A Cut-Free Sequent Calculus for Pure Type Systems Verifying the Structural Rules of Gentzen/Kleene

  • Francisco Gutiérrez
  • Blas Ruiz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2664)


In this paper, a new notion for sequent calculus (à la Gentzen) for Pure Type Systems (PTS) is introduced. This new calculus, \( \mathcal{K} \) , is equivalent to the standard PTS, and it has a cut-free subsystem, \( \mathcal{K}^{{\text{cf}}} \), 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 \( \mathcal{K}^{{\text{cf}}} \) 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.


lambda calculus with types pure type systems sequent calculi cut elimination 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Francisco Gutiérrez
    • 1
  • Blas Ruiz
    • 1
  1. 1.Departamento de Lenguajes y Ciencias de la ComputaciónUniversidad de MálagaMálagaSpain

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