Separate "probability expression" syntax

[phipsgabler]

I've been contemplating whether something like StatsModels formula syntax, but for probability expressions, might be useful to abstract out as well.

For example, this parses quite OK:

julia> :(f(first, @P(X | (; Y = 2)), model)) |> Meta.show_sexpr
(:call, :f, :first, (:macrocall, Symbol("@P"), :(#= REPL[13]:1 =#), (:call, :|, :X, (:tuple, (:parameters, (:kw, :Y, 2))))), :model)

There are currently two places where something similar is used:

1. In DynamicPPL's prob string macros for probability queries:

   prob"s = 1.0, m = 1.0 | model = gdemo, x = nothing, y = nothing"

   There, the string is really just split at the |, and then Meta.parsed. Separating out probability expressions would remove some awkwardness of "conditioned variables" which are not random variables, like the model.

2. In (future) Soss, you should be able to condition models: conditional models cscherrer/Soss.jl#216. Not quite the same thing, but going into a similar direction.

Perhaps other things, like prior/likelihood queries and transformations against models, can be subsumed under this, too.

CC @yebai @mohamed82008 @cscherrer

[cscherrer]

I like the @P macro idea. What would first be in this example?

Soss has | notation in dev already. I've been using it for a while, and I think it's working well. I need to get this into master; it's just going to be a giant merge at some point. Refactoring is hard.

I was also wondering about | notation for MeasureTheory, for restricting a measure to a subset. This is really what happens in any PPL anyway. We never compute the normalizing factor, so the logdensity or logpdf is really either not a probability measure, or it's no longer wrt Lebesgue measure. Might as well recognize this :)

[phipsgabler]

first is nothing relevant, just a leftover from when I tested how the @P call parses within a function call.

Although I had been thinking of notation like query(model, @P ...).