This is the first part of a three-part series in which we present a new approach to software functional design, starting from the dataflow diagram D of an algorithm. We introduce the notion of a path-closed set for characterizing the subsets of D that can be considered as function blocks for the software. We also define an equivalence relation and a partial order on the data-items in D, which together with the path-closed subsets, give rise to three design rules for creating a functional design. We illustrate our method using an algorithm with complex dataflows and data-structures.