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Fully Complete Minimal PER Models for the Simply Typed λ-Calculus

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Computer Science Logic (CSL 2001)

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

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Abstract

We show how to build a fully complete model for the maximal theory of the simply typed λ-calculus with k ground constants, λk. This is obtained by linear realizability over an affine combinatory algebra of partial involutions from natural numbers into natural numbers. For simplicitly, we give the details of the construction of a fully complete model for λk extended with ground permutations. The fully complete minimal model for λk can be obtained by carrying out the previous construction over a suitable subalgebra of partial involutions. The full completeness result is then put to use in order to prove some simple results on the maximal theory.

Work partially supported by TMR Linear FMRX-CT98-0170.

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Author information

Authors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, England

    Samson Abramsky

  2. Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100, Udine, Italy

    Marina Lenisa

Authors
  1. Samson Abramsky
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  2. Marina Lenisa
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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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Abramsky, S., Lenisa, M. (2001). Fully Complete Minimal PER Models for the Simply Typed λ-Calculus. 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_31

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  • DOI: https://doi.org/10.1007/3-540-44802-0_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42554-0

  • Online ISBN: 978-3-540-44802-0

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