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Domain algebras

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Automata, Languages and Programming (ICALP 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 172))

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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.

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Authors and Affiliations

  1. Programming Methodology Group Department of Computer Sciences, Chalmers Technical University, S-412 96, Gothenburg, Sweden

    Peter Dybjer

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  1. Peter Dybjer
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Jan Paredaens

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© 1984 Springer-Verlag Berlin Heidelberg

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Dybjer, P. (1984). Domain algebras. In: Paredaens, J. (eds) Automata, Languages and Programming. ICALP 1984. Lecture Notes in Computer Science, vol 172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13345-3_13

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  • DOI: https://doi.org/10.1007/3-540-13345-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13345-2

  • Online ISBN: 978-3-540-38886-9

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