Close composition

In SHARP APL and J, a close composition is one of the operators Atop, Over, or Under, defined so that the overall result has function rank equal to the right operand. "Close" is meant in the sense of distance; the left operand is applied nearer to the right operand relative to the corresponding rankless composition, in the sense that it is immediately applied to the result of each individual application of the right operand, as opposed to after the assembly of the right-operand results. In SHARP all composition operators follow this pattern, while in J, both close and non-close forms (with a result rank of infinity, matching the definition in most modern APLs) are provided.