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cs.LO2020
A complete equational axiomatisation of partial differentiation
Gordon D. Plotkin
We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is compl…
cs.LO2019
Reverse derivative categories
Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher +4
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivativ…
cs.LO2018
On the Axiomatizability of Quantitative Algebras
Radu Mardare, Prakash Panangaden, Gordon Plotkin
Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016.…