## Testing can be formal, too (1995)

Citations: | 84 - 2 self |

### BibTeX

@INPROCEEDINGS{Gaudel95testingcan,

author = {Marie-claude Gaudel},

title = {Testing can be formal, too},

booktitle = {},

year = {1995},

pages = {82--96},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. The paper presents a theory of program testing based on formal specifications. The formal semantics of the specifications is the basis for a notion of an exhaustive test set. Under some minimal hypotheses on the program under test, the success of this test set is equivalent to the satisfaction of the specification. The selection of a finite subset of the exhaustive test set can be seen as the introduction of more hypotheses on the program, called selection hypotheses. Several examples of commonly used selection hypotheses are presented. Another problem is the observability of the results of a program with respect to its specification: contrary to some common belief, the use of a formal specification is not always sufficient to decide whether a test execution is a success. As soon as the specification deals with more abstract entities than the program, program results may appear in a form which is not obviously equivalent to the specificied results. A solution to this problem is proposed in the case of algebraic specifications. 1

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Citation Context ...the formulas of ExhaustSP . The definition of ExhaustSP is very close to (and is derived from) the notion of satisfaction of a set of ∑-equations by a ∑-algebra as it has been defined for a long time =-=[17]-=-. In particular, the fact that each axiom can be tested independently comes from this definition. But several points prevent the success of an exhaustive test of P against SP from being equivalent to ... |

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Citation Context ...he use the LOFT system to assist the test of Lustre programs has been investigated [21]. Lustre is a description TAPSOFT'95-13slanguage for reactive systems which is based on the synchronous approach =-=[10]-=-. An algebraic semantics of Lustre has been stated and entered as a specification in LOFT. A Lustre program is considered as an enrichment of this specification, just a specific axiom to be tested. It... |

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Citation Context ... It is based on algebraic specifications and has been experimented on several significant case studies. Some underlying ideas have been reused for other kinds of formal specification or model: VDM in =-=[13]-=-, finite state automata and labelled transition systems in [26], and Lustre programs [21]. The interpretation of the results of a test is often very difficult. This difficulty is known as the oracle p... |

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Citation Context ...resentation of some recent results [2, 3, 22]. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and Gerhart =-=[18]-=- where the notion of testing criteria was first introduced and the work of Gourlay [19] who proposed a formal definition of a test method and pointed out the role of specifications in the testing proc... |

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Citation Context ...c specifications. 1 Introduction This paper is a survey of a research activity which has been led for several years in the area of program testing [5, 6, 7], and a presentation of some recent results =-=[2, 3, 22]-=-. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and Gerhart [18] where the notion of testing criteria was... |

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Citation Context ...ns are quite fundamental to a rigourous and systematic approach of program testing. For instance, an application area where testing has been extensively studied is the area of communication protocols =-=[8, 15, 27]-=-, etc: all these works are based on formal models of the protocol to be tested, generally finite state machines or transition systems. First, let us make more precise the background of the works repor... |

66 | On observational equivalence and algebraic specification
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Citation Context ...me more work is often needed. A solution to this problem is proposed in the case of algebraic specifications. It is based on a notion of observational equivalence of the specification and the program =-=[28, 20]-=-. The paper is organized as follows: part 2 presents a theory of black-box testing based on formal specifications and both the test data selection problem and the oracle problem are addressed in the c... |

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Citation Context ...n to this problem is proposed in the case of algebraic specifications. 1 Introduction This paper is a survey of a research activity which has been led for several years in the area of program testing =-=[5, 6, 7]-=-, and a presentation of some recent results [2, 3, 22]. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and... |

40 |
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Citation Context ...rch on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and Gerhart [18] where the notion of testing criteria was first introduced and the work of Gourlay =-=[19]-=- who proposed a formal definition of a test method and pointed out the role of specifications in the testing process. More recently, the growing interest in the use of formal methods has raised severa... |

31 |
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Citation Context ...c specifications. 1 Introduction This paper is a survey of a research activity which has been led for several years in the area of program testing [5, 6, 7], and a presentation of some recent results =-=[2, 3, 22]-=-. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and Gerhart [18] where the notion of testing criteria was... |

29 |
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Citation Context ...t stating definition 10, we have changed the notion of satisfaction of a specification SP by a program P into a notion of behavioural satisfaction (more precisely, the “behavioural satisfaction I” of =-=[25]-=-), and we have kept the fact that the exhaustive test only considers those values which are finitely generated by ∑. Thus there is no more need that P defines a finitely generated ∑-algebra: it is suf... |

29 |
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Citation Context ...ns are quite fundamental to a rigourous and systematic approach of program testing. For instance, an application area where testing has been extensively studied is the area of communication protocols =-=[8, 15, 27]-=-, etc: all these works are based on formal models of the protocol to be tested, generally finite state machines or transition systems. First, let us make more precise the background of the works repor... |

26 |
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Citation Context ...he axioms for all the terms which must be defined. Other definitions of ExhaustSP are possible, depending on the considered semantics (for instance all partial algebras or only minimally defined ones =-=[9]-=-) and on some conventions on what is a correct behaviour of the program for undefined terms. 2.2 Selection and Hypotheses ExhaustSP is obviously not usable in practice since it is generally infinite. ... |

20 | Using Specifications to Check Source Code
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Citation Context ...um hypotheses are static properties of the program. Some of them are (or could be) checkable: currently the tools for static checking of programs are often independant of the specifications. However, =-=[16]-=- reports some promising experiments on the use of specifications for statically detecting violations of abstraction barriers. 2.4 Equational test sets When the specification is sufficiently complete w... |

17 |
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Citation Context ...riving system of an automatic subway. An algebraic specification was written [12] . Then two modules of the specification were used for experiments with LOFT. The experiment is reported in details in =-=[11]-=-. We just give the conclusions here. It must be noted that this work was performed with the certification agency (INRETS), not with the development team of the system. The first module was the control... |

17 |
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Citation Context ...ted on several significant case studies. Some underlying ideas have been reused for other kinds of formal specification or model: VDM in [13], finite state automata and labelled transition systems in =-=[26]-=-, and Lustre programs [21]. The interpretation of the results of a test is often very difficult. This difficulty is known as the oracle problem: deciding whether the result of a test execution is acce... |

11 |
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Citation Context ...ns are quite fundamental to a rigourous and systematic approach of program testing. For instance, an application area where testing has been extensively studied is the area of communication protocols =-=[8, 15, 27]-=-, etc: all these works are based on formal models of the protocol to be tested, generally finite state machines or transition systems. First, let us make more precise the background of the works repor... |

10 |
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Citation Context ...ter passing, storage properties, etc) of some components. Such a set of variants is called a family. An experiment of “intensive” testing of a family have been led by Didier Buchs and Stéphane Barbey =-=[1]-=-. First an algebraic specification of the component was reengineered: the signature was derived from the package specifications of the family, and the axioms were written manually. Then the LOFT syste... |

4 |
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Citation Context ...me more work is often needed. A solution to this problem is proposed in the case of algebraic specifications. It is based on a notion of observational equivalence of the specification and the program =-=[28, 20]-=-. The paper is organized as follows: part 2 presents a theory of black-box testing based on formal specifications and both the test data selection problem and the oracle problem are addressed in the c... |

3 |
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Citation Context ...n to this problem is proposed in the case of algebraic specifications. 1 Introduction This paper is a survey of a research activity which has been led for several years in the area of program testing =-=[5, 6, 7]-=-, and a presentation of some recent results [2, 3, 22]. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and... |

3 |
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Citation Context ...c specifications. 1 Introduction This paper is a survey of a research activity which has been led for several years in the area of program testing [5, 6, 7], and a presentation of some recent results =-=[2, 3, 22]-=-. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and Gerhart [18] where the notion of testing criteria was... |

2 |
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Citation Context ... case studies. Some underlying ideas have been reused for other kinds of formal specification or model: VDM in [13], finite state automata and labelled transition systems in [26], and Lustre programs =-=[21]-=-. The interpretation of the results of a test is often very difficult. This difficulty is known as the oracle problem: deciding whether the result of a test execution is acceptable or not requires a p... |

2 |
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Citation Context ...ain. One possible way is to introduce some regularity hypothesis or some other uniformity hypotheses. This kind of symbolic manipulation of the specification is implemented by a tool, the LOFT system =-=[23]-=-. The kernel of this system is an equational resolution procedure since the implementation of uniformity hypotheses requires to solve conjunctions of equations in the theory defined by the specificati... |

1 | A Formal Approach to Software - Bernot, Gaudel, et al. - 1992 |

1 |
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Citation Context ...n to this problem is proposed in the case of algebraic specifications. 1 Introduction This paper is a survey of a research activity which has been led for several years in the area of program testing =-=[5, 6, 7]-=-, and a presentation of some recent results [2, 3, 22]. There has been surprisingly little research on the foundations of program testing. Some notable exceptions are the early paper by Goodenough and... |

1 |
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Citation Context ...aic Specifications A first experiment, performed at LRI by Pierre Dauchy and Bruno Marre, was on the on-board part of the driving system of an automatic subway. An algebraic specification was written =-=[12]-=- . Then two modules of the specification were used for experiments with LOFT. The experiment is reported in details in [11]. We just give the conclusions here. It must be noted that this work was perf... |

1 |
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Citation Context ...equalities are not tested: it rather corresponds to loose semantics. It is possible to choose another definition. For instance, as suggested in [4] and applied by Dong and Frankl in the ASTOOT system =-=[14]-=-, another possibility is to TAPSOFT'95-4sconsider the algebraic specification as a rewriting system, following a “normal-form” semantics. Under the condition that the specification, defines a ground-c... |

1 |
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Citation Context ...ractive process: the LOFT system aims at assisting this process, by guiding the choice of the uniformity subdomains and yielding unbiased and valid testing contexts A second experiment is reported in =-=[24]-=- and was performed within a collaboration between LRI and the LAAS laboratory in Toulouse. Our colleagues from LAAS have a good experience in evaluating the quality of test sets by mutation. The exper... |