Recalling a Witness

Recalling a Witness

Foundations and Applications of Monotonic State

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Danel Ahman1,2    Cătălin Hriţcu2    Cedric Fournet1   
Kenji Maillard2,3    Aseem Rastogi1    Nikhil Swamy1

1Microsoft Research    2Inria Paris    3ENS Paris   

Symposium on Principles of Programming Languages, POPL 2018


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.