Summary
The model theoretic basis for (abstract) data types is generalized from algebras to multi-algebr as in order to cope with non-deterministic operations. A programming oriented definition and a model theoretic criterion (called simulation) for implementation of data types are given. To justify the criterion w.r.t. the definition, an abstract framework linking denotational semantics of programming languages and model theory of data types is set up. A set of constraints on a programming language semantics are derived which guarantee that simulation implies implementation. It is argued that any language supporting data abstraction does fulfill these constraints. As an example a simple but expressive language L is defined and it is formally proved that L does conform to these restrictions.
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Nipkow, T. Non-deterministic data types: models and implementations. Acta Informatica 22, 629–661 (1986). https://doi.org/10.1007/BF00263649
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DOI: https://doi.org/10.1007/BF00263649