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A Complete Approach to Loop Verification with Invariants and Summaries
Invariants are the predominant approach to verify the correctness of loops.
As an alternative, loop contracts, which make explicit the premise and
conclusion of the underlying induction proof, can sometimes capture correctness
conditions more naturally. But despite this advantage, the second approach
receives little attention overall, and the goal of this paper is to lift it out
of its niche. We give the first comprehensive exposition of the theory of loop
contracts, including a characterization of its completeness. We show concrete
examples on standard algorithms that showcase their relative merits. Moreover,
we demonstrate a novel constructive translation between the two approaches,
which decouples the chosen specification approach from the verification
backend.Comment: This article extends a conference version at VMCAI'2