How does functional programming apply to simulations?

Question

Besides the general question in the title,

• How do functional programmers and functional languages approach the domain of simulations, which seem to be most natural

Answer 1

I'm writing a game in Clojure, using a mostly functional style. For example, the entire game state is modelled as an immutable data structure.

This has required some slightly convoluted coding. For example, you frequently end up creating functions with a lot of parameters to pass around various elements of game state and ensure that application of game state updates happens to the very latest game version.

But it has also thrown up some really nice advantages, for example concurrency has proved pretty trivial and you can do fun things like cloning the entire game state to run different simulations in the AI.

Overall, I'm delighted with Clojure as a language for simulations / games.

Based on this experience, the things I think would improve Clojure for games / simulations would be:

• Better support for primitives, especially as function parameters and return values
• Implementation of core language functions that are less hard on memory allocations (GC pressure is an issue for interactive games!)

You can see an early version of the game here: Ironclad - Generals of Steam. It's basically a steampunk themed strategy game.

Answer 2

To complement the other answers: There is a discipline called Functional Reactive Programming that addresses the issue of functional representation of systems that change in time and react to outer events. See

• What is (functional) reactive programming?
• Is functional GUI programming possible?
• Functional Reactive Programming at The Haskell Wiki.

Answer 3

Uncle Bob has been playing with Clojure lately and in particular writing an orbital simulator as his most public example.

Some links:

• Blog post
• Code on github

Answer 4

Michal's answer is excellent, but I thought I'd add a couple other neat examples I've personally found helpful/interesting.

The first is a post (and code) about functional fluid dynamics by Lau Jenson. Though he definitely goes the mutable route for speed here, the style is rather functional. I'd bet by Clojure 1.3 this could be done (mostly!) immutably with reasonable performance.

The next is a simple Snake game implemented in Clojure. Easy enough to read though in an hour or so, and the style is really pleasant and cohesive.

Also, some neat code to look at (I think!) is code modeling neural networks. Jeff Foster has some single layer perceptron code, and some more idiomatic revisions of the code. Worth looking at, even if you're not acquainted with NNs. He also has some more recent posts regarding fluid dynamics, though this time in Haskell. (Part I and Part II) Also fun, I think, is his implementation of the Game of Life (& Part II).

Finally, as Michal mentioned before me, Brian Carper is working on a RPG in Clojure. he recently posted some artwork for the game, so I'm betting it's still being worked on ;)

I love using the sequence libraries for working with tons of data; it feels more natural using abstractions like map and reduce, and fun, handy tools like juxt rather than simple imperative iterations. You do pay a tax, I've found, by using Clojure/functional langs in reimplementing well-known and well-implemented imperative algorithms.

Have fun!

Answer 5

I'm not sure that I'm up to the challenge of writing up a comprehensive analysis of the problem posed in the question, but I can at least post some links interesting on the FP vs. games front:

Jörg W. Mittag provides a number of interesting examples in this answer to a question on "real world" Haskell programming (with links to some interesting write-ups -- the Purely Functional Retrogames series is really worth a read).

In Clojure land, Phil Hagelberg has implemented a text-based adventure game for his PeepCode screencast on Clojure programming; the code is available on GitHub. Then there's Brian Carper's RPG project; no code publicly released yet and just that one post from a while ago (it looked very cool, though, so let's all come together to pressure Brian to continue ;-)). Finally, here's an example of a simple game using Penumbra (for some reason -- possibly unrelated to Clojure -- I couldn't get it to work, but may you will, plus there's a write-up attached).

As for simulations, studying ants.clj is a great idea. Also, I remember seeing a series of SICP-based lectures from an introductory programming course at UC Berkeley (I think...?) available somewhere (90% it was on their YouTube channel); they've got three lectures on OOP in Scheme and I think they mention simulation as a domain providing good use cases for the approach. Note that I have a pretty vague memory of this one, so it's hard for me to say how useful it might be to you.

Answer 6

Simulations are a form of interpreter -- which are easy to write in a functional style. They can be also designed as self-optimizing simulators, based on treating them as a compiler.