Skip to main content Accessibility help
×
Home

Computability over the partial continuous functionals

  • Dag Normann (a1)

Abstract

We show that to every recursive total continuous functional Φ there is a PCF-definable representative Ψ of Φ in the hierarchy of partial continuous functionals, where PCF is Plotkin's programming language for computable functionals. PCF-definable is equivalent to Kleene's S1–S9-computable over the partial continuous functionals.

Copyright

References

Hide All
[1]Bellantoni, S., Comments on two notions of higher type computability, unpublished notes, 1990.
[2]Berger, U., Totale objekte und mengen in der bereichtheorie, Thesis, München, 1990, in german.
[3]Berger, U., Total sets and objects in domain theory, Annals of Pure and Applied Logic, vol. 60 (1993), pp. 91–117.
[4]Ershov, Yu. L., Computable functionals of finite type, Algebra and Logic, vol. 11 (1972), pp. 203–277.
[5]Hyland, J. M. E., Filterspaces and continuous functionals, Annals of Mathematical Logic, vol. 16 (1979), pp. 101–143.
[6]Kleene, S.C., Countable functionals, Constructivity in mathematics (Heyting, A., editor), North-Holland, 1959, pp. 81–100.
[7]Kleene, S.C., Recursive functionals and quantifiers of finite types I, Transactions of the American Mathematical Society, vol. 91 (1959), pp. 1–52.
[8]Kreisel, G., Interpretation of analysis by means of functionals of finite type, Constructivity in mathematics (Heyting, A., editor), North-Holland, 1959, pp. 101–128.
[9]Longo, G. and Moggi, E., The hereditarily partial effective functionals and recursion theory in higher types, This Journal, vol. 49 (1984), pp. 1319–1332.
[10]Moldestad, J., Computation in higher types, Springer Lecture Notes in Mathematics, vol. 574, 1977.
[11]Normann, D., Nonobtainable continuous functionals, Logic, methodology and philosophy of science VI. Proceedings of the sixth international congress on logic, methodology and philosophy of science (Hannover), 1979, pp. 241–249.
[12]Normann, D., Recursion on the continuous functionals, Springer Lecture Notes in Mathematics, vol. 811, 1980.
[13]Normann, D., The continuous functionals; computations, recursions and degrees, Annals of Mathematical Logic, vol. 21 (1981), pp. 1–26.
[14]Normann, D., The continuous functionals, Handbook of computability theory (Griffor, E. R., editor), Elsevier, 1999, pp. 251–275.
[15]Plotkin, G., LCF considered as a programming language, Theoretical Computer Science, vol. 5 (1977), pp. 223–255.
[16]Plotkin, G., Full abstraction, totality and PCF, Mathematical Structures in Computer Science, vol. 11 (1999), pp. 1–20.
[17]Stoltenberg-Hansen, V., Lindström, I., and Griffor, E. R., Mathematical theory of domains, Cambridge Tracts in Theoretical Computer Science, vol. 22, Cambridge University Press, 1994.
[18]Tait, W. W., Continuity properties ofpartial recursive functionals offinite type, unpublished notes.

Related content

Powered by UNSILO

Computability over the partial continuous functionals

  • Dag Normann (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.