## Abstract

Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a region do not invalidate properties stated about the remainder of the heap. This concept is key to enabling modular reasoning and also extends to concurrency. While heaps are naturally related to mathematical graphs, many ubiquitous graph properties are non-local in character, such as reachability between nodes, path lengths, acyclicity and other structural invariants, as well as data invariants which combine with these notions. Reasoning modularly about such graph properties remains notoriously difficult, since a local modification can have side-effects on a global property that cannot be easily confined to a small region. In this paper, we address the question: What separation algebra can be used to avoid proof arguments reverting back to tedious global reasoning in such cases? To this end, we consider a general class of global graph properties expressed as fixpoints of algebraic equations over graphs. We present mathematical foundations for reasoning about this class of properties, imposing minimal requirements on the underlying theory that allow us to define a suitable separation algebra. Building on this theory, we develop a general proof technique for modular reasoning about global graph properties expressed over program heaps, in a way which can be directly integrated with existing separation logics. To demonstrate our approach, we present local proofs for two challenging examples: a priority inheritance protocol and the non-blocking concurrent Harris list.

Original language | English (US) |
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Title of host publication | Programming Languages and Systems- 29th European Symposium on Programming, ESOP 2020 held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Proceedings |

Editors | Peter Müller |

Publisher | Springer |

Pages | 308-335 |

Number of pages | 28 |

ISBN (Print) | 9783030449131 |

DOIs | |

State | Published - 2020 |

Event | 29th European Symposium on Programming, ESOP 2020, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020 - Dublin, Ireland Duration: Apr 25 2020 → Apr 30 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12075 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 29th European Symposium on Programming, ESOP 2020, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020 |
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Country/Territory | Ireland |

City | Dublin |

Period | 4/25/20 → 4/30/20 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science