Monoids, Monoids, Monoids
summary
Argues that monoids underlie many Scala patterns and shows concrete code-level uses: integer addition, string concat, set union, Option and tuple monoids, Map merge using a value monoid, and IO/Future sequencing. Demonstrates parallel aggregation with FS2 mapAsync + chunk + combineAll to fold large streams deterministically, and uses Cats + discipline for property tests. Notes Rubik's Cube as a permutation group (~4.6×10^19 permutations), experiments with Scala 3 union types as bounded semilattices, and reports the prototype designs compile and behave as expected.
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chapters (9)
- 0:00Introduction
- 1:57What are monoids
- 8:43Monoid laws
- 13:18Beyond monoids
- 24:13Advanced algebraic structures
- 30:51Type-level monoids
- 41:24Monoids in libraries
- 47:07Union/intersection types
- 53:05Conclusion and key takeaways
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