Mappings of MOF Metamodels and Algebraic Languages

Abstract

In this chapter we examine the relation between NEREUS and formal specification using CASL (Common Algebraic Specification Language) as a common algebraic language (Bidoit & Mosses, 2004). CASL is an expressive and simple language based on a critical selection of known constructs such as subsorts, partial functions, first-order logic, and structured and architectural specifications. A basic specification declares sorts, subsorts, operations and predicates, and gives axioms and constraints. Specifications are structured by means of specification building operators for renaming, extension and combining. Architectural specifications impose structure on implementations, whereas structured specifications only structure the text of specifications. CASL allows loose, free and generated specifications. The models of a loose specification include all those where the declared functions have the specified properties, without any restrictions on the set of values corresponding to the various sorts. In models of a generated specification, in contrast, it is required that all values can be expressed by terms formed from the specified constructors, i.e. unreachable values are prohibited. In models of free specifications, it is required that values of terms are distinct except when their equality follows from the specified axioms: the possibility of unintended coincidence between their axioms is prohibited.