[Haskell-beginners] Identifying general patterns / typeclass instances

[Tim Cowlishaw]

Hi there all,

I've come up with the following sketch for a simple agent-based
simulation program in Haskell. However, I'd be interested in knowing
whether there are any obvious instances of more general typeclasses
hidden in there that I haven't recognised!

https://gist.github.com/1129216

Some explanation: A simulation is comprised of a starting state, and a
set of agents which take in a state and output an updated state. The
particular simulation I'm working on has very specific timing
semantics in that, for each 'step' of the simulation, all the agents
must see the same state (so they cannot simply be composed and applied
sequentially), and the resulting states must be applied to create the
next state in a well-defined order (hence the monoid restriction on
the SimState type). For this reason, I'm having trouble coming up with
a monad instance (which would seem to me to imply that the 'agent'
functions would be applied sequentially). However, are there any other
more general typeclasses that might offer useful abstractions in this
case?

In addition, the 'building up' of a simulation from an initial state
also looks to me like an anamorphism of some kind - is this correct?

Many thanks,

Tim