The difference λ-calculus: a language for difference categories
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 inf...
| Autores principales: | , |
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| Formato: | Conference item |
| Lenguaje: | English |
| Publicado: |
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2020
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| Sumario: | 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 λ-calculus equipped with syntactic "infinitesimals" and show how its models correspond to difference λ-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials. |
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