Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Separation Logic: A Logic for Shared Mutable Data Structures
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Balanced Search Trees Made Simple
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Transition predicate abstraction and fair termination
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
BI-hyperdoctrines, higher-order separation logic, and abstraction
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Ynot: dependent types for imperative programs
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Structuring the verification of heap-manipulating programs
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Verifying event-driven programs using ramified frame properties
Proceedings of the 5th ACM SIGPLAN workshop on Types in language design and implementation
A realizability model for impredicative Hoare type theory
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Mechanized verification with sharing
ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
Verifying generics and delegates
ECOOP'10 Proceedings of the 24th European conference on Object-oriented programming
Concurrent abstract predicates
ECOOP'10 Proceedings of the 24th European conference on Object-oriented programming
Abstraction and refinement for local reasoning
VSTTE'10 Proceedings of the Third international conference on Verified software: theories, tools, experiments
Dafny: an automatic program verifier for functional correctness
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Kopitiam: modular incremental interactive full functional static verification of java code
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Verifying object-oriented programs with higher-order separation logic in Coq
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Verification of snapshotable trees using access permissions and typestate
TOOLS'12 Proceedings of the 50th international conference on Objects, Models, Components, Patterns
The ramifications of sharing in data structures
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
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We use separation logic to specify and verify a Java program that implements snapshotable search trees, fully formalizing the specification and verification in the Coq proof assistant. We achieve local and modular reasoning about a tree and its snapshots and their iterators, although the implementation involves shared mutable heap data structures with no separation or ownership relation between the various data. The paper also introduces a series of four increasingly sophisticated implementations and verifies the first one. The others are included as future work and as a set of challenge problems for full functional specification and verification, whether by separation logic or by other formalisms.