Practical Reasoning About Invocations and Implementations of Pure Methods

User-defined functions used in the specification of object-oriented programs are called pure methods. Providing sound and practical support for pure methods in a verification system faces many challenges, especially when pure methods have executable implementations and can be invoked from code at run time. This paper describes a design for reasoning about pure methods in the context of sound, modular verification. The design addresses (1) how to axiomatize pure methods as mathematical functions enabling reasoning about their result values; (2) preconditions and frame conditions for pure methods enabling reasoning about the implementation of a pure method. Two important considerations of the design are that it work with object invariants and that its logical encoding be suitable for fully automatic theorem provers. The design has been implemented in the Spec# programming system.

[1]  Brian Campbell,et al.  Amortised Memory Analysis Using the Depth of Data Structures , 2009, ESOP.

[2]  Martin C. Rinard,et al.  Purity and Side Effect Analysis for Java Programs , 2005, VMCAI.

[3]  Frank D. Valencia,et al.  Formal Methods for Components and Objects , 2002, Lecture Notes in Computer Science.

[4]  James Noble,et al.  Ownership types for flexible alias protection , 1998, OOPSLA '98.

[5]  Bertrand Meyer,et al.  Eiffel: The Language , 1991 .

[6]  Frank Piessens,et al.  Verification of programs using inspector methods , 2006 .

[7]  K. Rustan M. Leino,et al.  Object Invariants in Dynamic Contexts , 2004, ECOOP.

[8]  K. Rustan M. Leino,et al.  Verification of Object-Oriented Programs with Invariants , 2003, J. Object Technol..

[9]  K. Rustan M. Leino,et al.  The Spec# Programming System: An Overview , 2004, CASSIS.

[10]  Stephen Gilmore,et al.  Mobile Resource Guarantees for Smart Devices , 2004, CASSIS.

[11]  K. Rustan M. Leino,et al.  A Verification Methodology for Model Fields , 2006, ESOP.

[12]  Martin Odersky.  ECOOP 2004 – Object-Oriented Programming , 2004, Lecture Notes in Computer Science.

[13]  Ioannis T. Kassios.  Dynamic Frames: Support for Framing, Dependencies and Sharing Without Restrictions , 2006, FM.

[14]  David Detlefs,et al.  Simplify: a theorem prover for program checking , 2005, JACM.

[15]  Peter Müller,et al.  Reasoning About Method Calls in Interface Specifications , 2006, J. Object Technol..

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

[17]  Albert L. Baker,et al.  Preliminary design of JML: a behavioral interface specification language for java , 2006, SOEN.

[18]  Bor-Yuh Evan Chang,et al.  Boogie: A Modular Reusable Verifier for Object-Oriented Programs , 2005, FMCO.

[19]  Gavin M. Bierman,et al.  Separation logic and abstraction , 2005, POPL '05.

[20]  Tobias Nipkow,et al.  FM 2006: Formal Methods, 14th International Symposium on Formal Methods, Hamilton, Canada, August 21-27, 2006, Proceedings , 2006, FM.

[21]  Arnd Poetzsch-Heffter,et al.  A Programming Logic for Sequential Java , 1999, ESOP.

[22]  David R. Cok,et al.  Reasoning with specifications containing method calls and model fields , 2005, J. Object Technol..

[23]  Claude Marché,et al.  The KRAKATOA tool for certificationof JAVA/JAVACARD programs annotated in JML , 2004, J. Log. Algebraic Methods Program..