A Decidable Logic for Tree Data-Structures with Measurements

Qiu, Xiaokang; Wang, Yanjun

doi:10.1007/978-3-030-11245-5_15

Cited by 4 publications

(4 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a rich line of work in automating such reasoning within decidable fragments (e.g. [2,12,18,22,33,35]). However, recursive definitions are problematic for handling e.g.…”

Section: Related Workmentioning

confidence: 99%

Local Reasoning for Global Graph Properties

Krishna

Summers

Wies

2020

Programming Languages and Systems

View full text Add to dashboard Cite

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 over program heaps, in a way which can be 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. S. Krishna et al. 1 method acquire(p: Node, r: Node) { 2 if (r.next == null) { 3 r.next := p; update(p, -1, r.curr_prio) 4 } else { 5 p.next := r; update(r, -1, p.curr_prio) 6 } 7 } 8 method update(n: Node, from: Int, to: Int) { 9 n.prios := n.prios \ {from} 10 if (to >= 0) n.prios := n.prios ∪ {to} 11 from := n.curr_prio 12 n.curr_prio := max(n.prios ∪ {n.def_prio}) 13 to := n.curr_prio; 14 if (from != to && n.next != null) { 15 update(n.next, from, to) 16 } 17 }

show abstract

“…There is a rich line of work in automating such reasoning within decidable fragments (e.g. [2,12,18,22,33,35]). However, recursive definitions are problematic for handling e.g.…”

Section: Related Workmentioning

confidence: 99%

Local Reasoning for Global Graph Properties

Krishna

Summers

Wies

2020

Programming Languages and Systems

View full text Add to dashboard Cite

show abstract

“…Unbounded footprints have been encountered early on when computing the post image for recursive predicates [8]. This has spawned interest in separation logic fragments for which the reasoning can be efficiently automated [2,3,9,17,20,35,38]. A limitation that underlies all these works is an assumption of tree-regularity of the heap, in one way or another, which flows have been designed to overcome.…”

Section: Related Workmentioning

confidence: 99%

Make Flows Small Again: Revisiting the Flow Framework

Meyer

Wies

Wolff

2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows, rules out vanishing flows, and has an easy to understand notion of footprint as needed for soundness of the frame rule. In addition, we present algorithms for automating the frame rule, which we evaluate on graph updates extracted from linearizability proofs for concurrent data structures. The evaluation demonstrates that our algorithms help to automate key aspects of these proofs that have previously relied on user guidance or heuristics.

show abstract

“…Qiu and Wang [16] implemented a decidable fragment of the Dryad logic for reasoning about trees. Dryad dec is especially suited to analysing tree traversals which calculate some measurement of the tree.…”

Section: Fusing Tree Traversalsmentioning

confidence: 99%

“…Relying solely on developer intuition and testing leaves room for problematic corner cases to slip through the net. In most work on fusing tree traversals, soundness is formally proved, yielding stronger correctness guarantees [9,10,[16][17][18][19]. However, there are two factors that prevent the solutions proposed in such related work being directly useful in the case of miniphase-style fusion.…”

mentioning

confidence: 99%

Postcondition-preserving fusion of postorder tree transformations

Davies

Kalvala

2020

Proceedings of the 29th International Conference on Compiler Construction

View full text Add to dashboard Cite

Tree transformations are common in applications such as program rewriting in compilers. Using a series of simple transformations to build a more complex system can make the resulting software easier to understand, maintain, and reason about. Fusion strategies for combining such successive tree transformations promote this modularity, whilst mitigating the performance impact from increased numbers of tree traversals. However, it is important to ensure that fused transformations still perform their intended tasks. Existing approaches to fusing tree transformations tend to take an informal approach to soundness, or be too restrictive to consider the kind of transformations needed in a compiler. We use postconditions to define a more useful formal notion of successful fusion, namely postcondition-preserving fusion. We also present criteria that are sufficient to ensure postcondition-preservation and facilitate modular reasoning about the success of fusion. CCS Concepts • Software and its engineering → Compilers; • Theory of computation → Program reasoning.

show abstract

A Decidable Logic for Tree Data-Structures with Measurements

Cited by 4 publications

References 54 publications

Local Reasoning for Global Graph Properties

Local Reasoning for Global Graph Properties

Make Flows Small Again: Revisiting the Flow Framework

Postcondition-preserving fusion of postorder tree transformations

Contact Info

Product

Resources

About