Monoids and Software Engineering
summary
Defines monoid as set + associative binary op + identity, shows concrete Haskell examples (integers with + and , strings with concat) and uses HLearn Gaussians to demonstrate incremental aggregation: combine sample summaries without recomputing, and add inverses to remove data online. Builds a practical comparator by combining small accessor functions via the Ordering monoid to sort DB rows neatly. Notes a real-world monoid homomorphism* in protobufs where string concat length maps to integer addition, enabling a cheap merge refactor.
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chapters (10)
- 0:00Introduction to monoids
- 1:14Monoids in abstract algebra
- 3:45Examples of monoids
- 5:09Incremental aggregation with monoids
- 8:22Case study in machine learning
- 10:05Declarative interface benefits
- 21:20Monoids in function composition
- 23:32Monoid homomorphisms
- 25:58Monoids in protocol buffers
- 27:04Monoids and software complexity
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