Rank vs depth for array partitioning

Abstract

In some applications a subset of the dimensions of an array is used to define a framework which holds instances of cells defined by the complementary subset. A rank four array might be viewed as a page containing several rows of graphs. This structure could be used to apply a rotate function to each of the graphs. Existing proposals to implement a general scheme of program controlled distribution of functions over data arrays are compared. Nested arrays are suggested as the preferred technique. The analogy between the EACH operator and the ENCLOSE function in APL2/NARS leads to remarks on arrays of functions. In that context function distribution becomes a special case of scalar extension.