{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T09:05:17Z","timestamp":1726045517875},"publisher-location":"Cham","reference-count":80,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030310370"},{"type":"electronic","value":"9783030310387"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-31038-7_1","type":"book-chapter","created":{"date-parts":[[2019,9,22]],"date-time":"2019-09-22T23:03:06Z","timestamp":1569193386000},"page":"3-21","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Calculus of Space, Time, and Causality: Its Algebra, Geometry, Logic"],"prefix":"10.1007","author":[{"given":"Tony","family":"Hoare","sequence":"first","affiliation":[]},{"given":"Georg","family":"Struth","sequence":"additional","affiliation":[]},{"given":"Jim","family":"Woodcock","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,23]]},"reference":[{"issue":"2","key":"1_CR1","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/s00165-015-0343-1","volume":"28","author":"A Armstrong","year":"2016","unstructured":"Armstrong, A., Gomes, V.B.F., Struth, G.: Building program construction and verification tools from algebraic principles. Formal Asp. Comput. 28(2), 265\u2013293 (2016)","journal-title":"Formal Asp. Comput."},{"key":"1_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/3-540-51285-3_42","volume-title":"PARLE 1989 Parallel Architectures and Languages Europe","author":"RJR Back","year":"1989","unstructured":"Back, R.J.R.: A method for refining atomicity in parallel algorithms. In: Odijk, E., Rem, M., Syre, J.-C. (eds.) PARLE 1989. LNCS, vol. 366, pp. 199\u2013216. Springer, Heidelberg (1989). https:\/\/doi.org\/10.1007\/3-540-51285-3_42"},{"key":"1_CR3","volume-title":"Interactive Theorem Proving and Program Development: Coq\u2019Art The Calculus of Inductive Constructions","author":"Y Bertot","year":"2010","unstructured":"Bertot, Y., Castran, P.: Interactive Theorem Proving and Program Development: Coq\u2019Art The Calculus of Inductive Constructions. Springer, Heidelberg (2010)"},{"key":"1_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/978-3-642-03359-9_6","volume-title":"Theorem Proving in Higher Order Logics","author":"A Bove","year":"2009","unstructured":"Bove, A., Dybjer, P., Norell, U.: A brief overview of Agda\u2014a functional language with dependent types. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 73\u201378. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-03359-9_6"},{"issue":"3","key":"1_CR5","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s10270-005-0085-2","volume":"4","author":"A Cavalcanti","year":"2005","unstructured":"Cavalcanti, A., Sampaio, A., Woodcock, J.: Unifying classes and processes. Softw. Syst. Model. 4(3), 277\u2013296 (2005)","journal-title":"Softw. Syst. Model."},{"key":"1_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71999-1","volume-title":"All About Maude\u2014A High-Performance Logical Framework, How to Specify, Program and Verify Systems in Rewriting Logic","author":"M Clavel","year":"2007","unstructured":"Clavel, M., Dur\u00e1n, F., Eker, S., Lincoln, P., Mart\u00ed-Oliet, N., Meseguer, J., Talcott, C.: All About Maude\u2014A High-Performance Logical Framework, How to Specify, Program and Verify Systems in Rewriting Logic. LNCS, vol. 4350. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-71999-1"},{"key":"1_CR7","unstructured":"Dahl, O., Myhrhaug, B., Nygaard, K.: Simula 67 common base language. Technical report. NCC, May 1968"},{"key":"1_CR8","volume-title":"Introduction to Lattices and Order","author":"BA Davey","year":"1990","unstructured":"Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)"},{"key":"1_CR9","volume-title":"Stetigkeit und irrationale Zahlen","author":"R Dedekind","year":"1872","unstructured":"Dedekind, R.: Stetigkeit und irrationale Zahlen. Verlag von Friedrich Vieweg und Sohn, Braunschweig (1872)"},{"issue":"4","key":"1_CR10","doi-asserted-by":"publisher","first-page":"798","DOI":"10.1145\/1183278.1183285","volume":"7","author":"J Desharnais","year":"2006","unstructured":"Desharnais, J., M\u00f6ller, B., Struth, G.: Kleene algebra with domain. ACM Trans. Comput. Log. 7(4), 798\u2013833 (2006)","journal-title":"ACM Trans. Comput. Log."},{"issue":"3","key":"1_CR11","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.scico.2010.05.007","volume":"76","author":"J Desharnais","year":"2011","unstructured":"Desharnais, J., Struth, G.: Internal axioms for domain semirings. Sci. Comput. Program. 76(3), 181\u2013203 (2011)","journal-title":"Sci. Comput. Program."},{"key":"1_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/978-3-540-45236-2_18","volume-title":"FME 2003: Formal Methods","author":"A Duran","year":"2003","unstructured":"Duran, A., Cavalcanti, A., Sampaio, A.: A strategy for compiling classes, inheritance, and dynamic binding. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 301\u2013320. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/978-3-540-45236-2_18"},{"issue":"1\/2","key":"1_CR13","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF00625970","volume":"9","author":"EA Emerson","year":"1996","unstructured":"Emerson, E.A., Sistla, A.P.: Symmetry and model checking. Formal Methods Syst. Des. 9(1\/2), 105\u2013131 (1996)","journal-title":"Formal Methods Syst. Des."},{"key":"1_CR14","unstructured":"Fell, J., Hayes, I.J., Velykis, A.: Concurrent refinement algebra and rely quotients. Archive of Formal Proofs 2016 (2016)"},{"key":"1_CR15","doi-asserted-by":"crossref","unstructured":"Fitzgerald, J.S., Gamble, C., Larsen, P.G., Pierce, K., Woodcock, J.: Cyber-physical systems design: formal foundations, methods, and integrated tool chains. In: Gnesi, S., Plat, N. (eds.) 3rd IEEE\/ACM FME Workshop on Formal Methods in Software Engineering, FormaliSE 2015, Florence, 18 May 2015, pp. 40\u201346. IEEE Computer Society (2015)","DOI":"10.1109\/FormaliSE.2015.14"},{"key":"1_CR16","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.ipl.2018.02.017","volume":"135","author":"S Foster","year":"2018","unstructured":"Foster, S., Cavalcanti, A., Woodcock, J., Zeyda, F.: Unifying theories of time with generalised reactive processes. Inf. Process. Lett. 135, 47\u201352 (2018)","journal-title":"Inf. Process. Lett."},{"key":"1_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/978-3-642-39721-9_3","volume-title":"Unifying Theories of Programming and Formal Engineering Methods","author":"S Foster","year":"2013","unstructured":"Foster, S., Woodcock, J.: Unifying theories of programming in Isabelle. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Unifying Theories of Programming and Formal Engineering Methods. LNCS, vol. 8050, pp. 109\u2013155. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39721-9_3"},{"key":"1_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/978-3-030-02149-8_13","volume-title":"Relational and Algebraic Methods in Computer Science","author":"S Foster","year":"2018","unstructured":"Foster, S., Ye, K., Cavalcanti, A., Woodcock, J.: Calculational verification of reactive programs with reactive relations and Kleene algebra. In: Desharnais, J., Guttmann, W., Joosten, S. (eds.) RAMiCS 2018. LNCS, vol. 11194, pp. 205\u2013224. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-02149-8_13"},{"key":"1_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-3-319-14806-9_2","volume-title":"Unifying Theories of Programming","author":"S Foster","year":"2015","unstructured":"Foster, S., Zeyda, F., Woodcock, J.: Isabelle\/UTP: a mechanised theory engineering framework. In: Naumann, D. (ed.) UTP 2014. LNCS, vol. 8963, pp. 21\u201341. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-14806-9_2"},{"issue":"3","key":"1_CR20","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/BF01988052","volume":"3","author":"ND Gautam","year":"1957","unstructured":"Gautam, N.D.: The validity of equations of complex algebras. Archiv f\u00fcr mathematische Logik und Grundlagenforschung 3(3), 117\u2013124 (1957)","journal-title":"Archiv f\u00fcr mathematische Logik und Grundlagenforschung"},{"key":"1_CR21","doi-asserted-by":"crossref","unstructured":"Gent, I.P., Petrie, K.E., Puget, J.: Symmetry in constraint programming. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, Foundations of Artificial Intelligence, vol. 2, pp. 329\u2013376. Elsevier (2006)","DOI":"10.1016\/S1574-6526(06)80014-3"},{"key":"1_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1007\/978-3-642-10452-7_14","volume-title":"Formal Methods: Foundations and Applications","author":"R Gheyi","year":"2009","unstructured":"Gheyi, R., Massoni, T., Borba, P., Sampaio, A.: A complete set of object modeling laws for Alloy. In: Oliveira, M.V.M., Woodcock, J. (eds.) SBMF 2009. LNCS, vol. 5902, pp. 204\u2013219. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-10452-7_14"},{"issue":"2","key":"1_CR23","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s10009-015-0377-y","volume":"18","author":"T Gibson-Robinson","year":"2016","unstructured":"Gibson-Robinson, T., Armstrong, P.J., Boulgakov, A., Roscoe, A.W.: FDR3: a parallel refinement checker for CSP. STTT 18(2), 149\u2013167 (2016)","journal-title":"STTT"},{"key":"1_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1007\/978-3-319-48989-6_19","volume-title":"FM 2016: Formal Methods","author":"VBF Gomes","year":"2016","unstructured":"Gomes, V.B.F., Struth, G.: Modal Kleene algebra applied to program correctness. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 310\u2013325. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-48989-6_19"},{"key":"1_CR25","volume-title":"Transaction Processing: Concepts and Techniques","author":"J Gray","year":"1993","unstructured":"Gray, J., Reuter, A.: Transaction Processing: Concepts and Techniques. Morgan Kaufmann, Burlington (1993)"},{"key":"1_CR26","doi-asserted-by":"crossref","unstructured":"Grieves, M., Vickers, J.: Digital twin: mitigating unpredictable, undesirable emergent behavior in complex systems (excerpt). Technical report. University of Michigan, August 2016","DOI":"10.1007\/978-3-319-38756-7_4"},{"issue":"6","key":"1_CR27","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1007\/s00165-016-0384-0","volume":"28","author":"IJ Hayes","year":"2016","unstructured":"Hayes, I.J.: Generalised rely-guarantee concurrency: an algebraic foundation. Formal Asp. Comput. 28(6), 1057\u20131078 (2016)","journal-title":"Formal Asp. Comput."},{"issue":"2","key":"1_CR28","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s00165-018-0464-4","volume":"31","author":"IJ Hayes","year":"2019","unstructured":"Hayes, I.J., Meinicke, L.A., Winter, K., Colvin, R.J.: A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency. Formal Asp. Comput. 31(2), 133\u2013163 (2019)","journal-title":"Formal Asp. Comput."},{"issue":"7","key":"1_CR29","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1145\/366622.366644","volume":"4","author":"CAR Hoare","year":"1961","unstructured":"Hoare, C.A.R.: Algorithm 64: quicksort. Commun. ACM 4(7), 321 (1961)","journal-title":"Commun. ACM"},{"issue":"10","key":"1_CR30","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1145\/363235.363259","volume":"12","author":"CAR Hoare","year":"1969","unstructured":"Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576\u2013580 (1969)","journal-title":"Commun. ACM"},{"key":"1_CR31","volume-title":"Communicating Sequential Processes","author":"CAR Hoare","year":"1985","unstructured":"Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall, Upper Saddle River (1985)"},{"key":"1_CR32","first-page":"1","volume-title":"FM\u201999 \u2014 Formal Methods","author":"C. A. R. Hoare","year":"1999","unstructured":"Hoare, C.A.R.: Theories of programming: top-down and bottom-up and meeting in the middle. In: Wing, et al. [74], pp. 1\u201327"},{"issue":"2","key":"1_CR33","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/0020-0190(87)90106-2","volume":"24","author":"CAR Hoare","year":"1987","unstructured":"Hoare, C.A.R., He, J.: The weakest prespecification. Inf. Process. Lett. 24(2), 127\u2013132 (1987)","journal-title":"Inf. Process. Lett."},{"key":"1_CR34","volume-title":"Unifying Theories of Programming","author":"CAR Hoare","year":"1998","unstructured":"Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall, Upper Saddle River (1998)"},{"key":"1_CR35","unstructured":"Hoare, T.: Geometric theory of program testing. www.cl.cam.ac.uk\/~carh4\/19.Jan.18.Lecture1.pdf . Accessed 11 July 2019"},{"key":"1_CR36","doi-asserted-by":"crossref","unstructured":"Hoare, T., Mendes, A., Ferreira, J.F.: Logic, algebra, and geometry at the foundation of computer science. In: Formal Methods Teaching Workshop and Tutorial, FMTea 2019 (2019)","DOI":"10.1007\/978-3-030-32441-4_1"},{"issue":"6","key":"1_CR37","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.jlap.2011.04.005","volume":"80","author":"T Hoare","year":"2011","unstructured":"Hoare, T., M\u00f6ller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra and its foundations. J. Log. Algebr. Program. 80(6), 266\u2013296 (2011)","journal-title":"J. Log. Algebr. Program."},{"key":"1_CR38","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.entcs.2008.04.050","volume":"212","author":"T Hoare","year":"2008","unstructured":"Hoare, T., O\u2019Hearn, P.W.: Separation logic semantics for communicating processes. Electr. Notes Theoret. Comput. Sci. 212, 3\u201325 (2008)","journal-title":"Electr. Notes Theoret. Comput. Sci."},{"issue":"4","key":"1_CR39","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1016\/j.jlamp.2015.09.012","volume":"85","author":"T Hoare","year":"2016","unstructured":"Hoare, T., van Staden, S., M\u00f6ller, B., Struth, G., Zhu, H.: Developments in concurrent Kleene algebra. J. Log. Algebr. Methods Program. 85(4), 617\u2013636 (2016)","journal-title":"J. Log. Algebr. Methods Program."},{"issue":"1","key":"1_CR40","doi-asserted-by":"publisher","first-page":"14","DOI":"10.2307\/2268661","volume":"16","author":"A Horn","year":"1951","unstructured":"Horn, A.: On sentences which are true of direct unions of algebras. J. Symb. Log. 16(1), 14\u201321 (1951)","journal-title":"J. Symb. Log."},{"issue":"1\/2","key":"1_CR41","first-page":"41","volume":"9","author":"CN Ip","year":"1996","unstructured":"Ip, C.N., Dill, D.L.: Better verification through symmetry. Formal Methods Syst. Des. 9(1\/2), 41\u201375 (1996)","journal-title":"Formal Methods Syst. Des."},{"issue":"2","key":"1_CR42","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1145\/505145.505149","volume":"11","author":"D Jackson","year":"2002","unstructured":"Jackson, D.: Alloy: a lightweight object modelling notation. ACM Trans. Softw. Eng. Methodol. 11(2), 256\u2013290 (2002)","journal-title":"ACM Trans. Softw. Eng. Methodol."},{"key":"1_CR43","unstructured":"Jervis, C. (ed.): ITU-T: Recommendation Z.120 (04\/04), Message Sequence Charts (MSC). International Telecommunication Union, Geneva (2004)"},{"key":"1_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/978-3-540-69927-9_4","volume-title":"Theory and Practice of Model Transformations","author":"DS Kolovos","year":"2008","unstructured":"Kolovos, D.S., Paige, R.F., Polack, F.A.C.: The epsilon transformation language. In: Vallecillo, A., Gray, J., Pierantonio, A. (eds.) ICMT 2008. LNCS, vol. 5063, pp. 46\u201360. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-69927-9_4"},{"issue":"3","key":"1_CR45","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1145\/256167.256195","volume":"19","author":"D Kozen","year":"1997","unstructured":"Kozen, D.: Kleene algebra with tests. ACM Trans. Program. Lang. Syst. 19(3), 427\u2013443 (1997)","journal-title":"ACM Trans. Program. Lang. Syst."},{"key":"1_CR46","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1007\/978-3-642-22110-1_47","volume-title":"Computer Aided Verification","author":"M Kwiatkowska","year":"2011","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585\u2013591. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22110-1_47"},{"key":"1_CR47","unstructured":"Laurence, M.R., Struth, G.: Completeness theorems for pomset languages and concurrent Kleene algebras. CoRR abs\/1705.05896 (2017)"},{"issue":"3","key":"1_CR48","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1090\/S0002-9947-1937-1501929-X","volume":"42","author":"HM MacNeille","year":"1937","unstructured":"MacNeille, H.M.: Partially ordered sets. Trans. AMS 42(3), 416\u2013460 (1937)","journal-title":"Trans. AMS"},{"key":"1_CR49","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1007\/978-3-642-21070-9_20","volume-title":"Relational and Algebraic Methods in Computer Science","author":"A McIver","year":"2011","unstructured":"McIver, A., Rabehaja, T.M., Struth, G.: On probabilistic Kleene algebras, automata and simulations. In: de Swart, H. (ed.) RAMICS 2011. LNCS, vol. 6663, pp. 264\u2013279. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-21070-9_20"},{"key":"1_CR50","doi-asserted-by":"publisher","first-page":"97","DOI":"10.4204\/EPTCS.117.7","volume":"117","author":"Annabelle McIver","year":"2013","unstructured":"McIver, A., Rabehaja, T.M., Struth, G.: Probabilistic concurrent Kleene algebra. In: Bortolussi, L., Wiklicky, H. (eds.) 11th International Workshop on Quantitative Aspects of Programming Languages and Systems, QAPL 2013, Rome, 23\u201324 March 2013. EPTCS, vol. 117, pp. 97\u2013115 (2013)","journal-title":"Electronic Proceedings in Theoretical Computer Science"},{"key":"1_CR51","unstructured":"Microsoft: Time Travel Debugging in WinDbg Preview! blogs.msdn.microsoft.com\/windbg\/2017\/09\/25\/time-travel-debugging-in-windbg-preview\/ . Accessed 01 July 2019"},{"key":"1_CR52","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-10235-3","volume-title":"A Calculus of Communicating Systems","year":"1980","unstructured":"Milner, R. (ed.): A Calculus of Communicating Systems. LNCS, vol. 92. Springer, Heidelberg (1980). https:\/\/doi.org\/10.1007\/3-540-10235-3"},{"key":"1_CR53","doi-asserted-by":"crossref","unstructured":"Miyazawa, A., Ribeiro, P., Li, W., Cavalcanti, A.L.C., Timmis, J., Woodcock, J.C.P.: RoboChart: modelling and verification of the functional behaviour of robotic applications. Softw. Syst. Model. (2019)","DOI":"10.1007\/s10270-018-00710-z"},{"key":"1_CR54","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-319-52228-9_1","volume-title":"Unifying Theories of Programming","author":"B M\u00f6ller","year":"2017","unstructured":"M\u00f6ller, B., Hoare, T., M\u00fcller, M.E., Struth, G.: A discrete geometric model of concurrent program execution. In: Bowen, J.P., Zhu, H. (eds.) UTP 2016. LNCS, vol. 10134, pp. 1\u201325. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-52228-9_1"},{"key":"1_CR55","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1007\/978-3-319-21401-6_26","volume-title":"Automated Deduction \u2013 CADE-25","author":"L Moura de","year":"2015","unstructured":"de Moura, L., Kong, S., Avigad, J., van Doorn, F., von Raumer, J.: The Lean theorem prover (system description). In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS, vol. 9195, pp. 378\u2013388. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-21401-6_26"},{"key":"1_CR56","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/978-3-030-02149-8_14","volume-title":"Relational and Algebraic Methods in Computer Science","author":"JJ Huerta y Munive","year":"2018","unstructured":"Huerta y Munive, J.J., Struth, G.: Verifying hybrid systems with modal Kleene algebra. In: Desharnais, J., Guttmann, W., Joosten, S. (eds.) RAMiCS 2018. LNCS, vol. 11194, pp. 225\u2013243. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-02149-8_14"},{"key":"1_CR57","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.tcs.2012.02.009","volume":"433","author":"DA Naumann","year":"2012","unstructured":"Naumann, D.A., Sampaio, A., Silva, L.: Refactoring and representation independence for class hierarchies. Theoret. Comput. Sci. 433, 60\u201397 (2012)","journal-title":"Theoret. Comput. Sci."},{"key":"1_CR58","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45949-9","volume-title":"Isabelle\/HOL\u2014A Proof Assistant for Higher-Order Logic","year":"2002","unstructured":"Nipkow, T., Wenzel, M., Paulson, L.C. (eds.): Isabelle\/HOL\u2014A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-45949-9"},{"key":"1_CR59","unstructured":"Object Management Group: OMG: Unified Modeling Language: Superstructure 2.0 (2003)"},{"issue":"2","key":"1_CR60","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1145\/3211968","volume":"62","author":"PW O\u2019Hearn","year":"2019","unstructured":"O\u2019Hearn, P.W.: Separation logic. Commun. ACM 62(2), 86\u201395 (2019)","journal-title":"Commun. ACM"},{"issue":"1\u20132","key":"1_CR61","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s00165-007-0052-5","volume":"21","author":"M Oliveira","year":"2009","unstructured":"Oliveira, M., Cavalcanti, A., Woodcock, J.: A UTP semantics for Circus. Formal Asp. Comput. 21(1\u20132), 3\u201332 (2009)","journal-title":"Formal Asp. Comput."},{"issue":"3","key":"1_CR62","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1145\/356698.356702","volume":"9","author":"JL Peterson","year":"1977","unstructured":"Peterson, J.L.: Petri nets. ACM Comput. Surv. 9(3), 223\u2013252 (1977)","journal-title":"ACM Comput. Surv."},{"key":"1_CR63","unstructured":"Petri, C.A.: Communication with automata. DTIC Res. Rep. AD0630125, Defense Tech. Inf. Cntr., Fort Belvoir, VA (1966)"},{"key":"1_CR64","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BFb0018436","volume-title":"Logics in AI","author":"V Pratt","year":"1991","unstructured":"Pratt, V.: Action logic and pure induction. In: van Eijck, J. (ed.) JELIA 1990. LNCS, vol. 478, pp. 97\u2013120. Springer, Heidelberg (1991). https:\/\/doi.org\/10.1007\/BFb0018436"},{"key":"1_CR65","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/11494881_7","volume-title":"Formal Methods for Open Object-Based Distributed Systems","author":"R Ramos","year":"2005","unstructured":"Ramos, R., Sampaio, A., Mota, A.: A semantics for UML-RT active classes via mapping into Circus. In: Steffen, M., Zavattaro, G. (eds.) FMOODS 2005. LNCS, vol. 3535, pp. 99\u2013114. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11494881_7"},{"key":"1_CR66","unstructured":"Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: 17th IEEE Symposium on Logic in Computer Science (LICS 2002), Copenhagen, 22\u201325 July 2002, pp. 55\u201374. IEEE Computer Society (2002)"},{"key":"1_CR67","unstructured":"RoboTool: Graphical modelling, validation, and automatic generation of mathematical definitions for proof for RoboChart models. www.cs.york.ac.uk\/robostar\/robotool\/"},{"key":"1_CR68","unstructured":"Sakallah, K.A.: Symmetry and satisfiability. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 289\u2013338. IOS Press (2009)"},{"key":"1_CR69","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/11768173_2","volume-title":"Unifying Theories of Programming","author":"T Santos","year":"2006","unstructured":"Santos, T., Cavalcanti, A., Sampaio, A.: Object-orientation in the UTP. In: Dunne, S., Stoddart, B. (eds.) UTP 2006. LNCS, vol. 4010, pp. 18\u201337. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11768173_2"},{"key":"1_CR70","doi-asserted-by":"crossref","unstructured":"Silva, L., Sampaio, A., Liu, Z.: Laws of object orientation with reference semantics. In: Cerone, A., Gruner, S. (eds.) 6th IEEE International Conference on Software Engineering and Formal Methods, SEFM 2008, Cape Town, 10\u201314 November 2008, pp. 217\u2013226. IEEE Computer Society (2008)","DOI":"10.1109\/SEFM.2008.29"},{"key":"1_CR71","volume-title":"EMF: Eclipse Modeling Framework 2.0","author":"D Steinberg","year":"2009","unstructured":"Steinberg, D., Budinsky, F., Paternostro, M., Merks, E.: EMF: Eclipse Modeling Framework 2.0, 2nd edn. Addison-Wesley, Boston (2009)","edition":"2"},{"issue":"1","key":"1_CR72","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0167-6423(85)90004-8","volume":"5","author":"A Tarlecki","year":"1985","unstructured":"Tarlecki, A.: A language of specified programs. Sci. Comput. Program. 5(1), 59\u201381 (1985)","journal-title":"Sci. Comput. Program."},{"key":"1_CR73","doi-asserted-by":"publisher","first-page":"285","DOI":"10.2140\/pjm.1955.5.285","volume":"5","author":"A Tarski","year":"1955","unstructured":"Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pac. J. Math. 5, 285\u2013309 (1955)","journal-title":"Pac. J. Math."},{"key":"1_CR74","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48119-2","volume-title":"FM 1999\u2014Formal Methods, World Congress on Formal Methods in the Development of Computing Systems","year":"1999","unstructured":"Wing, J.M., Woodcock, J., Davies, J. (eds.): FM 1999. LNCS, vol. 1708. Springer, Heidelberg (1999). https:\/\/doi.org\/10.1007\/3-540-48119-2"},{"key":"1_CR75","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48118-4","volume-title":"FM 1999\u2014Formal Methods, World Congress on Formal Methods in the Development of Computing Systems","year":"1999","unstructured":"Wing, J.M., Woodcock, J., Davies, J. (eds.): FM 1999. LNCS, vol. 1709. Springer, Heidelberg (1999). https:\/\/doi.org\/10.1007\/3-540-48118-4"},{"key":"1_CR76","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1007\/3-540-45648-1_10","volume-title":"ZB 2002:Formal Specification and Development in Z and B","author":"J Woodcock","year":"2002","unstructured":"Woodcock, J., Cavalcanti, A.: The semantics of Circus. In: Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.) ZB 2002. LNCS, vol. 2272, pp. 184\u2013203. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-45648-1_10"},{"key":"1_CR77","unstructured":"Woodcock, S.F.J., Zeyda, F.: Unifying semantic foundations for automated verification tools in Isabelle\/UTP. CoRR abs\/1905.05500 (2019)"},{"issue":"1\u20132","key":"1_CR78","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.scico.2003.09.002","volume":"51","author":"J Wright von","year":"2004","unstructured":"von Wright, J.: Towards a refinement algebra. Sci. Comput. Program. 51(1\u20132), 23\u201345 (2004)","journal-title":"Sci. Comput. Program."},{"key":"1_CR79","unstructured":"Ye, K., Woodcock, J., Foster, S., Miyazawa, A., Cavalcanti, A.: RoboChart: formal modelling and verification of the probabilistic behaviour of robotic applications. Technical report. University of York (2019)"},{"key":"1_CR80","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1007\/978-3-319-06410-9_42","volume-title":"FM 2014: Formal Methods","author":"F Zeyda","year":"2014","unstructured":"Zeyda, F., Santos, T., Cavalcanti, A., Sampaio, A.: A modular theory of object orientation in higher-order UTP. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 627\u2013642. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-06410-9_42"}],"container-title":["Lecture Notes in Computer Science","Unifying Theories of Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-31038-7_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,7]],"date-time":"2019-12-07T18:55:20Z","timestamp":1575744920000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-31038-7_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030310370","9783030310387"],"references-count":80,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-31038-7_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"23 September 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"UTP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Unifying Theories of Programming","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Porto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 October 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 October 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"utp2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.cs.york.ac.uk\/circus\/utp2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"10","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"10","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"100% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}