Models for Polymorphism over Physical Dimension

Authors Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, Sam Staton

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Robert Atkey
Neil Ghani
Fredrik Nordvall Forsberg
Timothy Revell
Sam Staton

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Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton. Models for Polymorphism over Physical Dimension. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 45-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We provide a categorical framework for models of a type theory that has special types for physical quantities. The types are indexed by the physical dimensions that they involve. Fibrations are used to organize this index structure in the models of the type theory. We develop some informative models of this type theory: firstly, a model based on group actions, which captures invariance under scaling, and secondly, a way of constructing new models using relational parametricity.
  • Category Theory
  • Units of Measure
  • Dimension Types
  • Type Theory


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