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We present LT-PDR, a lattice-theoretic generalization of Bradley's propertydirected reachability analysis (PDR) algorithm. LT-PDR identifies the essenceof PDR to be an ingenious combination of verification and refutation attemptsbased on the Knaster-Tarski and Kleene theorems. We introduce four concreteinstances of LT-PDR, derive their implementation from a generic Haskellimplementation of LT-PDR, and experimentally evaluate them. We also present acategorical structural theory that derives these instances.

The Lattice-Theoretic Essence of Property Directed Reachability Analysis