%% %% %% BibTeX-file{ %% author = {Lars Birkedal} %% date = {June 1999} %% filename = {realizability.bib} %% url = {http://www.cs.cmu.edu/~birkedal/realizability.bib} %% abstract = {Bibiliography on Realizability} %% } %% %% The BibTeX entries are formatted following the guidelines %% for bibliography files in Hypatia, see %% http://www.hypatia.dcs.qmw.ac.uk/html/bibliography %% %% %% %% @inproceedings{AbadiM:modprt, author = {M. Abadi and G.D. Plotkin}, title = {A per Model of Polymorphism and Recursive Types}, pages = {355-365}, editor = {J. Mitchell}, booktitle = {5th Annual IEEE Symposium on Logic in Computer Science}, address = {Philadelphia}, publisher= {IEEE Computer Society Press}, year = 1990 } @book{AbadiM:theo, author = "M. Abadi and L. Cardelli", title = "A Theory of Objects", publisher = "Springer Verlag", Year = 1996 } @Unpublished{AbramskyS:typrea, author = {S. Abramsky}, title = {Typed Realizability}, note = {Talk at the workshop on Category Theory and Computer Science in Cambridge, England}, year = 1995, month = aug } @misc{AczelP:intiho, author="Aczel, P.H.G.", title="A note on interpreting intuitionistic higher-order logic", year=1980, note="Handwritten note" } @phdthesis{AltenkirchT:conits, author = "T. Altenkirch", title = "Constructions, Inductive Types and Strong Normalization", year = 1993, school = "University of Edinburgh", note = "Available as report ECS-LFCS-93-279" } @article{AmadioR:recor, author = {R. Amadio}, title = {Recursion over Realizability Structures}, journal = {Information and Computation}, year = 1991, volume = 91, pages = {55-85} } @techreport{AspertiA:intmpl, author = {A. Asperti}, title = {The Internal Model of Polymorphic Lambda Calculus}, year = 1988, number = {CMU-CS-88-155}, institution = {Carnegie Mellon University} } @InProceedings{AvigadJ:reaica, author = {J. Avigad}, title = {A realizability interpretation for classical arithmetic}, booktitle = {Logic Colloquium '98}, pages = {57--90}, year = 2000, editor = {Buss and H\'ajek and Pudl\'ak}, number = 13, series = {Lecture Notes in Logic}, publisher = {AK Peters} } @Unpublished{AwodeyS:locrtm, author = {S.~Awodey and L.~Birkedal and D.S.~Scott}, title = {Local Realizability Toposes and a Modal Logic for Computability}, note = {Presented at \emph{Tutorial Workshop on Realizability Semantics, FLoC'99}, Trento, Italy 1999.}, year = 1999 } @article{BainbridgeS:funp, author = {S. Bainbridge and P.J. Freyd and A. Scedrov and P. Scott}, title = {Functorial Polymorphism}, journal = {Theoretical Computer Science}, year = 1990, volume = 70, pages = {35-64} } @article{BarbaneraF:profcr, author="Barbanera, F. and Martini, S.", title="Proof--Functional Connectives and Realizability", journal="Archive for Mathematical Logic", volume=33, year=1994, pages="189--211" } @article{BarendregtHP:comlac, author="Barendregt, H.P.", title="Combinatory logic and the axiom of choice", journal="Indagationes Mathematicae", year=1973, volume=35, pages="203--221" } @article{BarendregtHP:intgts, author = {Barendregt, H.P.}, title = {Introduction to Generalized Type Systems}, journal = {Journal of Functional Programming}, volume = 1, number = 2, year = 1991, pages = {125--154}, source = {ftp://src.doc.ic.ac.uk/computing/bibliographies/Karlsruhe/Compiler/Functional.bib/}, source-date = {Tue 26 Aug 97}} @inproceedings{BarrM:exac, author = {M. Barr}, title = {Exact Categories}, pages = {1-120}, editor = {M. Barr and P.A. Grillet and D. Van Osdol}, booktitle = {Exact Categories and Categories of Sheaves}, series = {Lecture Notes in Mathematics}, volume = 236, publisher = {Springer-Verlag}, year = 1971 } @unpublished{BauerA:equs, author = {A. Bauer and L. Birkedal and D.S. 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International Workshop LCC '94, Indianapolis, IN, USA, October 1994", editor="Leivant, D.", year=1995, publisher={Springer-Verlag}, pages="77-97", volume=960, series="Lecture Notes in Computer Science" } @misc{BergerU:propms, author="Berger, U. and Schwichtenberg, H. and Seisenberger, M.", title="From Proofs to Programs in the {Minlog} System. {T}he {W}arshall algorithm and {H}igman's lemma", year=1997, note="To appear in {\it Journal of Automated Reasoning}" } @phdthesis{BethkeI:npca, author = {I. Bethke}, title = {Notes on Partial Combinatory Algebras}, school = {Universiteit van Amsterdam}, year = 1988 } @phdthesis{BezemM:barrff, author="Bezem, M.", title="Bar Recursion and Functionals of Finite Type", year=1986, school="Rijksuniversiteit Utrecht" } @article{BezemM:commff, author="Bezem, M.", title="Compact and Majorizable Functionals of Finite Type", journal={Journal of Symbolic Logic}, pages="271--280", year=1989, volume=54 } @article{BezemM:majfft, author="Bezem, M.", title="Strongly Majorizable Functionals of Finite Type: a Model for Bar Recursion Containing Discontinuous Functionals", journal={Journal of Symbolic Logic}, year=1985, volume=50, pages="652--660" } @PhdThesis{BirkedalL:devttc, author = {L. Birkedal}, title = {Developing Theories of Types and Computability}, school = {School of Computer Science, Carnegie Mellon University}, year = 1999, month = dec } @inproceedings{BirkedalL:ttec, author = {L. Birkedal and A. Carboni and G. Rosolini and D.S. Scott}, title = {Type Theory via Exact Categories}, booktitle = {Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science}, year = 1998, publisher = {IEEE Computer Society Press}, address = {Indianapolis, Indiana}, month = jun, pages = {188--198} } @inproceedings{BruceK:permod, author="Bruce, K. and Mitchell, J.C.", title="PER models of subtyping, recursive types and higher-order polymorphism", year=1992, booktitle={Proc.\ 19th ACM Symp.\ on Principles of Programming}, pages="316--327" } @book{BuchholzW:iteids, author="Buchholz, W. and Feferman, S. and Pohlers, W. and Sieg, W.", title="Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies", year=1981, publisher={Springer-Verlag}, } @inproceedings{BussS:polhiba, author="Buss, S.", title="The Polynomial Hierarchy and Intuitionistic Bounded Arithmetic", booktitle="Structure in Complexity Theory", publisher={Springer-Verlag}, year=1986, pages="77-103", series="Springer Lecture Notes in Computer Science", volume=223 } @inproceedings{CarboniA:catarp, author = {A. Carboni and P.J. Freyd and A. Scedrov}, title = {A Categorical Approach to Realizability and Polymorphic Types}, pages = {23-42}, editor = {M. Main and A. Melton and M. Mislove and D.Schmidt}, booktitle ={Mathematical Foundations of Programming Language Semantics}, address = {New Orleans}, series = {Lectures Notes in Computer Science}, volume = 298, publisher ={Springer-Verlag}, year = 1988 } @article{CarboniA:freecl, author = {A. Carboni and R. Celia Magno}, title = {The Free Exact Category on a Left Exact one}, journal = {Journal of Australian Mathematical Society}, volume = 33, year = 1982, number = {A}, pages = {295-301} } @misc{CarboniA:lccec, author = {A. Carboni and G. Rosolini}, title = {Locally Cartesian Closed Exact Completions}, journal = {Journal of Pure and Applied Algebra}, year = {1998}, OPTvolume = {}, note = {to appear} } @article{CarboniA:regec, author = {A. Carboni and E.M. Vitale}, title = {Regular and Exact Completions}, year = {1998}, volume = 125, journal = {Journal of Pure and Applied Algebra}, pages = {79-117} } @article{CarboniA:somfcr, author = {A. Carboni}, title = {Some Free Constructions in Realizability and Proof Theory}, journal = {Journal of Pure and Applied Algebra}, volume = 103, year = 1995, pages = {117-148} } @techreport{CardelliL:sembq, author = {L. Cardelli and G. Longo}, title = {A Semantic Basis for {Q}uest}, year = 1989, number = 55, institution = {Digital Equipment Corporation} } @article{CellucciC:opebrf, author="Cellucci, C.", title="Operazioni di {B}rouwer e Realizzabilita Formalizzata ({E}nglish Summary)", year=1971, journal="Annali della Scuola Normale Superiore di Pisa. Classe di Science. 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G{\"o}del}, title = {Zur intuitionistischen Arithmetik und Zahlentheorie}, journal = {Ergebnisse eines mathematisches Kolloquiums}, year = 1932, volume = 4, pages = {34-38} } @article{GoedelK:ubeefs, author="G{\"o}del, K.", title="{\"U}ber eine bisher noch nicht ben{\"u}tzte {E}rweiterung des finiten {S}tandpunktes", year=1958, journal="Dialectica", volume=12, pages="280--287", reviews="JSL 25.351; MR 21#1275; MR 81i:03094; ZBL 90.10" } @article{GoodmanN:relria, author="Goodman, N.D.", title="Relativized Realizability in Intuitionistic Arithmetic of all Finite Types", year=1978, journal={Journal of Symbolic Logic}, volume=43, pages="23--44", reviews="MR 81b:03061; RZH 79.2A46; ZBL 395#03038" } @inproceedings{Grayson:heymis, author = "R.J. Grayson", title = "Heyting-valued Models for Intuitionistic Set Theory", booktitle = "Application of Sheaves", editor = "M. Fourman and C. Mulvey and D.S. Scott", year = 1979, volume = 743, series = {Lecture Notes in Mathematics}, pages = "402--414", publisher = "Springer", address = "Berlin"} @misc{GraysonR:appmrt, title="Appendix to modified realisability toposes", author="Grayson, R.J.", note="Handwritten notes from M{\"u}nster University", year="1982" } @misc{GraysonR:derrmt, title="Derived Rules Obtained by a Model-Theoretic Approach to Realisability", author="Grayson, R.J.", note="Handwritten notes from M{\"u}nster University", year=1981, } @misc{GraysonR:extr, title="Note on extensional realizability", author="Grayson, R.J.", note="Handwritten notes from M{\"u}nster University", year="1981" } @misc{GraysonR:modrt, title="Modified realisability toposes", author="Grayson, R.J.", note="Handwritten notes from M{\"u}nster University", year=1981 } @misc{GraysonR:notr, author = {R. Grayson}, title = {Notes on realizability}, year = 1982 } @article{HarnikV:lamcpt, author="Harnik, V. and Makkai, M.", title="Lambek's Categorical Proof Theory and {L}{\"a}uchli's Abstract Realizability", year=1992, journal={Journal of Symbolic Logic}, volume=57, pages="200--230" } @article{HarnikV:protfi, author="Harnik, V.", title="Provably Total Functions of Intuitionistic Bounded Arithmetic", journal={Journal of Symbolic Logic}, year=1992, pages="466--477", volume=57 } @proceedings{HeytingA:conm, title="Constructivity in Mathematics", editor="Heyting, A.", year=1959, publisher={North-Holland Publishing Company} } @article{HiggsD:injtch, author="Higgs,D.", title="Injectivity in the Topos of Complete Heyting Algebra valued Sets", journal={Canadian Journal of Mathematics}, year=1984, pages="550--568", volume=36, number=3 } @book{HilbertD:grum, author = "D. Hilbert and P. Bernays", title = "Grundlagen der Mathematik I", publisher = "Springer Verlag", Year = 1934 } @InProceedings{HofmannM:semaho, author = {M.~Hofmann}, title = {Semantical Analysis of Higher-Order Abstract Syntax}, booktitle = {14th Annual Symposium on Logic in Computer Science}, publisher = {IEEE Computer Society Press, Washington}, year = 1999, pages = {?--?} } @incollection{HofmannM:ssdt, author = "Hofmann, M.", title = "Syntax and Semantics of Dependent Types", editors = "Dybjer, P. and Pitts, A.M.", booktitle = "Semantic and Logic of Computation", publisher = "Cambridge University Press", year=1997 } @incollection{HowardW:apphmf, author="Howard, W.A.", title="Appendix: Hereditarily Majorizable Functionals of Finite Type", year=1973, editor="Troelstra, A. S.", booktitle="Metamathematical Investigation of Intuitionistic Arithmetic and Analysis", publisher={Springer-Verlag}, reviews="MR 48#3699; MR 56#8334; RZH 74.6A90; ZBL 275#02025", note="With contributions by A. S. Troelstra, A. Smory{\'n}ski, J. I. Zucker and W. A. Howard", pages="454--461", reviews="MR 57#9493; RZH 74.6A114" } @inproceedings{HowardW:fortnc, author = "W.A. Howard", title = "To {H.B. Curry}: The Formulae-as-types Notion of Construction", year = 1969, booktitle = "Essays on Combinatory Logic, Lambda Calculus, and Formalism", publisher = "Academic Press", editor = "J. Hindley and J. Seldin" } @inproceedings{HylandJ:algtpm, author = {J.M.E. Hyland and E.P. Robinson and G. Rosolini}, title = {Algebraic Types in {PER} Models}, pages = {333-350}, editor = {M. Main and A. Melton and M. Mislove and D.Schmidt}, booktitle = {Mathematical Foundations of Programming Language Semantics}, address = {New Orleans}, series = {Lecture Notes in Computer Science}, volume = 442, publisher = {Springer-Verlag}, year = 1990 } @article{HylandJ:disote, author = {J.M.E. Hyland and E.P. Robinson and G. Rosolini}, title = {The discrete objects in the effective topos}, journal = {Proceedings of the London Mathematical Society}, year = 1990, volume = 60, pages = {1-60} } @inproceedings{HylandJ:efft, author = {J.M.E. Hyland}, title = {The effective topos}, pages = {165-216}, editor = {A.S. Troelstra and D. Van Dalen}, booktitle ={The {L.E.J. Brouwer} Centenary Symposium}, publisher ={North Holland Publishing Company}, year = 1982 } @inproceedings{HylandJ:firssd, author = {J.M.E. Hyland}, title = {First steps in Synthetic Domain Theory}, pages = {131-156}, editor = {A. Carboni and M.C. Pedicchio and G. Rosolini}, booktitle = {Category Theory '90}, address = {Como}, series = {Lectures Notes in Mathematics}, volume = 1144, publisher = {Springer-Verlag}, year = 1992 } @article{HylandJ:fsct, author = {J.M.E. Hyland}, title = {Filter Spaces and Continuous Functionals}, journal = {Annals of Mathematical Logic}, volume = 16, year = 1979 } @inproceedings{HylandJ:mrtsnp, author = {J.M.E. Hyland and C.-H. L. Ong}, title = {Modified Realizability Toposes and Strong Normalization Proofs}, booktitle = {Typed Lambda Calculi and Applications}, pages = {179--194}, editor = {J.F. Groote and M. Bezem}, series = {Lecture Notes in Computer Science}, volume = 664, publisher = {Springer-Verlag}, year = 1993 } @article{HylandJ:smacc, author = {J.M.E. Hyland}, title = {A Small Complete Category}, journal = {Journal of Pure and Applied Logic}, year = 1988, volume = 40, pages = {135-165} } @article{HylandJ:trit, author = {J.M.E. Hyland and P.T. Johnstone and A.M. Pitts}, title = {Tripos Theory}, journal = {Math. Proc. Camb. Phil. Soc.}, year = 1980, volume = 88, pages = {205-232} } @BOOK{JacobsB:cltt, author = "Jacobs, B.", title = "Categorical Logic and Type Theory", publisher = "Elsevier Science", year = 1999 } @article{JankovV:reafpl, author="Jankov, V.A.", title="Realizable Formulas of Propositional Logic ({R}ussian)", journal={Doklady}, volume=151, year=1963, pages="1035--1037", note="Translation {\em SM} 4, pp. 1146--1148" } @Book{JohnstonePT:indcta, editor = {P.T. Johnstone and R. Par{\'e}}, title = {Indexed Categories and Their Applications}, publisher = {Sringer-Verlag, Berlin}, year = 1978, volume = 661, series = {Lecture Notes in Mathematics} } @article{JohnstonePT:irt, author = {P.T. Johnstone and E.P. Robinson}, title = {A Note on Inequivalence of Realizability Toposes}, journal = {Mathematical Proceedings of Cambridge Philosophical Society}, volume = 105, year = 1989 } @article{JohnstonePT:locmt, author = "P.T. Johnstone and I. Moerdijk", title = "Local Maps of Toposes", journal = "Proc.\ London Math.\ Soc.", year = 1989, volume = 3, number = 58, pages = "281--305" } @Book{JohnstonePT:topt, author = {P.T. Johnstone}, title = {Topos Theory}, publisher = {Academic Press, London}, year = 1977, number = 10, series = {LMS Mathematical Monographs} } @book{JoyalA:algst, author = {Joyal, A. and Moerdijk, I.}, title = {Algebraic Set Theory}, series = {London Mathematical Society Lecture Note Series}, volume = {220}, publisher = {Cambridge University Press}, address = {Cambridge}, year = {1995}, pages = {viii+123} } @article{KabakovF:derrfs, author="Kabakov, F.A.", title="On the Derivability of some Realizable Formulae of the Sentential Calculus ({R}ussian)", journal="ZMLG", volume=9, year=1963, pages="97--104", reviews="MR26#4884,ZBL112.5" } @article{KabakovF:intdrf, author="Kabakov, F.A.", title="Intuitionistic Deducibility of some Realizable Formulae of Propositional Logic ({R}ussian)", journal={Doklady}, year=1970, volume=192, pages="269--271", note="Translation {\em SM} 11, pp. 612--614", reviews="MR41#8209, ZBL212.312" } @article{KabakovF:modpba, author="Kabakov, F.A.", title="On Modelling of Pseudo-Boolean Algebras by Realizability ({R}ussian)", journal={Doklady}, year=1970, volume=192, pages="16--18", note="Translation {\em SM} 11, pp. 562--564", reviews="MR42#43, ZBL278#02019" } @Article{KellyGM:comlel, author = "G.M. Kelly and F.W. Lawvere", title = "On the Complete Lattice of Essential Localizations", journal = "Bull.\ Soc.\ Math.\ Belg.\ Ser.\ A", year = 1989, volume = "XLI", number = 2, pages = "289--319" } @article{KhakhanyanV:comsct, author="Khakhanyan, V. {\protect{Kh}}.", title="Comparative Strength of Variants of {C}hurch's Thesis at the Level of Set Theory ({R}ussian)", year=1980, journal={Doklady}, volume=252, pages="1070--1074", note="Translation {\em SM} 21, pp. 894--898", reviews="MR 81g:03069; ZBL 482#03026" } @article{KhakhanyanV:conicp, author="Khakhanyan, V. {\protect{Kh}}.", title="The Consistency of some Intuitionistic and Constructive Principles with a Set Theory", year=1981, journal="Studia Logica", volume=40, pages="237--248", reviews="MR 84e:03061; ZBL 491#03019" } @article{KhakhanyanV:conistb, author="Khakhanyan, V. {\protect{Kh}}.", title="Consistency of the Intuitionistic Set Theory with {B}rouwer's Principle", journal="Matematika", volume=5, year=1979 } @article{KhakhanyanV:conistc, author="Khakhanyan, V. {\protect{Kh}}.", title="The Consistency of Intuitionistic Set Theory with {C}hurch's Principle and the Uniformization Principle ({R}ussian)", year=1980, journal="Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika", volume=5, pages="3--7", reviews="MR 82b:03106; ZBL 445#03031", note="Translation {\em Moscow University Mathematics Bulletin} 35/5, pp. 3--7" } @article{KhakhanyanV:conistf, author="Khakhanyan, V. {\protect{Kh}}.", title="The Consistency of Intuitionistic Set Theory with Formal Mathematical Analysis ({R}ussian)", year=1980, journal={Doklady}, volume=253, pages="48--52", reviews="MR 81h:03109; ZBL 531#03036", note="Translation {\em SM} 22, pp. 46--50" } @article{KhakhanyanV:nonupct, author="Khakhanyan, V. {\protect{Kh}}.", title="Nonderivability of the Uniformization Principle from {C}hurch's Thesis ({R}ussian)", journal="Matematicheskie Zametki", volume=43, year=1988, pages="685--691,703", note="Translation {\em Mathematical Notes} 43, pp. 394--398", review="MR89g:03089" } @incollection{KhakhanyanV:stct, author="Khakhanyan, V. {\protect{Kh}}.", title="Set Theory and {C}hurch's Thesis ({R}ussian)", year=1983, booktitle="Issledovaniya po Neklascheskims Logikam i Formal'nym Sistemam (Studies in Nonclassical logics and Formal Systems)", publisher="Nauka, Moskva", editor="Mikhajlov, A. I.", pages="198--208", reviews="MR 85d:03117" } @article{KipnisM:concap, author="Kipnis, M.M.", title="The Constructive Classification of Arithmetic Predicates and the Semantic Bases of Arithmetic ({R}ussian)", year=1968, journal="Zapiski", volume=8, pages="53--65", note="Translation {\em Seminars in Mathematics. V.A.Steklov Mathematical Institute Leningrad} 8(1970), pp. 22--27. This volume appeared as: A.O. Slisenko (ed.), {\em Studies in Constructive Mathematics and Mathematical Logic. Part II}. Consultants Bureau, New York, London" } @article{KipnisM:reapf, author="Kipnis, M.M.", title="On the Realizations of Predicate Formulas ({R}ussian) ({E}nglish summary)", journal={Zapiski}, year=1971, volume=20, pages="40--48", note="Translation {\em Journal of Soviet Mathematics} 1(1973), pp. 22--27", reviews="ZBL 222#02021" } @inproceedings{KleeneSC:claeim, author="Kleene, S.C.", title="Classical Extensions of Intuitionistic Mathematics", year=1965, booktitle="LMPS 2", editor="Bar-Hillel, Y.", publisher={North-Holland Publishing Company}, pages="31--44", reviews="JSL 40.508; MR 35#28 ; ZBL 192.30" } @inproceedings{KleeneSC:conffi, author="Kleene, S.C.", title="Constructive Functions in ``{T}he {F}oundations of {I}ntuitionistic {M}athematics''", year=1968, booktitle="LMPS 3", editor="van Rootselaar, B. and Staal, J. F.", publisher={North-Holland Publishing Company}, pages="137--144", reviews="MR 40#5424; ZBL 191.287" } @inproceedings{KleeneSC:couf, author = {S.C. Kleene}, title = {Countable Functionals}, pages = {81-100}, editor = {A. Heyting}, booktitle = {Constructivity in Mathematics}, publisher = {North Holland Publishing Company}, year = 1959 } @article{KleeneSC:diseie, author="Kleene, S.C.", title="Disjunction and Existence under Implication in Elementary Intuitionistic Formalisms", year=1962, journal={Journal of Symbolic Logic}, volume=27, pages="11--18", note="Addenda in {\em JSL} {\bf 28} (1963), pp. 154--156", reviews="JSL 28.166; JSL 29.146; MR 27#1368; MR 32#5515; ZBL 112.245" } @article{KleeneSC:ffqftII, author = {S.C. Kleene}, title = {Recursive Functionals and Quantifiers of Finite Types {II}}, journal = {Trans.\ Amer.\ Math.\ Soc}, volume = 108, year = 1963 } @book{KleeneSC:forrff, author="Kleene, S.C.", title="Formalized Recursive Functionals and Formalized Relizability", year=1969, series="Memoirs of the American Mathematical Society", publisher={American Mathematical Society}, volume="89", reviews="MR 39#5319; ZBL 184.20" } @book{KleeneSC:fouim, author="Kleene, S.C. and Vesley, R.E.", title="The Foundations of Intuitionistic Mathematics, especially in relation to recursive functions", year=1965, publisher={North-Holland Publishing Company}, reviews="JSL 31.258; MR 31#1190; ZBL 133.246", } @article{KleeneSC:intint, author="Kleene, S.C.", title="On the Interpretation of Intuitionistic Number Theory", year=1945, journal={Journal of Symbolic Logic}, volume=10, pages="109--124", reviews="JSL 12.91 ; MR 7.406" } @book{KleeneSC:intmm, author="Kleene, S.C.", title="Introduction to metamathematics", year=1952, publisher={North-Holland Publishing Company}, reviews="JSL 19.215; JSL 25.280; JSL 33.290; JSL 35.350; JSL38.333; MR 14.525 ; ZBL 47.7", note="Co-publisher: Wolters--Noordhoff; 8th revised ed.1980." } @article{KleeneSC:logcr, author="Kleene, S.C.", title="Logical Calculus and Realizability", year=1965, journal="Acta Philosophica Fennica", volume=18, pages="71--80", reviews="MR 33#5485; ZBL 133.252" } @inproceedings{KleeneSC:rea, author="Kleene, S. C.", title="Realizability", year=1957, booktitle="Summaries of Talks presented at the Summer Institute for Symbolic Logic", publisher="Institute for Defense Analyses, Communications Research Division, Princeton", pages="100--104", reviews="JSL 27.242; MR 21#2590; RZH 62.11A63; ZBL 88.249", note="Also in {\em \cite{HeytingA:conm}}, pp. 285--289. Errata in {\em \cite{KleeneSC:fouim}}, page 192" } @inproceedings{KleeneSC:rears, author = {S.C. Kleene}, title = {Realizability: a Retrospective Survey}, pages = {95-112}, editor = {A.R.D. Mathias and H. Rogers}, booktitle = {Cambridge Summer School in Mathematical Logic}, series = {Lecture Notes in Mathematics}, volume = 337, publisher = {Springer-Verlag}, year = 1973 } @article{KleeneSC:reasac, author="Kleene, S.C.", title="Realizability and {S}hanin's Algorithm for the Constructive Deciphering of Mathematical Sentences", year=1960, journal="Logique et Analyse, Nouvelle S{\'e}rie", volume=3, pages="154--165", reviews="JSL 27.243" } @article{KleeneSC:rfqftI, author = {S.C. Kleene}, title = {Recursive Functionals and Quantifiers of Finite Types {I}}, journal = {Trans.\ Amer.\ Math.\ Soc}, volume = 91, year = 1959 } @inproceedings{KleeneSC:rfqftrI, author = {S.C. Kleene}, title = {Recursive Functionals and Quantifiers of Finite Types Revisited {I}}, booktitle = {Generalized Recursion Theory {II}}, editor = {J.E. Fenstad and R.O. Gandy and G.E. Sacks}, pages = {185--222}, year = 1978 } @article{KobayashiS:reaigi, author="Kobayashi, S. and Tatsuta, M.", title="Realizability Interpretation of Generalized Inductive Definitions", year=1994, journal="Theoretical Computer Science", volume=131, pages="121--138" } @article{KohlenbachU:poihma, author="Kohlenbach, U.W.", title="Pointwise Hereditary Majorization and some Applications", year=1992, journal="Archive for Mathematical Logic", pages="227--241", volume=31 } @phdthesis{KohlenbachU:thesis, author="Kohlenbach, U.W.", title="Theorie der majorisierbaren und stetigen {F}unktionale und ihre {A}nwendung bei der {E}xtraktion von {S}chranken aus inkonstruktiven {B}eweisen: effektive {E}indeutigkeitsmodule bei besten {A}pproximationen aus ineffektiven {E}indeutigkeitsbeweisen", year=1990, school="J.W. Goethe-Universit{\"a}t, Frankfurt am Main" } @article{KreiselG:forsia, author="Kreisel, G. and Troelstra, A.S.", title="Formal Systems for some Branches of Intuitionistic Analysis", year=1970, journal={Annals of Pure and Applied Logic}, volume=1, pages="229--387", note="Addendum in {\em APAL} 3, pp. 437--439", reviews="MR 41#8210; MR 45#1729; ZBL 211.11; ZBL 231#02041" } @inproceedings{KreiselG:fouil, author="Kreisel, G.", title="Foundations of Intuitionistic Logic", year=1962, booktitle="LMPS", editor="Nagel, E. and Suppes, P. and Tarski, A.", publisher="Stanford University Press, Stanford", pages="198--210", reviews="JSL 30.243; MR 27#3529; ZBL 133.248" } @incollection{KreiselG:iafft, author = {G. Kreisel}, title = {Interpretation of Analysis by means of Functionals of Finite Type}, booktitle = {Constructivity in Mathematics}, pages = {101--128}, editor = {A. Heyting}, publisher = {North-Holland}, year = 1959, reviews="JSL 36.169; MR 21#5568; ZBL 134.10" } @article{KreiselG:varhtf, author="Kreisel, G.", title="A Variant to {H}ilbert's Theory of the Foundations of Arithmetic", journal="British Journal for the Philosophy of Science", year=1953, volume=4, pages="107--127" } @article{KreiselG:weacipl, author="Kreisel, G.", title="On Weak Completeness of Intuitionistic Predicate Logic", year=1962, journal={Journal of Symbolic Logic}, volume=27, pages="139--158", reviews="JSL 34.119; MR 28#5000; ZBL 117.10" } @article{KrolM:disepi, author="Krol', M.D.", title="Disjunctive and Existential Properties of Intuitionistic Analysis with {K}ripke's scheme ({R}ussian)", journal={Doklady}, volume=234, year=1977, note="Translation {\em SM} 18, pp. 755--758" } @article{KrolM:varfcp, author="Krol', M.D.", title="Various Forms of the Continuity Principle ({R}ussian)", year=1983, journal={Doklady}, volume=271, pages="33--36", note ="Translation {\em SM} 28, pp. 27--30", reviews="MR 84m:03094; ZBL 549#03052" } @inproceedings{KrolM:verr, author="Krol', M.D.", title="On a Version of Realizability ({R}ussian)", year=1992, booktitle="XI Interrepublican Conference on Mathematical Logic, University of Kazan, October 6--8, 1992", pages=81 } @techreport{KurtzS:confsc, author="Kurtz, S.A. and Mitchell, J.C. and O'Donnell, M.J.", title="Connecting Formal Semantics to Constructive Intuitions", institution="Department of Computer Science, University of Chicago", year=1992, number="CS 92--01" } @InProceedings{LambekJ:indpft, author = {J. Lambek and P.J. Scott}, title = {Independence of Premisses and the Free Topos}, booktitle = {Proc. Symp. Constructive Math}, volume = 873, series = {Lecture Notes in Mathematics}, year = 1981, pages = {191--207} } @book{LambekJ:inthoc, author="Lambek, J. and Scott, P. J.", title="Introduction to Higher Order Categorical Logic", publisher="Cambridge University Press, Cambridge", year=1986 } @Article{LambekJ:intttf, author = {J. Lambek and P.J. Scott}, title = {Intuitionistic Type Theory and the Free Topos}, journal = {Journal of Pure and Applied Algebra}, year = 1980, volume = 19, pages = {215--257} } @Article{LambekJ:proip, author = {J. Lambek and P.J. Scott}, title = {New Proofs of some Intutitionistic Principles}, journal = {Zeitschrift f{\"u}r Math. Log.}, year = 1983, volume = 29, pages = {493--504} } @inproceedings{LauchliH:absnri, author="L{\"a}uchli, H.", title="An Abstract Notion of Realizability for which Intuitionistic Predicate Calculus is Complete", year=1970, booktitle="Intuitionism and Proof Theory", editor="Kino, A. and Myhill, J.R. and Vesley, R.E.", publisher = {North-Holland}, pages="227--234", reviews="MR 42#5778; ZBL 216.5" } @article{LawvereFW:adjf, author={F.W.~Lawvere}, title={Adjointness in Foundations}, journal={Dialectica}, volume=23, year=1969, pages={281--296} } @incollection {LawvereFW:daccc, author = {F. W. 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Leivant}, title = {Reasoning about functional programs and complexity classes associated with type disciplines}, booktitle = {Proceedings of the Twenty Fourth Annual Symposium on the Foundations of Computer Science}, pages = {460--469}, year = 1983, publisher = {IEEE Computer Society, Washington} } @incollection{LifschitzV:calnn, author="Lifschitz, V.", title="Calculable Natural Numbers", year=1985, booktitle="Intensional Mathematics", editor="Shapiro, S.", publisher={North-Holland}, pages="173--190", reviews="MR 86m:03093; ZBL 606#03017" } @article{LifschitzV:conaec, author="Lifschitz, V.", title="Constructive Assertions in an Extension of Classical Mathematics", year=1982, journal={Journal of Symbolic Logic}, volume=47, pages="359--387", reviews="MR 84a:03075; ZBL 488#03034" } @article{LifschitzV:ct0, author="Lifschitz, V.", title="{CT$_0$ is stronger than CT$_0$!}", year=1979, journal="Proceedings of the American Mathematical Society", volume=73, pages="101--106", reviews="MR 80b:03094; RZH 79.9A42; ZBL 379#02012" } @inproceedings{LiptonJ:conksr, author="Lipton, J.", title="Constructive {K}ripke Semantics and Realizability", booktitle="Logic from Computer Science", editor="Moschovakis, Y.N.", year=1990, publisher={Springer}, note="Also as a Technical Report, from Cornell University, nr.90--71" } @article{LiptonJ:intrsc, author="Lipton, J. and {O'Donnell}, M.J.", title="Some Intuitions behind Realizability Semantics for Constructive Logic: Tableaux and {L}{\"a}uchli Countermodels", journal={Annals of Pure and Applied Logic}, year=1996, volume=81, pages="187--239" } @PhdThesis{LongleyJ:reatls, author = {J. 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Notes by Giovanni Sambin of a series of lectures given in Padua, June 1980", year=1984, publisher={Bibliopolis, Napoli}, pages="xii+92pp", reviews="JSL 51.1075; MR 86j:03005; ZBL 571#03030" } @inproceedings{MartinLofP:ittpp, author = "Martin-L{\"o}f, P.", title = "An intuitionisitc theory of types, Predicative part", editors = "Rose, E.H. and Sheperdson J.C.", pages = "73--118", booktitle = "Logic Colloquium 1973", poublisher = "North-Holland", year = "1975" } @inproceedings{McCartyD:infscr, author="McCarty, D.C.", title="Information Systems, Continuity and Realizability", year=1984, booktitle="Logics of Programs", editor="Clarke, E. and Kozen, D.", publisher={Springer}, series="Lecture Notes in Computer Science", volume=164, pages="341--359", reviews="ZBL 558#03031" } @incollection{McCartyD:iscr, author = {D.C. 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McCarty}, title = {Realizability and Recursive Mathematics}, year = 1984, school = {University of Oxford}, type = {D.{P}hil. {T}hesis} } @techreport{McCartyD:rearm, author="McCarty, D.C.", title="Realizability and Recursive Mathematics", institution="Department of Computer Science, Carnegie-Mellon University", year=1984, number="CMU--CS--84--131", note="Report version of the author's PhD thesis, Oxford University 1983" } @article{McCartyD:subcr, author="McCarty, D.C.", title="Subcountability under Realizability", journal="The Notre Dame Journal of Formal Logic", volume=27, year=1986, pages="210--220", reviews="MR87h:03108" } @Book{McLartyC:elecet, author = {C. {McL}arty}, title = {Elementary Categories, Elementary Toposes}, publisher = {Clarendon Press}, year = {1995} } @article{MedvedevY:finp, author="Medvedev, {\protect{Yu}}.T.", title="Finite Problems ({R}ussian)", year=1962, journal={Doklady}, volume=142, pages="1015--1018", note="Translation {\em SM} 3, pp. 227--230", reviews="JSL 38.330; MR 24#A3067; ZBL 286#02028" } @inproceedings{MedvedevY:intint, author="Medvedev, {\protect{Yu}}.T.", title="An Interpretation of Intuitionistic Number Theory", year=1973, booktitle="LMPS 4", editor="Suppes, P. and Moisil, G.C. and Joja, A.", publisher={North-Holland}, pages="129--136", reviews="MR 56#5240" } @article{MedvedevY:intlff, author="Medvedev, {\protect{Yu}}.T.", title="Interpretation of Logical Formulae by means of Finite Problems and its Relation to the Realizability Theory ({R}ussian)", year=1963, journal={Doklady}, volume=148, pages="771--774", note="Translation {\em SM} 4, pp. 180--183", reviews="JSL 38.330; MR 26#4904; ZBL 218#02048" } @article{MedvedevY:intlff66, author="Medvedev, {\protect{Yu}}.T.", title="Interpretation of Logical Formulae by means of Finite Problems ({R}ussian)", year=1966, journal={Doklady}, volume=169, pages="20--23", note="Translation {\em SM} 7, pp. 857--860", reviews="JSL 38.330; MR 38#37; ZBL 192.38" } @article{MedvedevY:locfap, author="Medvedev, {\protect{Yu}}.T.", title="Locally Finitary Algorithmic Problems ({R}ussian)", year=1972, journal={Doklady}, volume=203, pages="285--288", note="Errata {\em Ibidem} 204, pp. 1286. Translation {\em SM} 13, pp. 382--386", reviews="MR 47#24; RZH 72.8A90; ZBL 262#02034" } @article{MedvedevY:metpua, author="Medvedev, {\protect{Yu}}.T.", title="A Method for Proving the Unsolvability of Algorithmic Problems ({R}ussian)", year=1969, journal={Doklady}, volume=185, pages="1232--1235", note="Translation {\em SM} 10, pp. 495--498", reviews="MR 40#4112; ZBL 193.316" } @BOOK{MilnerR:defsml, author = "R.~Milner and M.~Tofte and R.~Harper", title = "The Definition of Standard ML", publisher = "MIT Press", year = 1990 } @article{MintsG:compr, author="Mints, G.E.", title="The Completeness of Provable Realizability", journal="The Notre Dame Journal of Formal Logic", year=1989, volume=30, pages="420--441" } @BOOK{MitchellJC:fpl, author = "Mitchell, J.C.", title = "Foundations of Programming Languages", publisher = "MIT Press", year = 1996 } @article{MoggiE:pmceo, author = {E. 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Phoa}, title = {Relative Computability in the Effective Topos}, journal = {Math.\ Proc.\ Camb.\ Phil.\ Soc}, volume = 106, year = 1989 } @article{PhoaW:relcet, author="Phoa, W.", title="Relative Computability in the Effective Topos", journal="Mathematical Proceedings of the Cambridge Philosophical Society", year=1989, pages="419--420", volume=106 } @inproceedings{PhoaW:tmd, author = {W.K.-S. 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Rosolini", title = "An {ExPer} Model for {Q}uest", booktitle = "MFPS'91", editor = "S. Brookes and M. Main and A. Melton and M. Mislove and D. Schmidt", year = 1991, publisher = "Springer", volume = 598, series = {Lecture Notes in Computer Science}, pages = "436--445" } @article{ScarpelliniB:modia, author="Scarpellini, B.", title="A Model for Intuitionistic Analysis", year=1970, journal="Commentarii Mathematici Helvetici", volume=45, pages="440--471", reviews="MR 43#7300; ZBL 213.12" } @article{ScarpelliniB:newrni, author="Scarpellini, B.", title="A New Realizability Notion for Intuitionistic Analysis", journal={ZLGM}, volume=23, year=1977, pages="137--167" } @article{ScedrovA:difeca, author="Scedrov, A.", title="Differential Equations in Constructive Analysis and in the Recursive Realizability Topos", journal="Journal of Pure and Applied Algebra", year=1984, volume=33, pages="69--80" } @inproceedings{ScedrovA:frisfc, author="Scedrov, A. and Scott, P. J.", title="A note on the {F}riedman slash and {F}reyd covers", year=1982, booktitle="The L.E.J. Brouwer Centenary Symposium", editor="Troelstra, A.S. and van~Dalen, D.", publisher={North-Holland}, pages="443--452", reviews="MR 85d:03118; ZBL 529#03039" } @article{ScedrovA:impeub, title="On the Impossibility of Explicit Upper Bounds on Lengths of some Provably Finite Algorithms in Computable Analysis", author="Scedrov, A.", journal={Annals of Pure and Applied Logic}, year=1986, volume=32, pages="291--297" } @inproceedings{ScedrovA:recrsc, author="Scedrov, A.", title="Recursive Realizability Semantics for {C}alculus of {C}onstructions. {P}reliminary Report", year=1990, booktitle="Logical Foundations of Functional Programming", editor="Huet, G.", publisher="Addison-Wesley Publishing Company", pages="419--430" } @article{ScedrovA:weamp, author="Scedrov, A. and R.E. 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Hughes", title = "{L}ogics of {T}ypes and {C}omputation at {C}arnegie {M}ellon {U}niversity", note = "\newline\texttt{http://www.cs.cmu.edu/Groups/LTC/}" } @inproceedings{ScowcroftP:disnep, author="Scowcroft, P.", title="The Disjunction and Numerical Existence Properties for Intuitionistic Analysis", booktitle="Logical Methods", editor="Crossley, J.N. and Remmel, J.B. and Shore, R.A. and Sweedler, M.E.", year=1993, publisher="Birkha{\"u}ser Boston, Inc., Boston MA", pages="747--781" } @article{ShaninN:algkdm, author="Shanin, N.A.", title="{\"U}ber einen {A}lgorithmus zur konstruktiven {D}echiffrierung mathematischer {U}rteile ({R}ussian) ({G}erman summary)", year=1958, journal="ZLGM", volume=4, pages="293--303", reviews="MR 21#5566; ZBL 92.11" } @article{ShaninN:coniaf, author="Shanin, N.A.", title="Concerning the Constructive Interpretation of Auxiliary Formulas {I} ({R}ussian)", year=1964, journal="Trudy Ordena Lenina Matematicheskogo Instituta imeni V. A. Steklova. 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Streicher", title = "Dependence and independece results for (impredicative) calculi of dependent types", journal = "Mathematical Structures in Computer Science", year = 1992, volume = 2, pages = "29--54" } %%%%%%%%%%%%%%%%%%%%%%% @article{StreicherT:indipa, author = "T. Streicher", title = "Independence of the Induction Principle and the Axiom of Choice in the Pure Calculus of Constructions", journal = "Theoretical Computer Science", year = 1992, volume = 103, pages = "395--408" } @booklet{StreicherT:invitt, author = "T. Streicher", title = "Investigations Into Intensional Type Theory", year = 1994, howpublished = "Habilitationsschrift, Universit{\"a}t M{\"u}nchen" } @techreport{StreicherT:matipc, author="Streicher, T.", title="Mathematical Independencies in the Pure Calculus of Constructions", institution="Fakult{\"a}t f{\"u}r {M}athematik und {I}nformatik, {U}niversit{\"a}t {P}assau", year=1991, number="MIP--909" } @book{StreicherT:semttc, author = "T. 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Taylor", title = "The Fixed Point Property in Synthetic Domain Theory", booktitle = "6th Symp. on {L}ogic in {C}omputer {S}cience", year = 1991, pages = "152--160", publisher = "IEEE Computer Society Press" } @article{TharpL:quaist, author="Tharp, L.H.", title="A Quasi--Intuitionistic Set Theory", year=1971, journal={Journal of Symbolic Logic}, volume=36, pages="456--460", reviews="MR 45#6617; RZH 72.6A59; ZBL 247#02055" } @article{TompkinsR:klerri, author="Tompkins, R.R.", title="On {K}leene's Recursive Realizability as an Interpretation for Intuitionistic Elementary Number Theory", year=1968, journal="Notre Dame Journal of Formal Logic", volume=9, pages="289--293", reviews="JSL 35.475; MR 39#3975; ZBL 179.11" } @inproceedings{TroelstraA:axiimi, author="Troelstra, A.S.", title="Axioms for Intuitionistic Mathematics Incompatible with Classical Logic", year=1977, booktitle="LMPS 5", editor="Butts, R.E. and Hintikka, J.", publisher="D. 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Troelstra, C.A. Smory{\'n}ski, J.I. Zucker and W.A. Howard" } @article{TroelstraA:modift, author="Troelstra, A.S.", title="Some Models for Intuitionistic Finite Type Arithmetic with Fan Functional", year=1977, journal={Journal of Symbolic Logic}, pages="194--202", volume=42 } @article{TroelstraA:noneoc, author="Troelstra, A.S.", title="A note on non--extensional operations in connection with continuity and recursiveness", year=1977, journal="Indagationes Mathematicae", volume=39, pages="455--462", reviews="MR 57#12186; RZH 78.7A62; ZBL 368#02026" } @techreport{HiggsD:catabs}, author="Higgs,D.", title="A Category Approach to Boolean-valued Set Theory", year=1973, institution="University of Waterloo" } @inproceedings{TroelstraA:notria, author="Troelstra, A.S.", title="Notions of Realizability for Intuitionistic Arithmetic and Intuitionistic Arithmetic in all Finite Types", year=1971, booktitle="The Second Scandinavian Logic Symposium", editor="Fenstad, J.E.", publisher={North-Holland}, pages="369--405", reviews="JSL 40.625; MR 49#23; RZH 72.1A72; ZBL 227#02015" } @inproceedings{TroelstraA:rea, author="Troelstra, A.S.", title="Realizability", year=1998, booktitle="Handbook of Proof Theory", editor="Buss, S.R.", publisher={North-Holland}, pages="407--473", } @article{TsejtinG:disrfc, author="Tsejtin, G. S.", title="The Disjunctive Rank of the Formulas of Constructive Arithmetic ({R}ussian)", year=1968, journal={Zapiski}, volume=8, pages="260--271", note="Translation {\em Seminars in Mathematics. V.A.Steklov Mathematical Institute Leningrad} 8(1970), pp. 126--132. This volume appeared as: A.O. Slisenko (ed.), {\em Studies in Constructive Mathematics and Mathematical Logic. Part II}. Consultants Bureau, New York, London" } @book{VanDalenD:conm, author = {D. van Dalen and A.S. Troelstra}, title = {Constructivism in Mathematics}, year = 1988, publisher = {North Holland Publishing Company} } @article{VarpahovskijF:clarpf, author="Varpahovskij, F.L.", title="A Class of Realizable Propositional Formulas", year=1971, journal={Zapiski}, volume=1, pages="8--23", note="Translation {\em Journal of Soviet Mathematics} {\bf 1},1--11 (1973)" } @inproceedings{VesleyR:palsks, author="Vesley, R.E.", title="A Palatable Substitute for {K}ripke's Schema", booktitle="Intuitionism and Proof Theory", editor="Kino, A. and Myhill, J.R. and Vesley, R.E.", year=1970, publisher={North-Holland}, pages="197--207" } @article{VesleyR:reabs, author="Vesley, R.E.", title="Realizing {B}rouwer's sequences", journal={Annals of Pure and Applied Logic}, volume=81, year=1996, pages="25--74" } @inproceedings{VoronkovA:compss, author="Voronkov, A.", title="On Completeness of Program Synthesis Systems", booktitle="Computer Science Logic. 5th workshop, CSL '91", editor="B{\"o}rger, E. and J{\"a}ger, G. and {Kleine B\"uning}, H. and Richter, M.M.", publisher={Springer}, year=1992, pages="411--418" } @techreport{VoronkovA:nreacs, author="Voronkov, A.", title="N-realizability: one more constructive semantics", year=1991, institution="Department of Mathematics, Monash University, Australia", number="71" } @misc{WehmeierK:fraha, author="Wehmeier, K.F.", title="Fragments of {HA} based on {$\Sigma_1$}-induction", year=1996, note="Preprint. Part of the author's dissertation project at the University of M{\"u}nster, Westphalia, Germany" }