Computability and totality in domains

Mathematical Structures in Computer Science / Volume 12 / Issue 03 / June 2002, pp 281 294 DOI: 10.1017/S0960129502003638, Published online: 16 August 2002 Link to this article: http://journals.cambridge.org/abstract_S0960129502003638 How to cite this article: ULRICH BERGER (2002). Computability and totality in domains. Mathematical Structures in Computer Science, 12, pp 281-294 doi:10.1017/S0960129502003638 Request Permissions : Click here

[1]  Viggo Stoltenberg-Hansen,et al.  Mathematical theory of domains , 1994, Cambridge tracts in theoretical computer science.

[2]  Michael Beeson,et al.  Recursive models for constructive set theories , 1982, Ann. Math. Log..

[3]  A. Troelstra.  Metamathematical investigation of intuitionistic arithmetic and analysis , 1973 .

[4]  Dag Normann,et al.  The continuous functionals of finite types over the reals , 1998, Workshop on Domains.

[5]  Viggo Stoltenberg-Hansen,et al.  Streams, Stream Transformers and Domain Representations , 1998, Prospects for Hardware Foundations.

[6]  Thomas Streicher,et al.  Real PCF extended with is universal (Extended Abstract) , 1996 .

[7]  Yiannis N. Moschovakis,et al.  Recursion in Higher Types , 1977 .

[8]  Dag Normann,et al.  Categories of domains with totality , 1997 .

[9]  J. Hyland,et al.  Filter spaces and continuous functionals , 1979 .

[10]  Erik Palmgren,et al.  Domain Interpretations of Martin-Löf's Partial Type Theory , 1990, Ann. Pure Appl. Log..

[11]  D. Normann.  Recursion on the countable functionals , 1980 .

[12]  Dieter Spreen,et al.  On effective topological spaces , 1998, Journal of Symbolic Logic.

[13]  Martín Hötzel Escardó,et al.  PCF Extended with Real Numbers , 1996, Theor. Comput. Sci..

[14]  Robert L. Constable,et al.  Computability Concepts for Programming Language Semantics , 1976, Theor. Comput. Sci..

[15]  Dag Normann.  Computability over The Partial Continuous Functionals , 2000, J. Symb. Log..

[16]  Y. Moschovakis.  Recursive metric spaces , 1964 .

[17]  Viggo Stoltenberg-Hansen,et al.  Concrete Models of Computation for Topological Algebras , 1999, Theor. Comput. Sci..

[18]  Robin Milner,et al.  Fully Abstract Models of Typed lambda-Calculi , 1977, Theor. Comput. Sci..

[19]  Robert L. Constable,et al.  Computability concepts for programming language semantics , 1975, Theor. Comput. Sci..

[20]  Johan Moldestad.  Computations in Higher Types , 1977 .

[21]  Ulrich Berger,et al.  Continuous Functionals of Dependent and Transfinite Types , 1999 .

[22]  Stephen A. Cook,et al.  Computability and Complexity of Higher Type Functions , 1992 .

[23]  Bruce M. Kapron,et al.  Characterizations of the basic feasible functionals of finite type , 1989, 30th Annual Symposium on Foundations of Computer Science.

[24]  Ulrich Berger,et al.  Total Sets and Objects in Domain Theory , 1993, Ann. Pure Appl. Log..

[25]  R. Platek.  Foundations of recursion theory , 1966 .

[26]  Helmut Schwichtenberg,et al.  Higher type recursion, ramification and polynomial time , 2000, Ann. Pure Appl. Log..

[27]  Geir Waagbø.  Denotational semantics for intuitionistic type theory using a hierarchy of domains with totality , 1999, Arch. Math. Log..

[28]  G.D. Plotkin,et al.  LCF Considered as a Programming Language , 1977, Theor. Comput. Sci..

[29]  Y. Moschovakis.  Review: G. Kriesel, D. Lacombe, J. Shoenfield, Effective Operations and Partial Recursive Functionals; G. Kreisel, D. Lacombe, J. R. Shoenfield, Partial Recursive Functionals and Effective Operations , 1966 .

[30]  Y. Ershov.  Model of Partial Continuous Functionals , 1977 .

[31]  J. Ersov.  Theorie der Numerierungen II , 1973 .

[32]  Solomon Feferman.  Inductive Schemata and Recursively Continuous Functionals , 1977 .

[33]  Helmut SchwichtenbergMathematisches,et al.  Density and Choice for Total Continuous Functionals* 1. Information Systems , 1996 .

[34]  R. Gandy,et al.  Computable and recursively countable functions of higher type , 1977 .

[35]  Bernhard Möller,et al.  Prospects for Hardware Foundations , 2002, Lecture Notes in Computer Science.

[36]  L. Kristiansen,et al.  Interpreting higher computations as types with totality , 1994, Arch. Math. Log..

[37]  Gordon D. Plotkin,et al.  Full abstraction, totality and PCF , 1999, Mathematical Structures in Computer Science.