Relation to Actors

[bblfish]

Watching David Spivak's course (see my twitter thread) which led me to this book, I came to wonder very quickly if Poly as Dynamical Systems could not be the mathematics for Actor based systems. That is an important question to me as I am using Actors to program a web server, and so understanding the relation would give me extra energy to read the books, and correct typos :-) If it did fit it could perhaps provide the maths for a general theory of the web.

The inventor of Actor Systems was Carl Hewitt and he wrote up a very personal explanation of them in a 2010 paper where he writes that it integrates:

1.the lambda calculus
2. interrupts
3. blocking method invocation
4. imperative programming using locks
5. capability systems
6 co-routines
7. packet networks
8. email systems
9. Petri nets
10. Smalltalk-72
11. Simula-67
12. pattern-directed invocation (from Planner)

I first came across an actor system using a language April by Keith Clark in 1993 doing my Masters, that could send messages to actors on the internet around the world as tuples. I am now using a different actor system - Akka - to build a Web Server used by many internet behemoths such as Paypal, that use it to execute over 1 billion transactions a day on relatively little hardware.

Akka Actors

• form open systems,
• maintain state
• have names (URLs) that can be used to address them
• can be typed by the messages they receive,
• they can change their own behavior
• the whole point is that they are individual execution contexts

Actor systems are excellent tools to build streaming libraries, which can be composed then using symmetric monoidal category like diagrams.

@alcestes has been working on pushing typesafe actors to the next level and I think he has a very good understanding of the theory of actors. I am not sure how much category theory he knows though.