Tests and proofs for custom data generators

We address automated testing and interactive proving of properties involving complex data structures with constraints, like the ones studied in enumerative combinatorics, e.g., permutations and maps. In this paper we show testing techniques to check properties of custom data generators for these str...

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Vydáno v:Formal aspects of computing Ročník 30; číslo 6; s. 659 - 684
Hlavní autoři: Dubois, Catherine, Giorgetti, Alain
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Springer London 01.11.2018
Association for Computing Machinery
Springer Verlag
Témata:
Combinatorial analysis
Combinatorics
Computer Science
Cryptography and Security
Data structures
Debugging
Distributed, Parallel, and Cluster Computing
Emerging Technologies
Generators
Logic programming
Math Applications in Computer Science
Modeling and Simulation
Multiagent Systems
Original Article
Permutations
Properties (attributes)
Software Engineering
Theory of Computation
Ubiquitous Computing
Random testing
Bounded-exhaustive testing
Permutations
Logic programming
Combinatorial enumeration
Interactive theorem proving
Rooted maps
nteractive theorem proving
rooted maps
bounded-exhaustive testing
logic programming
combinatorial enumeration
permutations
random testing
ISSN:0934-5043, 1433-299X
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Shrnutí:We address automated testing and interactive proving of properties involving complex data structures with constraints, like the ones studied in enumerative combinatorics, e.g., permutations and maps. In this paper we show testing techniques to check properties of custom data generators for these structures. We focus on random property-based testing and bounded exhaustive testing, to find counterexamples for false conjectures in the Coq proof assistant. For random testing we rely on the existing Coq plugin QuickChick and its toolbox to write random generators. For bounded exhaustive testing, we use logic programming to generate all the data up to a given size. We also propose an extension of QuickChick with bounded exhaustive testing based on generators developed inside Coq, but also on correct-by-construction generators developed with Why3. These tools are applied to an original Coq formalization of the combinatorial structures of permutations and rooted maps, together with some operations on them and properties about them. Recursive generators are defined for each combinatorial family. They are used for debugging properties which are finally proved in Coq. This large case study is also a contribution in enumerative combinatorics.
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ISSN:0934-5043
1433-299X
DOI:10.1007/s00165-018-0459-1