School of Computing and Mathematical Sciences,; Oxford Brookes University,
SVM HeaderParse 0.2
Gipsy Lane, Headington,; Oxford OX3 0BP, UK.
SVM HeaderParse 0.1
. A downwards accumulation is a higher-order operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular datatype; the resulting denition is co-inductive. 1 Introduction The notion of scans or accumulations on lists is well known, and has proved very fruitful for expressing and calculating with programs involving lists . Gibbons [7, 8] generalizes the notion of accumulation to various kinds of tree; that generalization too has proved fruitful, underlying the derivations of a number of tree algorithms, such as the parallel prex algorithm for prex sums [15, 8], Reingold and Tilford's algorithm for drawing trees tidily [21, 9], and algorithms for query evaluation in structured text [16, 23]. There are two varieties of accumulation on lists: leftwards and rightwards. Leftwards accumulation ...