A Discipline of Programming
The Mathematica Book
A framework for numeric analysis of array operations
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Combining abstract interpreters
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Discovering properties about arrays in simple programs
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Valigator: A Verification Tool with Bound and Invariant Generation
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Finding Loop Invariants for Programs over Arrays Using a Theorem Prover
FASE '09 Proceedings of the 12th International Conference on Fundamental Approaches to Software Engineering: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Program verification using templates over predicate abstraction
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Control-flow refinement and progress invariants for bound analysis
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
InvGen: An Efficient Invariant Generator
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Array abstractions from proofs
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Reasoning algebraically about P-solvable loops
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Invariant and type inference for matrices
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Invariant generation in vampire
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
Case studies on invariant generation using a saturation theorem prover
MICAI'11 Proceedings of the 10th Mexican international conference on Advances in Artificial Intelligence - Volume Part I
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This paper presents Aligators, a tool for the generation of universally quantified array invariants. Aligators leverages recurrence solving and algebraic techniques to carry out inductive reasoning over array content. The Aligators' loop extraction module allows treatment of multi-path loops by exploiting their commutativity and serializability properties. Our experience in applying Aligators on a collection of loops from open source software projects indicates the applicability of recurrence and algebraic solving techniques for reasoning about arrays.