Abstract
A desirable characteristic of formal system description languages is notational convenience for symbolic manipulation. As most natural and man-made objects are essentially non-algorithmic, syntactic and semantic concepts from traditional programming languages are ill-suited for more general system description. Syntactically, the function notation commonly used in mathematics and engineering provides a better match with the system concepts to be expressed. Depending on whether or not one may discern a (directional) signal flow in the system, lambda terms or sigma terms are appropriate. Semantically, the variety of systems and models has resulted in a corresponding variety of semantic domains and mathematical formalisms. Again based on “standard” notations from applied mathematics, a unifying (but not yet fully formalized) set of language concepts is proposed called Funmath ( Functional Mathematics). Two subsets of Funmath are intended to have, respectively, also an operational interpretation as a functional programming language and a structural interpretation as a system description language. Examples are given in various application areas.
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