The presented approach for equivalence and similarity refutation of probabilistic programs has significant implications for the design and compilation of probabilistic programming languages. By offering a method for automated formal analysis of relational properties of probabilistic program pairs, the approach enhances the correctness and reliability of probabilistic programming languages.
From a design perspective, the method provides a systematic way to verify equivalence and similarity of output distributions, which can inform the development of probabilistic programming languages with built-in verification mechanisms. This can lead to more robust and trustworthy probabilistic programming languages that are better equipped to handle complex probabilistic models and ensure the correctness of their output distributions.
In terms of compilation, the approach enables bug detection in probabilistic program compilers by comparing the source code to its intermediate representation without program execution. This can help identify and rectify compilation errors that may lead to incorrect output distributions. By providing formal guarantees on the correctness of results, the approach enhances the reliability of compilation processes for probabilistic programming languages. Overall, the approach contributes to the advancement of probabilistic programming languages by offering a method for automated verification and analysis of relational properties.