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The Logic of the Partial λ-Calculus with Equality

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Computer Science Logic (CSL 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3210))

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Abstract

We investigate the logical aspects of the partial λ-calculus with equality, exploiting an equivalence between partial λ-theories and partial cartesian closed categories (pcccs) established here. The partial λ-calculus with equality provides a full-blown intuitionistic higher order logic, which in a precise sense turns out to be almost the logic of toposes, the distinctive feature of the latter being unique choice. We give a linguistic proof of the generalization of the fundamental theorem of toposes to pcccs with equality; type theoretically, one thus obtains that the partial λ-calculus with equality encompasses a Martin-Löf-style dependent type theory. This work forms part of the semantical foundations for the higher order algebraic specification language HasCasl.

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Author information

Authors and Affiliations

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

    Lutz Schröder

Authors
  1. Lutz Schröder
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Editor information

Editors and Affiliations

  1. Wroclaw University, Poland

    Jerzy Marcinkowski

  2. Polish Academy of Sciences, Institute of Computer Science, Poland

    Andrzej Tarlecki

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Schröder, L. (2004). The Logic of the Partial λ-Calculus with Equality. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_30

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  • DOI: https://doi.org/10.1007/978-3-540-30124-0_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23024-3

  • Online ISBN: 978-3-540-30124-0

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