Look for the Proof to Find the Program: Decorated-Component-Based Program Synthesis

Adrià Gascón, Ashish Tiwari, Brent Carmer, Umang Mathur

Abstract: We introduce a technique for component-based program synthesis that relies on searching for a target program and its proof of correctness simultaneously using a purely constraint-based approach, rather than exploring the space of possible programs in an enumerate-and-check loop. Our approach solves a synthesis problem by checking satisfiability of an \(\exists \exists \) constraint \(\phi \), whereas traditional program synthesis approaches are based on solving an \(\exists \forall \) constraint. This enables the use of SMT-solving technology to decide \(\phi \), resulting in a scalable practical approach. Moreover, our technique uniformly handles both functional and nonfunctional criteria for correctness. To illustrate these aspects, we use our technique to automatically synthesize several intricate and non-obvious cryptographic constructions.