A cut-free sequent calculus for pure type systems verifying the structural rules of Gentzen/Kleene

Authors:
Francisco Gutiérrez;Blas Ruiz
Affiliations:
Departamento de Lenguajes y Ciencias de la Computación, Universidad de Málaga, Málaga, Spain;Departamento de Lenguajes y Ciencias de la Computación, Universidad de Málaga, Málaga, Spain
Venue:
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Year:
2002

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Abstract

In this paper, a new notion for sequent calculus (à la Gentzen) for Pure Type Systems (PTS) is introduced. This new calculus, κ, is equivalent to the standard PTS, and it has a cut-free subsystem, κcf, that will be proved to hold non-trivial properties such as the structural rules of Gentzen/Kleene: thinning, contraction, and interchange. An interpretation of completeness of the κcf system yields the concept of Cut Elimination, (CE), and it is an essential technique in proof theory; thus we think that it will have a deep impact on PTS and in logical frameworks based on PTS.