Bottom-Up Shape Analysis
In this paper we present a new shape analysis algorithm. The key distinguishing aspect of our algorithm is that it is completely compositional, bottom-up and non-iterative. We present our algorithm as an inference system for computing Hoare triples summarizing heap manipulating programs. Our inference rules are compositional: Hoare triples for a compound statement are computed from the Hoare triples of its component statements. These inference rules are used as the basis for a bottom-up shape analysis of programs.
Specifically, we present a logic of iterated separation formula (LISF) which uses the iterated separating conjunct of Reynolds  to represent program states. A key ingredient of our inference rules is a strong bi-abduction operation between two logical formulas. We describe sound strong bi-abduction and satisfiability decision procedures for LISF.
We have built a prototype tool that implements these inference rules and have evaluated it on standard shape analysis benchmark programs. Preliminary results show that our tool can generate expressive summaries, which are complete functional specifications in many cases.
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