There's some research on automatically deriving efficient algorithms for classes of distributions, e.g. getting a specialized EM-like algorithm for anything whe

There's some research on automatically deriving efficient algorithms for classes of distributions, e.g. getting a specialized EM-like algorithm for anything where EM-like algorithms are applicable: http://machinelearning.wustl.edu/mlpapers/paper_files/AA24.pdf http://machinelearning.wustl.edu/mlpapers/paper_files/AA24.p... But obviously that doesn't cover classes as big as "anything expressible in Church", so there's a pretty big gap. It's possible that languages like Church could use techniques like that as part of an optimizing compiler that recognizes specializable patterns, the way regular compilers do loop transformations and auto-vectorization and such. But, like auto-vectorization, not that easy to do.