4 ms·

Category theory in general, because it encompasses areas of computer science, mathematics, and physics.

• jules 19y ago
  Why should someone who is interested in programming languages learn category theory and what is the best (preferably online) text?
  • neilc 19y ago
    A Gentle Introduction to Category Theory looks pretty good: http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html
    • jules 19y ago
      After having read a few pages category theory somehow seems similar to OOP. As with OOP you package data with its operations (morphisms). > Quoting Asperti and Longo [1]: “The basic premise of category theory is that every kind of mathematically structured object comes equipped with a notion of [ . . . ] transformation, called ‘morphism’, that preserves the structure of the object.” By means of the categorical language one cannot express properties of the internal structure of objects. The internal structure of objects is accessible only externally through the morphisms between the objects. What is described here sounds a lot like information hiding/encapsulation. Is category theory similar to OOP in this way?
  • mattrepl 19y ago
    Category theory is important to type theory and semantics (Pierce, see below, also wrote several books on types in programming languages) and offers a different representation of computational flow (monads, arrows). Benjamin Pierce's "Basic Category Theory for Computer Scientists" (not online) is terse and complete [1]. Wikipedia is good for definitions and there's also a Wikibook on category theory: http://en.wikibooks.org/wiki/Category_theory http://en.wikibooks.org/wiki/Category_theory There are some brief, informative, and fun lectures on YouTube by the Catsters: http://www.youtube.com/profile_play_list?user=TheCatsters http://www.youtube.com/profile_play_list?user=TheCatsters The natural transformations playlist is where to start, just be ready to use the aforementioned references. __ [1] Natural transformations are the original point of category theory. A text that doesn't cover them is incomplete.
    • jules 19y ago
      Thank you and thanks neilc. What is the right order to watch the lectures by the Catsters? Top-to bottom as listed on that page? Are there any data structures based on category theory, like sets & graphs which are inspired by mathematical theories?
      • mattrepl 19y ago
        Category theory shares a lot with set theory, but they are different - they make different assumptions and each is better suited at describing certain types of systems. Graph theory is also its own topic in math, though sets can be used to talk about them As for the Catsters' videos, I'm unsure about the best order. The recommendation to start with the natural transformations playlist came from someone in #haskell (Cale, maybe?). I'd suggest diving in to whatever sounds interesting and backing up to review other videos that contain any new terms.