Category Theory for Programmers

  • redraw pictures of ƒ(A)=B so that the morphisms look like • and the objects look like →. Hey, why not?
  • string diagrams (process networks) are just as good as algebraic symbology
  • associativity
  • tensor products
  • if switch( switch( • )) ≠ • , then* you’ve got a braided category, which is described by the algebra of knots. “I’m not sure why you would want your programming language to include the algebra of knots at a basic level, but … you could.” I think braided code totally makes sense … in a visualising-a-big-system-of-code kind of way.

*Technically speaking: in Haskell it’s always true for every • input that switch( switch( • )) ≠ • . If we were talking about a language where switch( switch( • )) ≠ • is not always true — sometimes or possibly not true — then that language would be a braided category. ∃x | ¬ p(x) = ¬∀x p(x) — all symbols spoken in the subjunctive.

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