Substitution for Non-Wellfounded Syntax with Binders through Monoidal Categories
Abstract
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal categories and strong functors between them. A language is specified by a multi-sorted binding signature, say {\Sigma}. First, we provide sufficient criteria for {\Sigma} to generate a language of possibly infinite terms, through {\omega}-continuity. Second, we construct a monadic substitution operation for the language generated by {\Sigma}. A cornerstone in this construction is a mild generalization of the notion of heterogeneous substitution systems developed by Matthes and Uustalu; such a system encapsulates the necessary corecursion scheme for implementing substitution. The results are formalized in the Coq proof assistant, through the UniMath library of univalent mathematics.
Keywords
Cite
@article{arxiv.2308.05485,
title = {Substitution for Non-Wellfounded Syntax with Binders through Monoidal Categories},
author = {Ralph Matthes and Kobe Wullaert and Benedikt Ahrens},
journal= {arXiv preprint arXiv:2308.05485},
year = {2024}
}
Comments
v3: reworked introduction, expanded examples, changes in textual formulations; this is the full version for the upcoming FSCD'24 paper with the same title, the difference is the presence of Appendix B and Appendix D