Fostering Proof Scores in CafeOBJ

Proof scores are instructions to a proof engine such that when executed, if everything evaluates as expected, then a desired theorem is proved. Proof scores hide the detailed calculations done by machines, while revealing the proof plan created by humans. Although proof scores are executalbe by machines, they are also for human beings to read for proving (or verifying) desired properties on a system of interest. The technique of proof scores was brought up by the OBJ/CafeOBJ community, and substantial developments were done after a reliable implementation of CafeOBJ language system was available. This paper give an overview of evolution of proof scores which have been done under the efforts of verifying vearious kinds of formal specifications in CafeOBJ.

[1]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[2]  José Meseguer,et al.  Parameterized programming in OBJ2 , 1987, ICSE '87.

[3]  Kazuhiro Ogata,et al.  Flaw and modification of the iKP electronic payment protocols , 2003, Inf. Process. Lett..

[4]  Alexander Kurz,et al.  Algebra and Coalgebra in Computer Science, Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings , 2009, CALCO.

[5]  Stefania Gnesi,et al.  FME 2003: Formal Methods: International Symposium of Formal Methods Europe, Pisa, Italy, September 8-14, 2003. Proceedings , 2003, Lecture Notes in Computer Science.

[6]  Joseph A. Goguen,et al.  An Oxford survey of order sorted algebra , 1994, Mathematical Structures in Computer Science.

[7]  Doug DeGroot,et al.  Logic programming - functions, relations and equations , 1986 .

[8]  Bruce D. Shriver,et al.  Research Directions in Object-Oriented Programming , 1987 .

[9]  Kazuhiro Ogata,et al.  Rewriting-Based Verification of Authentication Protocols , 2002, Electron. Notes Theor. Comput. Sci..

[10]  Kazuhiro Ogata,et al.  Simulation-based Verification for Invariant Properties in the OTS/CafeOBJ Method , 2008, Electron. Notes Theor. Comput. Sci..

[11]  Razvan Diaconescu,et al.  Component-Based Algebraic Specification and Verification in CafeOBJ , 1999, World Congress on Formal Methods.

[12]  José Meseguer,et al.  Principles of OBJ2 , 1985, POPL.

[13]  Stephen J. Garland,et al.  Larch: Languages and Tools for Formal Specification , 1993, Texts and Monographs in Computer Science.

[14]  Joseph A. Goguen,et al.  Algebraic semantics of imperative programs , 1996, Foundations of computing series.

[15]  Joseph A. Goguen,et al.  A hidden agenda , 2000, Theor. Comput. Sci..

[16]  Kokichi Futatsugi,et al.  Specification Writing as Construction of Hierarchically Structured Clusters of Operators , 1980, IFIP Congress.

[17]  Michel Bidoit,et al.  Behavioural Theories and the Proof of Behavioural Properties , 1996, Theor. Comput. Sci..

[18]  Kazuhiro Ogata,et al.  Constructor-Based Institutions , 2009, CALCO.

[19]  Kazuhiro Ogata,et al.  CrÈme: an Automatic Invariant Prover of Behavioral Specifications , 2007, Int. J. Softw. Eng. Knowl. Eng..

[20]  José Meseguer,et al.  A logical theory of concurrent objects , 1990, OOPSLA/ECOOP '90.

[21]  Kazuhiro Ogata,et al.  Equational Approach to Formal Analysis of TLS , 2005, 25th IEEE International Conference on Distributed Computing Systems (ICDCS'05).

[22]  K. Futatsugi An overview of OBJ2 , 1988 .

[23]  Jean-Pierre Jouannaud,et al.  Algebra, Meaning, and Computation, Essays Dedicated to Joseph A. Goguen on the Occasion of His 65th Birthday , 2006, Essays Dedicated to Joseph A. Goguen.

[24]  Kazuhiro Ogata,et al.  Specification and Verification of Workflows with Rbac Mechanism and Sod Constraints , 2007, Int. J. Softw. Eng. Knowl. Eng..

[25]  José Meseguer,et al.  Unifying Functional, Object-Oriented and Relational Programming with Logical Semantics , 1987, Research Directions in Object-Oriented Programming.

[26]  Kazuhiro Ogata,et al.  Proof Scores in the OTS/CafeOBJ Method , 2003, FMOODS.

[27]  Kazuhiro Ogata,et al.  Algebraic Approaches to Formal Analysis of the Mondex Electronic Purse System , 2007, IFM.

[28]  Kazuhiro Ogata,et al.  Verifying Design with Proof Scores , 2005, VSTTE.

[29]  Kazuhiro Ogata,et al.  Formal Analysis of the iKP Electronic Payment Protocols , 2002, ISSS.

[30]  Akinori Yonezawa,et al.  Software Security — Theories and Systems , 2003, Lecture Notes in Computer Science.

[31]  Razvan Diaconescu,et al.  Behavioural Coherence in Object-Oriented Algebraic Specification , 2000, J. Univers. Comput. Sci..

[32]  Kokichi Futatsugi,et al.  CafeOBJ as a Tool for Behavioral System Verification , 2002, ISSS.

[33]  Kokichi Futatsugi Verifying Specifications with Proof Scores in CafeOBJ , 2006, 21st IEEE/ACM International Conference on Automated Software Engineering (ASE'06).

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

[35]  José Meseguer,et al.  Conditioned Rewriting Logic as a United Model of Concurrency , 1992, Theor. Comput. Sci..

[36]  K. Ogata,et al.  Equational approach to formal verification of SET , 2004, Fourth International Conference onQuality Software, 2004. QSIC 2004. Proceedings..

[37]  Joseph A. Goguen,et al.  Putting Theories Together to Make Specifications , 1977, IJCAI.

[38]  Yves Bertot,et al.  Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .

[39]  Joseph A. Goguen,et al.  Software Engineering with Obj: Algebraic Specification In Action , 2010 .

[40]  Tetsuo Tamai,et al.  CAFE: An Industrial-Strength Algebraic Formal Method , 2000 .

[41]  José Meseguer,et al.  From OBJ to Maude and Beyond , 2006, Essays Dedicated to Joseph A. Goguen.

[42]  Razvan Diaconescu,et al.  Logical foundations of CafeOBJ , 2002, Theor. Comput. Sci..

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

[44]  José Meseguer,et al.  EQLOG: Equality, Types, and Generic Modules For Logic Programming , 1986, Logic Programming: Functions, Relations, and Equations.

[45]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[46]  Kazuhiro Ogata,et al.  A Combination of Forward and Backward Reachability Analysis Methods , 2010, ICFEM.

[47]  Kazuhiro Ogata,et al.  Some Tips on Writing Proof Scores in the OTS/CafeOBJ Method , 2006, Essays Dedicated to Joseph A. Goguen.

[48]  Michel Bidoit,et al.  Observational Logic , 1998, AMAST.

[49]  Toshimi Sawada,et al.  Past, Present, and Future of SRA Implementation of CafeOBJ: Annex , 2003, FME.

[50]  Razvan Diaconescu,et al.  Cafeobj Report - The Language, Proof Techniques, and Methodologies for Object-Oriented Algebraic Specification , 1998, AMAST Series in Computing.

[51]  Donald Sannella,et al.  Horizontal Composability Revisited , 2006, Essays Dedicated to Joseph A. Goguen.

[52]  Kazuhiro Ogata,et al.  Modeling and verification of distributed real-time systems based on CafeOBJ , 2001, Proceedings 16th Annual International Conference on Automated Software Engineering (ASE 2001).

[53]  S. Anderson,et al.  Secure Synthesis of Code: A Process Improvement Experiment , 1999, World Congress on Formal Methods.

[54]  Kokichi Futatsugi,et al.  Verifying Behavioural Specifications in CafeOBJ Environment , 1999, World Congress on Formal Methods.

[55]  José Meseguer,et al.  Membership algebra as a logical framework for equational specification , 1997, WADT.

[56]  Kokichi Futatsugi,et al.  Formal Methods in CafeOBJ , 2002, FLOPS.

[57]  Grigore Rosu,et al.  Distributed cooperative formal methods tools , 1997, Proceedings 12th IEEE International Conference Automated Software Engineering.

[58]  Ataru T. Nakagawa,et al.  An overview of CAFE specification environment-an algebraic approach for creating, verifying, and maintaining formal specifications over networks , 1997, First IEEE International Conference on Formal Engineering Methods.

[59]  Kazuhiro Ogata,et al.  Formal Verification of the Horn-Preneel Micropayment Protocol , 2003, VMCAI.

[60]  Pierre Castéran,et al.  Interactive Theorem Proving and Program Development , 2004, Texts in Theoretical Computer Science An EATCS Series.

[61]  José Meseguer,et al.  Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations , 1992, Theor. Comput. Sci..

[62]  Kazuhiro Ogata,et al.  Specifying and verifying a railroad crossing with cafeOBJ , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.

[63]  K. Mani Chandy,et al.  Parallel program design - a foundation , 1988 .