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Datatypes as algebras

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Datatypes like Nat, List, Tree,... are constructed in a similar way: inductively according to some constructors. How can we understand these constructions in a uniform way? One solution is the simple category-theoretic idea of an algebra. This idea can be used to capture not just lists and trees, but also much more general notions like the abstract syntax of a type system. I will introduce algebras and show why they are good models of structure, and show how properties like induction principles arise naturally out of this perspective. (The only category theory assumed will be the idea of a category and a functor).

This talk is part of the Logic & Semantics for Dummies series.

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