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International Workshop on Computer Science Logic

CSL 2001: Computer Science Logic pp 429–442Cite as

Life without the Terminal Type

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2142))

Abstract

We introduce a method of extending arbitrary categories by a terminal object and apply this method in various type theoretic settings. In particular, we show that categories that are cartesian closed except for the lack of a terminal object have a universal full extension to a cartesian closed category, and we characterize categories for which the latter category is a topos. Both the basic construction and its correctness proof are extremely simple. This is quite surprising in view of the fact that the corresponding results for the simply typed λ-calculus with surjective pairing, in particular concerning the decision problem for equality of terms in the presence of a terminal type, are comparatively involved.

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Author information

Authors and Affiliations

  1. BISS, Department of Computer Science, Bremen University, Germany

    Lutz Schröder

Authors
  1. Lutz Schröder
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Editor information

Editors and Affiliations

  1. LSV (Ecole Normale Supérieure de Cachan and CNRS), 61, Avenue du Président Wilson, 94230, Cachan, France

    Laurent Fribourg

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© 2001 Springer-Verlag Berlin Heidelberg

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Schröder, L. (2001). Life without the Terminal Type. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_30

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  • DOI: https://doi.org/10.1007/3-540-44802-0_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42554-0

  • Online ISBN: 978-3-540-44802-0

  • eBook Packages: Springer Book Archive

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