The #LambdaCalculus is Algebraic
https://www.mscs.dal.ca/~selinger/papers/combinatory.pdf …pic.twitter.com/wp2SRSkAtE
In fact, those photos argue that (and then rebut it). There are different meanings of "algebraic" in play. Universal algebra forbids languages from using binders; without this restriction, things get harder to study and model.
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In a sense, this means lambda calculus doesn't actually need binders! Now, I think LC is algebraic in a more informal sense, but it's one that leads beyond algebra to category theory!
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