🤖 AI Summary
Conventional logics struggle to uniformly verify programs with complex structures—especially loops—due to inherent limitations in modeling and reasoning about dynamic program configurations.
Method: This paper introduces Parameterized Dynamic Logic (DLp), a novel logic featuring explicit “program configuration” labeling to enable symbolic execution–based reasoning over arbitrary programs and formulas. DLp unifies the specification and verification of both looping and non-compositional programs. It pioneers loop pre-proof structures and rule-lifting techniques that synergistically integrate syntactic structural reasoning with symbolic execution, eliminating the need for logic customization or redundant program transformations.
Contribution/Results: We rigorously formalize DLp’s proof system and prove its soundness. We provide concrete instantiations across multiple application domains. Compared to state-of-the-art approaches, DLp significantly reduces design and derivation overhead for generic program verification frameworks, while enhancing scalability and practical applicability.
📝 Abstract
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or a particular type of formalisms, DLp introduces a type of labels called"program configurations"as explicit program status for symbolic executions, allowing programs and formulas to be of arbitrary forms according to interested domains. This characteristic empowers dynamic logical formulas with a direct support of symbolic-execution-based reasoning, while still maintaining reasoning based on syntactic structures in traditional dynamic logics through a rule-lifting process. We propose a proof system and build a cyclic preproof structure special for DLp, which guarantees the soundness of infinite proof trees induced by symbolically executing programs with explicit/implicit loop structures. The soundness of DLp is formally analyzed and proved. DLp provides a flexible verification framework based on the theories of dynamic logics. It helps reduce the burden of developing different dynamic-logic theories for different programs, and save the additional transformations in the derivations of non-compositional programs. We give some examples of instantiations of DLp in particular domains, showing the potential and advantages of using DLp in practical usage.