Work

Modular abstract syntax trees (MAST): substitution tensors with second-class sorts

Year: 2025

Type: article

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.

Source: Electronic Notes in Theoretical Informatics and Computer Science

DOI: 10.46298/entics.16879

Authors: Marcelo P. Fiore, Ohad Kammar, Georg Moser, Sam Staton

Institutions: University of Cambridge, University of Oxford

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Austrian Science Fund

Award: Automated Amortised Resource Analysis of Data Structures