The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of U corresponding to each of these systems, and prove that, when a proof in U uses only symbols of a sub-theory, then it is a proof in that sub-theory.

@article{paperbot2238,
  title = {A modular construction of type theories},
  author = {Frédéric Blanqui and Gilles Dowek and Emilie Grienenberger and Gabriel Hondet and François Thiré},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 19, Issue 1},
  year = {2023},
  doi = {10.46298/lmcs-19(1:12)2023}
}