A formalization of abstraction in LAMBDA
In a mixed approach to system verification using theorem provers with an interface to specialized model-checking tools, it may be necessary to simplify models by considering abstract versions of them. We report on work in progress that aims to develop support within LAMBDA for a systematic approach to abstraction. We give a formalization in LAMBDA of a notion of abstraction for transition systems; the abstract systems have two sorts of transition, and are related to specifications in modal process logic. We prove that formulae in the modal mu-calculus are satisfied in an abstract version of a model only if they are satisfied in the model itself. We illustrate how the proof of an inductive step in the verification of a satisfaction relation for an infinite model can be reduced to the verification of a satisfaction relation for a very small finite model.
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