A sequent calculus for a semi-associative law

@article{Zeilberger2019ASC,
  title={A sequent calculus for a semi-associative law},
  author={Noam Zeilberger},
  journal={Log. Methods Comput. Sci.},
  year={2019},
  volume={15}
}
  • N. Zeilberger
  • Published 27 March 2018
  • Mathematics
  • Log. Methods Comput. Sci.
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused… 

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A Sequent Calculus for a Semi-Associative Law
TLDR
A sequent calculus with a simple restriction of Lambek's product rules is introduced that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words induced by a semi-associative law.
A sequent calculus for the Tamari order
TLDR
A sequent calculus with a simple restriction of Lambek's product rules is introduced that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words induced by a semi-associative law.
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