Kenji Maillard

Kenji Maillard, Catalin Hritcu, Exequiel Rivas et al.

We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an algebraic presentation of relational specifications as a class of relative monads, and link computations and specifications by introducing relational effect observations, which map pairs of monadic computations to relational specifications in a way that respects the algebraic structure. For an arbitrary relational effect observation, we generically define the core of a sound relational program logic, and explain how to complete it to a full-fledged logic for the monadic effect at hand. We show that this generic framework can be used to define relational program logics for effects as diverse as state, input-output, nondeterminism, and discrete probabilities. We, moreover, show that by instantiating our framework with state and unbounded iteration we can embed a variant of Benton's Relational Hoare Logic, and also sketch how to reconstruct Relational Hoare Type Theory. Finally, we identify and overcome conceptual challenges that prevented previous relational program logics from properly dealing with control effects, and are the first to provide a relational program logic for exceptions.

Danel Ahman, Cédric Fournet, Catalin Hritcu et al.

We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonic-state monad, a general yet compact interface for Hoare-style reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonic-state monad and use it as a unified foundation for reasoning about monotonic state in the F* verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications.

Niklas Grimm, Kenji Maillard, Cédric Fournet et al.

Relational properties describe multiple runs of one or more programs. They characterize many useful notions of security, program refinement, and equivalence for programs with diverse computational effects, and they have received much attention in the recent literature. Rather than developing separate tools for special classes of effects and relational properties, we advocate using a general purpose proof assistant as a unifying framework for the relational verification of effectful programs. The essence of our approach is to model effectful computations using monads and to prove relational properties on their monadic representations, making the most of existing support for reasoning about pure programs. We apply this method in F* and evaluate it by encoding a variety of relational program analyses, including information flow control, program equivalence and refinement at higher order, correctness of program optimizations and game-based cryptographic security. By relying on SMT-based automation, unary weakest preconditions, user-defined effects, and monadic reification, we show that, compared to unary properties, verifying relational properties requires little additional effort from the F* programmer.