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Metric Equational Theories
Radu Mardare (Heriot-Watt University, Edinburgh, Scotland), Neil Ghani (University of Strathclyde, Glasgow, Scotland), Eigil Rischel (University of Strathclyde, Glasgow, Scotland)
https://arxiv.org/abs/2509.14094

Metric Equational Theories
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric Equational Theories (METs) where operations no longer have finite sets as arities (as in QETs and the general theory of universal algebras), but arities are now drawn from countable metric spaces. This extension is inspired by the theory of Enriched Lawvere …