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Journal articles on the topic 'Coq formalization'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Boender, Jaap, Florian Kammüller, and Rajagopal Nagarajan. "Formalization of Quantum Protocols using Coq." Electronic Proceedings in Theoretical Computer Science 195 (November 4, 2015): 71–83. http://dx.doi.org/10.4204/eptcs.195.6.

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Cogumbreiro, Tiago, Jun Shirako, and Vivek Sarkar. "Formalization of Habanero phasers using Coq." Journal of Logical and Algebraic Methods in Programming 90 (August 2017): 50–60. http://dx.doi.org/10.1016/j.jlamp.2017.02.006.

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Cogumbreiro, Tiago, Jun Shirako, and Vivek Sarkar. "Formalization of Habanero phasers using Coq." Journal of Logical and Algebraic Methods in Programming 90 (August 1, 2017): 50–60. https://doi.org/10.1016/j.jlamp.2017.02.006.

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Phasers pose an interesting synchronization mechanism that generalizes many collective synchronization patterns seen in parallel programming languages, including barriers, clocks, and point-to-point synchronization using latches or semaphores. This work characterizes scheduling constraints on phaser operations, by relating the execution state of two tasks that operate on the same phaser. We propose a formalization of Habanero phasers, May-Happen-In-Parallel, and Happens-Before relations for phaser operations, and show that these relations conform with the semantics. Our formalization and proof

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Cohen, Joshua M., and Philip Johnson-Freyd. "A Formalization of Core Why3 in Coq." Proceedings of the ACM on Programming Languages 8, POPL (2024): 1789–818. http://dx.doi.org/10.1145/3632902.

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Intermediate verification languages like Why3 and Boogie have made it much easier to build program verifiers, transforming the process into a logic compilation problem rather than a proof automation one. Why3 in particular implements a rich logic for program specification with polymorphism, algebraic data types, recursive functions and predicates, and inductive predicates; it translates this logic to over a dozen solvers and proof assistants. Accordingly, it serves as a backend for many tools, including Frama-C, EasyCrypt, and GNATProve for Ada SPARK. But how can we be sure that these tools ar

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BOLDO, SYLVIE, CATHERINE LELAY, and GUILLAUME MELQUIOND. "Formalization of real analysis: a survey of proof assistants and libraries." Mathematical Structures in Computer Science 26, no. 7 (2015): 1196–233. http://dx.doi.org/10.1017/s0960129514000437.

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In the recent years, numerous proof systems have improved enough to be used for formally verifying non-trivial mathematical results. They, however, have different purposes and it is not always easy to choose which one is adapted to undertake a formalization effort. In this survey, we focus on properties related to real analysis: real numbers, arithmetic operators, limits, differentiability, integrability and so on. We have chosen to look into the formalizations provided in standard by the following systems: Coq, HOL4, HOL Light, Isabelle/HOL, Mizar, ProofPower-HOL, and PVS. We have also accoun

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PELAYO, ÁLVARO, VLADIMIR VOEVODSKY, and MICHAEL A. WARREN. "A univalent formalization of the p-adic numbers." Mathematical Structures in Computer Science 25, no. 5 (2015): 1147–71. http://dx.doi.org/10.1017/s0960129514000541.

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The goal of this paper is to report on a formalization of the p-adic numbers in the setting of the second author's univalent foundations program. This formalization, which has been verified in the Coq proof assistant, provides an approach to the p-adic numbers in constructive algebra and analysis.

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Rauber Du Bois, André, Rodrigo Ribeiro, and Maycon Amaro. "A Mechanized Proof of a Textbook Type Unification Algorithm." Revista de Informática Teórica e Aplicada 27, no. 3 (2020): 13–24. http://dx.doi.org/10.22456/2175-2745.100968.

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Unification is the core of type inference algorithms for modern functional programming languages, like Haskell and SML. As a first step towards a formalization of a type inference algorithm for such programming languages, we present a formalization in Coq of a type unification algorithm that follows classic algorithms presented in programming language textbooks. We also report on the use of such formalization to build a correct type inference algorithm for the simply typed λ-calculus.

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Xu, Yichi, Daniel J. Dougherty, and Rose Bohrer. "A Coq Formalization of Unification Modulo Exclusive-Or." Electronic Proceedings in Theoretical Computer Science 416 (February 11, 2025): 267–73. https://doi.org/10.4204/eptcs.416.23.

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VOEVODSKY, VLADIMIR. "An experimental library of formalized Mathematics based on the univalent foundations." Mathematical Structures in Computer Science 25, no. 5 (2015): 1278–94. http://dx.doi.org/10.1017/s0960129514000577.

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This is a short overview of an experimental library of Mathematics formalized in the Coq proof assistant using the univalent interpretation of the underlying type theory of Coq. I started to work on this library in February 2010 in order to gain experience with formalization of Mathematics in a constructive type theory based on the intuition gained from the univalent models (see Kapulkin et al. 2012).

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Fu, Yaoshun, and Wensheng Yu. "Formalizing Calculus without Limit Theory in Coq." Mathematics 9, no. 12 (2021): 1377. http://dx.doi.org/10.3390/math9121377.

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Formal verification of mathematical theory has received widespread concern and grown rapidly. The formalization of the fundamental theory will contribute to the development of large projects. In this paper, we present the formalization in Coq of calculus without limit theory. The theory aims to found a new form of calculus more easily but rigorously. This theory as an innovation differs from traditional calculus but is equivalent and more comprehensible. First, the definition of the difference-quotient control function is given intuitively from the physical facts. Further, conditions are added

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Boldo, Sylvie, François Clément, Florian Faissole, Vincent Martin, and Micaela Mayero. "A Coq Formalization of Lebesgue Integration of Nonnegative Functions." Journal of Automated Reasoning 66, no. 2 (2021): 175–213. http://dx.doi.org/10.1007/s10817-021-09612-0.

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Koprowski, Adam. "Coq formalization of the higher-order recursive path ordering." Applicable Algebra in Engineering, Communication and Computing 20, no. 5-6 (2009): 379–425. http://dx.doi.org/10.1007/s00200-009-0105-5.

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Wan, Xinyi, Ke Xu, and Qinxiang Cao. "Coq Formalization of ZFC Set Theory for Teaching Scenarios." International Journal of Software and Informatics 13, no. 3 (2023): 323–57. http://dx.doi.org/10.21655/ijsi.1673-7288.00303.

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Fu, Yaoshun, and Wensheng Yu. "Formalization of the Equivalence among Completeness Theorems of Real Number in Coq." Mathematics 9, no. 1 (2020): 38. http://dx.doi.org/10.3390/math9010038.

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The formalization of mathematics based on theorem prover becomes increasingly important in mathematics and computer science, and, particularly, formalizing fundamental mathematical theories becomes especially essential. In this paper, we describe the formalization in Coq of eight very representative completeness theorems of real numbers. These theorems include the Dedekind fundamental theorem, Supremum theorem, Monotone convergence theorem, Nested interval theorem, Finite cover theorem, Accumulation point theorem, Sequential compactness theorem, and Cauchy completeness theorem. We formalize th

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Chen, Gang. "Formalization of a Parameterized Parallel Adder Within the Coq Theorem Prover." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 29, no. 1 (2010): 149–53. http://dx.doi.org/10.1109/tcad.2009.2034346.

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Guo, Dakai, and Wensheng Yu. "A Comprehensive Formalization of Propositional Logic in Coq: Deduction Systems, Meta-Theorems, and Automation Tactics." Mathematics 11, no. 11 (2023): 2504. http://dx.doi.org/10.3390/math11112504.

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The increasing significance of theorem proving-based formalization in mathematics and computer science highlights the necessity for formalizing foundational mathematical theories. In this work, we employ the Coq interactive theorem prover to methodically formalize the language, semantics, and syntax of propositional logic, a fundamental aspect of mathematical reasoning and proof construction. We construct four Hilbert-style axiom systems and a natural deduction system for propositional logic, and establish their equivalences through meticulous proofs. Moreover, we provide formal proofs for ess

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Benzaken, Véronique, Évelyne Contejean, Mohammed Houssem Hachmaoui, et al. "Translating canonical SQL to imperative code in Coq." Proceedings of the ACM on Programming Languages 6, OOPSLA1 (2022): 1–27. http://dx.doi.org/10.1145/3527327.

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SQL is by far the most widely used and implemented query language. Yet, on some key features, such as correlated queries and NULL value semantics, many implementations diverge or contain bugs. We leverage recent advances in the formalization of SQL and query compilers to develop DBCert, the first mechanically verified compiler from SQL queries written in a canonical form to imperative code. Building DBCert required several new contributions which are described in this paper. First, we specify and mechanize a complete translation from SQL to the Nested Relational Algebra which can be used for q

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Endou, Noboru. "Antiderivatives and Integration." Formalized Mathematics 31, no. 1 (2023): 131–41. http://dx.doi.org/10.2478/forma-2023-0012.

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Summary In this paper, we introduce indefinite integrals [8] (antiderivatives) and proof integration by substitution in the Mizar system [2], [3]. In our previous article [15], we have introduced an indefinite-like integral, but it is inadequate because it must be an integral over the whole set of real numbers and in some sense it causes some duplication in the Mizar Mathematical Library [13]. For this reason, to define the antiderivative for a function, we use the derivative of an arbitrary interval as defined recently in [7]. Furthermore, antiderivatives are also used to modify the integrati

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Danvy, Olivier. "Getting There and Back Again." Fundamenta Informaticae 185, no. 2 (2022): 115–83. http://dx.doi.org/10.3233/fi-222106.

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“There and Back Again” (TABA) is a programming pattern where the recursive calls traverse one data structure and the subsequent returns traverse another. This article presents new TABA examples, refines existing ones, and formalizes both their control flow and their data flow using the Coq Proof Assistant. Each formalization mechanizes a pen-and-paper proof, thus making it easier to “get” TABA. In addition, this article identifies and illustrates a tail-recursive variant of TABA, There and Forth Again (TAFA) that does not come back but goes forth instead with more tail calls.

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Courtieu, Pierre, Maria Virginia Aponte, Tristan Crolard, et al. "Towards the formalization of SPARK 2014 semantics with explicit run-time checks using coq." ACM SIGAda Ada Letters 33, no. 3 (2013): 21–22. http://dx.doi.org/10.1145/2658982.2527278.

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GOTO, MATTHEW, RADHA JAGADEESAN, ALAN JEFFREY, CORIN PITCHER, and JAMES RIELY. "An extensible approach to session polymorphism." Mathematical Structures in Computer Science 26, no. 3 (2015): 465–509. http://dx.doi.org/10.1017/s0960129514000231.

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Session types describe and constrain the input/output behaviour of systems. Existing session typing systems have limited support for polymorphism. For example, existing systems cannot provide the most general type for a generic proxy process that forwards messages between two channels. We provide a polymorphic session typing system for the π calculus, and demonstrate the utility of session-type-level functions in combination with polymorphic session typing. The type system guarantees subject reduction and safety properties, but not deadlock freedom. We describe a formalization of the type syst

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Yan, Sheng, and Wensheng Yu. "Formal Verification of a Topological Spatial Relations Model for Geographic Information Systems in Coq." Mathematics 11, no. 5 (2023): 1079. http://dx.doi.org/10.3390/math11051079.

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Geographic information systems have undergone rapid growth for decades. Topology has provided valuable modeling tools in the development of this field. Formal verification of the model of topological spatial relations can provide a reliable guarantee for the correctness of geographic information systems. We present a proof of the topological spatial relations model that has been formally verified in the Coq proof assistant. After an introduction to the formalization of the axiomatic set theory of Morse--Kelley, the formal description of the elementary concepts and properties of general topolog

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RAHLI, VINCENT, and MARK BICKFORD. "Validating Brouwer's continuity principle for numbers using named exceptions." Mathematical Structures in Computer Science 28, no. 6 (2017): 942–90. http://dx.doi.org/10.1017/s0960129517000172.

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This paper extends the Nuprl proof assistant (a system representative of the class of extensional type theories with dependent types) withnamed exceptionsandhandlers, as well as a nominalfreshoperator. Using these new features, we prove a version of Brouwer's continuity principle for numbers. We also provide a simpler proof of a weaker version of this principle that only uses diverging terms. We prove these two principles in Nuprl's metatheory using our formalization of Nuprl in Coq and reflect these metatheoretical results in the Nuprl theory as derivation rules. We also show that these addit

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Tan, Jinhao, and Bruno C. d. S. Oliveira. "A Case for First-Class Environments." Proceedings of the ACM on Programming Languages 8, OOPSLA2 (2024): 2521–50. http://dx.doi.org/10.1145/3689800.

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Formalizations of programming languages typically adopt the substitution model from the lambda calculus. However, substitution creates notorious complications for reasoning and implementation. Furthermore, it is disconnected from practical implementations, which normally adopt environments and closures. In this paper we advocate for formalizing programming languages using a novel style of small-step environment-based semantics , which avoids substitution and is closer to implementations. We present a call-by-value statically typed calculus, called λ E , using our small-step environment semanti

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Muller, Jean-Michel, and Laurence Rideau. "Formalization of Double-Word Arithmetic, and Comments on “Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic”." ACM Transactions on Mathematical Software 48, no. 1 (2022): 1–24. http://dx.doi.org/10.1145/3484514.

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Recently, a complete set of algorithms for manipulating double-word numbers (some classical, some new) was analyzed [ 16 ]. We have formally proven all the theorems given in that article, using the Coq proof assistant. The formal proof work led us to: (i) locate mistakes in some of the original paper proofs (mistakes that, however, do not hinder the validity of the algorithms), (ii) significantly improve some error bounds, and (iii) generalize some results by showing that they are still valid if we slightly change the rounding mode. The consequence is that the algorithms presented in [ 16 ] ca

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BOVE, ANA, ALEXANDER KRAUSS, and MATTHIEU SOZEAU. "Partiality and recursion in interactive theorem provers – an overview." Mathematical Structures in Computer Science 26, no. 1 (2014): 38–88. http://dx.doi.org/10.1017/s0960129514000115.

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The use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalizing mathematics is becoming more common and feasible in practice. However, most mature theorem provers lack a direct treatment of partial and general recursive functions; overcoming this weakness has been the objective of intensive research during the last decades. In this article, we review several techniques that have been proposed in the literature to simplify the formalization of partial and general recursive functions in interactive theorem provers. Moreover, we c

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RÖCKL, CHRISTINE, та DANIEL HIRSCHKOFF. "A fully adequate shallow embedding of the π-calculus in Isabelle/HOL with mechanized syntax analysis". Journal of Functional Programming 13, № 2 (2003): 415–51. http://dx.doi.org/10.1017/s0956796802004653.

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This paper discusses an application of the higher-order abstract syntax technique to general-purpose theorem proving, yielding shallow embeddings of the binders of formalized languages. Higher-order abstract syntax has been applied with success in specialized logical frameworks which satisfy a closed-world assumption. As more general environments (like Isabelle/HOL or Coq) do not support this closed-world assumption, higher-order abstract syntax may yield exotic terms, that is, datatypes may produce more terms than there should actually be in the language. The work at hand demonstrates how suc

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Law, Tony, Delphine Demange, and Sandrine Blazy. "A Mechanized Semantics for Dataflow Circuits." Proceedings of the ACM on Programming Languages 9, OOPSLA1 (2025): 507–33. https://doi.org/10.1145/3720432.

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This paper proposes a mechanized formal semantics for dataflow circuits: rather than following a predetermined, static schedule, the execution of the circuit components is constrained solely by the availability of their input data. We model circuit components as abstract computing units, asynchronously connected with each other through unidirectional, unbounded FIFO. In contrast to Kahn’s classic, denotational semantic framework, our semantics is operational. It intends to reflect Dennis’ dataflow paradigm with firing, while still formalizing the observable behaviors of circuits as channels hi

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Xie, Guojun, Huanhuan Yang, Hao Deng, Zhengpu Shi, and Gang Chen. "Formal Verification of Robot Rotary Kinematics." Electronics 12, no. 2 (2023): 369. http://dx.doi.org/10.3390/electronics12020369.

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With the widespread application of robots in aerospace, medicine, automation, and other fields, their motion safety is essential for the well-being of humans and the accomplishment of vital socially beneficial programs. Conventional robot hardware and software designs mainly rely on experiential knowledge and manual testing to ensure safety, but this fails to cover all possible testing paths and adds risks. Alternatively, formal, mathematically rigorous verifications can provide predictable and reliable guarantees of robot motion safety. To demonstrate the feasibility of this approach, we form

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Coghetto, Roland. "A Case Study of Transporting Urysohn’s Lemma from Topology via Open Sets into Topology via Neighborhoods." Formalized Mathematics 28, no. 3 (2020): 227–37. http://dx.doi.org/10.2478/forma-2020-0020.

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Summary Józef Białas and Yatsuka Nakamura has completely formalized a proof of Urysohn’s lemma in the article [4], in the context of a topological space defined via open sets. In the Mizar Mathematical Library (MML), the topological space is defined in this way by Beata Padlewska and Agata Darmochwał in the article [18]. In [7] the topological space is defined via neighborhoods. It is well known that these definitions are equivalent [5, 6]. In the definitions, an abstract structure (i.e. the article [17, STRUCT 0] and its descendants, all of them directly or indirectly using Mizar structures [

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Wu, Mingguang, Taisheng Chen, Guonian Lv, Menglin Chen, Hong Wang, and Haoyu Sun. "Identification and formalization of knowledge for coloring qualitative geospatial data." Color Research & Application 43, no. 2 (2017): 198–208. http://dx.doi.org/10.1002/col.22183.

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Hamunen, Markus Veli Juhani. "On the grammaticalization of Finnish colorative construction." Constructions and Frames 9, no. 1 (2017): 101–38. http://dx.doi.org/10.1075/cf.9.1.04ham.

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Abstract This paper concentrates on the diachronic development of the so-called Colorative Construction (CoC) in Finnish, a two-verb expression consisting of an A-infinitive and an ideophonically based descriptive (or ‘colorative’) finite verb, e.g. susi juos-ta jolkottele-e [wolf run-inf col-prs.3sg] ‘wolf runs trotting’. The paper combines variationist dialectal data, grammaticalization theory, and Construction Grammar formalization. The detailed diachronic description demonstrates that the development from proto-CoC to modern CoC is the epitome of constructionalization, i.e., a gradual proc

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Nguyễn, Minh Hoàng, and Ly Khánh Đỗ. "Foreign innovation activities and CO2 emissions in Vietnam." Science & Technology Development Journal - Economics - Law and Management 5, no. 2 (2021): 1381–91. http://dx.doi.org/10.32508/stdjelm.v5i2.715.

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Vietnam is an emerging economy, CO2 emissions are a topic of interest to scientists and the Government, and innovation plays a very important role in ensuring sustainable growth. The year 1987 marked the formalization of the inflow of foreign investment into the country, from which the foreign-invested economic sector played an important role in the economic development of Vietnam. However, along with the benefits from foreign investment, there are still some shortcomings and limitations that can cause damage to the environment through CO2 emissions. The purpose of this study is to explore the

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Endou, Noboru. "Differentiation on Interval." Formalized Mathematics 31, no. 1 (2023): 9–21. http://dx.doi.org/10.2478/forma-2023-0002.

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Summary This article generalizes the differential method on intervals, using the Mizar system [2], [3], [12]. Differentiation of real one-variable functions is introduced in Mizar [13], along standard lines (for interesting survey of formalizations of real analysis in various proof-assistants like ACL2 [11], Isabelle/HOL [10], Coq [4], see [5]), but the differentiable interval is restricted to open intervals. However, when considering the relationship with integration [9], since integration is an operation on a closed interval, it would be convenient for differentiation to be able to handle de

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Lai, Ruxin, Xinwei Ma, Fan Zhang, and Yanjie Ji. "Life Cycle Assessment of Free-Floating Bike Sharing on Greenhouse Gas Emissions: A Case Study in Nanjing, China." Applied Sciences 11, no. 23 (2021): 11307. http://dx.doi.org/10.3390/app112311307.

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The free-floating bike sharing (FFBS) system appears in the form of low-carbon transport mode. Life cycle assessment (LCA) is a method to analyze the environmental impact of FFBS but has rarely considered the trip chain if the intermodal transport modes were employed. This paper proposes a mathematical formalization of LCA in response to the trip chain. The environmental benefit of FFBS was analyzed by this method considering the production, use, operation, and disposal phases in Nanjing. An online survey was conducted to analyze the mechanism of modal shift influenced by FFBS. The results sho

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Maliarenko, Olena, Nataliia Ivanenko, and Oleksandr Sudarykov. "Study of the relationship of environmental and energy efficiency indicators at the country level." System Research in Energy 2023, no. 4 (2023): 84–94. http://dx.doi.org/10.15407/srenergy2023.04.084.

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The world community strives to develop methods of assessing the most important factors of environmental impact, as well as to develop mechanisms for its adjustment in order to reduce greenhouse gas emissions to the minimum possible level. Increasing environmental efficiency should simultaneously contribute to increasing energy efficiency, which in turn can contribute to increasing the general living standard. When choosing energy-saving measures in industrial technologies, the primary fuel savings and the economic effect of the implementation of the up-to-date technologies are taken into accou

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Martínez-Rojas, María, Carlos Cano, Jesús Alcalá-Fdez, and José Manuel Soto-Hidalgo. "Interpretable Fuzzy Control for Energy Management in Smart Buildings Using JFML-IoT and IEEE Std 1855-2016." Applied Sciences 15, no. 15 (2025): 8208. https://doi.org/10.3390/app15158208.

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This paper presents an interpretable and modular framework for energy management in smart buildings based on fuzzy logic and the IEEE Std 1855-2016. The proposed system builds upon the JFML-IoT library, enabling the integration and execution of fuzzy rule-based systems on resource-constrained IoT devices using a lightweight and extensible architecture. Unlike conventional data-driven controllers, this approach emphasizes semantic transparency, expert-driven control logic, and compliance with fuzzy markup standards. The system is designed to enhance both operational efficiency and user comfort

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Perevaryukha, A. Yu. "UNIVERSAL METHOD FOR COMPUTATIONAL MODELING OF THRESHOLD PHENOMENON IN THE NONSTEADY BIOLOGICAL PROCESSES." Radio Electronics, Computer Science, Control 1, no. 1 (2021): 78–86. http://dx.doi.org/10.15588/1607-3274-2021-1-8.

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Context. In modern conditions occur abrupt changes in ecosystems. The species composition of Caspian Sea is changing rapidly. The dynamics of populations acquires an extreme character with the development of rapid invasions. The mathematical description of scale transformations requires new modeling methods. Complicated population regimes of changes have features of the threshold phenomenon in process of its development. Objective. We set the goal of computational modeling of practically important scenarios – groups of situations that relate to extreme and transitional dynamics of ecosys

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Sepadi, Maasago Mercy, and Vusumuzi Nkosi. "Health Risk Assessment of Informal Food Vendors: A Comparative Study in Johannesburg, South Africa." International Journal of Environmental Research and Public Health 20, no. 3 (2023): 2736. http://dx.doi.org/10.3390/ijerph20032736.

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According to the best of our knowledge, there are no critical studies to date about associations between the work environment and prevalence of respiratory diseases and their symptoms among urban informal vendors in South Africa. This study followed a risk assessment methodology to assess the risks associated with the occurrence of respiratory health problems among 617 indoor and outdoor market vendors in the inner city of Johannesburg, South Africa. A walkthrough survey using a checklist was conducted in 16 Markets for identification of respiratory risk factors and description of sanitary con

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Vysochyna, Alina, and Yuliia Puhovkina. "Mechanisms of national security post-pandemic recovery." Economic sustainability and business practices 1, no. 2 (2024): 61–67. https://doi.org/10.21272/esbp.2024.4-08.

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The COVID-19 pandemic has necessitated a critical review of pre-pandemic instruments and mechanisms for ensuring national security to identify drivers and inhibitors that determine the sensitivity of social, environmental and economic perspectives of national security to shocks, such as a pandemic. The objective of this study is to identify internal determinants (among individual indicators of economic, social and environmental security) and external drivers and inhibitors (among parameters of good governance) which act as relevant impacts on the resilience of national security of the studied

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AFFELDT, REYNALD, JACQUES GARRIGUE, DAVID NOWAK, and TAKAFUMI SAIKAWA. "A trustful monad for axiomatic reasoning with probability and nondeterminism." Journal of Functional Programming 31 (2021). http://dx.doi.org/10.1017/s0956796821000137.

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Abstract The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with both choices: the geometrically convex monad. This formalization has an immediate application: it provides a model for a monad that implements a nontrivial interface, which allows for proofs by equational reasoning using probabilistic and nondeterministic effects. We explain the technical choices we made to go from the literature to a complete Coq for

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Andrade Guzmán, Jesús Mauricio, and Francisco Hernández Quiroz. "Natural deduction and semantic models of justification logic in the proof assistant Coq." Logic Journal of the IGPL, June 25, 2020. http://dx.doi.org/10.1093/jigpal/jzaa007.

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Abstract The purpose of this paper is to present a formalization of the language, semantics and axiomatization of justification logic in Coq. We present proofs in a natural deduction style derived from the axiomatic approach of justification logic. Additionally, we present possible world semantics in Coq based on Fitting models to formalize the semantic satisfaction of formulas. As an important result, with this implementation, it is possible to give a proof of soundness for $\mathsf{L}\mathsf{P}$ with respect to Fitting models.

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Kupusinac, Aleksandar, and Dusan Malbaski. "Formalization of the General Hoare Logic Laws." TEM Journal, August 29, 2012, 145–50. http://dx.doi.org/10.18421/tem13-03.

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This paper presents a new approach to formalizing the general rules of the Hoare logic. Our way is based on formulas of the first-order predicate logic defined over the abstract state space of a virtual machine, i.e. so-called S-formulas. S-formulas are general tool for analyzing program semantics inasmuch as Hoare triples of total and partial correctness are not more than two S-formulas. The general rules of Hoare logic, such as the laws of consequence, conjunction, disjunction and negation can be derived using axioms and theorems of firstorder predicate logic. Every proof is based on derivin

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AFFELDT, REYNALD, JACQUES GARRIGUE, and TAKAFUMI SAIKAWA. "A practical formalization of monadic equational reasoning in dependent-type theory." Journal of Functional Programming 35 (2025). https://doi.org/10.1017/s0956796824000157.

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Abstract One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly because it is difficult to maintain pencil-and-paper proofs of large examples. We propose a formalization of a hierarchy of effects using monads in the Coq proof assistant that makes monadic equational reasoning practical. Our main idea is to formalize the hierarchy of effects and algebraic laws as interfaces like it is done when formalizing hierarc

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Dimitrantzou, Christina, Evangelos Psomas, and Fotios Vouzas. "The influence of competitive strategy and organizational structure on the cost of quality in food and beverage (F&B) companies." TQM Journal, August 17, 2023. http://dx.doi.org/10.1108/tqm-01-2023-0031.

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PurposeThis study aims at determining the influence of the competitive strategy types and organizational structure dimensions on Cost of Quality (CoQ) in Food and Beverage (F&B) small- and medium-sized enterprises (SMEs).Design/methodology/approachA survey questionnaire was sent to F&B companies in Greece and 307 responded positively and fully completed the questionnaire. The research model developed (consisting of the competitive strategy types, the organizational structure dimensions and CoQ) was tested using the exploratory and confirmatory factor analyses and the structural equatio

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Herbelin, Hugo, and Ramkumar Ramachandra. "A parametricity-based formalization of semi-simplicial and semi-cubical sets." Mathematical Structures in Computer Science 35 (2025). https://doi.org/10.1017/s096012952500009x.

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Abstract Semi-simplicial and semi-cubical sets are commonly defined as presheaves over, respectively, the semi-simplex or semi-cube category. Homotopy type theory then popularized an alternative definition, where the set of $n$ -simplices or $n$ -cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call indexed. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively, in their unary and binary variants. We exploit this correspondence to develop an original uniform ind

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Allamigeon, Xavier, Ricardo D. Katz, and Pierre-Yves Strub. "Formalizing the Face Lattice of Polyhedra." Logical Methods in Computer Science Volume 18, Issue 2 (May 18, 2022). http://dx.doi.org/10.46298/lmcs-18(2:10)2022.

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Faces play a central role in the combinatorial and computational aspects of polyhedra. In this paper, we present the first formalization of faces of polyhedra in the proof assistant Coq. This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps. Moreover, we design a special mechanism which automatically introduces an appropriate representation of a polyhedron or a face, depending on the context of the proof. We demonstrate the usability of this approach by establishing some of

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Ricciotti, Wilmer, and James Cheney. "A Formalization of SQL with Nulls." Journal of Automated Reasoning, July 27, 2022. http://dx.doi.org/10.1007/s10817-022-09632-4.

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AbstractSQL is the world’s most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal specification. Commercial SQL implementations interpret the standard in different ways, so that, given the same input data, the same query can yield different results depending on the SQL system it is run on. Even for a particular system, mechanically checked formalization of all widely-used features of SQL remains an open problem. The lack of a well-understo

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Konečný, Michal, Sewon Park, and Holger Thies. "Extracting efficient exact real number computation from proofs in constructive type theory." Journal of Logic and Computation, October 18, 2024. http://dx.doi.org/10.1093/logcom/exae066.

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Abstract Exact real computation is an alternative to floating-point arithmetic where operations on real numbers are performed exactly, without the introduction of rounding errors. When proving the correctness of an implementation, one can focus solely on the mathematical properties of the problem without thinking about the subtleties of representing real numbers. We propose a new axiomatization of the real numbers in a dependent type theory with the goal of extracting certified exact real computation programs from constructive proofs. Our formalization differs from similar approaches, in that

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de Boer, Frank S., Hans-Dieter A. Hiep, and Stijn de Gouw. "Dynamic Separation Logic." Electronic Notes in Theoretical Informatics and Computer Science Volume 3 - Proceedings of... (November 23, 2023). http://dx.doi.org/10.46298/entics.12297.

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This paper introduces a dynamic logic extension of separation logic. The assertion language of separation logic is extended with modalities for the five types of the basic instructions of separation logic: simple assignment, look-up, mutation, allocation, and de-allocation. The main novelty of the resulting dynamic logic is that it allows to combine different approaches to resolving these modalities. One such approach is based on the standard weakest precondition calculus of separation logic. The other approach introduced in this paper provides a novel alternative formalization in the proposed

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