In articles or Quora posts about category theory, I often find mentions of the programming language Haskell. I have little knowledge of category theory and even less of programming. Could someone please explain how category theory is important in Haskell?


1 Answer 1


Category theory is an abstract branch of mathematics and you do not need to learn it before you start writing Haskell code. Similarly, you do not need to learn Haskell before you start learning category theory.

Haskell has a beautiful relationship with category theory. For example, consider polymorphic functions. When we define some reasonable restrictions, it turns out that they are simply natural transformations on which category theory applies.

Another example is Haskell's relation with Cartesian closed categories (CCCs). Haskell, at its core, is pure typed lambda calculus and lambda expressions can be considered the composition of functions that come with a Cartesian closed category. Once you start dwelling into Haskell and category theory, you will develop a concrete understanding of this relationship.

Check out free theorems, CCCs and $\lambda$ calculus, category theory from Haskell's POV and monads.

  • 3
    $\begingroup$ Agree completely with the first paragraph. Just as an addendum, the way we generally learn abstract concepts and structures is by working through concrete examples first. Haskell is an excellent source of concrete examples for category theory. Personally, I never really understood natural transformations (what's so "natural" about them?) until I understood free theorems. Of course, your mileage may vary... $\endgroup$
    – Pseudonym
    Jun 12, 2022 at 10:46

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