Satisfiability and completeness Sample Clauses

Satisfiability and completeness. The traces of a test specification’s trace semantics describe the behavior that we expect from the unit under test and thus determines what we want to test. But a test which cannot be passed by any program is useless. Therefore, a specification should always describe only traces with incoming communication that is indeed implementable by a program of the programming language. Before we formalize this feature it is important to realize that a change of the viewpoint is involved: in the specification the expected behavior is given in terms of incoming commu- nication carried out by an (absent) external component. In contrast, saying that a program should exist which shows the desired behavior means that the communi- cation shows up in terms of outgoing communication within the semantics of the program. Thus, in order to formalize the satisfiability requirement, we use the dual of a given trace t, denoted by t¯, where in each label question marks and exclamation marks are exchanged, such that each incoming communication label becomes an outgoing communication label and vice versa. Lemma 3.7.1 (Satisfiability): Let s be a specification of our test specification language with ∆ ▶ s : Θ. Then for every trace t ∈ [[∆ ▶ s : Θ]] there exists a Japl program p such that Θ ▶ p : ∆ and t¯ ∈ [[Θ ▶ p : ∆]]. Note, that executability requires the existence of a single program, whereas satisfiability involves the existence of a program for each trace. This is a conse- quence of the input non-determinism introduced by the formal parameters in the incoming communication terms. That is, allowing different incoming values means also allowing different components to pass the test. The completeness requirement demands that each possible behavior of a Japl component can be formulated as a desired behavior in terms of a specification of the test specification language.
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