Paper: A Cartesian Closed Fibration of Higher-Order Regular Languages (at LICS 2026)

Authors: Paul-André Melliès Vincent Moreau

Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.73

Abstract

We explain how to construct in two different ways a cartesian closed fibration of higher-order regular languages in the sense of Salvati. In the first construction, we use fibrational techniques to derive the cartesian closed fibration from the various categories of regular languages of λ-terms associated to finite sets of ground states. In the second construction, we take advantage of the recent notion of profinite λ-calculus to define the cartesian closed fibration by a change-of-base from the fibration of clopen subsets over the category of Stone spaces, using an elegant idea coming from Hermida. We illustrate the expressive power of the cartesian closed fibration by generalizing the notion of Brzozowski derivative to higher-order regular languages, using an Isbell-like adjunction in the sense of Melliès and Zeilberger.

BibTeX

  @InProceedings{MelliesMoreau-ACartesianClosedFib,
    author = 	 {Paul-André Melliès and Vincent Moreau},
    title = 	 {A Cartesian Closed Fibration of Higher-Order Regular Languages},
    booktitle =  {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
    year =	 {2026},
    month =	 {July}, 
    pages =      {73:1--73:25},
    location =   {Lisbon, Portugal}, 
    publisher =	 {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
    doi =        {10.4230/LIPIcs.LICS.2026.73}
  }