Last time I talked about how algebraic abstractions like “monoid” and “semigroup” didn’t seem to be pulling their weight, despite love from functional programmers. That focused on a practical issue: do these abstractions aid or harm comprehension? Do they make programming easier or harder? (Of course, there’s not a simple answer to this question.)

This time, though, I want to talk about something more exploratory: do we have the right tools to talk about these abstractions? This post is therefore going to be much longer and contain a lot more rambling.

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Back in July I got myself into a discussion on Twitter about whether some of the more algebraic concepts in functional programming were net-useful, after reading Brandon Williams’ (great) articles on how they can be applied in Swift. Brandon Kase suggested I watch his talk “Beyond Types in Swift” from this year’s Functional Swift conference.

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