{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T01:51:09Z","timestamp":1725587469347},"publisher-location":"Berlin, Heidelberg","reference-count":48,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642214929"},{"type":"electronic","value":"9783642214936"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-21493-6_2","type":"book-chapter","created":{"date-parts":[[2011,6,20]],"date-time":"2011-06-20T12:42:44Z","timestamp":1308573764000},"page":"21-43","source":"Crossref","is-referenced-by-count":0,"title":["From Grammars and Automata to Algebras and Coalgebras"],"prefix":"10.1007","author":[{"given":"Peter","family":"Padawitz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"2_CR1","first-page":"157","volume":"14","author":"J. Ad\u00e1mek","year":"2005","unstructured":"Ad\u00e1mek, J.: Introduction to Coalgebra. Theory and Applications of Categories\u00a014, 157\u2013199 (2005)","journal-title":"Theory and Applications of Categories"},{"key":"2_CR2","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1093\/logcom\/12.2.217","volume":"12","author":"J. Ad\u00e1mek","year":"2002","unstructured":"Ad\u00e1mek, J.: Final coalgebras are ideal completions of initial algebras. Journal of Logic and Computation\u00a012, 217\u2013242 (2002)","journal-title":"Journal of Logic and Computation"},{"key":"2_CR3","series-title":"ENTCS","first-page":"1","volume-title":"Proc. Coalgebraic Methods in Computer Science","author":"P. Aczel","year":"2001","unstructured":"Aczel, P., Ad\u00e1mek, J., Velebil, J.: A Coalgebraic View of Infinite Trees and Iteration. In: Proc. Coalgebraic Methods in Computer Science. ENTCS, vol.\u00a044, pp. 1\u201326. Elsevier, Amsterdam (2001)"},{"key":"2_CR4","unstructured":"Ad\u00e1mek, J., Milius, S., Moss, L.S.: Initial algebras and terminal coalgebras: a survey, draft of February 7, TU Braunschweig (2011)"},{"key":"2_CR5","series-title":"ENTCS","first-page":"27","volume-title":"Proc. Coalgebraic Methods in Computer Science","author":"J. Ad\u00e1mek","year":"2001","unstructured":"Ad\u00e1mek, J., Porst, H.-E.: From varieties of algebras to covarieties of coalgebras. In: Proc. Coalgebraic Methods in Computer Science. ENTCS, vol.\u00a044, pp. 27\u201346. Elsevier, Amsterdam (2001)"},{"key":"2_CR6","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/S0304-3975(03)00378-5","volume":"311","author":"J. Ad\u00e1mek","year":"2004","unstructured":"Ad\u00e1mek, J., Porst, H.-E.: On Tree Coalgebras and Coalgebra Presentations. Theoretical Computer Science\u00a0311, 257\u2013283 (2004)","journal-title":"Theoretical Computer Science"},{"key":"2_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1007\/3-540-08442-8_88","volume-title":"Fundamentals of Computation Theory","author":"M.A. Arbib","year":"1977","unstructured":"Arbib, M.A.: Free dynamics and algebraic semantics. In: Karpinski, M. (ed.) FCT 1977. LNCS, vol.\u00a056, pp. 212\u2013227. Springer, Heidelberg (1977)"},{"key":"2_CR8","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/S0019-9958(82)80026-0","volume":"52","author":"M.A. Arbib","year":"1982","unstructured":"Arbib, M.A., Manes, E.G.: Parametrized Data Types Do Not Need Highly Constrained Parameters. Information and Control\u00a052, 139\u2013158 (1982)","journal-title":"Information and Control"},{"key":"2_CR9","series-title":"IFIP State-of-the-Art Report","volume-title":"Algebraic Foundations of Systems Specification","year":"1999","unstructured":"Astesiano, E., Kreowski, H.-J., Krieg-Br\u00fcckner, B. (eds.): Algebraic Foundations of Systems Specification. IFIP State-of-the-Art Report. Springer, Heidelberg (1999)"},{"key":"2_CR10","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/BF01111838","volume":"116","author":"M. Barr","year":"1970","unstructured":"Barr, M.: Coequalizers and Free Triples. Math. Zeitschrift\u00a0116, 307\u2013322 (1970)","journal-title":"Math. Zeitschrift"},{"key":"2_CR11","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/0304-3975(93)90076-6","volume":"114","author":"M. Barr","year":"1993","unstructured":"Barr, M.: Terminal coalgebras in well-founded set theory. Theoretical Computer Science\u00a0114, 299\u2013315 (1993)","journal-title":"Theoretical Computer Science"},{"key":"2_CR12","doi-asserted-by":"crossref","unstructured":"van den Brand, M.G.J., Heering, J., Klint, P., Olivier, P.A.: Compiling Rewrite Systems: The ASF+SDF Compiler. ACM TOPLAS\u00a024 (2002)","DOI":"10.1145\/567097.567099"},{"key":"2_CR13","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1145\/321239.321249","volume":"11","author":"J.A. Brzozowski","year":"1964","unstructured":"Brzozowski, J.A.: Derivatives of regular expressions. Journal ACM\u00a011, 481\u2013494 (1964)","journal-title":"Journal ACM"},{"key":"2_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69962-7","volume-title":"Fundamentals of Algebraic Specification","author":"H. Ehrig","year":"1985","unstructured":"Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specification, vol.\u00a01. Springer, Heidelberg (1985)"},{"key":"2_CR15","series-title":"ENTCS","first-page":"146","volume-title":"Proc. Coalgebraic Methods in Computer Science","author":"J. Gibbons","year":"2001","unstructured":"Gibbons, J., Hutton, G., Altenkirch, T.: When is a function a fold or an unfold? In: Proc. Coalgebraic Methods in Computer Science. ENTCS, vol.\u00a044, pp. 146\u2013159. Elsevier, Amsterdam (2001)"},{"key":"2_CR16","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/S0304-3975(99)00275-3","volume":"245","author":"J. Goguen","year":"2000","unstructured":"Goguen, J., Malcolm, G.: A Hidden Agenda. Theoretical Computer Science\u00a0245, 55\u2013101 (2000)","journal-title":"Theoretical Computer Science"},{"key":"2_CR17","first-page":"80","volume-title":"Current Trends in Programming Methodology","author":"J.A. Goguen","year":"1978","unstructured":"Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types. In: Yeh, R. (ed.) Current Trends in Programming Methodology, vol.\u00a04, pp. 80\u2013149. Prentice-Hall, Englewood Cliffs (1978)"},{"key":"2_CR18","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1145\/321992.321997","volume":"24","author":"J.A. Goguen","year":"1977","unstructured":"Goguen, J.A., Thatcher, J.W., Wagner, E.G., Wright, J.B.: Initial Algebra Semantics and Continuous Algebras. J. ACM\u00a024, 68\u201395 (1977)","journal-title":"J. ACM"},{"key":"2_CR19","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1017\/S0960129501003590","volume":"12","author":"H.P. Gumm","year":"2002","unstructured":"Gumm, H.P., Schr\u00f6der, T.: Coalgebras of bounded type. Math. Structures in Computer Science\u00a012, 565\u2013578 (2002)","journal-title":"Math. Structures in Computer Science"},{"key":"2_CR20","unstructured":"Gumm, H.P.: Universelle Coalgebra. In: Ihringer, T. (ed.) Allgemeine Algebra. Heldermann Verlag (2003)"},{"key":"2_CR21","doi-asserted-by":"publisher","first-page":"1048","DOI":"10.1145\/359657.359666","volume":"21","author":"J. Guttag","year":"1978","unstructured":"Guttag, J., Horowitz, E., Musser, D.R.: Abstract Data Types and Software Validation. Communications of the ACM\u00a021, 1048\u20131064 (1978)","journal-title":"Communications of the ACM"},{"key":"2_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/978-3-642-13321-3_13","volume-title":"Mathematics of Program Construction","author":"R. Hinze","year":"2010","unstructured":"Hinze, R.: Adjoint Folds and Unfolds. In: Bolduc, C., Desharnais, J., Ktari, B. (eds.) MPC 2010. LNCS, vol.\u00a06120, pp. 195\u2013228. Springer, Heidelberg (2010)"},{"key":"2_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/978-3-642-17685-2_3","volume-title":"Central European Functional Programming School","author":"R. Hinze","year":"2010","unstructured":"Hinze, R.: Reasoning about Codata. In: Horv\u00e1th, Z., Plasmeijer, R., Zs\u00f3k, V. (eds.) CEFP 2009. LNCS, vol.\u00a06299, pp. 42\u201393. Springer, Heidelberg (2010)"},{"key":"2_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1007\/BFb0000477","volume-title":"Algebraic Methodology and Software Technology","author":"B. Jacobs","year":"1997","unstructured":"Jacobs, B.: Invariants, Bisimulations and the Correctness of Coalgebraic Refinements. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol.\u00a01349, pp. 276\u2013291. Springer, Heidelberg (1997)"},{"key":"2_CR25","volume-title":"Introduction to Coalgebra","author":"B. Jacobs","year":"2005","unstructured":"Jacobs, B.: Introduction to Coalgebra. Radboud University, Nijmegen (2005)"},{"key":"2_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1007\/11780274_20","volume-title":"Algebra, Meaning, and Computation","author":"B. Jacobs","year":"2006","unstructured":"Jacobs, B.: A Bialgebraic Review of Deterministic Automata, Regular Expressions and Languages. In: Futatsugi, K., Jouannaud, J.-P., Bevilacqua, V. (eds.) Algebra, Meaning, and Computation. LNCS, vol.\u00a04060, pp. 375\u2013404. Springer, Heidelberg (2006)"},{"key":"2_CR27","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1145\/357195.357202","volume":"5","author":"S. Kamin","year":"1983","unstructured":"Kamin, S.: Final Data Type Specifications: A New Data Type Specification Method. ACM TOPLAS\u00a05, 97\u2013123 (1983)","journal-title":"ACM TOPLAS"},{"key":"2_CR28","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/BF01110627","volume":"103","author":"J. Lambek","year":"1968","unstructured":"Lambek, J.: A fixpoint theorem for complete categories. Math. Zeitschrift\u00a0103, 151\u2013161 (1968)","journal-title":"Math. Zeitschrift"},{"key":"2_CR29","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BF01752392","volume":"14","author":"D.J. Lehmann","year":"1981","unstructured":"Lehmann, D.J., Smyth, M.B.: Algebraic Specification of Data Types: A Synthetic Approach. Math. Systems Theory\u00a014, 97\u2013139 (1981)","journal-title":"Math. Systems Theory"},{"key":"2_CR30","first-page":"459","volume-title":"Algebraic Methods in Semantics","author":"J. Meseguer","year":"1985","unstructured":"Meseguer, J., Goguen, J.A.: Initiality, Induction and Computability. In: Nivat, M., Reynolds, J. (eds.) Algebraic Methods in Semantics, pp. 459\u2013541. Cambridge University Press, Cambridge (1985)"},{"key":"2_CR31","doi-asserted-by":"crossref","unstructured":"Meseguer, J., Rosu, G.: The Rewriting Logic Semantics Project. Theoretical Computer Science 373 (2007)","DOI":"10.1016\/j.tcs.2006.12.018"},{"key":"2_CR32","first-page":"277","volume-title":"Proc. 2nd AMAST","author":"E.A. Meulen van der","year":"1992","unstructured":"van der Meulen, E.A.: Deriving incremental implementations from algebraic specifications. In: Proc. 2nd AMAST, pp. 277\u2013286. Springer, Heidelberg (1992)"},{"key":"2_CR33","series-title":"IFIP State-of-the-Art Report","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/978-3-642-59851-7_10","volume-title":"Algebraic Foundations of Systems Specification","author":"P. Padawitz","year":"1999","unstructured":"Padawitz, P.: Proof in Flat Specifications. In: Astesiano, E., Kreowski, H.-J., Krieg-Br\u00fcckner, B. (eds.) Algebraic Foundations of Systems Specification. IFIP State-of-the-Art Report, pp. 321\u2013384. Springer, Heidelberg (1999)"},{"key":"2_CR34","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/S0304-3975(00)00171-7","volume":"243","author":"P. Padawitz","year":"2000","unstructured":"Padawitz, P.: Swinging Types = Functions + Relations + Transition Systems. Theoretical Computer Science\u00a0243, 93\u2013165 (2000)","journal-title":"Theoretical Computer Science"},{"key":"2_CR35","unstructured":"Padawitz, P.: Dialgebraic Specification and Modeling, slides, TU Dortmund (2011), http:\/\/fldit-www.cs.tu-dortmund.de\/~peter\/DialgSlides.pdf"},{"key":"2_CR36","unstructured":"Padawitz, P.: Algebraic compilers and their implementation in Haskell, Sierra Nevada IFIP WG 1.3 Meeting (January 14-18, 2008)"},{"key":"2_CR37","unstructured":"Padawitz, P.: Algebraic Model Checking. In: Drewes, F., Habel, A., Hoffmann, B., Plump, D. (eds.) Manipulation of Graphs, Algebras and Pictures. Electronic Communications of the EASST, vol.\u00a026 (2010), extended slides http:\/\/fldit-www.cs.tu-dortmund.de\/~peter\/CTL.pdf"},{"key":"2_CR38","unstructured":"Padawitz, P.: Expander2 as a Prover and Rewriter, http:\/\/fldit-www.cs.tu-dortmund.de\/~peter\/Prover.pdf"},{"key":"2_CR39","unstructured":"Padawitz, P.: \u00dcbersetzerbau, course notes, TU Dortmund (2010), http:\/\/fldit-www.cs.tu-dortmund.de\/~peter\/CbauFolien.pdf"},{"key":"2_CR40","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0304-3975(00)00056-6","volume":"249","author":"J.J.M.M. Rutten","year":"2000","unstructured":"Rutten, J.J.M.M.: Universal Coalgebra: A Theory of Systems. Theoretical Computer Science\u00a0249, 3\u201380 (2000)","journal-title":"Theoretical Computer Science"},{"key":"2_CR41","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1007\/BFb0055624","volume-title":"CONCUR \u201998 Concurrency Theory","author":"J.J.M.M. Rutten","year":"1998","unstructured":"Rutten, J.J.M.M.: Automata and coinduction (an exercise in coalgebra). In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol.\u00a01466, pp. 194\u2013218. Springer, Heidelberg (1998)"},{"key":"2_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0304-3975(02)00895-2","volume":"308","author":"J.J.M.M. Rutten","year":"2003","unstructured":"Rutten, J.J.M.M.: Behavioural differential equations: a coinductive calculus of streams, automata, and power series. Theoretical Computer Science\u00a0308, 1\u201353 (2003)","journal-title":"Theoretical Computer Science"},{"key":"2_CR43","doi-asserted-by":"crossref","unstructured":"Rutten, J.J.M.M., Turi, D.: Initial Algebra and Final Coalgebra Semantics for Concurrency, Report CS-R9409, CWI, Amsterdam (1994)","DOI":"10.1007\/3-540-58043-3_28"},{"key":"2_CR44","series-title":"ENTCS","first-page":"226","volume-title":"Proc. Runtime Verification 2003","author":"K. Sen","year":"2003","unstructured":"Sen, K., Rosu, G.: Generating Optimal Monitors for Extended Regular Expressions. In: Proc. Runtime Verification 2003. ENTCS, vol.\u00a089, pp. 226\u2013245. Elsevier, Amsterdam (2003)"},{"key":"2_CR45","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/0304-3975(81)90080-3","volume":"15","author":"J.W. Thatcher","year":"1981","unstructured":"Thatcher, J.W., Wagner, E.G., Wright, J.B.: More on Advice on Structuring Compilers and Proving Them Correct. Theoretical Computer Science\u00a015, 223\u2013249 (1981)","journal-title":"Theoretical Computer Science"},{"key":"2_CR46","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/978-3-540-25935-0_13","volume-title":"Domain-Specific Program Generation","author":"E. Visser","year":"2004","unstructured":"Visser, E.: Program Transformation with Stratego\/XT: Rules, Strategies, Tools, and Systems. In: Lengauer, C., Batory, D., Blum, A., Vetta, A. (eds.) Domain-Specific Program Generation. LNCS, vol.\u00a03016, pp. 216\u2013238. Springer, Heidelberg (2004)"},{"key":"2_CR47","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/0022-0000(79)90011-4","volume":"19","author":"M. Wand","year":"1979","unstructured":"Wand, M.: Final algebra semantics and data type extension. J. Comp. Syst. Sci.\u00a019, 27\u201344 (1979)","journal-title":"J. Comp. Syst. Sci."},{"key":"2_CR48","first-page":"675","volume-title":"Handbook of Theoretical Computer Science","author":"M. Wirsing","year":"1990","unstructured":"Wirsing, M.: Algebraic Specification. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, pp. 675\u2013788. Elsevier, Amsterdam (1990)"}],"container-title":["Lecture Notes in Computer Science","Algebraic Informatics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-21493-6_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T02:03:52Z","timestamp":1560305032000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-21493-6_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642214929","9783642214936"],"references-count":48,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-21493-6_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}