Domain algebras

Abstract

This paper proposes a way of relating domain-theoretic and algebraic interpretations of data types. It is different from Smyth, Plotkin, and Lehmann's T-algebra approach, and in particular the notion of homomorphism between higher-order algebras is not restricted in the same way, so that the usual initiality theorems of algebraic semantics, including one for inequational varieties, hold. Domain algebras are defined in terms of concepts from elementary category theory using Lambek's connection between cartesian closed categories and the typed λ-calculus. To this end axioms and inference rules for a theory of domain categories are given. Models of these are the standard categories of domains, such as Scott's information systems and Berry and Curien's sequential algorithms on concrete data structures. The set of axioms and inference rules are discussed and compared to the PPλ-logic of the LCF-system.KeywordsInference RuleDenotational SemanticAlgebraic SemanticDomain EquationQuotient CategoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.