Certified Refinement Types

Introduction

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.

Adoption of Refinement Types

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, such as:

• Safety of cryptographic protocols
• Memory and resource usage
• Web security

Limitations of Refinement Types

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.

Challenges in Applying Coq's Design

Coq's soundness design recipe, however, cannot be directly applied to refinement type checkers that aim to practically verify real-world programs.

Project Goal

The goal of CRETE is to design a sound and practical refinement type system.

Ambitious Objectives

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.

Risk and Reward

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 into mainstream software development.