Sum-Product Probabilistic Language

SPPL is a probabilistic programming language that delivers exact solutions to a broad range of probabilistic inference queries. The language handles continuous, discrete, and mixed-type probability distributions; many-to-one numerical transformations; and a query language that includes general predicates on random variables.

Users express generative models as probabilistic programs with standard imperative constructs, such as arrays, if/else branches, for loops, etc. The program is then translated to a sum-product expression (a generalization of sum-product networks) that statically represents the probability distribution of all random variables in the program. This expression is used to deliver answers to probabilistic inference queries.

A system description of SPPL is given in the following paper:

SPPL: Probabilistic Programming with Fast Exact Symbolic Inference. Saad, F. A.; Rinard, M. C.; and Mansinghka, V. K. In PLDI 2021: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, June 20-25, Virtual, Canada. ACM, New York, NY, USA. 2021.


This software is tested on Ubuntu 18.04 and requires a Python 3.6+ environment. SPPL is available on PyPI

$ python -m pip install sppl

To install the Jupyter interface, first obtain the system-wide dependencies in and then run

$ python -m pip install 'sppl[magics]'


The easiest way to use SPPL is via the browser-based Jupyter interface, which allows for interactive modeling, querying, and plotting. Refer to the .ipynb notebooks under the examples directory.


Please refer to the artifact at the ACM Digital Library:

Guide to Source Code

Please refer to for a description of the main source files in this repository.


To run the test suite as a user, first install the test dependencies:

$ python -m pip install 'sppl[tests]'

Then run the test suite:

$ python -m pytest --pyargs sppl

To run the test suite as a developer:

  • To run crash tests: $ ./
  • To run integration tests: $ ./ ci
  • To run a specific test: $ ./ [<pytest-opts>] /path/to/
  • To run the examples: $ ./ examples
  • To build a docker image: $ ./ docker
  • To generate a coverage report: $ ./ coverage

To view the coverage report, open htmlcov/index.html in the browser.

Language Reference

Coming Soon!


To cite this work, please use the following BibTeX.

title           = {{SPPL:} Probabilistic Programming with Fast Exact Symbolic Inference},
author          = {Saad, Feras A. and Rinard, Martin C. and Mansinghka, Vikash K.},
booktitle       = {PLDI 2021: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Design and Implementation},
pages           = {804--819},
year            = 2021,
location        = {Virtual, Canada},
publisher       = {ACM},
address         = {New York, NY, USA},
doi             = {10.1145/3453483.3454078},
address         = {New York, NY, USA},
keywords        = {probabilistic programming, symbolic execution, static analysis},