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Abstract:
We develop an abstract lattice-theoretic framework within which
we study soundness and other properties of circular assume-
guarantee (A-G) rules constrained by side conditions. We
identify a particular side condition, non-blockingness, which
admits an intelligible inductive proof of the soundness of
circular A-G reasoning. Besides, conditional circular rules
based on non-blockingness turn out to be complete in various
senses and stronger than a large class of sound conditional A-G
rules. In this respect, our framework enlightens the foundations
of circular A-G reasoning.
Due to its abstractness, the framework can be instantiated to
many concrete settings. We show several known circular A-G rules
for compositional verification to be instances of our generic
rules. Thus, we do the circularity-breaking inductive argument
once to establish soundness of our generic rules, which then
implies soundness of all the instances without resorting to
technically complicated circularity-breaking arguments for each
single rule. In this respect, our framework unifies many
approaches to circular A-G reasoning and provides a starting
point for the systematic development of new circular A-G rules.
