Abstract. We present a new modular shape analysis that can synthesize heap memory specification on a per method basis. We rely on a second-order biabduction mechanism that can give interpretations to unknown shape predicates. There are several novel features in our shape analysis. Firstly, it is grounded on second-order bi-abduction. Secondly, we distinguish unknown pre-predicates in pre-conditions, from unknown post-predicates in post-condition; since the former may be strengthened, while the latter may be weakened. Thirdly, we provide a new heap guard mechanism to support more precise preconditions for heap specification. Lastly, we formalise a set of derivation and normalization rules to give concise definitions for unknown predicates. Our approach has been proven sound and is implemented on top of an existing automated verification system. We show its versatility in synthesizing a wide range of intricate shape specifications.

We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the two. Unlike locks and critical sections, Pthreads barriers enable simultaneous resource redistribution between multiple threads and are inherently stateful, leading to significant complications in the design of the logic and its soundness proof. We show how our logic can be applied to a specific example program in a modular way. Our proofs are machine-checked in Coq.

Abstract. We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the two. Unlike locks and critical sections, Pthreads barriers enable simultaneous resource redistribution between multiple threads and are inherently stateful, leading to significant complications in the design of the logic and its soundness proof. We show how our logic can be applied to a specific example program in a modular way. Our proofs are machine-checked in Coq. We showcase a program verification toolset that automatically applies the logic rules and discharges the associated proof obligations.

Abstract. Fractional permissions enable sophisticated management of resource accesses in both sequential and concurrent programs. Entailment checkers for formulae that contain fractional permissions must be able to reason about said permissions to verify the entailments. We show how entailment checkers for separation logic with fractional permissions can extract equation systems over fractional shares. We develop a set decision procedures over equations drawn from the sophisticated boolean binary tree fractional permission model developed by Dockins et al. [4]. We prove that our procedures are sound and complete and discuss their computational complexity. We explain our implementation and provide benchmarks to help understand its performance in practice. We detail how our implementation has been integrated into the HIP/SLEEK verification toolset. We have machine-checked proofs in Coq.

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