By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.

@article{paperbot2773,
  title = {Variable binding and substitution for (nameless) dummies},
  author = {André Hirschowitz and Tom Hirschowitz and Ambroise Lafont and Marco Maggesi},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 20, Issue 1},
  year = {2024},
  doi = {10.46298/lmcs-20(1:18)2024}
}