Matching logic

Roşu, Grigore; Ștefănescu, Andrei

doi:10.1145/1985793.1985928

Cited by 43 publications

(53 citation statements)

References 57 publications

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“…The results proved in Section 4 allow the transfer of results between many-sorted hybrid modal logic and Matching logic. Note that, both in this paper, as well as in [6,12], there are two pairs of systems we can consider, the connection being stated by Theorem 30 and Theorem 31: H Σ (@ z , ∀) is related to Matching logic with Definedness [12], while H Σ (∀) is related to Matching logic without Definedness [6].…”

Section: Discussionmentioning

confidence: 96%

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From Hybrid Modal Logic to Matching Logic and Back

Leustean

Moanga

Şerbănuţă

2019

Electron. Proc. Theor. Comput. Sci.

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Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two approaches, which should benefit both systems. * All authors contributed equally to this work. 1 Note that Matching logic was further developed in [6], where techniques from modal logic are employed for the theoretical development. s = φ for any w ∈ W s ; in this case we write M | s = φ . The deductive system of H Σ is recalled in 1 and the completeness theorem is proved in [9]. The hybridization of our many-sorted modal logic is developed using a combination of ideas and techniques from [1,2,3,5,7,8], but for this section we drew our inspiration mainly form [3]. We refer to [10] for some similar proofs of the results presented in this section.Hybrid logic is defined on top of modal logic by adding nominals, states variables and specific operators and binders. Nominals allow us to directly refer the worlds (states) of a model, since they are evaluated in singletons in any model. However, a nominal may refer different worlds in different models. The sorts will be denoted by s, t, . . . and by PROP = {PROP s } s∈S , NOM = {NOM s } s∈S and SVAR = {SVAR s } s∈S we will denote some countable S-sorted sets. The elements of PROP are ordinary propositional variables and they will be denoted p, q,. . .; the elements of NOM are called nominals and they will be denoted by j, k, . . .; the elements of SVAR are called state variables and they are denoted x, y, . . .. We shall assume that for any distinct sorts s = t ∈ S, the corresponding sets of propositional variables, nominals and state variables are distinct. A state symbol is a nominal or a state variable.Definition 1 (H Σ (∀) formulas). For any s ∈ S we define the formulas of sort s: φ s := p | j | y s | ¬φ s | φ s ∨ φ s | σ (φ s 1 , . . . , φ s n ) s | ∀x t φ s

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Section: Discussionmentioning

confidence: 96%

“…Our research was inspired by Matching logic [12] which made some connections with modal logic 1 . Nevertheless, while the system we proposed in [10] was strong enough for performing specification and formal verification, its connection with Matching logic, its original motivation, was still to be established.…”

Section: Introductionmentioning

confidence: 99%

From Hybrid Modal Logic to Matching Logic and Back

Leustean

Moanga

Şerbănuţă

2019

Electron. Proc. Theor. Comput. Sci.

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“…Moreover, rl is built on top of Matching Logic (ml), which also exists in several versions [38,39,40]. (The situation is somewhat similar to the relationship between rewriting logic and the equational logics underneath it.)…”

Section: Reachability Logic ( Rl)mentioning

confidence: 99%

Executing and verifying higher-order functional-imperative programs in Maude

Rusu¹,

Arusoaie²

2017

Journal of Logical and Algebraic Methods in Programming

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We incorporate higher-order functions and state monads in Maude, thereby embedding a higher-order functional language with imperative features in the Maude framework. We illustrate, via simple programs in the resulting language: the concrete and symbolic execution of programs; their verification with respect to properties expressed in Reachability Logic, a languageparametric generalisation of Hoare Logic; and the verification of programequivalence properties. Our approach is proved sound and is implemented in Full Maude by taking advantage of its reflective features and module system.

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“…The main idea is to define a general logical system that is powerful enough to represent both the programs and their semantics in a uniform way. With respect to this, we follow the line of [13] and the recent work from [20]. 1 The logical system that we developed as support for our approach is a manysorted hybrid polyadic modal logic, built upon our general many-sorted polyadic modal logic defined in [17].…”

Section: Introductionmentioning

confidence: 99%

Operational Semantics and Program Verification Using Many-Sorted Hybrid Modal Logic

Leustean

Moanga

Şerbănuţă

2019

Lecture Notes in Computer Science

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We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal logic, for which we prove completeness results. We believe that our approach to program verification improves over the existing approaches within modal logic as (1) it is based on operational semantics which allows for a more natural description of the execution than Hoare's style weakest precondition used by dynamic logic; (2) being multi-sorted, it allows for a clearer encoding of semantics, with a smaller representational distance to its intended meaning.

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Matching logic

Cited by 43 publications

References 57 publications

From Hybrid Modal Logic to Matching Logic and Back

From Hybrid Modal Logic to Matching Logic and Back

Executing and verifying higher-order functional-imperative programs in Maude

Operational Semantics and Program Verification Using Many-Sorted Hybrid Modal Logic

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