Splitting \omega

[zenna]

From working on the probmods translation it's apparent that somethings are cumbersome to do with Omega as it stands. Let's take a geometric distribution, expressed recursively in WebPPL / javascript as:

var geometric = function(p) {
  return bernoulli(p) ? 1 + geometric(p) : 1
};

Compare with Omega

geometric(ω, p; i = 1) = (i ~ Bernoulli(p))(ω) ? 1 + geometric(ω, i + 1) : 1

There's this annoying passing around of indices. It'd be nice if we could do something like this:

geometric(ω, p) = (@~ Bernoulli(p))(ω) ? 1 + geometric(next(ω)) : 1

where next(ω) shifts ω to some independent ω.

But how would it work? The basic idea I've been following is to say that each ω lives on a subspace. I developed this idea for iid rvs, and it's all very similar.