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Intersection Logic

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Book cover Computer Science Logic (CSL 2001)

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

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Abstract

The intersection type assignment system IT uses the formulas of the negative fragment of the predicate calculus (LJ) as types for the λ-terms. However, the deductions of IT only correspond to the proper sub-set of the derivations of LJ, obtained by imposing a meta-theoretic condition about the use of the conjunction of LJ. This paper proposes a logical foundation for IT. This is done by introducing a logic IL. Intuitively, a derivation of IL is a set of derivations in LJ such that the derivations in the set can be thought of as writable in parallel. This way of looking at LJ, by means of IL, allows to transform the meta-theoretic condition, mentioned above, into a purely structural property of IL. The relation between IL and LJ surely has a first main benefit: the strong normalization of LJ directly implies the same property on IL, which translates in a very simple proof of the strong normalizability of the λ-terms typable with IT.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, C.so Svizzera, n.185, 10149, Torino, Italy

    Simona Ronchi Della Rocca & Luca Roversi

Authors
  1. Simona Ronchi Della Rocca
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  2. Luca Roversi
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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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Della Rocca, S.R., Roversi, L. (2001). Intersection Logic. 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_29

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  • DOI: https://doi.org/10.1007/3-540-44802-0_29

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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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