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arXiv · 2011.14476

The Difference Lambda-Calculus: A Language for Difference Categories

Mario Alvarez-Picallo·C. -H. Luke Ong
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Abstract

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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Mario Alvarez-Picallo, C. -H. Luke Ong. 2020-11-30. The Difference Lambda-Calculus: A Language for Difference Categories. https://arxiv.org/abs/2011.14476

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