An Introduction to Program Synthesis (mchav.github.io)

This post introduces program synthesis, the process of automatically generating small programs from input-output examples, exemplified by building a FlashFill-style string manipulator that converts names like “Joshua Nkomo” into “J. Nkomo.” It explains how to define a minimal domain-specific language (DSL) for string operations—such as head, tail, substring, concat, and case conversion—whose compositional building blocks enable systematic exploration of candidate programs to meet specified behaviors. The approach uses bottom-up enumerative search, starting from simple operations and incrementally creating more complex ones, testing each against example pairs until finding a solution. The significance lies in positioning program synthesis as a form of “System 2” AI—deliberate, symbolic reasoning—contrasted with the statistical “System 1” intuition of machine learning models like large language models (LLMs). While ML offers fast, pattern-based approximations prone to errors or hallucinations, synthesis provides exact, interpretable programs that guarantee correctness but traditionally face scalability challenges. By combining these complementary strengths, neuro-symbolic methods—such as DeepMind’s AlphaGeometry and OpenAI’s guided program search—are advancing toward more robust AI. The post highlights the crucial role of DSL design, balancing expressivity and search efficiency, showing that good DSLs encode domain knowledge allowing aggressive pruning of the search space and feasible synthesis. Overall, this series lays a practical foundation for building and understanding program synthesis systems, emphasizing that carefully constructed symbolic methods remain vital in the evolving AI landscape—offering principled solutions where pure statistical models struggle.