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Z. Dyment}, } @incollection {MR93g:68075, AUTHOR = {Hyland, J. M. E.}, TITLE = {First steps in synthetic domain theory}, BOOKTITLE = {Category theory (Como, 1990)}, SERIES = {Lecture Notes in Math.}, VOLUME = {1488}, PAGES = {131--156}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1991}, } @article {MR2003c:68044a, AUTHOR = {Hyland, J. M. E. and Ong, C.-H. L.}, TITLE = {On full abstraction for {PCF}: {I}, {II} and {III}}, JOURNAL = {Inform. and Comput.}, FJOURNAL = {Information and Computation}, VOLUME = {163}, YEAR = {2000}, NUMBER = {2}, PAGES = {285--408}, ISSN = {0890-5401}, MRCLASS = {68N18 (03B15 03D20 18D20 68Q05 91A05 91A40 91A80)}, MRNUMBER = {2003c:68044a}, MRREVIEWER = {Roberto Giacobazzi}, } @Article{brouwer:1920, author = "L.E.J. Brouwer", title = "Besitzt jede reelle {Z}ahl eine {D}ezimalbruchentwicklung?", journal = "Math. Ann.", year = 1920, volume = 83, pages = "201--210" } @Unpublished{ calculus:unknown, author = "?", note = "(I am trying to find out this reference)", title = "?" } @Article{cauchy, author = "Cauchy, A.", title = "Sur les moyens d'{\'e}viter les erreurs dans les calculs num{\'e}riques", journal = "Comptes Rendus 11", year = "Paris 1840", pages = "789--798", note = "Republished in: Augustin Cauchy, \OE{}vres compl{\`e}tes, 1{\'e}re s{\'e}rie, Tome V, pp 431--442." } @Article{claudio:escardo:franciosi, author = "D. Claudio and M. Escard\'o and B. Franciosi", title = "An order-theoretic approach to interval analysis", journal = "Interval Computations", year = 1992, volume = 3, number = 5, pages = "38--45" } @Book{ cohn, author = "Cohn, P.M.", title = "Algebra", edition = "2nd", publisher="John Willey \& Sons", year = 1991, address = "Chichester" } @Article{ colson, author = "Colson, L.", title = "About Primitive Recursive Algorithms", journal = TCS, year = 1991, volume = 83, number = 1, pages = "57--69" } @Book{ crole, author = "Crole, R.L.", title = "Categories for Types", publisher="Cambridge University Press", year = 1993, address = "Cambridge" } @article{stone:distributive, author="Stone, M. H.", title="{Topological representations of distributive lattices and Brouwerian logics.}", journal="Casopis, Mat. Fys., Praha, ", volume=67, pages="1-25", year=1937, } @article {MR0300949, AUTHOR = {Priestley, H. A.}, TITLE = {Ordered topological spaces and the representation of distributive lattices}, JOURNAL = {Proc. London Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {24}, YEAR = {1972}, PAGES = {507--530}, } @Book{ davey:priestley, AUTHOR = {Davey, B. A. and Priestley, H. A.}, TITLE = {Introduction to lattices and order}, EDITION = {Second}, PUBLISHER = {Cambridge University Press}, ADDRESS = {New York}, YEAR = {2002}, PAGES = {xii+298}, ISBN = {0-521-78451-4}, MRCLASS = {06-01 (68Q55)}, MRNUMBER = {2003e:06001}, MRREVIEWER = {T. S. Blyth}, } @article {day:kelly, AUTHOR = {Day, B. J. and Kelly, G. M.\}, TITLE = {On topological quotient maps preserved by pullbacks or products}, JOURNAL = {Proc. Cambridge Philos. Soc.}, VOLUME = {67}, YEAR = {1970}, PAGES = {553--558} } @article {day:reflection, AUTHOR = {Day, B. J.}, TITLE = {A reflection theorem for closed categories}, JOURNAL = {J. Pure Appl. Algebra}, VOLUME = {2}, YEAR = {1972}, NUMBER = {1}, PAGES = {1--11} } @book{ devaney, author = "Devaney, R. L.", title = "An Introduction to Chaotical Dynamical Systems", edition = "2nd", publisher="Addison-Wesley", year = 1989, address = "California" } @Book{ dieudonne, author = "Dieudonne, J.", title = "Foundations of Modern Analysis", edition = "2nd", publisher="Academic Press", address = "New York", year = 1969 } @Book{ dijkstra, author = "Dijkstra, E.W.", title = "A Discipline of Programming", year = 1976, publisher="Prentice Hall", address = "Englewood Cliffs" } @article {berger:total, AUTHOR = {Berger, U.}, TITLE = {Total sets and objects in domain theory}, JOURNAL = {Ann. Pure Appl. Logic}, FJOURNAL = {Annals of Pure and Applied Logic}, VOLUME = {60}, YEAR = {1993}, NUMBER = {2}, PAGES = {91--117}, ISSN = {0168-0072}, CODEN = {APALD7}, MRCLASS = {03D65 (68Q55)}, MRNUMBER = {94c:03061}, MRREVIEWER = {Andreas Blass}, } @Proceedings{domainsIII, title = "Workshop Domains III", year = 1997, editor = "U. Berger and K.-H. Niggl and B. Reus", address = "Institut f{\"u}r Informatik, Universit{\"a}t M{\"u}nchen", note = "Proceedings as Technical Report 9712" } @Book{dubuc, author = "E.J. Dubuc", title = "Kan Extensions in Enriched Category Theory", publisher = "Springer", year = 1970, OmitEditor = "A. Dold and B. Eckmann", volume = 145, series = "Lec. Not. Math." } @InCollection{dubuc:quasi, AUTHOR = {Dubuc, E.J.}, TITLE = {Concrete quasitopoi}, SERIES = {Lect. Notes Math.}, VOLUME = 753, PAGES = {239--254}, YEAR = 1979, MRCLASS = {18D20}, MRNUMBER = {81e:18010}, MRREVIEWER = {Hans-E. Porst}, } @Book{ dugundji:topology, author = "Dugundji, J.", title = "Topology", publisher="{Allin and Bacon, Inc.}", address = "Boston", year = 1966 } @InProceedings{edalat:escardo:intpcf, author = "Edalat, A. and Escard\'o, M.", title = "Integration in {R}eal {PCF}", year = 1996, pages = {382--393}, booktitle = "Proceedings of the Eleventh Annual IEEE Symposium on Logic In Computer Science", address = "New Brunswick, New Jersey, USA" } @Unpublished{edalat:escardo:intpcf:fullversion, author = "Edalat, A. and Escard\'o, M.H.", title = "Integration in {R}eal {PCF} (Full version)", year = 1995, month = "December", note = "www.dcs.ed.ac.uk/home/mhe/papers.html", } @Article{edalat:escardo:intpcf:infcomp, author = "Edalat, A. and Escard\'o, M.H.", title = "Integration in {R}eal {PCF}", journal = "Information and Computation", note = "To appear (available at {\footnotesize\tt www.dcs.st-and.ac.uk/\~{}mhe/})" } @Unpublished{ edalat:escardo:intpcf:submitted, author = "Edalat, A. and Escard\'o, M.H.", title = "Real {PCF} Extended with Integration (Full version)", year = 1995, month = "November", note = "{I}mperial {C}ollege, {L}ondon. www.dcs.ed.ac.uk/home/mhe/papers.html", } @Unpublished{ edalat:escardo:workshop, author = "Edalat, A. and Escard\'o, M.H.", title = "Real {PCF} Extended with Integration", year = 1995, month = "October", note = "Unpublished draft presented in the {C}omputational {M}easure and {I}ntegration {T}heory {W}orkshop, {I}mperial {C}ollege, {L}ondon. www.dcs.ed.ac.uk/home/mhe/papers.html" } @Unpublished{ edalat:fractals, author = "Edalat, A.", title = "Dynamical Systems, Measures, and Fractals via Domain Theory", note = "To appear in Information and Computation", } @Unpublished{ edalat:integration, author = "Edalat, A.", title = "Domain Theory and Integration (Extended Abstract)", note ="To appear in the proceedings of LICS94 Paris" } @Masterthesis{ escardo:mscthesis, author = "Escard\'o, M.H.", title = "N\'umeros Naturais Parciais (Partial Natural Numbers)", school = "Universidade Federal do Rio Grande do Sul (CPGCC)", year = 1993, address = "Porto Alegre, Brazil", month = "January" } @Unpublished{ edalat:patent, author = "A. Edalat", title = "Finite algorithms for decoding iterated function systems", note = "UK Patent Application No 9507586.7, filed by Imperial College on 11 May 1995", year=1995 } @Article{edalat:potts:mfps, author = "Edalat, A. and Potts, P.J.", title = "A New Representation for Exact Real Numbers", journal = "Electron. Notes Theor. Comput. Sci.", year = 1997, volume = 6 } @Article{egli:constable, author = "Egli, H. and Constable, R.L.", title = "Computability Concepts for Programming Languages", journal = "Theoret. Comput. Sci.", year = 1976, volume = 2, pages = "133--145" } @Article{erker:escardo:keimel:old, author = "T. Erker and M.H. Escard\'o and K. Keimel", title = "The way-below relation of function spaces of semantic domains", journal = {Topology and its Applications}, note = "To appear (available at www.dcs.ed.ac.uk/home/mhe/papers.html)", year = 1997 } @Article{erker:keimel:escardo, author = "T. Erker and M.H. Escard\'o and K. Keimel", title = "The way-below relation of function spaces over semantic domains", journal = "Topology Appl.", number = "1--2", volume = 89, pages = {61--74}, year = 1998 } @Unpublished{erker:waybelow, author = "T. Erker", title = "A note on the way-below relation on function spaces", note = "Fachbereich {M}athematik, Technische {H}ochschule {D}armstadt", year = 1996, month = "September" } @Techreport{ escardo:claudio, author = "Escard\'o, M.H. and Claudio, D.M.", title = "Scott Domain Theory as a foundation for Interval Analysis", institution="UFRGS/II", year = 1993, number = 218, address = "Porto Alegre, Brazil" } @Unpublished{ escardo:dedekind, author = "Escard\'o, M.H.", title = "Dedekind Cuts for Real Number Computation", year = 1993, month = "December", note = "Unpublished note" } @Unpublished{ escardo:formalisation, author = "Escard\'o, M.H.", title = "On the Formalisation of Real Number Computation", year = 1992, month = "August", note = "Unpublished draft" } @Unpublished{ escardo:induction, author = "Escard\'o, M.H.", title = "Induction, recursion, and computation on the real number system", year = 1993, month = "August", note = "Unpublished manuscript (in portuguese)" } @article {MR92m:03059, AUTHOR = {W., Klaus and Kreitz, C.}, TITLE = {Type $2$ computational complexity of functions on {C}antor's space}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = {82}, YEAR = {1991}, NUMBER = {1, Algorithms Automat. Complexity Games}, PAGES = {1--18}, ISSN = {0304-3975}, CODEN = {TCSDI}, MRCLASS = {03D15 (03D75 68Q15)}, MRNUMBER = {92m:03059}, } @book {MR37:7069, AUTHOR = {Moore, R.E.}, TITLE = {Interval analysis}, PUBLISHER = {Prentice-Hall Inc.}, ADDRESS = {Englewood Cliffs, N.J.}, YEAR = {1966}, PAGES = {xi+145}, MRCLASS = {65.10 (68.00)}, MRNUMBER = {37 #7069}, } @article {MR94i:65061, AUTHOR = {Vignes, J.}, TITLE = {A stochastic arithmetic for reliable scientific computation}, JOURNAL = {Math. Comput. Simulation}, FJOURNAL = {Mathematics and Computers in Simulation}, VOLUME = {35}, YEAR = {1993}, NUMBER = {3}, PAGES = {233--261}, ISSN = {0378-4754}, CODEN = {MCSIDR}, MRCLASS = {65G05}, MRNUMBER = {94i:65061}, MRREVR = {G. Alefeld}, } @article {MR94e:65053, AUTHOR = {Chesneaux, J.-M. and Vignes, J.}, TITLE = {Les fondements de l'arithm\'etique stochastique}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {315}, YEAR = {1992}, NUMBER = {13}, PAGES = {1435--1440}, ISSN = {0764-4442}, CODEN = {CASMEI}, MRCLASS = {65G10 (65Y99)}, MRNUMBER = {94e:65053}, MRREVR = {Bruno Codenotti}, } @InProceedings{Mue86a, author = {M{\"u}ller, N.Th.}, title = {Subpolynomial complexity classes of real functions and real numbers}, booktitle = {Proceedings of the 13th International Colloquium on Automata, Languages, and Programming}, editor = {Kott, Laurent}, year = {1986}, series = {Lec. Not. Comput. Sci.}, volume = {226}, pages = {284--293}, publisher = {Springer}, address = {Berlin}, keyword = {cca} } @book {MR99a:68070, AUTHOR = {Blum, L. and Cucker, F. and Shub, M. and Smale, S.}, TITLE = {Complexity and real computation}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = 1998, PAGES = {xvi+453}, ISBN = {0-387-98281-7}, MRCLASS = {68Q15 (03D15 13P99 14P99 65Y20 68-02)}, MRNUMBER = {99a:68070}, MRREVR = {Klaus Meer}, } @Article{escardo:injective, author = "M.H. Escard\'o", title = "Properly injective spaces and function spaces", journal = "Topology Appl.", number = "1--2", volume = 89, pages = {75--120}, year = {1998} } @Unpublished{escardo:keimel:waybelow, author = "M.H. Escard\'o and K. Keimel", title = "The way-below relation on function spaces", note = "Department of Computing, Imperial College of Science and Technology, University of London; Fachbereich {M}athematik, Technische {H}ochschule {D}armstadt", year = 1996, month = "February" } @Article{escardo:lazy, author = "M. Escard\'o", title = "On lazy natural numbers with applications to computability theory and functional programming ", journal = "SIGACT News", year = 1993, volume = 24, pages = "60--67" } @Unpublished{ escardo:logtrigo, author = "Escard\'o, M.H.", title = "(No title)", year = 1984, note = "A tentative proof of correctness of algorithms for computing logarithmic and trigonometric functions discovered in 1982; unpublished (in Portuguese)" } @Article{escardo:pcf, author = "Escard\'o, M.H.", title = "{PCF} extended with real numbers", journal = TCS, year = 1996, volume = 162, number = 1, pages = "79--115" } @Article{ escardo:pcf:old, author = "Escard\'o, M.H.", title = "{PCF} extended with real numbers", journal = TCS, year = "1996", volume = 162 } @PhdThesis{ escardo:phdthesis, author = "M.H. Escard\'o", title = "PCF extended with real numbers: A domain-theoretic approach to higher-order exact real number computation", school = "Imperial College, Department of Computing", year = 1996, month = "November" } @Unpublished{ escardo:realcomputation, author = "Escard\'o, M.H.", title = "Induction, Recursion, and Computation on the Real Line and Some of its Subspaces", year = 1994, note = "Unpublished work in progress" } @Unpublished{ escardo:recursive, author = "Escard\'o, M.H.", title = "Primitive Recursive Real Functions", year = 1993, month = "December", note = "Unpublished draft" } @Unpublished{escardo:streicher, author = "M.H. Escard\'o and T. Streicher", title = "Biquotients of bifree algebras", note = "Unpublished manuscript", year = 1996, month = "April" } @InProceedings{escardo:streicher:finductive, author = "Escard\'o, M.H. and Streicher, T.", title = "Induction and Recursion on the Partial Real Line via biquotients of bifree algebras", year = 1997, month = "Jun", booktitle = "Proceedings of the Twelveth Annual IEEE Symposium on Logic In Computer Science", address = "Warsaw, Polland" } @Inproceedings{ escardo:tfmrealpcfuniversal, author = "Escard\'o, M.H.", title = "Real {PCF} extended with $\exists$ is universal", booktitle = {Advances in Theory and Formal Methods of Computing: Proceedings of the Third Imperial College Workshop, April 1996}, editor = "A.~Edalat and S.~Jourdan and G.~McCusker", address = {Christ Church, Oxford}, publisher="IC Press", year = "1996", pages = {13--24} } @Inproceedings{ escardo:tfmworkshop, author = "Escard\'o, M.H.", title = "Induction and Recursion on the Real Line", booktitle = {Theory and Formal Methods 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods}, editor = "Hankin, C. and Mackie, I. and Nagarajan, R.", address = {{M{\o}ller} Centre, Cambridge}, publisher="IC Press", Note = "1995", pages = "259--282", year = "11--14 September 1994", } @Unpublished{ escardo:unitobj, author = "Escard\'o, M.H.", title = "Some numbers objects defined by initial algebras and finial coalgebras", year = 1995, note = "Working paper" } @Unpublished{ fiore, author = "M.~P. Fiore", title = "A Coinduction Principle for Recursive Data Types Based on Bisimulation", note = "Department of Computer Science, Laboratory for Foundations of Computer Science, University of Edinburgh" } @Article{flagg, author = "R.C. Flagg", title = "Algebraic theories of pospaces", journal = "Topology and Its Applications", year = 1997, Volume = 77, number = 3, pages = {277--290} } @Article{escardo:injective:old, author = "M.H. Escard\'o", title = "Properly Injective Spaces and Function Spaces", journal = {Topology and Its Applications}, note = "To appear (available at www.dcs.ed.ac.uk/home/mhe/papers.html)", year = 1997 } @Unpublished{flagg:note, author = "R.C. Flagg", title = "A simple proof of the {W}yler-{S}immons {T}heorem", note = "Unpublished manuscript, University of Southern Maine", year = 1997, month = "August" } @Unpublished{escardo:mgs, author = {M.H. Escard\'o}, title = {Mathematical foundations of functional programming with real numbers}, note = {University of Birmingham, lecture notes for a course in the Midlands Graduate School, available at the author's web page}, month = {March}, year = 2003 } @Article{fox, author = {R.H. Fox}, title = {On topologies for function spaces}, journal = {Bulletin of the American Mathematical Society}, year = 1945, volume = 51, pages = {429--432} } @Book{ gaal:topology, author = "Gaal, S.A.", title = "Point Set Topology", publisher="Academic Press", address = "London", year = 1964, } @Article{mislove:topology, AUTHOR = {Mislove, M.}, TITLE = {Topology, domain theory and theoretical computer science}, JOURNAL = {Topology Appl.}, FJOURNAL = {Topology and its Applications}, VOLUME = 89, YEAR = 1998, NUMBER = {1-2}, PAGES = {3--59}, ISSN = {0166-8641}, CODEN = {TIAPD9}, MRCLASS = {54F05 (06B35 06F30 18B30 54B20 68Q55)}, MRNUMBER = {99i:54046}, MRREVIEWER = {Peter Johnstone}, } @Book{ gierz:domains, author = "Gierz, G. and Hofmann, K.H. and Keimel, K. and Lawson, J.D. and Mislove, M. and Scott, D.S.", title = "Continuous Lattices and Domains", publisher="Cambridge University Press", year = 2003 } @Book{ gierz:compendium, author = "Gierz, G. and Hofmann, K.H. and Keimel, K. and Lawson, J.D. and Mislove, M. and Scott, D.S.", title = "A Compendium of Continuous Lattices", publisher="Springer", year = 1980 } @Book{ girard, author = "Girard, J.Y.", title = "Proofs and Types", publisher="Cambridge University Press", address = "Cambridge", year = 1989 } @Article{ goguen, author = "Goguen, J.A. and Thatcher J.W. and Wagner, E.G. and Wright, J.B.", title = "Initial Algebra Semantics and Continuous Algebras", Journal = "J. ACM", volume = 24, pages = "68--95", year = 1977 } @Book{ graham:knuth:patashnick, author = "Graham, L.R. and Knuth, D.E. and Patashnick, O.", title = "Concrete Mathematics", publisher="Addison-Wesley", address = "New York", year = 1989 } @Book{ gries, author = "Gries, D.", title = "The Science of Programming", publisher="Springer", address = "New York", year = 1981 } @Unpublished{ grue, author = "Grue, K.", title = "Unrestricted Lazy Numerical Algorithms", note = "Unpublished manuscript" } @Article{ grzegorczyk, author = "Grzegorczyk, A.", title = "On the Definition of Computable Real Continuous Functions", journal = "Fund. Math.", year = 1957, volume = 44, pages = "61-77" } @Book{ gunter, author = "Gunter, C.A.", title = "Semantics of Programming Languages---Structures and Techniques", publisher="The MIT Press", year = 1992 } @Inproceedings{ gunter:comparing, author = "Gunter, C.A.", title = "Comparing Categories of Domains", booktitle="Mathematical Foundations of Programming Semantics", year = 1986, editor = "Melton, A.", pages = "101--121", publisher="Springer", address = "New York", note = "LNCS 239", abstract= "***" } @article{heckmann:2nd-order, author = "R. Heckmann", title = "Power Domains and Second Order Predicates", journal = tcs, volume = 111, pages = {59--88}, year = 1993 } @Inproceedings{ herrlich:husek, author = "Herrlich, H and Husek, M.", title = "Galois Connections", booktitle="Mathematical Foundations of Programming Semantics", year = 1986, editor = "Melton, A.", pages = "121--134", publisher="Springer", address = "New York", note = "LNCS 239", abstract= "***" } @incollection {poigne:basic, AUTHOR = {Poign{\'e}, A.}, TITLE = {Basic category theory}, BOOKTITLE = {Handbook of logic in computer science, Vol.\ 1}, PAGES = {413--640}, PUBLISHER = {Oxford Univ. Press}, ADDRESS = {New York}, YEAR = {1992}, MRCLASS = {68Q65 (03G30 18-02 68Q55)}, MRNUMBER = {97i:68137}, } @Book{ herrlich:strecker, author = "Herrlich, H and Strecker, G.E.", title = "Category Theory", year = 1973, publisher= "Allyn and Bacon Inc.", adress = "Boston" } @Book{ hewitt, author = "Hewitt, E.", title = "Real and Abstract Analysis: a Modern Treatment of the Theory of Functions of a Real Variable", year = 1965, publisher= "Springer", adress = "New York" } @Book{ hocking:young, author = "Hocking, J.G. and Young, G.S.", title = "Topology", year = 1988, publisher= "Dover Publications", adress = "New York" } @InCollection{hofmann:lawson:82, author = "K.H. Hofmann and J.D. Lawson", title = "On the order theoretical foundation of a theory of quasicompactly generated spaces without separation axiom", booktitle = "Continuous Lattices and Related Topics", publisher = "University of Bremen", year = 1982, editor = "R.-E. 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Fundamenta Mathematicae}, VOLUME = {113}, YEAR = {1981}, NUMBER = {1}, PAGES = {21--35}, ISSN = {0016-2736}, CODEN = {FUMAAJ}, MRCLASS = {03E25 (03G30 54B10 54D30)}, MRNUMBER = {MR641111 (84h:03117)}, MRREVIEWER = {Andreas Blass}, } @InProceedings{hyland:functionspaces, author = {Hyland, M.}, title = {Function spaces in the category of locales.}, booktitle = {Continuous lattices}, pages = {264-281}, year = 1981, volume = 871, series = {Lect. Notes Math.}, } @InProceedings{achim:note, author = {A. Jung}, title = {Stably compact spaces and the probabilistic powerspace construction}, booktitle = {Domain-theoretic Methods in Probabilistic Processes}, year = 2004, editor = {J. Desharnais and P. Panangaden}, volume = 87, series = {Electron. Notes Theoret. Comp. Sci.}, publisher = {Elsevier}, note = {15pp.}, } @InProceedings{ hofmann:stablycontinuous, author = "K.H. 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(Basel)}, FJOURNAL = {Archiv der Mathematik}, VOLUME = {21}, YEAR = {1970}, PAGES = {1--10}, ISSN = {0003-889X}, MRCLASS = {18.10}, MRNUMBER = {MR0260825 (41 \#5446)}, MRREVIEWER = {Y. C. Wu}, } @article {kock:monoidal, AUTHOR = {Kock, A.}, TITLE = {Strong functors and monoidal monads}, JOURNAL = {Arch. Math. (Basel)}, FJOURNAL = {Archiv der Mathematik}, VOLUME = {23}, YEAR = {1972}, PAGES = {113--120}, ISSN = {0003-889X}, MRCLASS = {18D10}, MRNUMBER = {MR0304456 (46 \#3591)}, MRREVIEWER = {J. R. Isbell}, } @Article{moggi:monads, author = "E. 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Ku{\v{c}}era}, } @Book{weihrauch:2000, author = {Weirauch, K.}, title = {Computable analysis}, publisher = {Springer}, year = 2000, month = {September} } @Article{ plotkin:lcf, author = "G.D. Plotkin", title = "{LCF} considered as a programming language", journal = TCS, volume = 5, number = 1, pages = "223--255", year = 1977 } @Article{ plotkin:tomega, author = "Plotkin, G.D.", title = "$\mathbb{T}^{\omega}$ as a universal domain", journal = "J. Comput. System Sci.", volume = 17, pages = "209--236", year = 1978 } @Unpublished{plotkin:totality:old, author = "Gordon Plotkin", title = "Full Abstraction, Totality and {PCF}", note = "Department of Computer Science, University of Edinburgh, {\tt www.dcs.ed.ac.uk/home/gdp/totality.ps}", year = 1997, month = "June" } @article {MR1923914, AUTHOR = {Schr\"oder, M.}, TITLE = {Extended admissibility}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = 284, YEAR = 2002, NUMBER = 2, PAGES = {519--538}, ISSN = {0304-3975}, CODEN = {TCSDI}, MRCLASS = {03F60 (03D45 54B30)}, MRNUMBER = {MR1923914 (2003g:03105)}, } @article {stoughton, AUTHOR = {Stoughton, A.}, TITLE = {Interdefinability of parallel operations in {PCF}}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = {79}, YEAR = {1991}, NUMBER = {2, (Part B)}, PAGES = {357--358}, ISSN = {0304-3975}, CODEN = {TCSDI}, MRCLASS = {68Q60}, MRNUMBER = {1 122 583}, } @article {plotkin:totality, AUTHOR = {Plotkin, G.D.}, TITLE = {Full abstraction, totality and {PCF}}, JOURNAL = {Math. Structures Comput. Sci.}, FJOURNAL = {Mathematical Structures Comput. Sci..}, VOLUME = {9}, YEAR = {1999}, NUMBER = {1}, PAGES = {1--20}, ISSN = {0960-1295}, MRCLASS = {68Q55 (06B35)}, MRNUMBER = {2000d:68090}, MRREVIEWER = {Chris Brink}, } @incollection{ poigne, author = "A. Poign\'e", title = "Basic Category Theory", booktitle="Handbook of Logic in Computer Science", publisher="Clarendon Press", year = "1992", editor = "Abramsky, S. and Gabbay, D.M. and Maibaum,T.S.E", volume = "1", address = "Oxford", pages = "413--640" } @Unpublished{potts:continuedfractions, author = "P.J. Potts", title = "Computable Real Arithmetic using Linear Fractional Transformations", note = "Manuscript presented during the second Computation and Approximation Workshop, held in Darmstadt", year = 1996, month = "September" } @InProceedings{potts:edalat:escardo, author = "P.J. Potts and A. Edalat and M.H. Escard\'o", title = "Semantics of Exact Real Arithmetic", year = 1997, month = "Jun", booktitle = "Proceedings of the Twelveth Annual IEEE Symposium on Logic In Computer Science", address = "Warsaw, Polland" } @incollection {MR1720755, AUTHOR = {Normann, D.}, TITLE = {The continuous functionals}, BOOKTITLE = {Handbook of computability theory}, SERIES = {Stud. Logic Found. Math.}, VOLUME = {140}, PAGES = {251--275}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {1999}, MRCLASS = {03D65 (03D80)}, MRNUMBER = {MR1720755 (2000h:03084)}, MRREVIEWER = {Julia Y. Yasuda}, } @InProceedings{escardo:ho, author = "M.H. Escard\'o and W.K. Ho", title = "Operational domain theory and topology of a sequential programming language", year = 2005, pages = {427--436}, booktitle = "Proceedings of the 20th Annual IEEE Symposium on Logic In Computer Science", } @InProceedings{escardo:lics07, author = "M. 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Sci.}, VOLUME = {2064}, PAGES = {323--335}, PUBLISHER = {Springer}, YEAR = {2001}, MRCLASS = {54F45 (03F60)}, MRNUMBER = {2003b:54038}, } @Article{escardo:effective:comprox, author = "Escard{\'o}, M.H.", title = "Effective and sequential definition by cases on the reals via infinite signed-digit numerals", journal = "Electron. Notes Theor. Comput. Sci.", year = 1998, volume = 13, } @Book{ royden, author = "Royden, H.L.", title = "Real Analysis", publisher = "Collier Macmillan Publishing", year = 1988, edition = "Third" } @article {MR90b:06016, AUTHOR = {Simmons, H.}, TITLE = {Near-discreteness of modules and spaces as measured by {G}abriel and {C}antor}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = 56, YEAR = 1989, NUMBER = 2, PAGES = {119--162}, ISSN = {0022-4049}, CODEN = {JPAAA2}, MRCLASS = {06C05 (16A55)}, MRNUMBER = {90b:06016}, MRREVR = {J. R. Isbell}, } @article {MR82j:03082, AUTHOR = {MacNab, D.S.}, TITLE = {Modal operators on {H}eyting algebras}, JOURNAL = {Algebra Universalis}, FJOURNAL = {Algebra Universalis}, VOLUME = {12}, YEAR = {1981}, NUMBER = {1}, PAGES = {5--29}, ISSN = {0002-5240}, MRCLASS = {03G25 (03B45 06D20)}, MRNUMBER = {82j:03082}, MRREVR = {L. L. Maksimova}, } @Book{ rudin, author = "Rudin, W.", title = "Principles of Mathematical Analysis", edition = "3rd", publisher="McGraw-Hill", year = "1976", address = "New Yourk" } @TechReport{rutten:while, author = {Rutten, J.J.M.M.}, title = {A note on coinduction and weak bisimilarity for while programs}, institution = {CWI, Amsterdam}, year = 1998, number = {SEN-R9826, ISSN 1386-369X}, month = {October}, note = {\href{www.cwi.nl/static/publications/reports/reports.html}} } @PhdThesis{ schalk, author = "A. 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Conf., Wroc\l aw, 1977)}, PAGES = {239--251}, PUBLISHER = {North-Holland}, YEAR = {1978}, MRCLASS = {06B30 (18B30)}, MRNUMBER = {80b:06008}, MRREVR = {H. Herrlich}, } @Book{ simmons:book, author = "Simmons, G.F.", title = "Introduction to Topology and Modern Analysis", publisher="McGraw-Hill", address = "New York", year = 1963 } @article{simpson:integration, author = {A. Simpson}, title = {Lazy Functional Algorithms for Exact Real Functionals}, pages = {323--342}, year = 1998, volume = 1450, journal = {Lec. Not. Comput. Sci.}, publisher = {Springer} } @Article{ smale, author = "Smale, S.", title = "Some Remarks on the Foundations of Numerical Analysis", journal = "SIAM Review", volume = 32, number = 2, pages = "211--220", year = 1990, month = "June" } @article {schroeder:extended, AUTHOR = {Schr{\"o}der, M.}, TITLE = {Extended admissibility}, JOURNAL = {Theoret. Comput. 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