Relation-sorted algebraic specifications with built-in coercers: Basic notions and results
A relation-sorted algebraic specification SPEC with built-in coercers is, syntactically seen, quite similar to an order-sorted specification, i.e. SPEC consists of a signature, a set of equations and an arbitrary relation ⊳ on the set of sorts. But our notion of SPEC-algebras is more general. In particular, if two sorts are in the sort relation s⊳s′, then we assume that, in each SPEC-algebra A, the corresponding carriers AS and AS′, are related by an operator AS⊳S′:AS→AS′, which is considered as a component of A, rather than by inclusion AS\(\subseteq\)AS, as required in order-sorted algebras. This allows us to map a sort into a sort and simultaneously forget about some aspects as it occurs in object-oriented programming. Although our approach is more general than order-sorted specification, we et similar results, e.g. concerning the construction of initial algebras and a complete deduction system. Our approach may serve as a general framework for investigating subtypes as injective as well as non-injective conversion.
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