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Explore a 15-minute conference presentation that introduces a novel denotational semantics theory for verifying properties across infinite sets of programs defined by grammars. Learn how current verification frameworks fail when dealing with loops in program sets, and discover why existing Hoare-style logics lack relative completeness for such scenarios. Understand the fundamental requirement of tracking distinct program behaviors over unboundedly many executions for compositional verification of simple properties in infinite program sets. Examine the construction of minimal compositional semantics that captures simple properties of program sets and see how this leads to the first sound and relatively complete Hoare-style logic for infinite sets of programs. Gain insights into designing minimally complex, compositional verification techniques for sets of programs, with applications in program synthesis where proving properties must hold for all infinitely many programs described by a grammar. The presentation covers theoretical foundations, practical implications, and demonstrates how this work addresses limitations in current verification approaches for program synthesis applications.
