메뉴 건너뛰기




Volumn 87, Issue , 2004, Pages 21-156

Synthetic topology of data types and classical spaces

(1)  Escardó, Martín a  

a NONE

Author keywords

Computability; Data types; Denotational semantics; Domain theory; Equilogical spaces; Functional programming; Operational semantics; Programming language semantics; Recursion theory; Scott model of PCF; Synthetic topology; Topological spaces; calculus

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; COMPUTER PROGRAMMING LANGUAGES; COMPUTER SCIENCE; DATA STRUCTURES; SEMANTICS; SET THEORY; THEOREM PROVING;

EID: 23844479323     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2004.09.017     Document Type: Conference Paper
Times cited : (87)

References (145)
  • 1
    • 19144373216 scopus 로고
    • Domain theory in logical form
    • Abramsky, S., Domain theory in logical form, Ann. Pure Appl. Logic 51 (1991), pp. 1-77.
    • (1991) Ann. Pure Appl. Logic , vol.51 , pp. 1-77
    • Abramsky, S.1
  • 3
    • 0001847686 scopus 로고
    • Domain theory
    • S. Abramsky, D. Gabbay and T. Maibaum, editors, Oxford science publications 3, Clarendon Press, Oxford
    • Abramsky, S. and A. Jung, Domain theory, in: S. Abramsky, D. Gabbay and T. Maibaum, editors, Handbook of Logic in Computer Science, Oxford science publications 3, Clarendon Press, Oxford, 1994 pp. 1-168.
    • (1994) Handbook of Logic in Computer Science , pp. 1-168
    • Abramsky, S.1    Jung, A.2
  • 5
    • 4444329616 scopus 로고    scopus 로고
    • Local readability toposes and a modal logic for computability
    • Awodey, S., L. Birkedal and D. Scott, Local readability toposes and a modal logic for computability, Math. Struct. Comput. Sci. 12 (2002), pp. 319-334.
    • (2002) Math. Struct. Comput. Sci. , vol.12 , pp. 319-334
    • Awodey, S.1    Birkedal, L.2    Scott, D.3
  • 6
    • 0036435280 scopus 로고    scopus 로고
    • A relationship between equilogical spaces and type two effectivity
    • Bauer, A., A relationship between equilogical spaces and type two effectivity, MLQ Math. Log. Q. 48 (2002), pp. 1-15.
    • (2002) MLQ Math. Log. Q , vol.48 , pp. 1-15
    • Bauer, A.1
  • 7
    • 85030746594 scopus 로고    scopus 로고
    • Equilogical spaces as imaginary spaces
    • university of Ljubljana , LMU, Department of Mathematics, University of Munich, 1-2 November 2003
    • Bauer, A., Equilogical spaces as imaginary spaces (2003), university of Ljubljana. Presented at the Workshop on Domains, Topology and Constructive Logic, LMU, Department of Mathematics, University of Munich, 1-2 November 2003.
    • (2003) Workshop on Domains, Topology and Constructive Logic
    • Bauer, A.1
  • 8
    • 2042461992 scopus 로고    scopus 로고
    • Continuous functionals of dependent types and equilogical spaces
    • Bauer, A. and L. Birkedal, Continuous functionals of dependent types and equilogical spaces, Lec. Not. Comput. Sci. 1862 (2000), pp. 202-216.
    • (2000) Lec. Not. Comput. Sci. , vol.1862 , pp. 202-216
    • Bauer, A.1    Birkedal, L.2
  • 10
    • 33847701636 scopus 로고    scopus 로고
    • Comparing functional paradigms for exact real-number computation
    • Bauer, A., M. Escardó and A. Simpson, Comparing functional paradigms for exact real-number computation, Lect. Not. Comp. Sci. 2380, 2002, pp. 488-500.
    • (2002) Lect. Not. Comp. Sci. , vol.2380 , pp. 488-500
    • Bauer, A.1    Escardó, M.2    Simpson, A.3
  • 11
    • 33645269090 scopus 로고    scopus 로고
    • A new category for semantics
    • notes from D.S. Scott's talk at. CMU, available from Scott's web page
    • Bauer, A. and D. Scott, A new category for semantics (2001), notes from D.S. Scott's talk at MFCS 2001. CMU, available from Scott's web page.
    • (2001) MFCS 2001
    • Bauer, A.1    Scott, D.2
  • 14
    • 0001770258 scopus 로고
    • Total sets and objects in domain theory
    • Berger, U., Total sets and objects in domain theory, Ann. Pure Appl. Logic 60 (1993), pp. 91-117.
    • (1993) Ann. Pure Appl. Logic , vol.60 , pp. 91-117
    • Berger, U.1
  • 18
    • 11944257741 scopus 로고    scopus 로고
    • Computability over topological structures
    • S. Cooper and S. Goncharov, editors, Kluwer Academic
    • Brattka, V., Computability over topological structures, in: S. Cooper and S. Goncharov, editors, Computability and Models, Kluwer Academic, 2003 pp. 93-136.
    • (2003) Computability and Models , pp. 93-136
    • Brattka, V.1
  • 19
    • 0037189790 scopus 로고    scopus 로고
    • Topological properties of real number representations
    • Brattka, V. and P. Hertling, Topological properties of real number representations, Theoret. Comput. Sci. 284 (2002), pp. 241-257.
    • (2002) Theoret. Comput. Sci. , vol.284 , pp. 241-257
    • Brattka, V.1    Hertling, P.2
  • 20
    • 0039078785 scopus 로고
    • Besitzt jede reelle Zahl eine Dezimalbruchentwicklung?
    • Brouwer, L., Besitzt jede reelle Zahl eine Dezimalbruchentwicklung?, Math. Ann. 83 (1920), pp. 201-210.
    • (1920) Math. Ann. , vol.83 , pp. 201-210
    • Brouwer, L.1
  • 21
    • 0003447193 scopus 로고
    • Ellis Horwood Ltd., Chichester, second edition
    • Brown, R., "Topology," Ellis Horwood Ltd., Chichester, 1988, second edition.
    • (1988) Topology
    • Brown, R.1
  • 22
    • 0034258762 scopus 로고    scopus 로고
    • Formal topologies on the set of first-order formulae
    • Coquand, T., S. Sadocco, G. Sambin and J. Smith, Formal topologies on the set of first-order formulae, J. Symbolic Logic 65 (2000), pp. 1183-1192.
    • (2000) J. Symbolic Logic , vol.65 , pp. 1183-1192
    • Coquand, T.1    Sadocco, S.2    Sambin, G.3    Smith, J.4
  • 23
    • 0004020078 scopus 로고
    • Cambridge University Press, Cambridge
    • Croie, R., "Categories for Types," Cambridge University Press, Cambridge, 1993.
    • (1993) Categories for Types
    • Croie, R.1
  • 25
    • 84972371238 scopus 로고
    • On topological quotient maps preserved by pullbacks or products
    • Day, B. J. and G. M. Kelly, On topological quotient maps preserved by pullbacks or products, Proc. Cambridge Philos. Soc. 67 (1970), pp. 553-558.
    • (1970) Proc. Cambridge Philos. Soc. , vol.67 , pp. 553-558
    • Day, B.J.1    Kelly, G.M.2
  • 26
    • 33645272061 scopus 로고    scopus 로고
    • An approach to effective. functionals on the real numbers via filter spaces
    • DeJaeger, F., An approach to effective. functionals on the real numbers via filter spaces, Topology Proceedings 26 (2001-2002), pp. 485-504.
    • (2001) Topology Proceedings , vol.26 , pp. 485-504
    • Dejaeger, F.1
  • 27
    • 85030740486 scopus 로고    scopus 로고
    • On the computational content of the Lawson topology
    • available at Escardó's web page
    • DeJaeger, F., M. Escardó and G. Santini, On the computational content of the Lawson topology, presented at MFPS XVI, available at Escardó's web page.
    • MFPS XVI
    • DeJaeger, F.1    Escardó, M.2    Santini, G.3
  • 28
    • 0001790104 scopus 로고    scopus 로고
    • Real number computability and domain theory
    • Di Gianantonio, P., Real number computability and domain theory, Inform, and Comput. 127 (1996), pp. 11-25.
    • (1996) Inform, and Comput. , vol.127 , pp. 11-25
    • Di Gianantonio, P.1
  • 29
    • 0002511180 scopus 로고
    • Concrete quasitopoi
    • Dubuc, E., Concrete quasitopoi, Lect. Notes Math. 753, 1979 pp. 239-254.
    • (1979) Lect. Notes Math. , vol.753 , pp. 239-254
    • Dubuc, E.1
  • 30
    • 84974313061 scopus 로고
    • Objets compacts dans les topos, J
    • Dubuc, E. and J. Penon, Objets compacts dans les topos, J. Austral. Math. Soc. Ser. A 40 (1986), pp. 203-217.
    • (1986) Austral. Math. Soc. Ser. A , vol.40 , pp. 203-217
    • Dubuc, E.1    Penon, J.2
  • 31
    • 0003535772 scopus 로고
    • Allin and Bacon, Inc., Boston
    • Dugundji, J., "Topology," Allin and Bacon, Inc., Boston, 1966.
    • (1966) Topology
    • Dugundji, J.1
  • 32
    • 0001643398 scopus 로고    scopus 로고
    • Domains for computation in mathematics, physics and exact real arithmetic
    • Edalat, A., Domains for computation in mathematics, physics and exact real arithmetic, Bulletin of Symbolic Logic 3 (1997), pp. 401-452.
    • (1997) Bulletin of Symbolic Logic , vol.3 , pp. 401-452
    • Edalat, A.1
  • 34
  • 35
    • 0004516209 scopus 로고
    • Computability concepts for programming languages
    • Egli, H. and R. Constable, Computability concepts for programming languages, Theoret. Comput. Sci. 2 (1976), pp. 133-145.
    • (1976) Theoret. Comput. Sci. , vol.2 , pp. 133-145
    • Egli, H.1    Constable, R.2
  • 37
    • 0004339461 scopus 로고    scopus 로고
    • The way-below relation of function spaces over semantic domains
    • Erker, T., M. Escardó and K. Keimel, The way-below relation of function spaces over semantic domains, Topology Appl. 89 (1998), pp. 61-74.
    • (1998) Topology Appl. , vol.89 , pp. 61-74
    • Erker, T.1    Escardó, M.2    Keimel, K.3
  • 38
    • 0000260572 scopus 로고
    • Computable functional of finite types
    • Ershov, Y., Computable functional of finite types, Algebra Logic 11 (1972), pp. 203-242.
    • (1972) Algebra Logic , vol.11 , pp. 203-242
    • Ershov, Y.1
  • 39
    • 33645273152 scopus 로고
    • Continuous lattices and A-spaces
    • Ershov, Y., Continuous lattices and A-spaces, Soviet Mathematics Doklady 13 (1973), pp. 1551-1555.
    • (1973) Soviet Mathematics Doklady , vol.13 , pp. 1551-1555
    • Ershov, Y.1
  • 40
    • 0030570676 scopus 로고    scopus 로고
    • PCF extended with real numbers
    • Escardó, M., PCF extended with real numbers, Theoret. Comput. Sci. 162 (1996), pp. 79-115.
    • (1996) Theoret. Comput. Sci. , vol.162 , pp. 79-115
    • Escardó, M.1
  • 42
    • 77956457690 scopus 로고    scopus 로고
    • Injective spaces via the filter monad
    • Escardó, M., Injective spaces via the filter monad, Topology Proceedings 22 (1997), pp. 97-110.
    • (1997) Topology Proceedings , vol.22 , pp. 97-110
    • Escardó, M.1
  • 43
    • 0004054172 scopus 로고    scopus 로고
    • PCF extended with real numbers: A domain-theoretic, approach to higher-order exact real number computation
    • University of Edinburgh , phD thesis at Imperial College
    • Escardó, M., PCF extended with real numbers: A domain-theoretic, approach to higher-order exact real number computation, Technical Report ECS-LFCS-97-374, University of Edinburgh (1997), phD thesis at Imperial College.
    • (1997) Technical Report , vol.ECS-LFCS-97-374
    • Escardó, M.1
  • 44
    • 18944399783 scopus 로고    scopus 로고
    • Effective and sequential definition by cases on the reals via infinite signed-digit numerals
    • Escardó, M., Effective and sequential definition by cases on the reals via infinite signed-digit numerals, Electron. Notes Theor. Comput. Sci. 13 (1998).
    • (1998) Electron. Notes Theor. Comput. Sci. , vol.13
    • Escardó, M.1
  • 45
    • 0004511730 scopus 로고    scopus 로고
    • A metric model of PCF
    • LFCS, University of Edinburgh Federated Logic Conference, Trento, June 29-July 12, 1999. Available at the author's web page
    • Escardó, M., A metric model of PCF (1998), LFCS, University of Edinburgh. Presented at the Workshop on Realizability Semantics and Applications, Federated Logic Conference, Trento, June 29-July 12, 1999. Available at the author's web page.
    • (1998) Workshop on Realizability Semantics and Applications
    • Escardó, M.1
  • 46
    • 0001897066 scopus 로고    scopus 로고
    • Properly injective spaces and function spaces
    • Escardó, M., Properly injective spaces and function spaces, Topology Appl. 89 (1998), pp. 75-120.
    • (1998) Topology Appl. , vol.89 , pp. 75-120
    • Escardó, M.1
  • 47
    • 0038351004 scopus 로고    scopus 로고
    • Function-space compactifications of function spaces
    • Escardó, M., Function-space compactifications of function spaces, Topology Appl. 120 (2002), pp. 441-463.
    • (2002) Topology Appl. , vol.120 , pp. 441-463
    • Escardó, M.1
  • 48
    • 85030741437 scopus 로고    scopus 로고
    • Mathematical foundations of functional programming with real numbers
    • university of Birmingham, available at the author's web page.
    • Escardó, M., Mathematical foundations of functional programming with real numbers (2003), university of Birmingham, lecture notes for a course in the Midlands Graduate School, available at the author's web page.
    • (2003) Lecture Notes for a Course in the Midlands Graduate School
    • Escardó, M.1
  • 50
    • 4243149930 scopus 로고    scopus 로고
    • Topologies on spaces of continuous functions
    • Escardó, M. and R. Heckmann, Topologies on spaces of continuous functions, Topology Proceedings 26 (2001-2002), pp. 545-564.
    • (2001) Topology Proceedings , vol.26 , pp. 545-564
    • Escardó, M.1    Heckmann, R.2
  • 51
    • 85030739986 scopus 로고    scopus 로고
    • On the non-sequential nature of the interval-domain model of exact real-number computation
    • to appear
    • Escardó, M., M. Hofmann and T. Streicher, On the non-sequential nature of the interval-domain model of exact real-number computation, Math. Struct. Comput. Sci. (to appear).
    • Math. Struct. Comput. Sci.
    • Escardó, M.1    Hofmann, M.2    Streicher, T.3
  • 52
    • 85030744588 scopus 로고    scopus 로고
    • Comparing categories of (core) compactly generated spaces
    • To appear
    • Escardó, M., J. Lawson and A. Simpson, Comparing categories of (core) compactly generated spaces, Topology Appl. (To appear).
    • Topology Appl.
    • Escardó, M.1    Lawson, J.2    Simpson, A.3
  • 53
    • 0000650008 scopus 로고    scopus 로고
    • Induction and recursion on the partial real line with applications to Real PCF
    • Escardó, M. and T. Streicher, Induction and recursion on the partial real line with applications to Real PCF, Theoret. Comput. Sci. 210 (1999), pp. 121-157.
    • (1999) Theoret. Comput. Sci. , vol.210 , pp. 121-157
    • Escardó, M.1    Streicher, T.2
  • 56
    • 0346934040 scopus 로고    scopus 로고
    • Bisimilarity as a theory of functional programming
    • mathematical foundations of programming semantics (New Orleans, LA, 1995)
    • Gordon, A. D., Bisimilarity as a theory of functional programming, Theoret. Comput. Sci. 228 (1999), pp. 5-47, mathematical foundations of programming semantics (New Orleans, LA, 1995).
    • (1999) Theoret. Comput. Sci. , vol.228 , pp. 5-47
    • Gordon, A.D.1
  • 58
    • 0027575864 scopus 로고
    • Power domains and second-order predicates
    • Heckmann, R., Power domains and second-order predicates, Theoret. Comput. Sci. 111 (1993), pp. 59-88.
    • (1993) Theoret. Comput. Sci. , vol.111 , pp. 59-88
    • Heckmann, R.1
  • 59
    • 0041528439 scopus 로고    scopus 로고
    • A non-topological view of dcpo's as convergence spaces
    • Heckmann, R., A non-topological view of dcpo's as convergence spaces, Theoret. Comp. Sci. 305 (2003), pp. 159-186.
    • (2003) Theoret. Comp. Sci. , vol.305 , pp. 159-186
    • Heckmann, R.1
  • 60
    • 0042895975 scopus 로고    scopus 로고
    • Quantitative semantics, topology, and possibility measures
    • Heckmann. R. and M. Huth, Quantitative semantics, topology, and possibility measures, Topology Appl. 89 (1998), pp. 151-178.
    • (1998) Topology Appl. , vol.89 , pp. 151-178
    • Heckmann, R.1    Huth, M.2
  • 61
    • 0021974161 scopus 로고
    • Algebraic laws for nondeterminism and concurrency
    • Hennessy, M. and R. Milner, Algebraic laws for nondeterminism and concurrency, J. Assoc. Comput. Mach. 32 (1985), pp. 137-161.
    • (1985) J. Assoc. Comput. Mach. , vol.32 , pp. 137-161
    • Hennessy, M.1    Milner, R.2
  • 62
    • 84968484601 scopus 로고
    • The spectral theory of distributive continuous lattices
    • Hofmann, K. and J. Lawson, The spectral theory of distributive continuous lattices, Trans. Amer. Math. Soc. 246 (1978), pp. 285-310.
    • (1978) Trans. Amer. Math. Soc. , vol.246 , pp. 285-310
    • Hofmann, K.1    Lawson, J.2
  • 63
    • 0013457461 scopus 로고
    • Local compactness and continuous lattices
    • Continuous Lattices
    • Hofmann, K. and M. Mislove, Local compactness and continuous lattices, in: Continuous Lattices, Lect. Notes Math. 871, 1981, pp. 209-248.
    • (1981) Lect. Notes Math. , vol.871 , pp. 209-248
    • Hofmann, K.1    Mislove, M.2
  • 64
    • 0001556003 scopus 로고
    • Filter spaces and continuous functional
    • Hyland, J., Filter spaces and continuous functional, Ann. Math. Logic 16 (1979), pp. 101-143.
    • (1979) Ann. Math. Logic , vol.16 , pp. 101-143
    • Hyland, J.1
  • 65
    • 0002177623 scopus 로고
    • First steps in synthetic domain theory
    • Category theory (Como, 1990), Springer, Berlin
    • Hyland, J. M. E., First steps in synthetic domain theory, in: Category theory (Como, 1990), Lecture Notes in Math. 1488, Springer, Berlin, 1991 pp. 131-156.
    • (1991) Lecture Notes in Math. , vol.1488 , pp. 131-156
    • Hyland, J.M.E.1
  • 66
    • 0034672932 scopus 로고    scopus 로고
    • On full abstraction for PCF: I, II and III
    • Hyland, J. M. E. and C.-H. L. Ong, On full abstraction for PCF: I, II and III, Inform. and Comput. 163 (2000), pp. 285-408.
    • (2000) Inform. and Comput. , vol.163 , pp. 285-408
    • Hyland, J.M.E.1    Ong, C.-H.L.2
  • 67
    • 0000574281 scopus 로고
    • Function spaces in the category of locales
    • Continuous lattices
    • Hyland, M., Function spaces in the category of locales., in: Continuous lattices, Lect. Notes Math. 871, 1981, pp. 264-281.
    • (1981) Lect. Notes Math. , vol.871 , pp. 264-281
    • Hyland, M.1
  • 68
    • 84976003627 scopus 로고
    • General function spaces, products and continuous lattices
    • Isbell, J., General function spaces, products and continuous lattices, Math. Proc. Camb. Phil. Soc. 100 (1986), pp. 193-205.
    • (1986) Math. Proc. Camb. Phil. Soc. , vol.100 , pp. 193-205
    • Isbell, J.1
  • 69
    • 0004072372 scopus 로고
    • Cambridge University Press, Cambridge
    • Johnstone, P., "Stone Spaces," Cambridge University Press, Cambridge, 1982.
    • (1982) Stone Spaces
    • Johnstone, P.1
  • 74
    • 9544225976 scopus 로고    scopus 로고
    • Stably compact spaces and the probabilistic powerspace construction
    • J. Desharnais and P. Panangaden, editors, Domain-theoretic Methods in Probabilistic Processes
    • Jung, A., Stably compact spaces and the probabilistic powerspace construction, in: J. Desharnais and P. Panangaden, editors, Domain-theoretic Methods in Probabilistic Processes, Electron. Notes Theoret. Comp. Sci. 87 (2004), 15pp.
    • (2004) Electron. Notes Theoret. Comp. Sci. , vol.87
    • Jung, A.1
  • 76
    • 33645263928 scopus 로고
    • Halbstetige Funktionen und stetige Verbände
    • R.-E. Hoffmann, editor, Continuous Lattices and Related Topics, Universität Bremen
    • Keimel, K. and G. Gierz, Halbstetige Funktionen und stetige Verbände, in: R.-E. Hoffmann, editor, Continuous Lattices and Related Topics, Mathematik-Arbeitspapiere 27, Universität Bremen, 1982, pp. 59-67.
    • (1982) Mathematik-arbeitspapiere , vol.27 , pp. 59-67
    • Keimel, K.1    Gierz, G.2
  • 77
    • 84966247356 scopus 로고
    • A direct proof of the Hofmann-Mislove theorem
    • Keimel, K. and J. Paseka, A direct proof of the Hofmann-Mislove theorem, Proc. Amer. Math. Soc. 120 (1994), pp. 301-303.
    • (1994) Proc. Amer. Math. Soc. , vol.120 , pp. 301-303
    • Keimel, K.1    Paseka, J.2
  • 78
  • 80
    • 0001805522 scopus 로고
    • Countable functionals
    • Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (edited by A. Heyting)
    • Kleene, S., Countable functionals, in: Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (edited by A. Heyting), Studies in Logic and the Foundations of Mathematics (1959), pp. 81-100.
    • (1959) Studies in Logic and the Foundations of Mathematics , pp. 81-100
    • Kleene, S.1
  • 82
    • 0003362604 scopus 로고
    • Synthetic differential geometry
    • Cambridge University Press, Cambridge
    • Kock, A., "Synthetic differential geometry," London Mathematical Society Lecture Note Series 51, Cambridge University Press, Cambridge, 1981.
    • (1981) London Mathematical Society Lecture Note Series , vol.51
    • Kock, A.1
  • 83
    • 0001776862 scopus 로고
    • Interpretation of analysis by means of constructive functionals of finite types
    • Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (edited by A. Heyting)
    • Kreisel, G., Interpretation of analysis by means of constructive functionals of finite types, in: Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (edited by A. Heyting), Studies in Logic and the Foundations of Mathematics (1959), pp. 101-128.
    • (1959) Studies in Logic and the Foundations of Mathematics , pp. 101-128
    • Kreisel, G.1
  • 85
    • 0346268480 scopus 로고    scopus 로고
    • Spaces of maximal points
    • Lawson, J., Spaces of maximal points, Math. Struct. Comput. Sci. 7 (1997), pp. 543-555.
    • (1997) Math. Struct. Comput. Sci. , vol.7 , pp. 543-555
    • Lawson, J.1
  • 87
    • 0037107689 scopus 로고    scopus 로고
    • The sequentially realizable functionals
    • Longley, J., The sequentially realizable functionals, Ann. Pure Appl. Logic 117 (2002), pp. 1-93.
    • (2002) Ann. Pure Appl. Logic , vol.117 , pp. 1-93
    • Longley, J.1
  • 91
    • 84991395657 scopus 로고    scopus 로고
    • Topological and limit-space subcategories of countably-based equilogical spaces
    • Menni, M. and A. Simpson, Topological and limit-space subcategories of countably-based equilogical spaces, Math. Struct. Comput. Sci. 12 (2002), pp. 739-770.
    • (2002) Math. Struct. Comput. Sci. , vol.12 , pp. 739-770
    • Menni, M.1    Simpson, A.2
  • 92
    • 0001862336 scopus 로고
    • Fully abstract models of typed λ-calculi
    • Milner, R., Fully abstract models of typed λ-calculi, Theoret. Comput. Sci. 4 (1977), pp. 1-22.
    • (1977) Theoret. Comput. Sci. , vol.4 , pp. 1-22
    • Milner, R.1
  • 93
    • 0038817831 scopus 로고    scopus 로고
    • Topology, domain theory and theoretical computer science
    • Mislove, M., Topology, domain theory and theoretical computer science, Topology Appl. 89 (1998), pp. 3-59.
    • (1998) Topology Appl. , vol.89 , pp. 3-59
    • Mislove, M.1
  • 94
    • 84982375633 scopus 로고
    • Effective operations on partial recursive functions
    • Myhill, J. and J. C. Shepherdson, Effective operations on partial recursive functions, Z. Math. Logik Grundlagen Math, l (1955), pp. 310-317.
    • (1955) Z. Math. Logik Grundlagen Math , vol.1 , pp. 310-317
    • Myhill, J.1    Shepherdson, J.C.2
  • 95
    • 84972507784 scopus 로고
    • Some Stone spaces and recursion theory
    • Nerode, A., Some Stone spaces and recursion theory, Duke Math. J. 26 (1959), pp. 397-406.
    • (1959) Duke Math. J. , vol.26 , pp. 397-406
    • Nerode, A.1
  • 96
    • 0008056690 scopus 로고
    • Recursion on the countable functionals
    • Springer, Berlin
    • Normann, D., "Recursion on the countable functionals," Lee. Not. Math. 811, Springer, Berlin, 1980, viii-191 pp.
    • (1980) Lee. Not. Math. , vol.811
    • Normann, D.1
  • 97
    • 0034258671 scopus 로고    scopus 로고
    • Computability over the partial continuous functionals
    • Normann, D., Computability over the partial continuous functionals, J. Symbolic Logic 65 (2000), pp. 1133-1142.
    • (2000) J. Symbolic Logic , vol.65 , pp. 1133-1142
    • Normann, D.1
  • 98
    • 85030748525 scopus 로고    scopus 로고
    • Hierarchies of total functionals over the reals
    • to appear
    • Normann, D., Hierarchies of total functionals over the reals, Theoret. Comput. Sci. (to appear).
    • Theoret. Comput. Sci.
    • Normann, D.1
  • 100
    • 0002057409 scopus 로고    scopus 로고
    • Operationally-based theories of program equivalence
    • Semantics and logics of computation (Cambridge, 1995), Cambridge Univ. Press, Cambridge
    • Pitts, A., Operationally-based theories of program equivalence, in: Semantics and logics of computation (Cambridge, 1995), Publ. Newton Inst. 14, Cambridge Univ. Press, Cambridge, 1997 pp. 241-298.
    • (1997) Publ. Newton Inst. , vol.14 , pp. 241-298
    • Pitts, A.1
  • 101
    • 0000230630 scopus 로고
    • LCF considered as a programming language
    • Plotkin, G., LCF considered as a programming language, Theoret. Comput. Sci. 5 (1977), pp. 223-255.
    • (1977) Theoret. Comput. Sci. , vol.5 , pp. 223-255
    • Plotkin, G.1
  • 102
    • 27744566785 scopus 로고
    • ω as a universal domain
    • ω as a universal domain, J. Comput. System Sci. 17 (1978), pp. 209-236.
    • (1978) J. Comput. System Sci. , vol.17 , pp. 209-236
    • Plotkin, G.1
  • 103
    • 33645260950 scopus 로고
    • department of Computer Science, University of Edinburgh. Available at the author's web page
    • Plotkin, G., Pisa notes on domains (1983), department of Computer Science, University of Edinburgh. Available at the author's web page.
    • (1983) Pisa Notes on Domains
    • Plotkin, G.1
  • 104
    • 33645248150 scopus 로고    scopus 로고
    • lectures given at McGill University's Bellairs Research Institute, Barbados
    • Plotkin, G., Ignorance and uncertainty (2003), lectures given at McGill University's Bellairs Research Institute, Barbados.
    • (2003) Ignorance and Uncertainty
    • Plotkin, G.1
  • 105
    • 0011642118 scopus 로고
    • Basic category theory
    • Oxford Univ. Press, New York
    • Poigne, A., Basic category theory, in: Handbook of logic in computer science, Vol. 1, Oxford Univ. Press, New York, 1992 pp. 413-640.
    • (1992) Handbook of Logic in Computer Science , vol.1 , pp. 413-640
    • Poigne, A.1
  • 107
    • 85034666637 scopus 로고
    • Logical aspects of denotational semantics
    • Robinson, E., Logical aspects of denotational semantics, Lec. Not. Comput. Sci. 283, 1987 pp. 238-253.
    • (1987) Lec. Not. Comput. Sci. , vol.283 , pp. 238-253
    • Robinson, E.1
  • 109
    • 15544377971 scopus 로고    scopus 로고
    • Equilogical spaces and filter spaces
    • categorical studies in Italy (Perugia, 1997)
    • Rosolini, G., Equilogical spaces and filter spaces, Rend. Circ. Mat. Palermo (2) Suppl. 64 (2000), pp. 157-175, categorical studies in Italy (Perugia, 1997).
    • (2000) Rend. Circ. Mat. Palermo (2) Suppl. , vol.64 , pp. 157-175
    • Rosolini, G.1
  • 111
    • 0001995203 scopus 로고
    • Continuous lattices
    • Scott, D., Continuous lattices, Lee. Not. Math. 274, 1972, pp. 97-136.
    • (1972) Lee. Not. Math. , vol.274 , pp. 97-136
    • Scott, D.1
  • 112
    • 0000889413 scopus 로고
    • Data types as lattices
    • Scott, D., Data types as lattices, SIAM J. Comput. 5 (1976), pp. 522-587.
    • (1976) SIAM J. Comput. , vol.5 , pp. 522-587
    • Scott, D.1
  • 113
    • 0027910876 scopus 로고
    • A type-theoretical alternative to CUCH, ISWIM and OWHY
    • reprint of a 1969 manuscript
    • Scott, D., A type-theoretical alternative to CUCH, ISWIM and OWHY, Theoret. Comput. Sci. 121 (1993), pp. 411-440, reprint of a 1969 manuscript.
    • (1993) Theoret. Comput. Sci. , vol.121 , pp. 411-440
    • Scott, D.1
  • 114
    • 0009950548 scopus 로고    scopus 로고
    • computer Science Department, Carnagie Mellon University. Available at the author's web page
    • Scott, D., A new category? Domains, spaces and equivalence relations (1996), computer Science Department, Carnagie Mellon University. Available at the author's web page.
    • (1996) A New Category? Domains, Spaces and Equivalence Relations
    • Scott, D.1
  • 116
    • 84974693335 scopus 로고    scopus 로고
    • A new category for semantics
    • Scott, D., A new category for semantics, Lec. Not. Comput. Sci. 2136 (2001), pp. 1-2.
    • (2001) Lec. Not. Comput. Sci. , vol.2136 , pp. 1-2
    • Scott, D.1
  • 118
    • 84896801813 scopus 로고    scopus 로고
    • Lazy functional algorithms for exact real functionals
    • Simpson, A., Lazy functional algorithms for exact real functionals, Lec. Not. Comput. Sci. 1450 (1999), pp. 323-342.
    • (1999) Lec. Not. Comput. Sci. , vol.1450 , pp. 323-342
    • Simpson, A.1
  • 119
    • 33746068266 scopus 로고    scopus 로고
    • Towards a convenient category of topological domains
    • Kyoto University
    • Simpson, A., Towards a convenient category of topological domains, in: Proceedings of 13th ALGI Workshop, RIMS, Kyoto University, 2003.
    • (2003) Proceedings of 13th ALGI Workshop, RIMS
    • Simpson, A.1
  • 120
    • 0003275966 scopus 로고
    • Effectively given domains
    • Smyth, M., Effectively given domains, Theoret. Comput. Sci. 5 (1977), pp. 256-274.
    • (1977) Theoret. Comput. Sci. , vol.5 , pp. 256-274
    • Smyth, M.1
  • 121
    • 0021011078 scopus 로고
    • Power domains and predicate transformers: A topological view
    • Smyth, M., Power domains and predicate transformers: a topological view, Lec. Not. Comput. Sci. 154, 1983, pp. 662-675.
    • (1983) Lec. Not. Comput. Sci. , vol.154 , pp. 662-675
    • Smyth, M.1
  • 122
    • 0001744565 scopus 로고
    • Topology
    • S. Abramsky, D. Gabbay and T. Maibaum, editors, Oxford science publications 1, Clarendon Press, Oxford
    • Smyth, M., Topology, in: S. Abramsky, D. Gabbay and T. Maibaum, editors, Handbook of Logic, in Computer Science, Oxford science publications 1, Clarendon Press, Oxford, 1992 pp. 641-761.
    • (1992) Handbook of Logic, in Computer Science , pp. 641-761
    • Smyth, M.1
  • 123
    • 0000874096 scopus 로고
    • The category-theoretic solution of recursive, domain equations
    • Smyth, M. and G. Plotkin, The category-theoretic solution of recursive, domain equations, SIAM J. Comput. 11 (1982), pp. 761-783.
    • (1982) SIAM J. Comput. , vol.11 , pp. 761-783
    • Smyth, M.1    Plotkin, G.2
  • 125
    • 0000234877 scopus 로고    scopus 로고
    • Concrete models of computation for topological algebras
    • Stoltenberg-Hansen, V. and J. Tucker, Concrete models of computation for topological algebras, Theoret. Comput. Sci. 219 (1999), pp. 347-378.
    • (1999) Theoret. Comput. Sci. , vol.219 , pp. 347-378
    • Stoltenberg-Hansen, V.1    Tucker, J.2
  • 126
    • 84968486072 scopus 로고
    • The theory of representations for Boolean algebras
    • Stone, M. H., The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), pp. 37-111.
    • (1936) Trans. Amer. Math. Soc. , vol.40 , pp. 37-111
    • Stone, M.H.1
  • 127
    • 84968483087 scopus 로고
    • Applications of the theory of Boolean rings to general topology
    • Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), pp. 375-481.
    • (1937) Trans. Amer. Math. Soc. , vol.41 , pp. 375-481
    • Stone, M.H.1
  • 128
    • 85030739573 scopus 로고    scopus 로고
    • department of mathematics, University of Darmstadt. Available at the author's web page
    • Streicher, T., Mathematical foundations of functional programming (2003), department of mathematics, University of Darmstadt. Available at the author's web page.
    • (2003) Mathematical Foundations of Functional Programming
    • Streicher, T.1
  • 131
    • 0012651251 scopus 로고    scopus 로고
    • Geometric and higher order logic in terms of abstract Stone duality
    • Taylor, P., Geometric and higher order logic in terms of abstract Stone duality, Theory Appl. Categ. 7 (2000), pp. No. 15, 284-338.
    • (2000) Theory Appl. Categ. , vol.7 , pp. 15
    • Taylor, P.1
  • 132
    • 14544276425 scopus 로고    scopus 로고
    • Local compactness and the Baire category theorem in ASD: A feasibility study
    • Taylor, P., Local compactness and the Baire category theorem in ASD: a feasibility study, Electron. Notes Theor. Comput. Sci. 69 (2002).
    • (2002) Electron. Notes Theor. Comput. Sci. , vol.69
    • Taylor, P.1
  • 133
    • 2442549417 scopus 로고    scopus 로고
    • Sober spaces and continuations
    • Taylor, P., Sober spaces and continuations, Theory Appl. Categ. 10 (2002), pp. No. 12, 248-300.
    • (2002) Theory Appl. Categ. , vol.10 , pp. 12
    • Taylor, P.1
  • 134
    • 18444391452 scopus 로고    scopus 로고
    • Subspaces in abstract Stone duality
    • Taylor, P., Subspaces in abstract Stone duality, Theory Appl. Categ. 10 (2002), pp. No. 13, 301-368.
    • (2002) Theory Appl. Categ. , vol.10 , pp. 13
    • Taylor, P.1
  • 135
    • 0012720413 scopus 로고
    • Denotational semantics
    • Oxford Sci. Publ., Oxford Univ. Press, New York
    • Tennent, R. D., Denotational semantics, in: Handbook of logic in computer science, Vol. 3, Oxford Sci. Publ., Oxford Univ. Press, New York, 1994 pp. 169-322.
    • (1994) Handbook of Logic in Computer Science , vol.3 , pp. 169-322
    • Tennent, R.D.1
  • 136
    • 85030748365 scopus 로고    scopus 로고
    • A universal characterization of the double power locale
    • to appear
    • Townsend, C. and S. Vickers, A universal characterization of the double power locale, Theoret. Comput. Sci. (to appear).
    • Theoret. Comput. Sci.
    • Townsend, C.1    Vickers, S.2
  • 137
    • 84974676530 scopus 로고    scopus 로고
    • Computational dimension of topological spaces
    • Tsuiki, H., Computational dimension of topological spaces, Lee. Not. Comput. Sci. 2064 (2001), pp. 323-335.
    • (2001) Lee. Not. Comput. Sci. , vol.2064 , pp. 323-335
    • Tsuiki, H.1
  • 139
    • 84960561455 scopus 로고
    • On computable numbers, with an application to the Entscheidungsproblem
    • Turing, A., On computable numbers, with an application to the Entscheidungsproblem., Proc. Lond. Math. Soc., II. Ser. 42 (1936), pp. 230-265.
    • (1936) Proc. Lond. Math. Soc., II. Ser. , vol.42 , pp. 230-265
    • Turing, A.1
  • 143
    • 0000793128 scopus 로고
    • Representations of the real numbers and the open subsets of the set of real numbers
    • Weihrauch, K. and C. Kreitz, Representations of the real numbers and the open subsets of the set of real numbers, Ann. Pure and Appl. Logic 35 (1987), pp. 247-260.
    • (1987) Ann. Pure and Appl. Logic , vol.35 , pp. 247-260
    • Weihrauch, K.1    Kreitz, C.2
  • 144
    • 0000162476 scopus 로고
    • Computing with infinite objects
    • Wiedmer, E., Computing with infinite objects, Theoret. Comput. Sci. 10 (1980), pp. 133-155.
    • (1980) Theoret. Comput. Sci. , vol.10 , pp. 133-155
    • Wiedmer, E.1
  • 145
    • 0004273499 scopus 로고
    • The formal semantics of programming languages
    • MIT Press, Cambridge, MA, an introduction
    • Winskel, G., "The formal semantics of programming languages," Foundations of Computing Series, MIT Press, Cambridge, MA, 1993, xx+361 pp., an introduction.
    • (1993) Foundations of Computing Series
    • Winskel, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.