Towards a unified proof framework for automated fixpoint reasoning using matching logic

Chen, Xiaohong; Trinh, Minh-Thai; Rodrigues, Nishant; Peña, Lucas; Roşu, Grigore

doi:10.1145/3428229

Cited by 8 publications

(8 citation statements)

References 71 publications

(73 reference statements)

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“…A proof system based on coinduction (i.e. forward reasoning) that generalizes loop verification to any recurring program locations is [15], a similar approach to tackle interleavings in concurrency is [52]. Brotherston [10] takes a similar route to construct cyclic proofs, implicitly making use of induction.…”

Section: Related Workmentioning

confidence: 99%

A Complete Approach to Loop Verification with Invariants and Summaries

Ernst¹

2020

Preprint

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Loop invariants characterize the partial result computed by a loop so far up to an intermediate state. It has been noted, however, that complementing invariants by summaries, which characterize the remaining iterations of a loop, can often lead to simpler correctness proofs. In this paper, we derive sound verification conditions for this approach, and moreover characterize completeness relative to a class of "safe" invariants, alongside with fundamental and novel insights in the relation between invariants and summaries. All theoretical results have immediate practical consequences for tool use and construction. Summaries should therefore be regarded as a principal alternative to invariants. To substantiate this claim experimentally, we evaluate the automation potential using stateof-the-art Horn solvers, which shows that the the proposed approach is competitive, even without specialized solving strategies.

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Section: Related Workmentioning

confidence: 99%

A Complete Approach to Loop Verification with Invariants and Summaries

Ernst¹

2020

Preprint

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“…Matching logic [8,9,11,35] is a relatively new logical formalism used for both specifying and proving logical systems and properties of logics by means of patterns and pattern matching. Matching logic admits a sound proof system, and many important theories have already been defined as matching logic theories, including separation logic with recursive definitions [14,15], linear-temporal logic [11,33], and reachability logic [11,37] for semantics-based formal verification.…”

Section: Introductionmentioning

confidence: 99%

Mechanizing Matching Logic In Coq

Bereczky,

Chen,

Horpácsi

et al. 2022

Preprint

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Matching logic is a formalism for specifying and reasoning about structures using patterns and pattern matching. Growing in popularity, matching logic has been used to define many logical systems such as separation logic with recursive definitions and linear-temporal logic. Despite this, there is no way for a user to define his or her own matching logic theories using a theorem prover, with maximal assurance of the properties being proved. Hence, in this work, we formalized a version of matching logic using the Coq proof assistant. Specifically, we create a new version of matching logic that uses a locally nameless representation, where quantified variables are unnamed in order to aid verification. We formalize the syntax, semantics, and proof system of this representation of matching logic using the Coq proof assistant. Crucially, we also verify the soundness of the formalized proof system, thereby guaranteeing that any matching logic properties proved in our Coq formalization are indeed correct. We believe this work provides a previously unexplored avenue for defining and proving matching logic theories and properties.

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“…So far, the authors of [9] focused on formalising program executions as mathematical proofs and generating their corresponding proof objects. This required the development of a proof generator which uses an improved proof system of ML [16], and a proof checker implementation in Metamath [27]. The K definition of a language L corresponds to a ML theory Γ L which consists of a set of symbols (that represents the formal syntax of L) and a set of axioms (that specify the formal semantics of L).…”

Section: Introductionmentioning

confidence: 99%

Proof-Carrying Parameters in Certified Symbolic Execution: The Case Study of Antiunification

Arusoaie,

Lucanu

2021

Preprint

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Unification and antiunification are essential algorithms used by symbolic execution engines and verification tools. Complex frameworks for defining programming languages, such as K, aim to generate various tools (e.g., interpreters, symbolic execution engines, deductive verifiers, etc.) using only the formal definition of a language. K is the best effort implementation of matching logic, a logical framework for defining languages. When used at an industrial scale, a tool like the K framework is constantly updated, and in the same time it is required to be trustworthy. Ensuring the correctness of such a framework is practically impossible. A solution is to generate proof objects as correctness certificates that can be checked by an external trusted checker. In K, symbolic execution makes intensive use of unification and antiunification algorithms to handle conjunctions and disjunctions of term patterns. Conjunctions and disjunctions of formulae have to be automatically normalised and the generation of proof objects needs to take such normalisations into account. The executions of these algorithms can be seen as parameters of the symbolic execution steps and they have to provide proof objects that are used then to generate the proof object for the program execution step. We show in this paper that Plotkin's antiunification can be used to normalise disjunctions and to generate the corresponding proof objects. We provide a prototype implementation of our proof object generation technique and a checker for certifying the generated objects.

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Towards a unified proof framework for automated fixpoint reasoning using matching logic

Cited by 8 publications

References 71 publications

A Complete Approach to Loop Verification with Invariants and Summaries

A Complete Approach to Loop Verification with Invariants and Summaries

Mechanizing Matching Logic In Coq

Proof-Carrying Parameters in Certified Symbolic Execution: The Case Study of Antiunification

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