Theory Interpretations in PVS

Abstract

The purpose of this task was to provide a mechanism for theory interpretations in a prototype verification system (PVS) so that it is possible to demonstrate the consistency of a theory by exhibiting an interpretation that validates the axioms. The mechanization makes it possible to show that one collection of theories is correctly interpreted by another collection of theories under a user-specified interpretation for the uninterpreted types and constants. A theory instance is generated and imported, while the axiom instances are generated as proof obligations to ensure that the interpretation is valid. Interpretations can be used to show that an implementation is a correct refinement of a specification, that an axiomatically defined specification is consistent, or that a axiomatically defined specification captures its intended models. In addition, the theory parameter mechanism has been extended with a notion of theory as parameter so that a theory instance can be given as an actual parameter to an imported theory. Theory interpretations can thus be used to refine an abstract specification or to demonstrate the consistency of an axiomatic theory. In this report we describe the mechanism in detail. This extension is a part of PVS version 3.0, which will be publicly released in mid-2001.