A Monadic Approach to Relational Verification:
Applied to Information Security, Program Equivalence, and Optimizations

Niklas Grimm (Logics and Computation, Vienna University of Technology, Vienna, Austria)
Kenji Maillard (Prosecco, INRIA, Paris, France)
Cédric Fournet (Programming Principles and Tools, Microsoft Research, Cambridge, United Kingdom)
Catalin Hritcu (Prosecco)
Matteo Maffei (Logics and Computation, Vienna UT)
Jonathan Protzenko (RiSE: Research in Software Engineering, Microsoft Research, Redmond, WA, USA)
Tahina Ramananandro (RiSE)
Aseem Rastogi (Microsoft Research, Bengaluru, Karnataka, India)
Nikhil Swamy (RiSE)
Santiago Zanella-Béguelin (Programming Principles and Tools)

CPP 2018

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, semantic declassification, program equivalence and refinement at higher order, correctness of program optimizations. 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.