Aligators for Arrays (Tool Paper)

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.

[1]  Sumit Gulwani,et al.  Control-flow refinement and progress invariants for bound analysis , 2009, PLDI '09.

[2]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[3]  Thomas A. Henzinger,et al.  Valigator: A Verification Tool with Bound and Invariant Generation , 2008, LPAR.

[4]  Kousha Etessami,et al.  Analysis of Recursive Game Graphs Using Data Flow Equations , 2004, VMCAI.

[5]  Bruno Buchberger,et al.  Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..

[6]  Ranjit Jhala,et al.  Array Abstractions from Proofs , 2007, CAV.

[7]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[8]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[9]  Laura Kovács,et al.  Reasoning Algebraically About P-Solvable Loops , 2008, TACAS.

[10]  Andrei Voronkov,et al.  Finding Loop Invariants for Programs over Arrays Using a Theorem Prover , 2009, FASE.

[11]  Thomas W. Reps,et al.  A framework for numeric analysis of array operations , 2005, POPL '05.

[12]  Sumit Gulwani,et al.  Program verification using templates over predicate abstraction , 2009, PLDI '09.

[13]  Xavier Leroy.  The objective caml system release 3 , 2001 .

[14]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[15]  Thomas A. Henzinger,et al.  Invariant and Type Inference for Matrices , 2010, VMCAI.

[16]  Edsger W. Dijkstra,et al.  A Discipline of Programming , 1976 .

[17]  Ashutosh Gupta,et al.  InvGen: An Efficient Invariant Generator , 2009, CAV.

[18]  Sumit Gulwani,et al.  Combining abstract interpreters , 2006, PLDI '06.

[19]  Perdita Stevens,et al.  Modelling Recursive Calls with UML State Diagrams , 2003, FASE.

[20]  Nicolas Halbwachs,et al.  Discovering properties about arrays in simple programs , 2008, PLDI '08.

[21]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.