Journal Article10.1007/BF00263649
Non-deterministic data types: models and implementations
88
TL;DR: The model theoretic basis for (abstract) data types is generalized from algebras to multi-algebr as in order to cope with non-deterministic operations.
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Abstract: 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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Citations
Nondeterministic Algebraic Specifications and Nonconfluent Term Rewriting
Heinrich Hußmann
- 14 Nov 1988
TL;DR: Algebraic specifications are generalized to the case of nondeterministic operations by admitting models with set-valued functions (multi-algebras) and term rewriting systems are considered as a specification language for this semantic framework.
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