@article(abelAlti:predicative, author = "Andreas Abel and Thorsten Altenkirch", year = "2002", title = "A Predicative Analysis of Structural Recursion", journal = "J. Func. Program.", volume = "12", number = "1", pages = "1--41", doi = "10.1017/S0956796801004191", ) @phdthesis(abel:PhD, author = "Andreas Abel", year = "2006", title = "A Polymorphic Lambda-Calculus with Sized Higher-Order Types", type = "Ph.D. thesis", school = "Ludwig-Maximilians-Universit\"at M\"unchen", ) @inproceedings(abel:aplas07, author = "Andreas Abel", year = "2007", title = "Mixed Inductive/Coinductive Types and Strong Normalization", editor = "Zhong Shao", booktitle = "Proc. of the 5th Asian Symp. on Programming Languages and Systems, APLAS 2007", series = "Lect. Notes in Comput. Sci.", volume = "4807", publisher = "Springer", pages = "286--301", doi = "10.1007/978-3-540-76637-7\_19", ) @article(abel:mscs06, author = "Andreas Abel", year = "2008", title = "Polarized Subtyping for Sized Types", journal = "Math. Struct. in Comput. Sci.", volume = "18", pages = "797--822", doi = "10.1017/S0960129508006853", note = "Special issue on subtyping, edited by Healfdene Goguen and Adriana Compagnoni.", ) @article(abel:lmcs07, author = "Andreas Abel", year = "2008", title = "Semi-continuous Sized Types and Termination", journal = "Logical Meth. in Comput. Sci.", volume = "4", number = "2", doi = "10.2168/LMCS-4(2:3)2008", note = "CSL'06 special issue.", ) @inproceedings(abel:par10, author = "Andreas Abel", year = "2010", title = "{MiniAgda}: {I}ntegrating Sized and Dependent Types", editor = "Ana Bove and Ekaterina Komendantskaya and Milad Niqui", booktitle = "Wksh. on Partiality And Recursion in Interactive Theorem Provers (PAR 2010)", series = "Electr. Proc. in Theor. Comp. Sci.", volume = "43", pages = "14--28", doi = "10.4204/EPTCS.43.2", ) @inproceedings(abel:fossacs11, author = "Andreas Abel", year = "2011", title = "Irrelevance in Type Theory with a Heterogeneous Equality Judgement", editor = "Martin Hofmann", booktitle = "Proc. of the 14th Int. Conf. on Foundations of Software Science and Computational Structures, FOSSACS 2011", series = "Lect. Notes in Comput. Sci.", volume = "6604", publisher = "Springer", pages = "57--71", doi = "10.1007/978-3-642-19805-2\_5", ) @article(aspinallCompagnoni:tcs01, author = "David Aspinall and Adriana B. Compagnoni", year = "2001", title = "Subtyping dependent types", journal = "Theor. Comput. Sci.", volume = "266", number = "1-2", pages = "273--309", doi = "10.1016/S0304-3975(00)00175-4", ) @inproceedings(amadio:guardcondition, author = "Roberto M. Amadio and Solange Coupet-Grimal", year = "1998", title = "Analysis of a Guard Condition in Type Theory (Extended Abstract).", editor = "Maurice Nivat", booktitle = "Proc. of the 1st Int. Conf. on Foundations of Software Science and Computation Structure, FoSSaCS'98", series = "Lect. Notes in Comput. Sci.", volume = "1378", publisher = "Springer", pages = "48--62", doi = "10.1007/BFb0053541", ) @misc(altenkirchDanielsson:par10, author = "Thorsten Altenkirch and Nils Anders Danielsson", year = "2010", title = "Termination Checking in the Presence of Nested Inductive and Coinductive Types", howpublished = "Short note supporting a talk given at PAR 2010, Workshop on Partiality and Recursion in Interactive Theorem Provers, FLoC 2010", url = "http://www.cse.chalmers.se/~nad/publications/altenkirch-danielsson-par2010.pdf", ) @inproceedings(alti:flops10, author = "Thorsten Altenkirch and Nils Anders Danielsson and Andres L{\"o}h and Nicolas Oury", year = "2010", title = "PiSigma: Dependent Types without the Sugar", editor = "Matthias Blume and Naoki Kobayashi and Germ{\'a}n Vidal", booktitle = "Proc. of the 10th Int. Symp. on Functional and Logic Programming, FLOPS 2010", series = "Lect. Notes in Comput. Sci.", volume = "6009", publisher = "Springer", pages = "40--55", doi = "10.1007/978-3-642-12251-4\_5", ) @inproceedings(altenkirchMcBrideSwierstra:plpv07, author = "Thorsten Altenkirch and Conor McBride and Wouter Swierstra", year = "2007", title = "Observational equality, now!", editor = "Aaron Stump and Hongwei Xi", booktitle = "Proc. of the Wksh. Programming Languages meets Program Verification, PLPV 2007", publisher = "ACM Press", pages = "57--68", doi = "10.1145/1292597.1292608", ) @book(aczelRathjen:constructiveSetTheory, author = "Peter Aczel and Michael Rathjen", year = "2008", title = "Notes on Constructive Set Theory", url = "http://www.maths.manchester.ac.uk/logic/mathlogaps/workshop/CST-book-June-08.pdf", note = "Draft.", ) @phdthesis(barras:PhD, author = "Bruno Barras", year = "1999", title = "Auto-validation d'un syst\`eme de preuves avec familles inductives", type = "Ph.D. thesis", school = "Universit\'e Paris 7", ) @article(barras:jfr10, author = "Bruno Barras", year = "2010", title = "Sets in Coq, Coq in Sets", journal = "J. Formalized Reasoning", volume = "3", number = "1", url = "http://jfr.cib.unibo.it/article/view/1695", ) @misc(barras:jfla10, author = "Bruno Barras", year = "2010", title = "The syntactic guard condition of Coq", howpublished = "Talk at the Journ\'ee ``\'egalit\'e et terminaison'' du 2 f\'evrier 2010 in conjunction with JFLA 2010", url = "http://coq.inria.fr/files/adt-2fev10-barras.pdf", ) @inproceedings(barrasBernardo:fossacs08, author = "Bruno Barras and Bruno Bernardo", year = "2008", title = "The Implicit Calculus of Constructions as a Programming Language with Dependent Types", editor = "Roberto M. Amadio", booktitle = "FoSSaCS", series = "Lect. Notes in Comput. Sci.", volume = "4962", publisher = "Springer", pages = "365--379", doi = "10.1007/978-3-540-78499-9\_26", ) @inproceedings(bartheGregoirePastawski:lpar06, author = "Gilles Barthe and Benjamin Gr{\'e}goire and Fernando Pastawski", year = "2006", title = "{CIC\^{}}: Type-Based Termination of Recursive Definitions in the {C}alculus of {I}nductive {C}onstructions", editor = "Miki Hermann and Andrei Voronkov", booktitle = "Proc. of the 13th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2006", series = "Lect. Notes in Comput. Sci.", volume = "4246", publisher = "Springer", pages = "257--271", doi = "10.1007/11916277\_18", ) @inproceedings(bartheGregoireRiba:lernet08, author = "Gilles Barthe and Benjamin Gr{\'e}goire and Colin Riba", year = "2008", title = "A Tutorial on Type-Based Termination", editor = "Ana Bove and Lu\'{\i }s Soares Barbosa and Alberto Pardo and Jorge Sousa Pinto", booktitle = "LerNet ALFA Summer School", series = "Lect. Notes in Comput. Sci.", volume = "5520", publisher = "Springer", pages = "100--152", doi = "10.1007/978-3-642-03153-3\_3", ) @inproceedings(bartheGregoireRiba:csl08, author = "Gilles Barthe and Benjamin Gr{\'e}goire and Colin Riba", year = "2008", title = "Type-Based Termination with Sized Products", editor = "Michael Kaminski and Simone Martini", booktitle = "Computer Science Logic, 22nd Int. Wksh., CSL 2008, 17th Annual Conf. of the EACSL", series = "Lect. Notes in Comput. Sci.", volume = "5213", publisher = "Springer", pages = "493--507", doi = "10.1007/978-3-540-87531-4\_35", ) @inproceedings(blanqui:rta04, author = "Fr\'ed\'eric Blanqui", year = "2004", title = "A Type-Based Termination Criterion for Dependently-Typed Higher-Order Rewrite Systems", editor = "Vincent van Oostrom", booktitle = "Rewriting Techniques and Applications (RTA 2004), Aachen, Germany", series = "Lect. Notes in Comput. Sci.", volume = "3091", publisher = "Springer", pages = "24--39", doi = "10.1007/978-3-540-25979-4\_2", ) @article(cousot:constructiveTarski, author = "Patrick Cousot and Radhia Cousot", year = "1979", title = "Constructive Versions of {T}arski's Fixed Point Theorems", journal = "Pacific Journal of Mathematics", volume = "81", number = "1", pages = "43--57", ) @inproceedings(chen:subtypingCC, author = "Gang Chen", year = "1997", title = "Subtyping Calculus of Construction (Extended Abstract)", editor = "Igor Pr\'{\i }vara and Peter Ruzicka", booktitle = "Proc. of the 22nd Int. Symb. on Mathematical Foundations of Computer Science, MFCS'97", series = "Lect. Notes in Comput. Sci.", volume = "1295", publisher = "Springer", pages = "189--198", doi = "10.1007/BFb0029962", ) @inproceedings(chen:popl03, author = "Gang Chen", year = "2003", title = "Coercive subtyping for the calculus of constructions", booktitle = "Proc. of the 30st ACM Symp. on Principles of Programming Languages, POPL 2003", series = "ACM SIGPLAN Notices", volume = "38", publisher = "ACM Press", pages = "150--159", doi = "10.1145/640128.604145", ) @inproceedings(coquand:infiniteObjects, author = "Thierry Coquand", year = "1993", title = "Infinite Objects in Type Theory", editor = "H. Barendregt and T. Nipkow", booktitle = "Types for Proofs and Programs (TYPES '93)", series = "Lect. Notes in Comput. Sci.", volume = "806", publisher = "Springer", pages = "62--78", doi = "10.1007/3-540-58085-9\_72", ) @inproceedings(danielssonAltenkirch:mpc10, author = "Nils Anders Danielsson and Thorsten Altenkirch", year = "2010", title = "Subtyping, Declaratively", editor = "Claude Bolduc and Jules Desharnais and B{\'e}chir Ktari", booktitle = "Proc. of the 10th Int. Conf. on Mathematics of Program Construction, MPC 2010", series = "Lect. Notes in Comput. Sci.", volume = "6120", publisher = "Springer", pages = "100--118", doi = "10.1007/978-3-642-13321-3\_8", ) @article(damGurov:jlc02, author = "Mads Dam and Dilian Gurov", year = "2002", title = "$\mu $-Calculus with Explicit Points and Approximations", journal = "J. Log. Comput.", volume = "12", number = "2", pages = "255--269", doi = "10.1093/logcom/12.2.255", ) @phdthesis(frade:PhD, author = "Maria {Jo\~{a}o} Frade", year = "2003", title = "Type-Based Termination of Recursive Definitions and Constructor Subtyping in Typed Lambda Calculi", type = "Ph.D. thesis", school = "Universidade do Minho, Departamento de Inform\'{a}tica", ) @article(ghaniHancockPattinson:entcs06, author = "Neil Ghani and Peter Hancock and Dirk Pattinson", year = "2006", title = "Continuous Functions on Final Coalgebras", journal = "Electr. Notes in Theor. Comp. Sci.", volume = "164", number = "1", pages = "141--155", doi = "10.1016/j.entcs.2006.06.009", ) @article(ghaniHancockPattinson:lmcs09, author = "Neil Ghani and Peter Hancock and Dirk Pattinson", year = "2009", title = "Representations of Stream Processors Using Nested Fixed Points", journal = "Logical Meth. in Comput. Sci.", volume = "5", number = "3", doi = "10.2168/LMCS-5(3:9)2009", ) @inproceedings(gimenez:guardeddefinitions, author = "Eduardo Gim\'enez", year = "1995", title = "Codifying Guarded Definitions with Recursive Schemes", editor = "Peter Dybjer and Bengt Nordstr\"{o}m and Jan Smith", booktitle = "Types for Proofs and Programs, Int. Wksh., TYPES'94", series = "Lect. Notes in Comput. Sci.", volume = "996", publisher = "Springer", pages = "39--59", doi = "10.1007/3-540-60579-7\_3", ) @inproceedings(gimenez:strec, author = "Eduardo Gim\'enez", year = "1998", title = "Structural Recursive Definitions in Type Theory", editor = "K. G. Larsen and S. Skyum and G. Winskel", booktitle = "Int. Colloquium on Automata, Languages and Programming (ICALP'98), Aalborg, Denmark", series = "Lect. Notes in Comput. Sci.", volume = "1443", publisher = "Springer", pages = "397--408", doi = "10.1007/BFb0055070", ) @phdthesis(girard:thesis, author = "Jean-Yves Girard", year = "1972", title = "Interpr{\'e}tation fonctionnelle et {\'e}limination des coupures dans l'arithm{\'e}tique d'ordre sup{\'e}rieur", type = "Th{\`e}se de {D}octorat {d'{\'E}tat}", school = "Universit{\'e} de Paris VII", ) @inproceedings(hughesParetoSabry:popl96, author = "John Hughes and Lars Pareto and Amr Sabry", year = "1996", title = "Proving the Correctness of Reactive Systems Using Sized Types", booktitle = "Proc. of the 23rd ACM Symp. on Principles of Programming Languages, POPL'96", pages = "410--423", doi = "10.1145/237721.240882", ) @inproceedings(hutchins:popl10, author = "DeLesley S. Hutchins", year = "2010", title = "Pure subtype systems", editor = "Manuel V. Hermenegildo and Jens Palsberg", booktitle = "Proc. of the 37th ACM Symp. on Principles of Programming Languages, POPL 2010", publisher = "ACM Press", pages = "287--298", doi = "10.1145/1706299.1706334", ) @manual(inria:coq83, author = "INRIA", year = "2010", title = "The Coq Proof Assistant Reference Manual", edition = "version 8.3", organization = "INRIA", url = "http://coq.inria.fr/", ) @article(luoAdams:mscs08, author = "Zhaohui Luo and Robin Adams", year = "2008", title = "Structural subtyping for inductive types with functorial equality rules", journal = "Math. Struct. in Comput. Sci.", volume = "18", number = "5", pages = "931--972", doi = "10.1017/S0960129508006956", ) @inproceedings(mcBride:calco09, author = "Conor McBride", year = "2009", title = "Let's See How Things Unfold: Reconciling the Infinite with the Intensional", editor = "Alexander Kurz and Marina Lenisa and Andrzej Tarlecki", booktitle = "3rd Int. Conf. on Algebra and Coalgebra in Computer Science, CALCO 2009", series = "Lect. Notes in Comput. Sci.", volume = "5728", publisher = "Springer", pages = "113--126", doi = "10.1007/978-3-642-03741-2\_9", ) @inproceedings(mendler:lics, author = "Nax Paul Mendler", year = "1987", title = "Recursive Types and Type Constraints in Second-Order Lambda Calculus", booktitle = "Proc. of the 2nd IEEE Symp. on Logic in Computer Science (LICS'87)", publisher = "IEEE Computer Soc. Press", pages = "30--36", ) @article(milner:goWrong, author = "Robin Milner", year = "1978", title = "A Theory of Type Polymorphism in Programming", journal = "J. Comput. Syst. Sci.", volume = "17", pages = "348--375", doi = "10.1016/0022-0000(78)90014-4", ) @phdthesis(norell:PhD, author = "Ulf Norell", year = "2007", title = "Towards a Practical Programming Language Based on Dependent Type Theory", type = "Ph.D. thesis", school = "Dept of Comput. Sci. and Engrg., Chalmers", address = "G\"{o}teborg, Sweden", ) @phdthesis(pareto:PhD, author = "Lars Pareto", year = "2000", title = "Types for Crash Prevention", type = "Ph.D. thesis", school = "Chalmers University of Technology", ) @inproceedings(pientka:termination, author = "Brigitte Pientka", year = "2001", title = "Termination and Reduction Checking for Higher-Order Logic Programs", editor = "Rajeev Gor\'{e} and Alexander Leitsch and Tobias Nipkow", booktitle = "Automated Reasoning, First International Joint Conference, IJCAR 2001", series = "Lect. Notes in Art. Intell.", volume = "2083", publisher = "Springer", pages = "401--415", doi = "10.1007/3-540-45744-5\_32", ) @article(qianNipkow:jar94, author = "Zhenyu Qian and Tobias Nipkow", year = "1994", title = "Reduction and Unification in Lambda Calculi with a General Notion of Subtype", journal = "J. of Autom. Reasoning", volume = "12", number = "3", pages = "389--406", doi = "10.1007/BF00885767", ) @inproceedings(reynolds:systemF, author = "John C. Reynolds", year = "1974", title = "Towards a Theory of Type Structure", editor = "B. Robinet", booktitle = "Programming Symposium", series = "Lect. Notes in Comput. Sci.", volume = "19", publisher = "Springer", address = "Berlin", pages = "408--425", doi = "10.1007/3-540-06859-7\_148", ) @phdthesis(sacchini:PhD, author = "Jorge Luis Sacchini", year = "2011", title = "On Type-Based Termination and Pattern Matching in the Calculus of Inductive Constructions", type = "Ph.D. thesis", school = "INRIA Sophia-Antipolis and \'Ecole des Mines de Paris", ) @inproceedings(sprengerDam:fossacs03, author = "Christoph Sprenger and Mads Dam", year = "2003", title = "On the Structure of Inductive Reasoning: Circular and Tree-Shaped Proofs in the $\mu $-Calculus", editor = "Andrew D. Gordon", booktitle = "Proc. of the 6th Int. Conf. on Foundations of Software Science and Computational Structures, FoSSaCS 2003", series = "Lect. Notes in Comput. Sci.", volume = "2620", publisher = "Springer", pages = "425--440", doi = "10.1007/3-540-36576-1\_27", ) @inproceedings(schoeppSimpson:fossacs02, author = "Ulrich Sch{\"o}pp and Alex K. Simpson", year = "2002", title = "Verifying Temporal Properties Using Explicit Approximants: Completeness for Context-free Processes", editor = "Mogens Nielsen and Uffe Engberg", booktitle = "Proc. of the 5th Int. Conf. on Foundations of Software Science and Computational Structures, FoSSaCS 2002", series = "Lect. Notes in Comput. Sci.", volume = "2303", publisher = "Springer", pages = "372--386", doi = "10.1007/3-540-45931-6\_26", ) @phdthesis(steffen:PhD, author = "Martin Steffen", year = "1998", title = "Polarized Higher-Order Subtyping", type = "Ph.D. thesis", school = "Technische Fakult{\"a}t, Universit{\"a}t Erlangen", ) @article(tait:functionalsFiniteTypeI, author = "William W. Tait", year = "1967", title = "Intensional Interpretations of Functionals of Finite Type {I}", journal = "J. Symb. Logic", volume = "32", number = "2", pages = "198--212", ) @mastersthesis(wahlstedt:master, author = "David Wahlstedt", year = "2000", title = "Detecting termination using size-change in parameter values", type = "Master's thesis", school = "G{\"o}teborgs Universitet", ) @article(xi:terminationHOSC, author = "Hongwei Xi", year = "2002", title = "Dependent Types for Program Termination Verification", journal = "J. Higher-Order and Symb. Comput.", volume = "15", number = "1", pages = "91--131", doi = "10.1023/A:1019916231463", )