A111788 Order of the domain D_n (n >= 0) in the inverse limit domain D_infinity.

2, 3, 10, 120549

Offset

0,1

Comments

D_infinity is the limit of the sequence of domains D_n that constitute the minimal nontrivial solution to the requirements that D_0 be a continuous lattice containing at least two elements and that D_(n+1) be the space of functions from D_n to D_n.

References

J. G. Sanderson, The Lambda Calculus, Lattice Theory and Reflexive Domains, Mathematical Institute Lecture Notes, University of Oxford, 1973.

J. E. Stoy, Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory, MIT Press, Cambridge, MA, 1977, pp. 113-115.

Links

Table of n, a(n) for n=0..3.

Encyclopedia of Mathematics, Continuous lattice.

Martin Richards, Backtracking algorithms in MCPL using bit patterns and recursion, University of Cambridge, 1997; see pp. 48-50. [It contains a program for the calculation of a(3) = |D_3|.]

A. W. [Bill] Roscoe, Notes on domain theory, 2007; see p. 131.

A. W. [Bill] Roscoe, Notes on domain theory, 2007; see p. 131.

Dana S. Scott, Continuous lattices, Technical Monograph PRG-7, Oxford University Computing Laboratory, 1971.

Dana S. Scott, Continuous Lattices, pp. 97-136 in F. W. Lawvere (ed.), Toposes, Algebraic Geometry and Logic, Springer-Verlag, Berlin, 1972.

Crossrefs

Sequence in context: A351775 A070239 A002443 * A238455 A098929 A073098

Adjacent sequences: A111785 A111786 A111787 * A111789 A111790 A111791

Keyword

nonn,more

Author

Jon Awbrey, Aug 16 2005

Status

approved