The Difference Lambda-Calculus: A Language for Difference Categories [article]

Mario Alvarez-Picallo, C.-H. Luke Ong
2020 arXiv   pre-print
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
more » ... lambda-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials.
arXiv:2011.14476v1 fatcat:m5jt5is6svgkll2xtibxsqzkny