This article describes a new approach to the unit testing of object-oriented programs, a set of tools based on this approach, and two case studies. In this approach, each test case consists of a tuple of sequences of messages, along with tags indicating whether these sequences should put objects of the class under test into equivalent states and\or return objects that are in equivalent states. Tests are executed by sending the sequences to objects of the class under test, then invoking a user-supplied equivalence-checking mechanism. This approach allows for substantial automation of many aspects of testing, including test case generation, test driver generation, test execution, and test checking. Experimental prototypes of tools for test generation and test execution are described. The test generation tool requires the availability of an algebraic specification of the abstract data type being tested, but the test execution tool can be used when no formal specification is available. Using the test execution tools, case studies involving execution of tens of thousands of test cases, with various sequence lengths, parameters, and combinations of operations were performed. The relationships among likelihood of detecting an error and sequence length, range of parameters, and relative frequency of various operations were investigated for priority queue and sorted-list implementations having subtle errors. In each case, long sequences tended to be more likely to detect the error, provided that the range of parameters was suffkiently large and likelihood of detecting an error tended to increase up to a threshold value as the parameter range increased. Categories and Subject Descriptors: D.2.1 [Software Engineering]: Requirements/Specificstions—languages; D.2.5 [Software Engineering]: Testing and Debugging-symbolzc execution;

Roughly speaking, an equational problem is a first order formula whose only predicate symbol is =. We propose some rules for the transformation of equational problems and study their correctness in various models. Then, we give completeness results with respect to some “simple ” problems called solved forms. Such completeness results still hold when adding some control which moreover ensures termination. The termination proofs are given for a “weak ” control and thus hold for the (large) class of algorithms obtained by restricting the scope of the rules. Finally, it must be noted that a by-product of our method is a decision procedure for the validity in the Herbrand Universe of any

Abstract data types have proved to be a useful technique for structuring systems. In large systems it is sometimes useful to have different regions of the system use different representations for the abstract data values. A technique is described for communicating abstract values between such regions. The method was developed for use in constructing distributed systems, where the regions exist at different computers and the values are communicated over a network. The method defines a call-by-value semantics; it is also useful in nondistributed systems wherever call by value is the desired semantics. An important example of such a use is a repository, such as a file system, for storing long-lived data.

We present and evaluate an automatic tool for extracting algebraic specifications from Java classes. Our tool maps a Java class to an algebraic signature and then uses the signature to generate a large number of terms. The tool evaluates these terms and based on the results of the evaluation, it proposes equations. Finally, the tool generalizes equations to axioms and eliminates many redundant axioms. Since our tool uses dynamic information, it is not guaranteed to be sound or complete. However, we manually inspected the axioms generated in our experiments and found them all to be correct.

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Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey these works and bring them together in a same framework. R'esum'e On appelle habituellement (algorithme d') unification un algorithme de r'esolution d'une 'equation dans une alg`ebre de termes. La r'esolution de formules plus complexes, comportant en particulier des n'egations, est appel'ee ici disunification. Avec une d'efinition aussi 'etendue, de nombreux travaux peuvent etre consid'er'es comme portant sur la disunification. L'objet de cet article de synth`ese est de rassembler tous ces travaux dans un meme formalisme. Laboratoire de Recherche en Informatique, Bat. 490, Universit'e de Paris-Sud, 91405 ORSAY cedex, France. E-mail: comon@lri.lri.fr i Contents 1 Syntax 5 1.1 Basic Defini...

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The state of knowledge in how to specify sequential programs in object-oriented languages such as Java and C# and the state of the art in automated verification tools for such programs have made measurable progress in the last several years. This paper describes several remaining challenges and approaches to their solution.

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