Duality and How to Delete Half (minus ε) of Your Code
summary
Claims that 96% minus ε of duplicated recursion-schemes code disappears by abstracting folds/unfolds over comonads and arrow categories, collapsing monadic, cofree, para/histo variants into one generalized cata. Implements this in Scala using Cats, kind-projector, typelevel/Dotty features and ports a Haskell dualizer to Scala. Demonstrates concrete types (CoFree, tuple comonad, Kleisli-like arrows), compiles with typelevel Scala, and notes tradeoffs: naming headaches, poorer type inference and compile-time cost, but no runtime penalty thanks to erasure.
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chapters (10)
- 0:00Talk introduction
- 1:06About the speaker
- 2:29What is a catamorphism
- 5:40Expanding the library
- 9:10Library growth problem
- 9:54Abstracting over comonads
- 12:43Abstracting function arrows
- 15:32Duality in recursion
- 18:00Kind polymorphism solution
- 20:28Final thoughts and summary
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