Abstract and Model Check While You Prove

The construction of abstractions is essential for reducing large or innnite state systems to small or nite state systems. Boolean abstractions, where boolean variables replace concrete predicates, are an important class that subsume several abstraction schemes. We show how boolean abstractions can be constructed simply, eeciently, and precisely for innnite state systems while preserving properties in the full-calculus. We also propose an automatic reenement algorithm which reenes the abstraction until the property is veriied or a counterexample is found. Our algorithm is implemented as a proof rule in the PVS verii-cation system. With the abstraction proof rule, proof strategies combining deductive proof construction, model checking, and abstraction can be deened entirely within the PVS framework.