ABSTRACT
Shape analyses are concerned with precise abstractions of the heap to capture detailed structural properties. To do so, they need to build and decompose summaries of disjoint memory regions. Unfortunately, many data structure invariants require relations be tracked across disjoint regions, such as intricate numerical data invariants or structural invariants concerning back and cross pointers. In this paper, we identify issues inherent to analyzing relational structures and design an abstract domain that is parameterized both by an abstract domain for pure data properties and by user-supplied specifications of the data structure invariants to check. Particularly, it supports hybrid invariants about shape and data and features a generic mechanism for materializing summaries at the beginning, middle, or end of inductive structures. Around this domain, we build a shape analysis whose interesting components include a pre-analysis on the user-supplied specifications that guides the abstract interpretation and a widening operator over the combined shape and data domain. We then demonstrate our techniques on the proof of preservation of the red-black tree invariants during insertion.
- Gilad Arnold. Specialized 3-valued logic shape analysis using structure-based refinement and loose embedding. In Static Analysis (SAS), 2006. Google ScholarDigital Library
- Josh Berdine, Cristiano Calcagno, Byron Cook, Dino Distefano, Peter W. O'Hearn, Thomas Wies, and Hongseok Yang. Shape analysis for composite data structures. In Computer-Aided Verification (CAV), 2007. Google ScholarDigital Library
- Bor-Yuh Evan Chang, Xavier Rival, and George C. Necula. Shape analysis with structural invariant checkers. In Static Analysis (SAS), 2007. Google ScholarDigital Library
- Shaunak Chatterjee, Shuvendu K. Lahiri, Shaz Qadeer, and Zvonimir Rakamaric. A reachability predicate for analyzing low-level software. In Tools and Algorithms for the Construction and Analysis of Systems (TACAS), 2007. Google ScholarDigital Library
- Sigmund Cherem and Radu Rugina. Maintaining doubly-linked list invariants in shape analysis with local reasoning. In Verification, Model Checking, and Abstract Interpretation (VMCAI), 2007. Google ScholarDigital Library
- Patrick Cousot. Verification by abstract interpretation. In Verification: Theory and Practice, 2003.Google ScholarCross Ref
- Patrick Cousot and Radhia Cousot. Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In Principles of Programming Languages (POPL), 1977. Google ScholarDigital Library
- Dino Distefano, Peter W. O'Hearn, and Hongseok Yang. A local shape analysis based on separation logic. In Tools and Algorithms for the Construction and Analysis of Systems (TACAS), 2006. Google ScholarDigital Library
- Denis Gopan, Thomas W. Reps, and Shmuel Sagiv. A framework for numeric analysis of array operations. In Principles of Programming Languages (POPL), 2005. Google ScholarDigital Library
- Sumit Gulwani and Ashish Tiwari. An abstract domain for analyzing heapmanipulating low-level software. In Computer-Aided Verification (CAV), 2007. Google ScholarDigital Library
- Bolei Guo, Neil Vachharajani, and David I. August. Shape analysis with inductive recursion synthesis. In Programming Language Design and Implementation (PLDI), 2007. Google ScholarDigital Library
- Michael Karr. Affine relationships among variables of a program. Acta Inf., 6, 1976.Google Scholar
- Oukseh Lee, Hongseok Yang, and Kwangkeun Yi. Automatic verification of pointer programs using grammar-based shape analysis. In European Symposium on Programming (ESOP), 2005. Google ScholarDigital Library
- Tal Lev-Ami, Thomas W. Reps, Shmuel Sagiv, and Reinhard Wilhelm. Putting static analysis to work for verification: A case study. In Software Testing and Analysis (ISSTA), 2000. Google ScholarDigital Library
- Stephen Magill, Josh Berdine, Edmund Clarke, and Byron Cook. Arithmetic strengthening for separation logic based shape analyses. In Static Analysis (SAS), 2007. Google ScholarDigital Library
- Scott McPeak and George C. Necula. Data structure specifications via local equality axioms. In Computer-Aided Verification (CAV), 2005. Google ScholarDigital Library
- Antoine Mine. The octagon abstract domain. Higher-Order and Symbolic Computation, 19(1), 2006. Google ScholarDigital Library
- Anders Møller and Michael I. Schwartzbach. The pointer assertion logic engine. In Programming Language Design and Implementation (PLDI), 2001. Google ScholarDigital Library
- Huu Hai Nguyen, Cristina David, Shengchao Qin, and Wei-Ngan Chin. Automated verification of shape and size properties via separation logic. In Verification, Model Checking, and Abstract Interpretation (VMCAI), 2007. Google ScholarDigital Library
- John C. Reynolds. Separation logic: A logic for shared mutable data structures. In Logic in Computer Science (LICS), 2002. Google ScholarDigital Library
- Radu Rugina. Quantitative shape analysis. In Static Analysis (SAS), 2004.Google ScholarCross Ref
- Shmuel Sagiv, Thomas W. Reps, and Reinhard Wilhelm. Parametric shape analysis via 3-valued logic. ACM Trans. Program. Lang. Syst., 24(3), 2002. Google ScholarDigital Library
- Arnaud Venet. Abstract cofibered domains: Application to the alias analysis of untyped programs. In Static Analysis (SAS), 1996. Google ScholarDigital Library
Index Terms
- Relational inductive shape analysis
Recommendations
Relational inductive shape analysis
POPL '08Shape analyses are concerned with precise abstractions of the heap to capture detailed structural properties. To do so, they need to build and decompose summaries of disjoint memory regions. Unfortunately, many data structure invariants require ...
Calling context abstraction with shapes
POPL '11: Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languagesInterprocedural program analysis is often performed by computing procedure summaries. While possible, computing adequate summaries is difficult, particularly in the presence of recursive procedures. In this paper, we propose a complementary framework ...
Calling context abstraction with shapes
POPL '11Interprocedural program analysis is often performed by computing procedure summaries. While possible, computing adequate summaries is difficult, particularly in the presence of recursive procedures. In this paper, we propose a complementary framework ...
Comments