Verifying a Plaftorm for Digital Imaging: A Multi-tool Strategy

Fiji is a Java platform widely used by biologists and other experimental scientists to process digital images. In our research, made together with a biologists team, we use Fiji in some pre-processing steps before undertaking a homological digital processing of images. In a previous work, we have formalised the correctness of the programs which use homological techniques to analyse digital images. However, the verification of Fiji's pre-processing step was missed. In this paper, we present a multi-tool approach (based on the combination of Why/Krakatoa, Coq and ACL2) filling this gap.

[1]  Francisco-Jesús Martín-Mateos,et al.  Formalization of a normalization theorem in simplicial topology , 2011, Annals of Mathematics and Artificial Intelligence.

[2]  Till Mossakowski,et al.  Towards Logical Frameworks in the Heterogeneous Tool Set Hets , 2010, WADT.

[3]  Stephen M. Watt,et al.  Intelligent Computer Mathematics , 2014, Lecture Notes in Computer Science.

[4]  Steven Obua,et al.  Importing HOL into Isabelle/HOL , 2006, IJCAR.

[5]  Jeremy Avigad,et al.  A Machine-Checked Proof of the Odd Order Theorem , 2013, ITP.

[6]  Michael D. Ernst,et al.  An overview of JML tools and applications , 2003, International Journal on Software Tools for Technology Transfer.

[7]  Jesús Aransay,et al.  A Mechanized Proof of the Basic Perturbation Lemma , 2008, Journal of Automated Reasoning.

[8]  Johannes E. Schindelin,et al.  Fiji: an open-source platform for biological-image analysis , 2012, Nature Methods.

[9]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[10]  Matt Kaufmann,et al.  Non-Standard Analysis in ACL2 , 2001 .

[11]  Holger Hermanns,et al.  Proceedings of the 19th international conference on Computer aided verification , 2007 .

[12]  David Pointcheval,et al.  Verified security of redundancy-free encryption from Rabin and RSA , 2012, CCS.

[13]  Evelyne Contejean,et al.  Software - The Alt-Ergo theorem prover , 2010 .

[14]  Sandip Ray,et al.  The Right Tools for the Job: Correctness of Cone of Influence Reduction Proved Using ACL2 and HOL4 , 2011, Journal of Automated Reasoning.

[15]  David Delahaye,et al.  Verifying B Proof Rules Using Deep Embedding and Automated Theorem Proving , 2011, SEFM.

[16]  Claude Marché,et al.  The Why/Krakatoa/Caduceus Platform for Deductive Program Verification , 2007, CAV.

[17]  Ana Romero,et al.  Homotopy groups of suspended classifying spaces: An experimental approach , 2013, Math. Comput..

[18]  César Domínguez,et al.  Effective homology of bicomplexes, formalized in Coq , 2011, Theor. Comput. Sci..

[19]  Rolf Dach,et al.  Technical Report 2012 , 2013 .

[20]  W. S. Rasband,et al.  ImageJ: Image processing and analysis in Java , 2012 .

[21]  Jónathan Heras,et al.  Verifying an Algorithm Computing Discrete Vector Fields for Digital Imaging , 2012, AISC/MKM/Calculemus.

[22]  Benjamin Werner,et al.  Importing HOL Light into Coq , 2010, ITP.

[23]  T. W. Körner,et al.  On the Fundamental Theorem of Algebra , 2006, Am. Math. Mon..

[24]  Martin Wirsing,et al.  Extraction of Structured Programs from Specification Proofs , 1999, WADT.

[25]  B. Fine,et al.  The Fundamental Theorem of Algebra , 1997 .

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

[27]  Thierry Coquand,et al.  Computing persistent homology within Coq/SSReflect , 2013, TOCL.

[28]  Ewen Denney A Prototype Proof Translator from HOL to Coq , 2000, TPHOLs.

[29]  David Aspinall,et al.  Formalising Java's Data Race Free Guarantee , 2007, TPHOLs.

[30]  Georges Gonthier,et al.  Formal Proof—The Four- Color Theorem , 2008 .

[31]  S. Griffis EDITOR , 1997, Journal of Navigation.

[32]  Matt Kaufmann,et al.  Nonstandard Analysis in ACL2 , 2001, Journal of Automated Reasoning.

[33]  David S. Hardin Design and Verification of Microprocessor Systems for High-Assurance Applications , 2010 .

[34]  Hanbing Liu,et al.  Java Program Verification via a JVM Deep Embedding in ACL2 , 2004, TPHOLs.