By Hussmann

Algebraic specification, nondeterminism and time period rewriting are 3 lively examine components aiming at thoughts for the summary description of software program structures: Algebraic requisites are well-suited for describing facts buildings and sequential software program platforms in an summary manner. time period rewriting tools are utilized in many prototyping structures and shape the root for executing specifi­ cations. Nondeterminism performs an incredible position in formal language idea; in programming it serves for delaying layout judgements in application improvement and happens in a "natural" approach in formalisations of dispensed procedures. Heinrich Hussmann offers a sublime extension of equational specification and time period rewriting to incorporate nondeterminism. in response to a fresh modeltheoretic semantics he considers time period rewriting structures with no confluence regulations as a specification language and exhibits that basic homes reminiscent of the life of preliminary types or the stability and completeness of narrowing, the elemental mechanism for executing equational standards, should be prolonged to nondeterministic computations. The paintings of Heinrich Hussmann is a wonderful contribution to Algebraic Programming; it offers a framework that admits an immediate method of software verification, is acceptable for describing concurrent and dispensed approaches, and it may be finished as quickly as Prolog.

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Extra resources for Nondeterminism in Algebraic Specifications and Algebraic Programs

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Therefore, the following deduction rule is sound, too: (AXIOM-I-RUN) DET(ox}), ... , DET(oxn) aI-Of if <1- f> E R, a E SUBST(~, X), {XI, ... 4, which is simpler in its structure. 4 is preferred within this manuscript. The other reason is that there is no significant gain in completeness if the more complex rule (AXIOM-I~ RUN) is used. The next section studies completeness issues in more detail. 4 is complete in some sense. Unfortunately, there exist counterexamples which demonstrate the incompleteness of the calculus.

Relationally described nondeterministic specifications obviously are an equivalent, interesting alternative. But for the purposes followed here, this approach has too few similarities with the functional viewpoint of algebraic specifications. In particular, we are interested here in a formal framework which explicitly shows the principle of uni-directionality (for instance from input to output) which is central to most programming paradigms. This is the reason why we prefer here the set-valued approach listed above as (c).

In order to ensure the welldefinedness of such a model, two properties must be fulfilled: • For every nondeterministic term there must be a deterministic term it can be reduced to. This ensures that the interpretation of every term is a nonempty set. This property is called DET-completeness below. 7 from above must be avoided. This property is called DET-additivity below. 1 DET -Completeness and DET -Additivity The first and rather simple condition for the construction of a term model is DET-completeness.

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