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I took a brief look at the first paper you cite, and I think Max New's answer does have some relevance to it. The purpose of this answer is to explain how I think the 'finally tagless' stuff gets a bit confused itself about the idea. The paper starts with a simple algebraic signature for a language with literal numbers, addition and negation. It says that ...


Final Algebra semantics was introduced by Mitch Wand in his paper "Final Algebra Semantics and Data Type Extensions", see this freely available tech report: . It does not mean final coalgebra semantics, which is a very different idea. The wrinkle is that the algebra is not final in the same category that ...

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