Elementary Algebraic Specifications of the Rational Complex Numbers

Electronic Notes in Theoretical Computer Science

Middelburg

2008

We propose a process algebra which is concerned with processes that have an implicit computational capital. This process algebra is intended to be helpful when designing computer-based systems of which the behaviour is related to money handling. It goes along with the development that the behaviour of computer-based systems, organizations and persons is increasingly more related to money handling.

Section: Parallel Processes With Computational Capitalmentioning

confidence: 99%

Parallel Processes with Implicit Computational Capital

Electronic Notes in Theoretical Computer Science

Middelburg

2008

“…In [7] we have discussed a very limited specification technique which we have termed elementary algebraic specification (EAS). In fact EAS limits the expressive power of specifications to the original minimum of features that were used when algebraic specification of abstract data types was developed as a topic in the 1970s.…”

Section: Elementary Algebraic Specifications and Totalitymentioning

confidence: 99%

“…In particular, the elementary specifications require total functions, allow hidden functions and sorts, and may or may not be complete term rewriting systems. Clearly, there are plenty of restrictions in force in EAS as there are many properties ruled out-see [7] for a long list with arguments for their omission. The EAS specification problem is this: Given a algebra A, can one find an elementary algebraic specification ( , E ) such that I ( , E )| ∼ = A.…”

Section: Elementary Algebraic Specifications and Totalitymentioning

confidence: 99%

“…In [1,7,8], we have begun to investigate the field of rationals, and fields in general, using the elementary methods of abstract data type theory, especially equations, initial algebras and term rewriting. Calculations in fields are commonplace and the aim is to simplify algebraic reasoning and term rewriting for fields by removing the complications of partial functions and non-equational axioms.…”

Section: Introductionmentioning

confidence: 99%

“…The fact that only a single hidden function is used depends upon special properties of the field of rational numbers. In [7] the specification found for the rational numbers was extended to the complex rationals with conjugation, and in [1] a specification was given of the algebra of rational functions with field and degree operations that are all total.…”

Section: Introductionmentioning

confidence: 99%

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We introduce the notion of an ACP process algebra and the notion of a meadow enriched ACP process algebra. The former notion originates from the models of the axiom system ACP. The latter notion is a simple generalization of the former notion to processes in which data are involved, the mathematical structure of data being a meadow. Moreover, for all associative operators from the signature of meadow enriched ACP process algebras that are not of an auxiliary nature, we introduce variable-binding operators as generalizations. These variable-binding operators, which give rise to comprehended terms, have the property that they can always be eliminated. Thus, we obtain a process calculus whose terms can be interpreted in all meadow enriched ACP process algebras. Use of the variable-binding operators can have a major impact on the size of terms.