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International Conference on Mathematical Foundations of Programming Semantics

MFPS 1993: Mathematical Foundations of Programming Semantics pp 438–453Cite as

Linear domains and linear maps

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 802))

Abstract

We study the symmetric monoidal closed category LIN of linear domains. Its objects are inverse limits of finite, bounded complete posets with respect to projection-embedding pairs preserving all suprema. The full reflective subcategory LL of linear lattices is a denotational model of linear logic; the negation is A ↦ A op and !(A) is the lattice of all Scott-closed sets of A. The Scott-continuous function space [A → B] models intuitionistic implication. Prime-algebraic lattices are linear and ℘ equals ⊗ for these lattices; in general, ℘ ≠ ⊗ in LL. Distributive, linear domains are exactly the prime-algebraic ones.

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Authors and Affiliations

  1. Department of Computing, Imperial College, SW7 2BZ, London, England

    Michael Huth

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  1. Michael Huth
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Editor information

Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1994 Springer-Verlag Berlin Heidelberg

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Huth, M. (1994). Linear domains and linear maps. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_21

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  • DOI: https://doi.org/10.1007/3-540-58027-1_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58027-0

  • Online ISBN: 978-3-540-48419-6

  • eBook Packages: Springer Book Archive

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