The Derivative of a Regular Type is its Type of One-Hole Contexts (2001) [pdf]
Some related links (specifically that they perform &quot;high school&quot; algebra on types):<p>- Seven trees in one [0], a paper showing a bijection between binary trees and seven-tuples of binary trees.<p>- The algebra of algebraic data types [1] discusses Taylor expansions of data types.<p>- Differentiation of higher-order types [2] is commenting on OP&#x27;s paper.<p>I used to be really interested in type theory, but haven&#x27;t had as much time to explore it, but over the years I&#x27;ve saved these links (and the one posted).<p>[0]: <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;math&#x2F;9405205.pdf" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;math&#x2F;9405205.pdf</a><p>[1]: <a href="https:&#x2F;&#x2F;codewords.recurse.com&#x2F;issues&#x2F;three&#x2F;algebra-and-calculus-of-algebraic-data-types" rel="nofollow">https:&#x2F;&#x2F;codewords.recurse.com&#x2F;issues&#x2F;three&#x2F;algebra-and-calcu...</a><p>[2]: <a href="http:&#x2F;&#x2F;conal.net&#x2F;blog&#x2F;posts&#x2F;differentiation-of-higher-order-types" rel="nofollow">http:&#x2F;&#x2F;conal.net&#x2F;blog&#x2F;posts&#x2F;differentiation-of-higher-order-...</a>