Verification of object-oriented programs: A transformational approach

Abstract

We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation suggests natural proofs rules and its correctness helps us to establish soundness and relative completeness of the proposed proof system. One of the difficulties is how to properly deal in the assertion language with the instance variables and aliasing. The discussed programming language supports arrays, instance variables, failures and recursive methods with parameters. We also explain how the transformational approach can be extended to deal with other features of object-oriented programming, like classes, inheritance, subtyping and dynamic binding.

Weak Arithmetic Completeness of Object-Oriented First-Order Assertion Networks

“…The features to which this transformational approach applies include failures and bounded arrays. Inheritance and dynamic binding have been addressed in [3]. These transformations allow us to treat object creation orthogonally to such features, and thereby indicates our approach scales up to modern languages.…”

“…This completeness result however is based on the expressibility of the strongest postcondition in a weak second-order language which contains quantification over finite sequences. In [3] completeness for an object-oriented core language without object creation is proven assuming the standard interpretation of Peano arithmetic for the expressibility of the weakest precondition. We are not aware of any other completeness result based on weak arithmetic structures using only Presburger arithmetic and an assertion language which only contains quantification over basic types., i.e., integer, Boolean and Object.…”

Proof Pearl: The KeY to Correct and Stable Sorting

“…We formalize stability with the help of the auxiliary array variable idx. 3 This variable should store for each index in the sorted array, the index of that element in the original input. For example, in Listing 1, directly after line 9, we add the assignment…”

“…But even without the conjunction rule, the proof system is relative complete [3], so it is always possible to avoid the conjunction rule.…”

Integrating deductive verification and symbolic execution for abstract object creation in dynamic logic

“…The set of program variables consists of both local and global variables. For technical convenience, we restrict local variables to formal parameters (for a treatment of blocks, we refer to [9]). …”