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A mathematical algebra has three parts:

  • Objects. The collection of objects defines what we’re talking about.
  • Operations
  • Laws are relationships between the objects and the operations.

In high school algebra:

  • the objects are numbers
  • and the operations are addition, multiplication and friends.

In the algebra of Haskell types,

  • the objects are types, for example Bool and Int.
  • the operators take types that already exist, and generate new types from them.