Variable binding and substitution for (nameless) dummies

André Hirschowitz (1) , Tom Hirschowitz (2) , Ambroise Lafont (3) , Marco Maggesi (4)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 LAMA - Laboratoire de Mathématiques
3 UNSW - University of New South Wales [Sydney]
4 DiMal - Dipartimento di Matematica e Informatica [Firenze]

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.

Mots clés: syntax; variable binding; substitution; category theory

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

André Hirschowitz, Tom Hirschowitz, Ambroise Lafont, Marco Maggesi. Variable binding and substitution for (nameless) dummies. 25th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2022), Apr 2022, Munich, Germany. ⟨hal-03547002⟩