On the sub model syntax

[yebai]

We recently added support for submodels (#233). There are follow-up discussions in #267 (comment) and slack on the proposed submodel syntax. I thought it may be helpful to open an issue for some discussions.

Current syntax:

    @submodel x = model(args...)
    @submodel prefix x = model(args...)
Treats `model` as a distribution, where `x` is the return-value of `model`.

I think we can support both tilde and assignment, but with different semantics, i.e.

1. @submodel x = model(args...) will assign returned value of model to variable x.
2. @submodel x ~ model(args...) will assign a named tuple to variable x. This named tuple is a "SimpleVarInfo" style object, e.g. it contains all variables in the sub-model.

Here option 2 is slightly more general since a user can manipulate the returned named tuple x to for specific purposes. It is also more consistent with the Turing modelling syntax.

cc @devmotion @phipsgabler @torfjelde @mohamed82008

EDIT: we can also remove the @submodel annotation eventually, and use a unified notation ~ for both Distributions and sub-models.

[torfjelde]

Current syntax:

    @submodel x = model(args...)
    @submodel prefix x = model(args...)
Treats `model` as a distribution, where `x` is the return-value of `model`.

I think we can support both tilde and assignment, but with different semantics, i.e.

1. @submodel x = model(args...) will assign returned value of model to variable x.
2. @submodel x ~ model(args...) will assign a named tuple to variable x. This named tuple is a "SimpleVarInfo" style object, e.g. it contains all variables in the sub-model.

Here option 2 is slightly more general since a user can manipulate the returned named tuple x to for specific purposes. It is also more consistent with the Turing modelling syntax.

After #269 (2) seems not as useful maybe, since __varinfo__ will essentially be this? If the point is that we only want the information that was added from within the submodel, the best approach would probably be to diff the varinfo before running the submodel with the resulting varinfo and then "un-prefix" the variables. But I'm not so certain people would ever use this when they can access the return-values anyways? 😕

EDIT: we can also remove the @submodel annotation eventually, and use a unified notation ~ for both Distributions and sub-models.

We could actually do this for (1) quite easily if we decided to use ~ for it (but again, this has issues):

function tilde_assume!!(context, right::Model, vn, inds, vi)
    retval, new_vi = _evaluate(right, vi, PreficContext(vn, context))
    return retval, new_vi
end

PrefixContext(vn::VarName, context) = PrefixContext{Symbol(vn)}(context)
# Just to make it inferrable at compile-time when it's possible.
function PrefixContext(::VarName{sym, Tuple{}}, context) where {sym}
    return PrefixContext{sym}(context)
end

But this of course suffers the same issues as (2) since it requires using the ~ notation + it's not so easy to override the prefix being used, which can be annoying.

[mhauru]

This conversation has been overtaken by the conversation in #696