Year: 2025
Type: article
Abstract: Nominal techniques have been praised for their ability to formalize grammars with binding structures closer to their informal developments.At its core, there lies the definition of nominal sets, which capture the notion of name (in)dependence through a simple, and uniform, metatheory based on name permutations.We present a formal constructive development of nominal sets in Rocq (formerly known as Coq), with its main design and project decisions.Furthermore, we formalize the concepts of freshness, nominal α-equivalence, name abstraction, and finitely supported functions.Our implementation relies on a type class hierarchy which, combined with Rocq generalized rewriting mechanism, achieves concise definitions and proofs, whilst easing the well-known "setoid hell" scenario.We conclude with a discussion on how to obtain the constructive α-structural recursion and induction combinators, towards a nominal framework.
DOI: 10.4204/eptcs.430.5
Authors: Fabrício Sanches Paranhos, Daniel Ventura
Institutions: Nethermind (United Kingdom), Universidade Federal de Goiás
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414584970