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1

KOZEN, DEXTER, and ALEXANDRA SILVA. "Practical coinduction." Mathematical Structures in Computer Science 27, no. 7 (2016): 1132–52. http://dx.doi.org/10.1017/s0960129515000493.

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Induction is a well-established proof principle that is taught in most undergraduate programs in mathematics and computer science. In computer science, it is used primarily to reason about inductively defined datatypes such as finite lists, finite trees and the natural numbers. Coinduction is the dual principle that can be used to reason about coinductive datatypes such as infinite streams or trees, but it is not as widespread or as well understood. In this paper, we illustrate through several examples the use of coinduction in informal mathematical arguments. Our aim is to promote the princip
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Kidney, Donnacha Oisín, and Nicolas Wu. "Formalising Graph Algorithms with Coinduction." Proceedings of the ACM on Programming Languages 9, POPL (2025): 1657–86. https://doi.org/10.1145/3704892.

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Graphs and their algorithms are fundamental to computer science, but they can be difficult to formalise, especially in dependently-typed proof assistants. Part of the problem is that graphs aren’t as well-behaved as inductive data types like trees or lists; another problem is that graph algorithms (at least in standard presentations) often aren’t structurally recursive. Instead of trying to find a way to make graphs behave like other familiar inductive types, this paper builds a formal theory of graphs and their algorithms where graphs are treated as coinductive structures from the beginning.
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MANTADELIS, THEOFRASTOS, RICARDO ROCHA, and PAULO MOURA. "Tabling, Rational Terms, and Coinduction Finally Together!" Theory and Practice of Logic Programming 14, no. 4-5 (2014): 429–43. http://dx.doi.org/10.1017/s147106841400012x.

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AbstractTabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling often improves computational performance. Rational term are terms with one or more infinite sub-terms but with a finite representation. Rational terms can be generated in Prolog by omitting the occurs check when unifying two terms. Applications of rational terms include definite clause grammars, constraint handling systems, and coinduction. In this paper, we report our extension of YAP's Prolog tabling mechanism
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4

BARTELS, FALK. "Generalised coinduction." Mathematical Structures in Computer Science 13, no. 2 (2003): 321–48. http://dx.doi.org/10.1017/s0960129502003900.

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Bartels, F. "Generalised Coinduction." Electronic Notes in Theoretical Computer Science 44, no. 1 (2001): 67–87. http://dx.doi.org/10.1016/s1571-0661(04)80903-4.

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6

HINZE, RALF. "Concrete stream calculus: An extended study." Journal of Functional Programming 20, no. 5-6 (2010): 463–535. http://dx.doi.org/10.1017/s0956796810000213.

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AbstractThis paper shows how to reason about streams concisely and precisely. Streams, infinite sequences of elements, live in a coworld: they are given by a coinductive datatype, operations on streams are implemented by corecursive programs, and proofs are typically concocted using coinduction. This paper offers an alternative to coinduction. Suitably restricted, stream equations possessunique solutions. This property gives rise to a simple and attractive proof technique, essentially bringing equational reasoning to the coworld. We redevelop the theory of recurrences, finite calculus and gene
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7

Upchurch, R. C. C., and A. P. Hall. "Propofol/midazolam coinduction." Anaesthesia 54, no. 6 (1999): 608–9. http://dx.doi.org/10.1046/j.1365-2044.1999.96794n.x.

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8

Anderson, L., and H. Robb. "Propofol/midazolam coinduction." Anaesthesia 54, no. 6 (1999): 609. http://dx.doi.org/10.1046/j.1365-2044.1999.96794o.x.

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9

Lenisa, Marina. "From Set-theoretic Coinduction to Coalgebraic Coinduction: some results, some problems." Electronic Notes in Theoretical Computer Science 19 (1999): 2–22. http://dx.doi.org/10.1016/s1571-0661(05)80265-8.

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10

Yesua, I. Nyoman, Puger Rahardjo, and Pesta Parulian Maurid Edwar. "Keamanan Penggunaan Propofol Auto-Coinduction Dibandingkan Dengan Midazolam Coinduction Berdasarkan Perubahan Hemodinamik Pada Induksi Anestesi Pasien Yang Dilakukan General Anestesi." JAI (Jurnal Anestesiologi Indonesia) 11, no. 1 (2019): 1. http://dx.doi.org/10.14710/jai.v11i1.22039.

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Latar Belakang: Pemilihan obat anestesi untuk induksi bagi seorang ahli anestesi merupakan hal yang krusial dan didasarkan atas efek farmakodinamik terhadap sistem kardiovaskular.Tujuan: Menganalisa apakah penggunaan propofol auto-coinduction (pre-dosing propofol) dapat digunakan sebagai alternatif midazolam sebagai obat coinduction, dilihat dari segi keamanan pasien (perubahan hemodinamik yang terjadi) dan biaya yang dikeluarkan.Metode: Penelitian eksperimental dengan desain pre-posttest single blind group ini melibatkan 52 pasien yang menjalani operasi elektif dengan anestesi umum di Kamar O
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11

Cockett, Robin, and Luigi Santocanale. "Induction, Coinduction, and Adjoints." Electronic Notes in Theoretical Computer Science 69 (February 2003): 101–19. http://dx.doi.org/10.1016/s1571-0661(04)80561-9.

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12

Diaconescu, Răzvan. "Coinduction for preordered algebra." Information and Computation 209, no. 2 (2011): 108–17. http://dx.doi.org/10.1016/j.ic.2010.11.001.

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13

TURI, DANIELE, and JAN RUTTEN. "On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces." Mathematical Structures in Computer Science 8, no. 5 (1998): 481–540. http://dx.doi.org/10.1017/s0960129598002588.

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This paper, a revised version of Rutten and Turi (1993), is part of a programme aiming at formulating a mathematical theory of structural operational semantics to complement the established theory of domains and denotational semantics to form a coherent whole (Turi 1996; Turi and Plotkin 1997). The programme is based on a suitable interplay between the induction principle, which pervades modern mathematics, and a dual, non-standard ‘coinduction principle’, which underlies many of the recursive phenomena occurring in computer science.The aim of the present survey is to show that the elementary
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14

Sangiorgi, Davide. "From enhanced coinduction towards enhanced induction." Proceedings of the ACM on Programming Languages 6, POPL (2022): 1–29. http://dx.doi.org/10.1145/3498679.

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There exist a rich and well-developed theory of enhancements of the coinduction proof method, widely used on behavioural relations such as bisimilarity. We study how to develop an analogous theory for inductive behaviour relations, i.e., relations defined from inductive observables. Similarly to the coinductive setting, our theory makes use of (semi)-progressions of the form R->F(R), where R is a relation on processes and F is a function on relations, meaning that there is an appropriate match on the transitions that the processes in R can perform in which the process derivatives are in F(R
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15

Abrams, Gene, and Claudia Menini. "Coinduction for semigroup-graded rings." Communications in Algebra 27, no. 7 (1999): 3283–301. http://dx.doi.org/10.1080/00927879908826627.

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16

Ciaffaglione, Alberto. "Towards Turing computability via coinduction." Science of Computer Programming 126 (September 2016): 31–51. http://dx.doi.org/10.1016/j.scico.2016.02.004.

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17

Forster, Thomas. "Better-quasi-orderings and coinduction." Theoretical Computer Science 309, no. 1-3 (2003): 111–23. http://dx.doi.org/10.1016/s0304-3975(03)00131-2.

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18

Komenda, Jan. "Coinduction in Concurrent Timed Systems." Electronic Notes in Theoretical Computer Science 264, no. 2 (2010): 177–97. http://dx.doi.org/10.1016/j.entcs.2010.07.020.

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19

El Kaoutit, L., and J. Gómez-Torrecillas. "Coinduction functor and simple comodules." ANNALI DELL'UNIVERSITA' DI FERRARA 56, no. 1 (2009): 21–35. http://dx.doi.org/10.1007/s11565-009-0086-0.

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20

Aparanji, Koduri, Manta Radhasundari, and Kommula Gopalakrishna. "INDUCTION OF PROPOFOL WITH COINDUCTION OF PROPOFOL, MIDAZOLAM VERSUS PROPOFOL AUTO COINDUCTION- A COMPARATIVE STUDY." Journal of Evidence Based Medicine and Healthcare 4, no. 93 (2017): 5670–74. http://dx.doi.org/10.18410/jebmh/2017/1138.

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21

Chawla, Davinder, Reiya Goyal, Parmod Kumar, and Mandeep Kaur. "COMPARATIVE STUDY OF PROPOFOL AUTO-COINDUCTION VERSUS KETAMINE PROPOFOL COINDUCTION USING PRIMING PRINCIPLE BY BISPECTRAL INDEX ANALYSIS FOR DAY CARE SURGERY." International Journal of Advanced Research 12, no. 11 (2024): 1093–99. https://doi.org/10.21474/ijar01/19924.

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Aim:The aim of our study was to do the comparison of Propofol Auto-coinduction versus Ketamine Propofol coinduction using priming principle by bispectral index analysis for day care surgery. Methods:150 patients participated in our study at Govt. Medical College and Rajindra Hospital, Patiala. Patients aged above 18 years and ASA Grade I and II scheduled to undergo elective surgery were included in this prospective, randomized controlled trial. All patients were randomly assigned into 3 groups of 50 each. Group A- patients were given Propofol 0.5mg/kg body wt., Group B- patients were given Ket
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22

MIYAMOTO, KENJI, and HELMUT SCHWICHTENBERG. "Program extraction in exact real arithmetic." Mathematical Structures in Computer Science 25, no. 8 (2014): 1692–704. http://dx.doi.org/10.1017/s0960129513000327.

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The importance of an abstract approach to a computation theory over general data types has been stressed by Tucker in many of his papers. Berger and Seisenberger recently elaborated the idea for extraction out of proofs involving (only) abstract reals. They considered a proof involving coinduction of the proposition that any two reals in [−1, 1] have their average in the same interval, and informally extract a Haskell program from this proof, which works with stream representations of reals. Here we formalize the proof, and machine extract its computational content using the Minlog proof assis
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23

Gan, Wee Liang, and Liping Li. "Coinduction functor in representation stability theory." Journal of the London Mathematical Society 92, no. 3 (2015): 689–711. http://dx.doi.org/10.1112/jlms/jdv043.

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24

Bonchi, Filippo, and Damien Pous. "Hacking nondeterminism with induction and coinduction." Communications of the ACM 58, no. 2 (2015): 87–95. http://dx.doi.org/10.1145/2713167.

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25

&NA;. "Deeper neuromuscular block with desflurane coinduction." Inpharma Weekly &NA;, no. 1265 (2000): 20. http://dx.doi.org/10.2165/00128413-200012650-00051.

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26

Berger, Ulrich, and Tie Hou. "Coinduction for Exact Real Number Computation." Theory of Computing Systems 43, no. 3-4 (2007): 394–409. http://dx.doi.org/10.1007/s00224-007-9017-6.

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27

MARTINS, MANUEL A., and DON PIGOZZI. "Behavioural reasoning for conditional equations." Mathematical Structures in Computer Science 17, no. 5 (2007): 1075–113. http://dx.doi.org/10.1017/s0960129507006305.

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Object-oriented (OO) programming techniques can be applied to equational specification logics by distinguishing visible data from hidden data (that is, by distinguishing the output of methods from the objects to which the methods apply), and then focusing on the behavioural equivalence of hidden data in the sense introduced by H. Reichel in 1984. Equational specification logics structured in this way are called hidden equational logics, HELs. The central problem is how to extend the specification of a given HEL to a specification of behavioural equivalence in a computationally effective way. S
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28

HONSELL, FURIO, and MARINA LENISA. "Coinductive characterizations of applicative structures." Mathematical Structures in Computer Science 9, no. 4 (1999): 403–35. http://dx.doi.org/10.1017/s096012959900287x.

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We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on λ-terms and, more generally, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles for reasoning on program equivalences, which are not based on Abramsky's applicative bisimulation. We discuss, in particular, what we call the cartesian coinduction principle, which arises when we exploit the elementary observation that functional behaviours can be expressed as cartesian graphs. Using the paradigm of final semantics, the
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29

Correnson, Arthur, and Bernd Finkbeiner. "Coinductive Proofs for Temporal Hyperliveness." Proceedings of the ACM on Programming Languages 9, POPL (2025): 1568–95. https://doi.org/10.1145/3704889.

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Temporal logics for hyperproperties have recently emerged as an expressive specification technique for relational properties of reactive systems. While the model checking problem for such logics has been widely studied, there is a scarcity of deductive proof systems for temporal hyperproperties. In particular, hyperproperties with an alternation of universal and existential quantification over system executions are rarely supported. In this paper, we focus on hyperproperties of the form ∀ * ∃ * ψ, where ψ is a safety relation. We show that hyperproperties of this class – which includes many hy
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30

Oddby-Muhrbeck, Eva, Staffan Eksborg, Henrik T. G. Bergendahl, Olle Muhrbeck, and Per Arne Lönnqvist. "Effects of Clonidine on Postoperative Nausea and Vomiting in Breast Cancer Surgery." Anesthesiology 96, no. 5 (2002): 1109–14. http://dx.doi.org/10.1097/00000542-200205000-00013.

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Background Postoperative nausea and vomiting (PONV) is still common, especially among female patients. Our hypothesis is that coinduction with clonidine reduces the incidence of PONV in adult patients undergoing breast cancer surgery. Methods Sixty-eight women premedicated with midazolam were randomly allocated to coinduction with intravenous clonidine (group C) or placebo (group P) in this prospective, double-blind study. Anesthesia was standardized (laryngeal mask airway, fentanyl, propofol, sevoflurane, nitrous oxide, and oxygen). Hemodynamic parameters and the requirements for propofol, se
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31

DAGNINO, FRANCESCO, DAVIDE ANCONA, and ELENA ZUCCA. "Flexible coinductive logic programming." Theory and Practice of Logic Programming 20, no. 6 (2020): 818–33. http://dx.doi.org/10.1017/s147106842000023x.

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AbstractRecursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations, necessary in some cases to get the correct meaning. We provide a detailed formal account of an extension of logic programming supporting flexible coinduction. Syntactically, programs are enriched by coclauses, clauses with a special meaning used to tune the interpretation of predicates. As usual, the declarative semantics can be expressed as a fixed point
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32

Wong, W. H., K. F. Cheong, and S. L. C. Tham. "Propofol auto-coinduction for laryngeal mask insertion." European Journal of Anaesthesiology 17, Supplement 19 (2000): 7. http://dx.doi.org/10.1097/00003643-200000002-00022.

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33

GOGUEN, JOSEPH A., and GRANT MALCOLM. "Hidden coinduction: behavioural correctness proofs for objects." Mathematical Structures in Computer Science 9, no. 3 (1999): 287–319. http://dx.doi.org/10.1017/s0960129599002777.

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This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering. We begin with an outline of our general goals, continue with an overview of results, and conclude with a discussion of some future plans. The main contribution is powerful hidden coinduction techniques for proving behavioural correctness of concurrent systems, and several mechanical proofs are given using OBJ3. We also show how modularization, bisimulation, transition systems, concurrency and combinations of the functional, constraint, logic and object paradigms fit into hidden algebra
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34

Komenda, Jan. "Coalgebra and Coinduction in Decentralized Supervisory Control." IFAC Proceedings Volumes 36, no. 18 (2003): 193–98. http://dx.doi.org/10.1016/s1474-6670(17)34667-0.

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35

Niqui, M., and J. J. M. M. Rutten. "A proof of Moessner’s theorem by coinduction." Higher-Order and Symbolic Computation 24, no. 3 (2011): 191–206. http://dx.doi.org/10.1007/s10990-012-9082-7.

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36

Pous, Damien, and Davide Sangiorgi. "Bisimulation and Coinduction Enhancements: A Historical Perspective." Formal Aspects of Computing 31, no. 6 (2019): 733–49. http://dx.doi.org/10.1007/s00165-019-00497-w.

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37

Rot, Jurriaan, Marcello Bonsangue, and Jan Rutten. "Proving language inclusion and equivalence by coinduction." Information and Computation 246 (February 2016): 62–76. http://dx.doi.org/10.1016/j.ic.2015.11.009.

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38

Bonchi, Filippo, Daniela Petrişan, Damien Pous, and Jurriaan Rot. "A general account of coinduction up-to." Acta Informatica 54, no. 2 (2016): 127–90. http://dx.doi.org/10.1007/s00236-016-0271-4.

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39

CAPRETTA, Venanzio. "Wander types : A formalization of coinduction-recursion." Progress in Informatics, no. 10 (March 2013): 47. http://dx.doi.org/10.2201/niipi.2013.10.4.

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40

Sangiorgi, Davide. "On the origins of bisimulation and coinduction." ACM Transactions on Programming Languages and Systems 31, no. 4 (2009): 1–41. http://dx.doi.org/10.1145/1516507.1516510.

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41

Caenepeel, S., S. Raianu, and F. Vanoystaeyen. "Induction and Coinduction for Hopf Algebras: Applications." Journal of Algebra 165, no. 1 (1994): 204–22. http://dx.doi.org/10.1006/jabr.1994.1107.

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42

BERGER, ULRICH, and TIE HOU. "A realizability interpretation of Church's simple theory of types." Mathematical Structures in Computer Science 27, no. 8 (2016): 1364–85. http://dx.doi.org/10.1017/s0960129516000104.

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We give a realizability interpretation of an intuitionistic version of Church's Simple Theory of Types (CST) which can be viewed as a formalization of intuitionistic higher-order logic. Although definable in CST we include operators for monotone induction and coinduction and provide simple realizers for them. Realizers are formally represented in an untyped lambda–calculus with pairing and case-construct. The purpose of this interpretation is to provide a foundation for the extraction of verified programs from formal proofs as an alternative to type-theoretic systems. The advantages of our app
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43

Areces, Carlos, and Daniel Gorín. "Coinductive models and normal forms for modal logics (or how we learned to stop worrying and love coinduction)." Journal of Applied Logic 8, no. 4 (2010): 305–18. http://dx.doi.org/10.1016/j.jal.2010.08.010.

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44

Komenda, Jan, Sébastien Lahaye, and Jean-Louis Boimond. "Decentralized Control of Product (max+)-automata using Coinduction." IFAC Proceedings Volumes 45, no. 29 (2012): 122–27. http://dx.doi.org/10.3182/20121003-3-mx-4033.00023.

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45

Paulson, L. "Mechanizing coinduction and corecursion in higher-order logic." Journal of Logic and Computation 7, no. 2 (1997): 175–204. http://dx.doi.org/10.1093/logcom/7.2.175.

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46

Hermida, Claudio, and Bart Jacobs. "Structural Induction and Coinduction in a Fibrational Setting." Information and Computation 145, no. 2 (1998): 107–52. http://dx.doi.org/10.1006/inco.1998.2725.

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47

Komenda, Jan. "Coinduction in Control of Partially Observed Discrete-Event Systems." Electronic Notes in Theoretical Computer Science 82, no. 1 (2003): 150–69. http://dx.doi.org/10.1016/s1571-0661(04)80637-6.

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48

Matsumoto, Michihiro, and Kokichi Futatsugi. "Test Set Coinduction -- Toward Automated Verification of Behavioural Properties —." Electronic Notes in Theoretical Computer Science 15 (1998): 242–62. http://dx.doi.org/10.1016/s1571-0661(05)80015-5.

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49

Lescanne, Pierre, and Matthieu Perrinel. "“Backward” coinduction, Nash equilibrium and the rationality of escalation." Acta Informatica 49, no. 3 (2012): 117–37. http://dx.doi.org/10.1007/s00236-012-0153-3.

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50

MOMIGLIANO, ALBERTO, BRIGITTE PIENTKA, and DAVID THIBODEAU. "A case study in programming coinductive proofs: Howe’s method." Mathematical Structures in Computer Science 29, no. 8 (2018): 1309–43. http://dx.doi.org/10.1017/s0960129518000415.

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Bisimulation proofs play a central role in programming languages in establishing rich properties such as contextual equivalence. They are also challenging to mechanize, since they require a combination of inductive and coinductive reasoning on open terms. In this paper, we describe mechanizing the property that similarity in the call-by-name lambda calculus is a pre-congruence using Howe’s method in the Beluga formal reasoning system. The development relies on three key ingredients: (1) we give a higher order abstract syntax (HOAS) encoding of lambda terms together with their operational seman
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