Aligator.jl

Automated Loop Invariant Generation by Algebraic Techniques Over the Rationals.

Aligator.jl is a Julia package for the automated generation of loop invariants. It supersedes the Mathematica package Aligator.

Installation

pkg> add https://github.com/ahumenberger/Recurrences.jl
pkg> add https://github.com/ahumenberger/AlgebraicDependencies.jl
pkg> add https://github.com/ahumenberger/Aligator.jl

Quick Start

julia> using Aligator
julia> loop = quote
         while true
           x = 2*x
           y = 1/2*y
         end
       end
julia> aligator(loop)
Invariant ideal with 1-element basis:
 y*x-y00*x00

Publications

1. A. Humenberger, M. Jaroschek, L. Kovács. Invariant Generation for Multi-Path Loops with Polynomial Assignments. In Verification, Model Checking, and Abstract Interpretation (VMCAI), 2018. https://arxiv.org/abs/1801.03967

2. A. Humenberger, M. Jaroschek, L. Kovács. Aligator.jl - A Julia Package for Loop Invariant Generation. In Intelligent Computer Mathematics (CICM), 2018. https://arxiv.org/abs/1808.05394

3. A. Humenberger, M. Jaroschek, L. Kovács. Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences. In International Symposium on Symbolic and Algebraic Computation (ISSAC), 2017. https://arxiv.org/abs/1705.02863

4. L. Kovács. A Complete Invariant Generation Approach for P-solvable Loops. In Proceedings of the International Conference on Perspectives of System Informatics (PSI), volume 5947 of LNCS, pages 242–256, 2009.

5. L. Kovács. Reasoning Algebraically About P-solvable Loops. In Proceedings of the International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS), volume 4963 of LNCS, pages 249–264, 2008.

6. L. Kovács. Aligator: A Mathematica Package for Invariant Generation (System Description). In Proceedings of the International Joint Conference on Automated Reasoning (IJCAR), volume 5195 of LNCS, pages 275–282, 2008.

7. L. Kovács. Invariant Generation with Aligator. In Proceedings of Austrian-Japanese Workshop on Symbolic Computation in Software Science (SCCS), number 08-08 in RISC-Linz Report Series, pages 123–136, 2008.

8. L. Kovács. Aligator: a Package for Reasoning about Loops. In Proceedings of the International Conference on Logic for Programming, Artificial Intelligence and Reasoning – Short Papers (LPAR-14), pages 5–8, 2007.