{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T20:59:50Z","timestamp":1725569990160},"publisher-location":"Berlin, Heidelberg","reference-count":45,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642171635"},{"type":"electronic","value":"9783642171642"}],"license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"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":[[2010]]},"DOI":"10.1007\/978-3-642-17164-2_4","type":"book-chapter","created":{"date-parts":[[2010,11,19]],"date-time":"2010-11-19T10:54:39Z","timestamp":1290164079000},"page":"34-46","source":"Crossref","is-referenced-by-count":1,"title":["Reasoning about Computations Using Two-Levels of Logic"],"prefix":"10.1007","author":[{"given":"Dale","family":"Miller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"4_CR1","first-page":"3","volume-title":"35th ACM Symp. on Principles of Programming Languages","author":"B. Aydemir","year":"2008","unstructured":"Aydemir, B., Chargu\u00e9raud, A., Pierce, B.C., Pollack, R., Weirich, S.: Engineering formal metatheory. In: 35th ACM Symp. on Principles of Programming Languages, pp. 3\u201315. ACM, New York (January 2008)"},{"key":"4_CR2","unstructured":"Baelde, D.: A linear approach to the proof-theory of least and greatest fixed points. PhD thesis, Ecole Polytechnique (December 2008)"},{"key":"4_CR3","unstructured":"Baelde, D.: On the expressivity of minimal generic quantification. In: Abel, A., Urban, C. (eds.) International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2008). ENTCS, vol.\u00a0228, pp. 3\u201319 (2008)"},{"key":"4_CR4","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/978-3-540-73595-3_28","volume-title":"Automated Deduction \u2013 CADE-21","author":"D. Baelde","year":"2007","unstructured":"Baelde, D., Gacek, A., Miller, D., Nadathur, G., Tiu, A.: The bedwyr system for model checking over syntactic expressions. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol.\u00a04603, pp. 391\u2013397. Springer, Heidelberg (2007)"},{"key":"4_CR5","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/978-3-540-75560-9_9","volume-title":"Logic for Programming, Artificial Intelligence, and Reasoning","author":"D. Baelde","year":"2007","unstructured":"Baelde, D., Miller, D.: Least and greatest fixed points in linear logic. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol.\u00a04790, pp. 92\u2013106. Springer, Heidelberg (2007)"},{"key":"4_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1007\/978-3-642-14203-1_24","volume-title":"Automated Reasoning","author":"D. Baelde","year":"2010","unstructured":"Baelde, D., Miller, D., Snow, Z.: Focused inductive theorem proving. In: Giesl, J., H\u00e4hnle, R. (eds.) Automated Reasoning. LNCS, vol.\u00a06173, pp. 278\u2013292. Springer, Heidelberg (2010)"},{"key":"4_CR7","unstructured":"Baelde, D., Miller, D., Snow, Z., Viel, A.: Tac: A generic and adaptable interactive theorem prover (2009), http:\/\/slimmer.gforge.inria.fr\/tac\/"},{"key":"4_CR8","series-title":"Texts in Theoretical Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07964-5","volume-title":"Interactive Theorem Proving and Program Development. Coq\u2019Art: The Calculus of Inductive Constructions","author":"Y. Bertot","year":"2004","unstructured":"Bertot, Y., Cast\u00e9ran, P.: Interactive Theorem Proving and Program Development. Coq\u2019Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. Springer, Heidelberg (2004)"},{"key":"4_CR9","doi-asserted-by":"publisher","first-page":"56","DOI":"10.2307\/2266170","volume":"5","author":"A. Church","year":"1940","unstructured":"Church, A.: A formulation of the simple theory of types. J. of Symbolic Logic\u00a05, 56\u201368 (1940)","journal-title":"J. of Symbolic Logic"},{"key":"4_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/3-540-52335-9_47","volume-title":"COLOG-88","author":"T. Coquand","year":"1990","unstructured":"Coquand, T., Paulin, C.: Inductively defined types. In: Martin-L\u00f6f, P., Mints, G. (eds.) COLOG 1988. LNCS, vol.\u00a0417, pp. 50\u201366. Springer, Heidelberg (1990)"},{"key":"4_CR11","unstructured":"Felty, A., Momigliano, A.: Hybrid: A definitional two-level approach to reasoning with higher-order abstract syntax. To appear in the J. of Automated Reasoning"},{"key":"4_CR12","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/978-3-540-71070-7_13","volume-title":"Automated Reasoning","author":"A. Gacek","year":"2008","unstructured":"Gacek, A.: The Abella interactive theorem prover (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol.\u00a05195, pp. 154\u2013161. Springer, Heidelberg (2008)"},{"key":"4_CR13","unstructured":"Gacek, A.: A Framework for Specifying, Prototyping, and Reasoning about Computational Systems. PhD thesis, University of Minnesota (2009)"},{"key":"4_CR14","first-page":"33","volume-title":"23th Symp. on Logic in Computer Science","author":"A. Gacek","year":"2008","unstructured":"Gacek, A., Miller, D., Nadathur, G.: Combining generic judgments with recursive definitions. In: Pfenning, F. (ed.) 23th Symp. on Logic in Computer Science, pp. 33\u201344. IEEE Computer Society Press, Los Alamitos (2008)"},{"key":"4_CR15","doi-asserted-by":"crossref","unstructured":"Gacek, A., Miller, D., Nadathur, G.: Reasoning in Abella about structural operational semantics specifications. In: Abel, A., Urban, C. (eds.) International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2008). ENTCS, vol.\u00a0228, pp. 85\u2013100 (2008)","DOI":"10.1016\/j.entcs.2008.12.118"},{"key":"4_CR16","unstructured":"Gacek, A., Miller, D., Nadathur, G.: A two-level logic approach to reasoning about computations (November 16, 2009) (submitted )"},{"key":"4_CR17","unstructured":"Girard, J.-Y.: A fixpoint theorem in linear logic. An email posting to the mailing list linear@cs.stanford.edu (February 1992)"},{"issue":"1","key":"4_CR18","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1145\/138027.138060","volume":"40","author":"R. Harper","year":"1993","unstructured":"Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. J. of the ACM\u00a040(1), 143\u2013184 (1993)","journal-title":"J. of the ACM"},{"key":"4_CR19","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/0304-3975(75)90011-0","volume":"1","author":"G. Huet","year":"1975","unstructured":"Huet, G.: A unification algorithm for typed \u03bb-calculus. Theoretical Computer Science\u00a01, 27\u201357 (1975)","journal-title":"Theoretical Computer Science"},{"issue":"46","key":"4_CR20","doi-asserted-by":"publisher","first-page":"4747","DOI":"10.1016\/j.tcs.2009.07.041","volume":"410","author":"C. Liang","year":"2009","unstructured":"Liang, C., Miller, D.: Focusing and polarization in linear, intuitionistic, and classical logics. Theoretical Computer Science\u00a0410(46), 4747\u20134768 (2009)","journal-title":"Theoretical Computer Science"},{"key":"4_CR21","unstructured":"McDowell, R.: Reasoning in a Logic with Definitions and Induction. PhD thesis, University of Pennsylvania (December 1997)"},{"key":"4_CR22","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/S0304-3975(99)00171-1","volume":"232","author":"R. McDowell","year":"2000","unstructured":"McDowell, R., Miller, D.: Cut-elimination for a logic with definitions and induction. Theoretical Computer Science\u00a0232, 91\u2013119 (2000)","journal-title":"Theoretical Computer Science"},{"issue":"1","key":"4_CR23","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1145\/504077.504080","volume":"3","author":"R. McDowell","year":"2002","unstructured":"McDowell, R., Miller, D.: Reasoning with higher-order abstract syntax in a logical framework. ACM Trans. on Computational Logic\u00a03(1), 80\u2013136 (2002)","journal-title":"ACM Trans. on Computational Logic"},{"issue":"4","key":"4_CR24","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1093\/logcom\/1.4.497","volume":"1","author":"D. Miller","year":"1991","unstructured":"Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. J. of Logic and Computation\u00a01(4), 497\u2013536 (1991)","journal-title":"J. of Logic and Computation"},{"key":"4_CR25","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/3-540-44957-4_16","volume-title":"Computational Logic - CL 2000","author":"D. Miller","year":"2000","unstructured":"Miller, D.: Abstract syntax for variable binders: An overview. In: Lloyd, J., et al. (eds.) CL 2000. LNCS (LNAI), vol.\u00a01861, pp. 239\u2013253. Springer, Heidelberg (2000)"},{"key":"4_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-540-30124-0_4","volume-title":"Computer Science Logic","author":"D. Miller","year":"2004","unstructured":"Miller, D.: Bindings, mobility of bindings, and the $\\nabla$ -quantifier. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol.\u00a03210, p. 24. Springer, Heidelberg (2004)"},{"key":"4_CR27","doi-asserted-by":"crossref","unstructured":"Miller, D.: Formalizing operational semantic specifications in logic. Concurrency Column of the Bulletin of the EATCS (October 2008)","DOI":"10.1016\/j.entcs.2009.07.020"},{"key":"4_CR28","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/0168-0072(91)90068-W","volume":"51","author":"D. Miller","year":"1991","unstructured":"Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic\u00a051, 125\u2013157 (1991)","journal-title":"Annals of Pure and Applied Logic"},{"key":"4_CR29","first-page":"118","volume-title":"18th Symp. on Logic in Computer Science","author":"D. Miller","year":"2003","unstructured":"Miller, D., Tiu, A.: A proof theory for generic judgments: An extended abstract. In: Kolaitis, P. (ed.) 18th Symp. on Logic in Computer Science, pp. 118\u2013127. IEEE, Los Alamitos (June 2003)"},{"issue":"4","key":"4_CR30","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1145\/1094622.1094628","volume":"6","author":"D. Miller","year":"2005","unstructured":"Miller, D., Tiu, A.: A proof theory for generic judgments. ACM Trans. on Computational Logic\u00a06(4), 749\u2013783 (2005)","journal-title":"ACM Trans. on Computational Logic"},{"key":"4_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/978-3-540-24849-1_19","volume-title":"Types for Proofs and Programs","author":"A. Momigliano","year":"2004","unstructured":"Momigliano, A., Tiu, A.: Induction and co-induction in sequent calculus. In: Coppo, M., Berardi, S., Damiani, F. (eds.) TYPES 2003. LNCS, vol.\u00a03085, pp. 293\u2013308. Springer, Heidelberg (2004)"},{"key":"4_CR32","first-page":"810","volume-title":"Fifth International Logic Programming Conference","author":"G. Nadathur","year":"1988","unstructured":"Nadathur, G., Miller, D.: An Overview of \u03bbProlog. In: Fifth International Logic Programming Conference, Seattle, pp. 810\u2013827. MIT Press, Cambridge (August 1988)"},{"key":"4_CR33","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/3-540-48660-7_25","volume-title":"Automated Deduction - CADE-16","author":"G. Nadathur","year":"1999","unstructured":"Nadathur, G., Mitchell, D.J.: System description: Teyjus \u2014 A compiler and abstract machine based implementation of \u03bbProlog. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol.\u00a01632, pp. 287\u2013291. Springer, Heidelberg (1999)"},{"key":"4_CR34","doi-asserted-by":"crossref","unstructured":"Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle\/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol.\u00a02283. Springer, Heidelberg (2002)","DOI":"10.1007\/3-540-45949-9"},{"key":"4_CR35","first-page":"199","volume-title":"Proceedings of the ACM-SIGPLAN Conference on Programming Language Design and Implementation","author":"F. Pfenning","year":"1988","unstructured":"Pfenning, F., Elliott, C.: Higher-order abstract syntax. In: Proceedings of the ACM-SIGPLAN Conference on Programming Language Design and Implementation, pp. 199\u2013208. ACM Press, New York (1988)"},{"key":"4_CR36","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1007\/3-540-48660-7_14","volume-title":"Automated Deduction - CADE-16","author":"F. Pfenning","year":"1999","unstructured":"Pfenning, F., Sch\u00fcrmann, C.: System description: Twelf \u2014 A meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol.\u00a01632, pp. 202\u2013206. Springer, Heidelberg (1999)"},{"key":"4_CR37","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1145\/1328438.1328483","volume-title":"35th Annual ACM Symposium on Principles of Programming Languages (POPL 2008)","author":"B. Pientka","year":"2008","unstructured":"Pientka, B.: A type-theoretic foundation for programming with higher-order abstract syntax and first-class substitutions. In: 35th Annual ACM Symposium on Principles of Programming Languages (POPL 2008), pp. 371\u2013382. ACM, New York (2008)"},{"key":"4_CR38","doi-asserted-by":"crossref","unstructured":"Poswolsky, A., Sch\u00fcrmann, C.: System description: Delphin - A functional programming language for deductive systems. In: Abel, A., Urban, C. (eds.) International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2008), vol.\u00a0228, pp. 113\u2013120 (2008)","DOI":"10.1016\/j.entcs.2008.12.120"},{"key":"4_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0031929","volume-title":"Nonclassical Logics and Information Processing","author":"P. Schroeder-Heister","year":"1992","unstructured":"Schroeder-Heister, P.: Cut-elimination in logics with definitional reflection. In: Pearce, D., Wansing, H. (eds.) All-Berlin 1990. LNCS, vol.\u00a0619, Springer, Heidelberg (1992)"},{"key":"4_CR40","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1109\/LICS.1993.287585","volume-title":"Eighth Annual Symposium on Logic in Computer Science","author":"P. Schroeder-Heister","year":"1993","unstructured":"Schroeder-Heister, P.: Rules of definitional reflection. In: Vardi, M. (ed.) Eighth Annual Symposium on Logic in Computer Science, pp. 222\u2013232. IEEE Computer Society Press, Los Alamitos (June 1993)"},{"key":"4_CR41","unstructured":"Sch\u00fcrmann, C.: Automating the Meta Theory of Deductive Systems. PhD thesis, Carnegie Mellon University (October 2000) CMU-CS-00-146"},{"key":"4_CR42","unstructured":"Tiu, A.: A Logical Framework for Reasoning about Logical Specifications. PhD thesis, Pennsylvania State University (May 2004)"},{"key":"4_CR43","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/11539452_7","volume-title":"CONCUR 2005 \u2013 Concurrency Theory","author":"A. Tiu","year":"2005","unstructured":"Tiu, A.: Model checking for \u03c0-calculus using proof search. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol.\u00a03653, pp. 36\u201350. Springer, Heidelberg (2005)"},{"key":"4_CR44","doi-asserted-by":"crossref","unstructured":"Tiu, A., Miller, D.: Proof search specifications of bisimulation and modal logics for the \u03c0-calculus. ACM Trans. on Computational Logic\u00a011(2) (2010)","DOI":"10.1145\/1656242.1656248"},{"issue":"4","key":"4_CR45","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10817-008-9097-2","volume":"40","author":"C. Urban","year":"2008","unstructured":"Urban, C.: Nominal reasoning techniques in Isabelle\/HOL. J. of Automated Reasoning\u00a040(4), 327\u2013356 (2008)","journal-title":"J. of Automated Reasoning"}],"container-title":["Lecture Notes in Computer Science","Programming Languages and Systems"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-17164-2_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T20:00:59Z","timestamp":1636833659000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-17164-2_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642171635","9783642171642"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-17164-2_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}