babble: Learning Better Abstractions with E-Graphs and Anti-Unification

POPL 2023, January 2023
  author = {Cao, David and Kunkel, Rose and Nandi, Chandrakana and Willsey, Max and Tatlock, Zachary and Polikarpova, Nadia},
  title = {Babble: Learning Better Abstractions with E-Graphs and Anti-Unification},
  year = {2023},
  issue_date = {January 2023},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  volume = {7},
  number = {POPL},
  url = {},
  doi = {10.1145/3571207},
  journal = {Proc. ACM Program. Lang.},
  month = {jan},
  articleno = {14},
  numpages = {29},
  keywords = {e-graphs, anti-unification, library learning}


Library learning compresses a given corpus of programs by extracting common structure from the corpus into reusable library functions. Prior work on library learning suffers from two limitations that prevent it from scaling to larger, more complex inputs. First, it explores too many candidate library functions that are not useful for compression. Second, it is not robust to syntactic variation in the input.

We propose library learning modulo theory (LLMT), a new library learning algorithm that additionally takes as input an equational theory for a given problem domain. LLMT uses e-graphs and equality saturation to compactly represent the space of programs equivalent modulo the theory, and uses a novel e-graph anti-unification technique to find common patterns in the corpus more directly and efficiently.

We implemented LLMT in a tool named babble. Our evaluation shows that babble achieves better compression orders of magnitude faster than the state of the art. We also provide a qualitative evaluation showing that babble learns reusable functions on inputs previously out of reach for library learning.