Quati: An Automated Tool for Proving Permutation Lemmas

  • Vivek Nigam
  • Giselle Reis
  • Leonardo Lima
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)


The proof of many foundational results in structural proof theory, such as the admissibility of the cut rule and the completeness of the focusing discipline, rely on permutation lemmas. It is often a tedious and error prone task to prove such lemmas as they involve many cases. This paper describes the tool Quati which is an automated tool capable of proving a wide range of inference rule permutations for a great number of proof systems. Given a proof system specification in the form of a theory in linear logic with subexponentials, Quati outputs in Open image in new window the permutation transformations for which it was able to prove correctness and also the possible derivations for which it was not able to do so. As illustrated in this paper, Quati’s output is very similar to proof derivation figures one would normally find in a proof theory book.


Inference Rule Proof System Linear Logic Automate Tool Proof Theory 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Vivek Nigam
    • 1
  • Giselle Reis
    • 2
  • Leonardo Lima
    • 1
  1. 1.Universidade Federal da ParaíbaBrazil
  2. 2.Technische Universität WienAustria

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