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Nonflatness and totality

Published online by Cambridge University Press:  16 April 2018

BASIL A. KARÁDAIS
BASIL A. KARÁDAIS*
Affiliation:
Mathematisches Institut, Ludwig-Maximilians-Universität München, Munich 80333, Germany Email: karadais@math.lmu.de
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Abstract

We interpret finite types as domains over nonflat inductive base types in order to bring out the finitary core that seems to be inherent in the concept of totality. We prove a strong version of the Kreisel density theorem by providing a total compact element as a witness, a result that we cannot hope to have if we work with flat base types. To this end, we develop tools that deal adequately with possibly inconsistent finite sets of information. The classical density theorem is reestablished via a ‘finite density theorem,’ and corollaries are obtained, among them Berger's separation property.

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Mathematical Structures in Computer Science , Volume 29 , Issue 2 , February 2019 , pp. 309 - 338
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Copyright © Cambridge University Press 2018 

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