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Idealized Haskell type class lattice
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lattice.md

This is a personal mental model of how I would classify Haskell main type classes if semigroupoids were first-class.

Functor: <$>

  • Apply: <*>, <.>
    • Applicative: pure, return
    • Bind: join, =<<, <=<
  • Alternative (Alt): <|>, <!>
    • Zero (Alternative): zero, empty
  • CoApply: <@>
    • CoApplicative: copure, extract
    • Extend: duplicate
  • SemiGroup: <>
    • Monoid: empty, mempty
  • SemiGroupoid: >>>
    • Category: id
      • Arrow: arr first

  • Plus -> Apply + Zero: <+>, mplus (Left Distribution)

  • Or -> Applicative + Zero: <!>, morelse (Left Catch)

  • Monad -> Bind + Applicative

  • MonadPlus -> Monad + Plus

  • MonadOr -> Monad + Or

  • CoMonad -> Extend + CoApplicative

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