Type systems for programs respecting dimensions

@article{McBride2022TypeSF,
  title={Type systems for programs respecting dimensions},
  author={Conor McBride and Fredrik Nordvall-Forsberg},
  journal={Series on Advances in Mathematics for Applied Sciences},
  year={2022}
}
Type systems can be used for tracking dimensional consistency of numerical computations: we present an extension from dimensions of scalar quantities to dimensions of vectors and matrices, making use of dependent types from programming language theory. We show that our types are unique, and most general. We further show that we can give straightforward dimensioned types to many common matrix operations such as addition, multiplication, determinants, traces, and fundamental row operations. 

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