Abstract
We study generalised polynomial functors between presheaf categories, developing their mathematical theory together with computational applications. The main theoretical contribution is the introduction of discrete generalised polynomial functors, a class that lies in between the classes of cocontinuous and finitary functors, and is closed under composition, sums, finite products, and differentiation. A variety of applications are given: to the theory of nominal algebraic effects; to the algebraic modelling of languages, and equational theories there of, with variable binding and polymorphism; and to the synthesis of dependent zippers.
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Fiore, M. (2012). Discrete Generalised Polynomial Functors. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_22
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DOI: https://doi.org/10.1007/978-3-642-31585-5_22
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