Red-black trees in a functional setting

Okasaki, Chris

doi:10.1017/s0956796899003494

Cited by 53 publications

(25 citation statements)

References 11 publications

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“…1 shows a recursive Haskell predicate bst that checks whether a given tree with labels strictly between low and high satisfies the standard binary-search tree (BST) invariant [56]. It is followed by a QuickCheck generator genTree, which generates BSTs with a given maximum depth, controlled by the size parameter.…”

Section: Luck By Examplementioning

confidence: 99%

Beginner's luck: a language for property-based generators

Lampropoulos

Gallois-Wong

Hriţcu

et al. 2017

Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

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Property-based random testingà la QuickCheck requires building efficient generators for well-distributed random data satisfying complex logical predicates, but writing these generators can be difficult and error prone. We propose a domain-specific language in which generators are conveniently expressed by decorating predicates with lightweight annotations to control both the distribution of generated values and the amount of constraint solving that happens before each variable is instantiated. This language, called Luck, makes generators easier to write, read, and maintain.We give Luck a formal semantics and prove several fundamental properties, including the soundness and completeness of random generation with respect to a standard predicate semantics. We evaluate Luck on common examples from the property-based testing literature and on two significant case studies, showing that it can be used in complex domains with comparable bug-finding effectiveness and a significant reduction in testing code size compared to handwritten generators.

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Section: Luck By Examplementioning

confidence: 99%

Beginner's luck: a language for property-based generators

Lampropoulos

Gallois-Wong

Hriţcu

et al. 2017

Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

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“…1 A red-black tree is a self-balancing binary search tree in which each non-leaf node stores a data item and is colored either Red or Black [36]. We define the type of red-black trees of naturals in Coq as follows:…”

Section: Example: Red-black Treesmentioning

confidence: 99%

Foundational Property-Based Testing

Paraskevopoulou

Hriţcu

Dénès

et al. 2015

Lecture Notes in Computer Science

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Integrating property-based testing with a proof assistant creates an interesting opportunity: reusable or tricky testing code can be formally verified using the proof assistant itself. In this work we introduce a novel methodology for formally verified property-based testing and implement it as a foundational verification framework for QuickChick, a port of QuickCheck to Coq. Our framework enables one to verify that the executable testing code is testing the right Coq property. To make verification tractable, we provide a systematic way for reasoning about the set of outcomes a random data generator can produce with non-zero probability, while abstracting away from the actual probabilities. Our framework is firmly grounded in a fully verified implementation of QuickChick itself, using the same underlying verification methodology. We also apply this methodology to a complex case study on testing an information-flow control abstract machine, demonstrating that our verification methodology is modular and scalable and that it requires minimal changes to existing code.

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“…For denoting individual states, we will use the letter s, possibly with indices. The For efficiency, we represent the maps in each level of the abstract state as persistent red-black trees [35] (using Eker's optimizations [19]) to allow fast functional updates with sharing. Regions use interval trees to efficiently detect overlap, and we use hash consing to avoid constructing duplicate objects.…”

Section: Abstract Domainsmentioning

confidence: 99%

Statically-directed dynamic automated test generation

Babić

Martignoni

McCamant

et al. 2011

Proceedings of the 2011 International Symposium on Software Testing and Analysis

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We present a new technique for exploiting static analysis to guide dynamic automated test generation for binary programs, prioritizing the paths to be explored. Our technique is a three-stage process, which alternates dynamic and static analysis. In the first stage, we run dynamic analysis with a small number of seed tests to resolve indirect jumps in the binary code and build a visibly pushdown automaton (VPA) reflecting the global control-flow of the program. Further, we augment the computed VPA with statically computable jumps not executed by the seed tests. In the second stage, we apply static analysis to the inferred automaton to find potential vulnerabilities, i.e., targets for the dynamic analysis. In the third stage, we use the results of the prior phases to assign weights to VPA edges. Our symbolic-execution based automated test generation tool then uses the weighted shortest-path lengths in the VPA to direct its exploration to the target potential vulnerabilities. Preliminary experiments on a suite of benchmarks extracted from real applications show that static analysis allows exploration to reach vulnerabilities it otherwise would not, and the generated test inputs prove that the static warnings indicate true positives.

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Red-black trees in a functional setting

Cited by 53 publications

References 11 publications

Beginner's luck: a language for property-based generators

Beginner's luck: a language for property-based generators

Foundational Property-Based Testing

Statically-directed dynamic automated test generation

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