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Register a new userThe Difference Lambda-Calculus: A Language for Difference Categories
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Added by
Mario Alvarez-Picallo
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of infinitesimal arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian differential category being satisfied only up to an infinitesimal perturbation. In this work, we construct a simply-typed calculus in the spirit of the differential lambda-calculus equipped with syntactic infinitesimals and show how its models correspond to difference lambda-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials.
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