WebPPL

Per-target obligations of Transpilation correctness for \(\mathsf{T} = \mathrm{WebPPL}\).

Semantics

WebPPL's denotational semantics is the continuation-passing-style trace semantics of Goodman and Stuhlmüller (2014). A program is a JavaScript-syntax WebPPL function whose sample and observe calls are reified by the WebPPL compiler into CPS-transformed continuations; the trace is the sequence of (address, distribution, value) triples visited. The repository's numeric probe rewrites rendered sample and observe sites into calls to each distribution object's score(value) method at clamped parameter and data values. It does not estimate the density through importance sampling.

Unconstrained-space change of variables

Identity. WebPPL distributions are operationally defined; no automatic reparametrization layer.

Family parameterizations

WebPPL families use JavaScript-object keyword arguments: Dirichlet({alpha: ...}), Categorical({ps: ...}), Gaussian({mu: ..., sigma: ...}), Bernoulli({p: ...}), etc. The QVR ↔ WebPPL arg mapping requires non-trivial aliases that live in FAMILY_META.arg_aliases["webppl"]:

QVR arg	WebPPL arg
loc	mu
scale	sigma
concentration (Dirichlet)	alpha
probs	ps

The renamings are syntactic; \(c_{F, \mathsf{WebPPL}} = 0\) for every family with native WebPPL support.

Per-construct emit

Sample / observe. var <name> = sample(<Family>({args})); for latents; observe(<Family>({args}), <obs>); for observations.

Plate. repeat(B, function() { return sample(<dist>); }) for index-independent batches; mapIndexed(function(m, _) { return sample(<dist using m>); }, repeat(B, 0)) for index-dependent. Per Goodman & Stuhlmüller 2014, repeat denotes the documented \(B\)-fold product measure.

Marginalize. Explicit-latent rewrite (head the marginalization discussion). WebPPL natively samples discrete latents via the trace mechanism.

Score / let / return. factor(expr) for score; var <name> = <expr>; for let; native return.

Acceptance

• Tier 1 structural. Every emit has var model = function(...) { ... }; whose body uses sample, observe, factor, repeat, and mapIndexed.
• Tier 1 pipeline composition. Direct and composed pipeline calls agree.
• Tier 2 external syntax. node --check /dev/stdin accepts the JavaScript syntax. This does not validate WebPPL primitive names or runtime semantics.
• Tier 3 numeric equivalence. The rewritten .score(value) probe is compared with the QVR reference on selected fixture grids.