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arXiv · 2511.03946

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

Marcelo P. Fiore·Ohad Kammar·Georg Moser·Sam Staton
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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.

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Marcelo P. Fiore, Ohad Kammar, Georg Moser, Sam Staton. 2025-11-06. Modular abstract syntax trees (MAST): substitution tensors with second-class sorts. https://doi.org/10.46298/entics.16879

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