foerster

A "bit" of information is definable as a difference that makes a difference. — Gregory Bateson, Steps to an Ecology of Mind

Act always so as to increase the number of choices. — Heinz von Foerster

Probabilistic inference in forkable worlds, for Clojure.

A Förster is a forester: someone who tends a forest, grows branches, prunes them, and decides which trees continue. That is what inference over spindel worlds does. Particles branch from a world, resampling prunes the unlikely ones and copies the likely ones, and Markov chains walk the tree of worlds. The name also honours Heinz von Foerster, whose cybernetics put the observer inside the system it observes, as agents inferring inside the worlds they act in are here.

What it does

A probabilistic program is a spindel spin with sample, observe and factor sites. Every site is a spindel savepoint, so an inference algorithm is a handler that decides, scores, forks, copies or abandons those savepoints:

• SMC and streaming SMC, importance sampling, tempered SMC, resample-move and SMCP3; arrival-batched SMC and the particle cascade, which do not wait for the slowest particle
• particle MCMC: PIMH, particle Gibbs, PGAS, IPMCMC; PMMH and SMC² for static parameters
• MCMC over traces: single-site and random-walk Metropolis–Hastings, block Gibbs, involutive MCMC, HMC on numerical blocks; kernels composed by k/cycle and k/mixture
• BBVI (black-box variational inference)
• steering a process — a language model's turns, a simulator — by SMC over scored steps, twisted by a value estimate (foerster.steer), with the trajectories as training data (foerster.learn)
• guides: a sample site's :proposal draws from a distribution the program computes, weighted by log p − log q
• counterfactuals and interventions (Pearl's do), selectors over sites
• a Gen-style generative function interface

(require '[org.replikativ.foerster.core :as infer]
         '[org.replikativ.foerster.dist :as dist]
         '[org.replikativ.foerster.effects :refer [sample observe]]
         '[org.replikativ.spindel.core :as sp]
         '[org.replikativ.spindel.spin.cps :refer [spin]])

;; programs run in a spindel world (an execution context)
(def world (sp/create-execution-context))

(defn model []
  (spin
   (let [mu (sample (dist/normal 0.0 1.0) :id :mu)]
     (observe (dist/normal mu 1.0) 1.0 :id :y)
     mu)))

;; inference returns a spin; at the REPL, deref it
(def posterior (sp/with-context world @(infer/smc-infer (model) 1000)))

(:mean (infer/query posterior identity))   ; ≈ 0.5, the posterior is N(0.5, 0.707²)

Inside another spin, await it instead of dereferencing (org.replikativ.spindel.effects.await).

Documentation

• Tutorials — runnable notebooks, rendered at replikativ.github.io/foerster: getting started, choosing an algorithm, models in worlds, blocks and HMC, streaming SMC, programmable inference, interventions and counterfactuals, steering a process.
• Guides — doc/: the language, the algorithms, posteriors, checking a model and its inference, coming from Stan, PyMC, Turing, Gen, Anglican or WebPPL, extending, worlds, distributions and reproducibility, the design, the literature.
• API reference — cljdoc.

Worlds

Pure models run in fresh worlds (:world-policy :fresh, the default). The particle methods (importance sampling, SMC, particle MCMC, BBVI) also run in canonical forks of the caller's world (:world-policy :fork), for models that read or change the systems of the world they run in (databases, repositories, a business book); Markov chains run in fresh worlds only:

• every particle is a frozen copy of the caller's world and runs the whole model, so nothing a particle writes reaches the caller;
• on the JVM particles are copies of worlds: systems that must not be duplicated (live handles, unsettleable linear state) are refused before the model runs, and with a resource authority particles split the inference's budget instead of multiplying it (in ClojureScript particles are forks, without these checks);
• however inference ends, every world is discarded before the result is delivered, and the posterior keeps each particle's world descriptor.

See the worlds guide.

Numerical blocks

A block is a group of latents sampled at one site, with a log density and its gradient. HMC moves blocks jointly. foerster-raster compiles block densities with raster (JVM, WASM, GPU) and reverse-mode AD.

Platforms

The sources are .cljc, and inference runs on the JVM and in JavaScript. Distributions (foerster.dist) are portable Clojure, named and parameterized like raster's, and the random generator draws the same numbers for a seed on both platforms. Copying worlds for canonical particles is JVM-only; in ClojureScript canonical particles are forks.

History

Monte Carlo began on ENIAC: Stanisław Ulam's idea (1946), John von Neumann's design, Klára Dán von Neumann's code for the first runs (1948), and Nicholas Metropolis's name for it. The Metropolis algorithm followed in 1953.

The idea was to try out thousands of such possibilities and, at each stage, to select by chance, by means of a "random number" with suitable probability, the fate or kind of event, to follow it in a line, so to speak, instead of considering all branches. — Stanisław Ulam

Lineage

foerster stands on earlier probabilistic programming systems:

• Anglican, probabilistic programming in Clojure: a model is a program whose sample and observe are checkpoints, and inference is a continuation-passing interpreter over them (SMC, PIMH, PGibbs, PGAS, IPMCMC, LMH, BBVI). foerster's sites are those checkpoints as spindel savepoints, and its benchmarks reuse Anglican's ground truths.
• Daphne, a probabilistic programming compiler in Clojure, following An Introduction to Probabilistic Programming: first-order programs compiled to graphical models, and those to amortized inference networks.
• Gen (Gen.jl), programmable inference through the generative function interface — simulate, generate, assess, update, regenerate over traces — which foerster implements (foerster.gfi), and involutive MCMC.

foerster grew inside spindel and was split out with its history.

License

Copyright © 2026 Christian Weilbach. Apache License 2.0.