Cartesian Reachability Logic: A Language-parametric Logic for Verifying k-Safety Properties

52 pages•Published: June 3, 2023

Jan Tušil, Traian Serbanuta and Jan Obdrzalek

Abstract

We introduce a language-parametric calculus for k-safety verification - Cartesian Reach- ability logic (CRL).
In recent years, formal verification of hyperproperties has become an important topic in the formal methods community. An interesting class of hyperproperties is known as k-safety properties, which express the absence of a bad k-tuple of execution traces. Many security policies, such as noninterference, and functional properties, such as commutativity, monotonicity, and transitivity, are k-safety properties. A prominent example of a logic that can reason about k-safety properties of software systems is Cartesian Hoare logic (CHL). However, CHL targets a specific, small imperative language. In order to use it for sound verification of programs in a different language, one needs to extend it with the desired features or hand-craft a translation. Both these approaches require a lot of tedious, error- prone work.
Unlike CHL, CRL is language-parametric: it can be instantiated with an operational semantics (of a certain kind) of any deterministic language. Its soundness theorem is proved once and for all, with no need to adapt or re-prove it for different languages or their variants. This approach can significantly reduce the development costs of tools and techniques for sound k-safety verification of programs in deterministic languages: for exam- ple, of smart contracts written for EVM (the language powering the Ethereum blockchain), which already has an operational semantics serving as a reference.

Keyphrases: hyperproperties, k safety, language parametric, logic

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 405-456.

Links:	https://easychair.org/publications/paper/8vTf
	https://doi.org/10.29007/1874

BibTeX entry

@inproceedings{LPAR2023:Cartesian_Reachability_Logic_Language,
  author    = {Jan Tušil and Traian Serbanuta and Jan Obdrzalek},
  title     = {Cartesian Reachability Logic: A Language-parametric Logic for Verifying k-Safety Properties},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/8vTf},
  doi       = {10.29007/1874},
  pages     = {405-456},
  year      = {2023}}

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