论文信息 - Total Sets and Objects in Domain Theory

Total Sets and Objects in Domain Theory

Abstract Berger, U., Total sets and objects in domain theory, Annals of Pure and Applied Logic 60 (1993) 91-117. Total sets and objects generalizing total functions are introduced into the theory of effective domains of Scott and Ersov. Using these notions Kreisel's Density Theorem and the Theorem of Kreisel-Lacombe-Shoenfield are generalized. As an immediate consequence we obtain the well-known continuity of computable functions on the constructive reals as well as a domain-theoretic characterization of the Heriditarily Effective Operations.

Ulrich Berger | Ulrich Berger

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

[2] Paola Giannini,et al. Effectively Given Domains and Lambda-Calculus Models , 1984, Inf. Control..

[3] P. Young,et al. Effective operators in a topological setting , 1984 .

[4] John C. Shepherdson,et al. Effective operations on partial recursive functions , 1955 .

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

[6] H. Schwichtenberg. Proofs as programs , 1993 .

[7] Dana S. Scott,et al. Some Domain Theory and Denotational Semantics in Coq , 2009, TPHOLs.

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

[9] Ulrich Berger,et al. An inverse of the evaluation functional for typed lambda -calculus , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

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

[11] Jean-Yves Girard,et al. A new constructive logic: classic logic , 1991, Mathematical Structures in Computer Science.

[12] Jean-Yves Girard,et al. The System F of Variable Types, Fifteen Years Later , 1986, Theor. Comput. Sci..

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

[14] Yu. L. Ershov,et al. Maximal and everywhere-defined functionals , 1974 .