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Quotients over Minimal Type Theory

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Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

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Abstract

We consider an extensional version, called qmTT, of the intensional Minimal Type Theory mTT, introduced in a previous paper with G. Sambin, enriched with proof-irrelevance of propositions and effective quotient sets. Then, by using the construction of total setoid à la Bishop we build a model of qmTT over mTT.

The design of an extensional type theory with quotients and its interpretation in mTT is a key technical step in order to build a two level system to serve as a minimal foundation for constructive mathematics as advocated in the mentioned paper about mTT.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Genova, Italy

    Maria Emilia Maietti

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  1. Maria Emilia Maietti
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Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

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Maietti, M.E. (2007). Quotients over Minimal Type Theory. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_54

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  • DOI: https://doi.org/10.1007/978-3-540-73001-9_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

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