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Transactional objects combine the performance of classical concurrent objects with the high-level programmability of transactional memory. However, verifying the correctness of transactional objects is tricky, requiring reasoning simultaneously about classical concurrent objects, which guarantee the atomicity of individual methods—the property known as linearizability—and about software-transactional-memory libraries, which guarantee the atomicity of user-defined sequences of method calls—or serializability. We present a formal-verification framework called C4, built up from the familiar notion of linearizability and its compositional properties, that allows proof of both kinds of libraries, along with composition of theorems from both styles to prove correctness of applications or further libraries. We apply the framework in a significant case study, verifying a transactional set object built out of both classical and transactional components following the technique oftransactional predication; the proof is modular, reasoning separately about the transactional and nontransactional parts of the implementation. Central to our approach is the use of syntactic transformers oninteraction trees—i.e., transactional libraries that transform client code to enforce particular synchronization disciplines. Our framework and case studies are mechanized in Coq.
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A verified decision procedure for univariate real arithmetic with the BKR algorithm.
We formalize the univariate fragment of Ben-Or, Kozen, and Reif’s (BKR) decision procedure for first-order real arithmetic in Isabelle/HOL. BKR’s algorithm has good potential for parallelism and was designed to be used in practice. Its key insight is a clever recursive procedure that computes the set of all consistent sign assignments for an input set of univariate polynomials while carefully managing intermediate steps to avoid exponential blowup from naively enumerating all possible sign assignments (this insight is fundamental for both the univariate case and the general case). Our proof combines ideas from BKR and a follow-up work by Renegar that are well-suited for formalization. The resulting proof outline allows us to build substantially on Isabelle/HOL’s libraries for algebra, analysis, and matrices. Our main extensions to existing libraries are also detailed.
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- Award ID(s):
- 1739629
- PAR ID:
- 10276733
- Editor(s):
- Cohen, Liron; Kaliszyk, Cezary
- Date Published:
- Journal Name:
- 12th International Conference on Interactive Theorem Proving (ITP 2021)
- Volume:
- 193
- Page Range / eLocation ID:
- 14:1-14:20
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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