On the Length of Medial-Switch-Mix Derivations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10388)


Switch and medial are two inference rules that play a central role in many deep inference proof systems. In specific proof systems, the mix rule may also be present. In this paper we show that the maximal length of a derivation using only the inference rules for switch, medial, and mix, modulo associativity and commutativity of the two binary connectives involved, is quadratic in the size of the formula at the conclusion of the derivation. This shows, at the same time, the termination of the rewrite system.



We are grateful to Alessio Guglielmi and Tom Gundersen, for their encouragements and checks, and to the anonymous referees. Paola Bruscoli was funded by EPSRC Project EP/K018868/1 “Efficient and Natural Proof Systems”. This research is also supported by ANR Project FISP – “The Fine Structure of Formal Proof Systems and their Computational Interpretations.”


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.University of BathBathUK
  2. 2.InriaPalaiseauFrance

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