Type Assisted Synthesis of Programs with Algebraic Data Types

In this paper, we show how synthesis can help implement interesting functions involving pattern matching and algebraic data types. One of the novel aspects of this work is the combination of type inference and counterexample-guided inductive synthesis (CEGIS) in order to support very high-level notations for describing the space of possible implementations that the synthesizer should consider. The paper also describes a new encoding for synthesis problems involving immutable data-structures that significantly improves the scalability of the synthesizer. The approach is evaluated on a set of case studies which most notably include synthesizing desugaring functions for lambda calculus that force the synthesizer to discover Church encodings for pairs and boolean operations, as well as a procedure to generate constraints for type inference.