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Monotonic versus antimonotonic exponentiation

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Typed Lambda Calculi and Applications (TLCA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 664))

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Abstract

We investigate the relationship between the monotonic (→) and the antimonotonic exponentiation (➾) in a type system with subtyping. We present a model in which we can develop both exponentiations at the same time. In this model the monotonic and the antimonotonic exponentiation enjoy a duality, namely α➾β=∁(α→∁β) where ∁ is the type constructor complement. We give a sound and complete system of axioms for the type system with the type constructors →, ➾, ∪, ∩, ∁, ⊥, T.

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References

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Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, 545 Technology Square, 02139, Cambridge, MA, USA

    Daniel F. Otth

Authors
  1. Daniel F. Otth
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Marc Bezem Jan Friso Groote

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© 1993 Springer-Verlag Berlin Heidelberg

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Otth, D.F. (1993). Monotonic versus antimonotonic exponentiation. In: Bezem, M., Groote, J.F. (eds) Typed Lambda Calculi and Applications. TLCA 1993. Lecture Notes in Computer Science, vol 664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037115

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  • DOI: https://doi.org/10.1007/BFb0037115

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56517-8

  • Online ISBN: 978-3-540-47586-6

  • eBook Packages: Springer Book Archive

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