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
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
KEYWORD
nonn,more
AUTHOR
Jon Awbrey, Aug 16 2005
STATUS
approved