Modular abstract syntax trees (MAST): substitution tensors with second-class sorts
Programming Languages
2026-03-03 v5
Abstract
We adapt Fiore, Plotkin, and Turi's treatment of abstract syntax with binding, substitution, and holes to account for languages with second-class sorts. These situations include programming calculi such as the Call-by-Value lambda-calculus (CBV) and Levy's Call-by-Push-Value (CBPV). Prohibiting second-class sorts from appearing in variable contexts changes the characterisation of the abstract syntax from monoids in monoidal categories to actions in actegories. We reproduce much of the development through bicategorical arguments. We apply the resulting theory by proving substitution lemmata for varieties of CBV.
Keywords
Cite
@article{arxiv.2511.03946,
title = {Modular abstract syntax trees (MAST): substitution tensors with second-class sorts},
author = {Marcelo P. Fiore and Ohad Kammar and Georg Moser and Sam Staton},
journal= {arXiv preprint arXiv:2511.03946},
year = {2026}
}