Certified Refinement Types

Refinement types are a type-based, static verification technique designed to be practical. They enrich the types of an existing programming language with logical predicates to specify program properties and automatically validate these specifications using SMT solvers. Refinement types are a promising verification technology that in the last decade has spread to mainstream languages (e.g., Haskell, C, Ruby, Scala, and the ML-family) to verify sophisticated properties of real world applications, e.g., safety of cryptographic protocols, memory and resource usage, and web security. The weakness of refinement types is that they do not meet the soundness standards set by theorem provers. A sound verification system accepts as safe only those programs that never violate their specifications. Refinement type checkers (e.g., Liquid Haskell, F*, and Stainless) approximately report five unsoundness bugs per year, as opposed to only one reported by the Coq theorem prover. This rarity of unsoundness bugs in Coq is unsurprising since Coq is designed to soundly machine check mathematical proofs. Coq's soundness design recipe though cannot be directly applied to refinement type checkers that aim to practically verify real world programs. The goal of CRETE is to design a sound and practical refinement type system.This is an ambitious goal that entails the development of a verification system that is as practical as refinement types and constructs machine-checked mathematical proofs. The system will be implemented on refinement type systems for mainstream languages (i.e., Haskell and Rust) and will be evaluated on real-world code, such as web applications and cryptographic protocols. CRETE is high-risk since it aims to develop a novel program logic in which SMT automation co-exists with real world programming. Yet, CRETE is high-gain since it proposes a low-cost, high-profit approach to formal verification that aims to be integrated in mainstream software development.