A Monoid for All Seasons

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In this keynote at Haskell Exchange 2017, I decided to tell people why I love monoids so much. Before I started learning Haskell, I’d never heard the word “monoid” and didn’t know what an algebra meant. But I recognized a pattern when I learned about the Monoid typeclass, a pattern of conjunction and disjunction, that pervades Haskell and all its monoids, including the type system.

I recognized the pattern from some common, well-known examples: arithmetic, Boolean arithmetic, and set theory. Understanding the pattern helped me see connections all through Haskell and mathematics.

Near the end of the talk, I go briefly into category theory, the way I was first introduced to category theory and try to explain that sums and products are deeply connected, which validates our intuitions about their connections that we’ve seen through concrete examples.

There is some Haskell code, and I don’t explain much about what typeclasses are for, so some basic Haskell knowledge is assumed.

Slides are available here.

Video is here. Perhaps someday we’ll get it embedded here.


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