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International Symposium on Mathematical Foundations of Computer Science

MFCS 1996: Mathematical Foundations of Computer Science 1996 pp 135–155Cite as

A sequent calculus for subtyping polymorphic types

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1113))

Abstract

We present two complete systems for subtyping polymorphic types. One system is in the style of natural deduction, while another is a Gentzen style sequent calculus system. We prove several metamathematical properties for these systems including cut elimination, subject reduction, coherence, and decidability of type reconstruction. Following the approach by J.Mitchell, the sequents are given a simple semantics using logical relations over applicative structures. The systems are complete with respect to this semantics. The logic which emerges from this paper can be seen as a successor to the original Hilbert style system proposed by J. Mitchell in 1988, and to the “half way” sequent calculus of G. Longo, K. Milsted and S. Soloviev proposed in 1995.

This work is partly supported by NSF Grants CCR-9417382, CCR-9304144, and by Polish KBN Grant 2 P301 031 06.

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Author notes

  1. Jerzy Tiuryn

    Present address: Institute of Informatics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

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    1. Jerzy Tiuryn
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    Correspondence to Jerzy Tiuryn .

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    Wojciech Penczek Andrzej Szałas

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    © 1996 Springer-Verlag Berlin Heidelberg

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    Tiuryn, J. (1996). A sequent calculus for subtyping polymorphic types. In: Penczek, W., Szałas, A. (eds) Mathematical Foundations of Computer Science 1996. MFCS 1996. Lecture Notes in Computer Science, vol 1113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61550-4_144

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    • DOI: https://doi.org/10.1007/3-540-61550-4_144

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    • Print ISBN: 978-3-540-61550-7

    • Online ISBN: 978-3-540-70597-0

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