Steps to an advanced Ada programming environment

Conceptual simplicity, tight coupling of tools, and effective support of host-target software development will characterize advanced Ada programming support environments. Several important principles have been demonstrated in the Arcturus system, including template-assisted Ada editing, command completion using Ada as a command language, and combining the advantages of interpretation and compliation. Other principles, relating to analysis, testing, and debugging of concurrent Ada programs, have appeared in other contexts. This paper discusses several of these topics, considers how they can be integrated, and argues for their inclusion in an environment appropriate for software development in the late 1980's

The Number of Hierarchical Orderings

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single ``hierarchy''; these are enumerated by the ordered Bell numbers. In this note we determine the number of ``hierarchical orderings'' or ``societies'', where the n elements are first partitioned into m <= n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case.Comment: 7 page

Special Geometry and Twisted Moduli in Orbifold Theories with Continuous Wilson Lines

Target space duality symmetries, which acts on K\"ahler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These spaces described by the cosets $SU(n,1)\over SU(n)\times U(1)$ are $special$ K\"ahler, a fact which is exploited in deriving the extension of tree level duality transformation to include higher orders of the twisted moduli. Also, restrictions on these higher order terms are derived.Comment: 13 page