My background came from imperative languages, primarily C, C++, and Python. I picked up Scala, Erlang, and a bit of Haskell a few years later and have since become very interested in functional programming and the formalisms behind it.

I am also interested in concurrent and distributed programming and have been looking into formalisms behind that, especially those that have seen at least a tiny bit of the "light of day" (e.g. real world use, or at least an implementation somewhere). So far I know of Communicating Sequential Processes, the Actor model, Algebra of Communicating Processes, and the Calculus of Communicating Systems. Among these I know the Actor model has realized itself in languages like Erlang, Scala, and Haskell.

I am wondering if there are foundations I should learn and practice before tackling these fields, if there is a "classic" one that I should study first, and if there are any other popular ones that I may have missed?


The most widely used formalism is the $\pi$-calculus by Milner, Parrow and Walker. It is an extension of CCS, and comes in many variants, some of which (the asynchronous $\pi$-calculus) attempt to be a formalisation of the actor model. There are now many typing disciplines for $\pi$-calculi, the simplest of which are probably Honda's session types. Such types are slowly diffusing from research papers to research implementations.

  • $\begingroup$ Ah very interesting, thanks! What sort of mathematical background do you recommend before tackling such a field, or is it more or less self-contained? $\endgroup$
    – adelbertc
    Apr 30 '13 at 6:10
  • 2
    $\begingroup$ It's more or less self-contained. At least the basics. Milner's Communicating and Mobile Systems is a friendly introduction. If you want to get into types for concurrency, I suggest to understand the untyped $\pi$-calculus first, and maybe also to be familiar with typed $\lambda$-calculi. $\endgroup$ Apr 30 '13 at 19:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.