Approximate Relational Reasoning for Higher-Order Probabilistic Programs - Formalization Artifact

This artifact contains the Coq development accompanying the POPL 2025 submission "Approximate Relational Reasoning for Higher-Order Probabilistic Programs".

Contents

• The file docker-approxis.tar.gz contains a (compressed) Docker image that contains a working, compiled version of Approxis and all of its dependencies.
• The file coq-approxis.tar.gz contains the Coq development.
• The file Dockerfile was used to create the Docker image by running the command docker build -t approxis . && docker save approxis:latest | gzip > docker-approxis.tar.gz. The Docker image was created on Arch Linux, with a current version of Docker (date: 2024-10-16, version: 27.3.1, build ce1223035a). To successfully build the image, the files coq-approxis.tar.gz and Dockerfile should be in the current working directory.

Usage

Please refer to the file README.md in coq-approxis.tar.gz for information about the main results of the POPL submission as well as manual installation instructions.

The Docker image can be loaded via the command docker load < docker-approxis.tar.gz. We recommend either working with the provided image or following the installation instructions in the readme. 

To run an interactive Docker shell, execute the command docker run -i --name approxis -t approxis. From the interactive shell, one can check that the results of the paper have been proven without "admits" by examining the file collecting the main results and re-compiling it:

cat theories/approxis/approxis_examples.v
touch theories/approxis/approxis_examples.v
make

This sequence of commands will print Coq's the mathematical axioms for real numbers and classical logic.