splitting a way programmatically

I am assuming that you want to detect actual intersection nodes, i.e. nodes that are shared between more than one way and are not the start or end node for the ways that share the node.

Without pre-processing, there is no way to detect those, because the way objects do not possess geometry, only the nodes do. So you would at least keep all the node IDs in memory or in a temporary file and then check for each way member node whether that node is also used by another way.

If you import your OSM file into an Osmosis schema PostGIS database, you will find the way_nodes table useful for checking intersections.

Assume you have extracted/created all the poly-lines in accordance with ways-nodes relations. From that point your question may be understood more generally than the former answer is suggesting. Namely, you are looking for a function that converts a set of poly-lines into a set of simple poly-lines (a simple poly-line has no common point with any other poly-line except maybe the end-points). But then, if a crossing point can be anywhere on poly-lines the issue is more complex and complicated. I am not shore you can find standard and open-source solution to it (you know, any computer calculated crossing of two vectors/straight line segments is never on any of them except maybe in some trivial cases). At the same time, the mentioned function is essential in vector map data preparation phase (e.g. finding a simple area coverage for complicated area structures with overlaps or like a hole having a common border section with container/outer border, or even slightly crossing it, or when recognizing wrong/not tagged roundabouts in a road class and so on). So, if you don’t mind, here is a model how I/we handle your issue: First, we decompose all poly-lines into single (independent) vectors. Next, any crossing or overlapping vectors are divided into none-crossing and none overlapping vectors. So, neighboring vectors (those having one and only one common end-point) are linear-connected to (simple) poly-lines again. Finally, there are some cosmetic updates regarding orientations, name assignments, rule assignments and so on. Now, these poly-lines are what you are looking for. The whole poly_lines-to-simple-poly_lines (how we call it) process takes some seconds or minutes (in case of huge data-sets like the Planet forests, river-lines…) on a medium strong laptop.