{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T02:46:33Z","timestamp":1743129993801,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":25,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642198045"},{"type":"electronic","value":"9783642198052"}],"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\/978-3-642-19805-2_5","type":"book-chapter","created":{"date-parts":[[2011,3,14]],"date-time":"2011-03-14T13:05:14Z","timestamp":1300107914000},"page":"57-71","source":"Crossref","is-referenced-by-count":6,"title":["Irrelevance in Type Theory with a Heterogeneous Equality Judgement"],"prefix":"10.1007","author":[{"given":"Andreas","family":"Abel","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"5_CR1","unstructured":"Abel, A.: Extensional normalization in the logical framework with proof irrelevant equality. In: Danvy, O. (ed.) 2009 Wksh. on Normalization by Evaluation (2009)"},{"key":"5_CR2","unstructured":"Abel, A.: MiniAgda: Integrating sized and dependent types. In: Bove, A., Komendantskaya, E., Niqui, M. (eds.) Wksh. on Partiality And Recursion in Interactive Theorem Provers (PAR 2010) (2010)"},{"key":"5_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/978-3-540-70594-9_4","volume-title":"Mathematics of Program Construction","author":"A. Abel","year":"2008","unstructured":"Abel, A., Coquand, T., Dybjer, P.: Verifying a semantic \u03b2\u03b7-conversion test for martin-l\u00f6f type theory. In: Audebaud, P., Paulin-Mohring, C. (eds.) MPC 2008. LNCS, vol.\u00a05133, pp. 29\u201356. Springer, Heidelberg (2008)"},{"key":"5_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/978-3-642-02273-9_3","volume-title":"Typed Lambda Calculi and Applications","author":"A. Abel","year":"2009","unstructured":"Abel, A., Coquand, T., Pagano, M.: A modular type-checking algorithm for type theory with singleton types and proof irrelevance. In: Curien, P.-L. (ed.) TLCA 2009. LNCS, vol.\u00a05608, pp. 5\u201319. Springer, Heidelberg (2009)"},{"key":"5_CR5","series-title":"Lecture Notes in Computer Science","volume-title":"Foundations of Software Science and Computational Structures","year":"2008","unstructured":"Amadio, R.M. (ed.): FOSSACS 2008. LNCS, vol.\u00a04962. Springer, Heidelberg (2008)"},{"key":"5_CR6","series-title":"SIGPLAN Notices","first-page":"239","volume-title":"Proc. of the 3rd ACM SIGPLAN Int. Conf. on Functional Programming (ICFP 1998)","author":"L. Augustsson","year":"1999","unstructured":"Augustsson, L.: Cayenne - a language with dependent types. In: Proc. of the 3rd ACM SIGPLAN Int. Conf. on Functional Programming (ICFP 1998). SIGPLAN Notices, vol.\u00a034, pp. 239\u2013250. ACM Press, New York (1999)"},{"issue":"4","key":"5_CR7","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1093\/logcom\/14.4.447","volume":"14","author":"S. Awodey","year":"2004","unstructured":"Awodey, S., Bauer, A.: Propositions as [Types]. J. Log. Comput.\u00a014(4), 447\u2013471 (2004)","journal-title":"J. Log. Comput."},{"key":"5_CR8","doi-asserted-by":"crossref","unstructured":"Barras, B., Bernardo, B.: The implicit calculus of constructions as a programming language with dependent types. In: Amadio [5], pp. 365\u2013379","DOI":"10.1007\/978-3-540-78499-9_26"},{"key":"5_CR9","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 \u2013 A Functional Language with Dependent Types. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol.\u00a05674, pp. 73\u201378. Springer, Heidelberg (2009)"},{"key":"5_CR10","series-title":"Sci. Comput. Program.","first-page":"167","volume-title":"Proc. of the 3rd Int. Conf. on Mathematics of Program Construction, MPC 1995","author":"T. Coquand","year":"1996","unstructured":"Coquand, T.: An algorithm for type-checking dependent types. In: Proc. of the 3rd Int. Conf. on Mathematics of Program Construction, MPC 1995. Sci. Comput. Program., vol.\u00a026, pp. 167\u2013177. Elsevier, Amsterdam (1996)"},{"key":"5_CR11","unstructured":"Goguen, H.: A Typed Operational Semantics for Type Theory. PhD thesis, University of Edinburgh, Available as LFCS Report ECS-LFCS-94-304 (August 1994)"},{"issue":"1","key":"5_CR12","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1145\/1042038.1042041","volume":"6","author":"R. Harper","year":"2005","unstructured":"Harper, R., Pfenning, F.: On equivalence and canonical forms in the LF type theory. ACM Transactions on Computational Logic\u00a06(1), 61\u2013101 (2005)","journal-title":"ACM Transactions on Computational Logic"},{"key":"5_CR13","unstructured":"INRIA. The Coq Proof Assistant Reference Manual. INRIA, version 8.2 edition (2008), http:\/\/coq.inria.fr\/"},{"key":"5_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1007\/3-540-39185-1_12","volume-title":"Types for Proofs and Programs","author":"P. Letouzey","year":"2003","unstructured":"Letouzey, P.: A new extraction for coq. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol.\u00a02646, pp. 200\u2013219. Springer, Heidelberg (2003)"},{"key":"5_CR15","doi-asserted-by":"crossref","unstructured":"McBride, C., McKinna, J.: The view from the left. J. Func. Program (2004)","DOI":"10.1017\/S0956796803004829"},{"key":"5_CR16","doi-asserted-by":"crossref","unstructured":"Miquel, A.: A model for impredicative type systems, universes, intersection types and subtyping. In: Proc. of the 15th IEEE Symp. on Logic in Computer Science (LICS 2000), pp. 18\u201329 (2000)","DOI":"10.1109\/LICS.2000.855752"},{"key":"5_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1007\/3-540-45413-6_27","volume-title":"Typed Lambda Calculi and Applications","author":"A. Miquel","year":"2001","unstructured":"Miquel, A.: The Implicit Calculus of Constructions. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol.\u00a02044, pp. 344\u2013359. Springer, Heidelberg (2001)"},{"key":"5_CR18","unstructured":"Miquel, A.: Le Calcul des Constructions implicite: syntaxe et s\u00e9mantique. PhD thesis, Universit\u00e9 Paris 7 (December 2001)"},{"key":"5_CR19","doi-asserted-by":"crossref","unstructured":"Mishra-Linger, N., Sheard, T.: Erasure and polymorphism in pure type systems. In: Amadio [5], pp. 350\u2013364","DOI":"10.1007\/978-3-540-78499-9_25"},{"key":"5_CR20","unstructured":"Mishra-Linger, R.N.: Irrelevance, Polymorphism, and Erasure in Type Theory. PhD thesis, Portland State University (2008)"},{"issue":"5\/6","key":"5_CR21","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1016\/S0747-7171(06)80007-6","volume":"15","author":"C. Paulin-Mohring","year":"1993","unstructured":"Paulin-Mohring, C., Werner, B.: Synthesis of ML programs in the system Coq. J. Symb. Comput.\u00a015(5\/6), 607\u2013640 (1993)","journal-title":"J. Symb. Comput."},{"key":"5_CR22","unstructured":"Pfenning, F.: Intensionality, extensionality, and proof irrelevance in modal type theory. In: LICS 2001: IEEE Symposium on Logic in Computer Science (June 2001)"},{"key":"5_CR23","unstructured":"Reed, J.: Proof irrelevance and strict definitions in a logical framework, Senior Thesis, published as Carnegie-Mellon University technical report CMU-CS-02-153 (2002)"},{"key":"5_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/10930755_16","volume-title":"Theorem Proving in Higher Order Logics","author":"J. Reed","year":"2003","unstructured":"Reed, J.: Extending Higher-Order Unification to Support Proof Irrelevance. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol.\u00a02758, pp. 238\u2013252. Springer, Heidelberg (2003)"},{"key":"5_CR25","doi-asserted-by":"crossref","unstructured":"Werner, B.: On the strength of proof-irrelevant type theories. Logical Meth. in Comput. Sci.\u00a04 (2008)","DOI":"10.2168\/LMCS-4(3:13)2008"}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computational Structures"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-19805-2_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T07:09:52Z","timestamp":1741072192000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-19805-2_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642198045","9783642198052"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-19805-2_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}