Type-Directed Synthesis of Products

TL;DR

This paper extends a type-directed program synthesis system to handle product types, improving its expressiveness and efficiency by integrating logical conjunctions and focusing techniques, while maintaining performance.

Contribution

The thesis introduces the handling of product types into the synthesis engine, enhancing its theoretical foundation and practical implementation for more expressive program synthesis.

Findings

Successfully integrated product types into the synthesis system.

Maintained performance competitiveness with the original synthesizer.

Enhanced the system's extensibility for future improvements.

Abstract

Software synthesis - the process of generating complete, general-purpose programs from specifications - has become a hot research topic in the past few years. For decades the problem was thought to be insurmountable: the search space of possible programs is far too massive to efficiently traverse. Advances in efficient constraint solving have overcome this barrier, enabling a new generation of effective synthesis systems. Most existing systems compile synthesis tasks down to low-level SMT instances, sacrificing high-level semantic information while solving only first-order problems (i.e., filling integer holes). Recent work takes an alternative approach, using the Curry-Howard isomorphism and techniques from automated theorem proving to construct higher-order programs with algebraic datatypes. My thesis involved extending this type-directed synthesis engine to handle product types, which required significant modifications to both the underlying theory and the tool itself. Product types streamline other language features, eliminating variable-arity constructors among other workarounds employed in the original synthesis system. A form of logical conjunction, products are invertible, making it possible to equip the synthesis system with an efficient theorem-proving technique called focusing that eliminates many of the nondeterministic choices inherent in proof search. These theoretical enhancements informed a new version of the type-directed synthesis prototype implementation, which remained performance-competitive with the original synthesizer. A significant advantage of the type-directed synthesis framework is its extensibility; this thesis is a roadmap for future such efforts to increase the expressive power of the system.