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Schrodinger is an (early-stage) project for probabilistic programming in Scala 3, built for the Cats ecosystem. At its heart is the RVT monad transformer for modeling pseudo-random effects that is designed to fully compose with asynchronous effects such as IO. The goal is that this construct will facilitate the implementation of high-performance, concurrent Monte Carlo algorithms for simulation and inference.

Furthermore, Schrodinger encodes the foundational probability distributions as a set of typeclasses to be used to write "universal" probabilistic programs, for which simulators and inference algorithms can be automatically derived by implementing interpreters in terms of these same typeclasses.


libraryDependencies += "com.armanbilge" %% "schrodinger" % "0.3-193-ed9a8ba"


  • kernel: essential typeclasses for writing probabilistic programs.
    • Random[F[_]] encodes the primitive of generating random bits in the form of Int and Long.
    • PseudoRandom[F[_], G[_], S]: encodes the ability to pseudo-randomly simulate ("compile") a Random effect F to another effect G via a seed S. Extends Random[F].
    • Distribution[F[_], P, X]: the Kleisli P => F[X], encoding the mapping from parameters P (e.g., the mean and standard deviation of a Gaussian) for a distribution on X (e.g., the reals represented as Double) to an instance of an effect F[X] (e.g., an effect implementing the Random typeclass).
    • Various case classes parameterizing different distribution families, to be used as arguments for P above, as well as convenient aliases that can be used with the usual typeclass syntax.
    • Density[F[_], X, R]: the Kleisli X => F[R], encoding the probability density (or probability mass) function in some effect F.
  • random: samplers for the distribution families in kernel. These are implemented purely monadically, in terms of Random[F] or each other.
  • schrodinger: the core module, also brings in random.
    • RVT[F[_], S, A]: a monad transformer for pseudo-random effects. Use this to simulate your probabilistic programs. Externally it is pure, although internally it is implemented with a mutable RNG for performance. Notably, it implements all the Cats Effect typeclasses up to Async (given that F is equally capable) by utilizing the underlying RNG's capability to deterministically "split" itself, such that each fiber has its own source of randomness. Not only does this avoid contention and synchronization, it makes it possible to write pseudo-random programs that are concurrent yet deterministic, and thus reproducible. Anyone who has debugged a complex Monte Carlo algorithm knows this is a big deal.
    • Rng[S]: a mutable and thus unsafe random number generator with state S.
    • RngDispatcher[F[_], S]: "dispatches" a mutable RNG that can be used to run pseudo-random imperative programs, for interop with unsafe lands. This also relies on the splitting capability described above.
  • stats: Density implementations for the distribution families in kernel.
  • monte-carlo: algorithms and datastructures for Monte Carlo inference.
    • Weighted and WeightedT: encodes a sample from a distribution along with its weight and probability density. This is useful for implementing importance sampling-based algorithms.
    • ImportanceSampler: derives a sampler for a distribution P in terms of a sampler for a distribution Q.
  • math: assorted math stuff.
  • laws: currently empty besides a silly law for PseudoRandom. Still figuring this one out in #2.
  • kernel-testkit: currently mostly used to test random.
    • the PureRVT monad, implemented in terms of Cats' StateT. It is completely pure, unlike RVT in core which is run with an unsafe mutable RNG.
    • *waves hands* Eq for a pseudo-random effect F.
  • testkit: used to test RVT.

If not readily apparent, various aspects of the design are heavily influenced by Cats Effect 3.

  • monte-carlo is like a "std" lib, and so-called middlewares can ideally be implemented only in terms of that and kernel. The implementations provided by the random and stats modules and RVT itself are only needed at runtime and indeed can be substituted with (more performant!) alternatives.
  • The unsafe Rng that is used to simulate an RVT is kind of like the unsafe IORuntime that runs IO.
  • RngDispatcher facilitates interop with "unsafe lands" inspired by the Dispatcher in CE3.