I think your integrate function looks like a good idea:
integrate :: TimeStep -> World -> World
For bodies, I think you should have a BodyID type, and then to add a body to the world you could have a function:
newBody :: (Position, Velocity) -> World -> (BodyID, World)
To delete a body:
deleteBody :: BodyID -> World -> World
So your World type will need to contain all of the bodies "inside" it, something like this: data World = World { gravity :: Vector, bodies :: [(BodyID, (Position, Velocity, BodyProperties))] This is pretty much the way things are done in the FRP paper "The Yampa Arcade", where they use an "Identity List" where the type ILKey = Int. See section 5.5 of the paper: http://www.haskell.org/yale/papers/haskell-workshop03/index.html