Over the last few years, Jean-Philippe Bernardy and I have been exploring how to express tensor calculus (the Einstein notation, Penrose diagrams, and the categorical view) in Haskell. The paper is under review and we have just uploaded a new version to arXiv, after receiving lots of good feedback from reviewers (and acting on the 86 suggestions...). https://arxiv.org/abs/2312.02664
Now hoping it will soon be accepted for the journal.
(Here is an earlier blog post from when it was first submitted to JFP: https://patrikja.owlstown.net/posts/2002-domain-specific-tensor-languages )
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