stagesfrom

Stagesfrom is a term used in process modeling and graph theory to denote an operator that, given a directed graph of stages and a starting node, yields the set or sequence of stages reachable from that node under the graph’s transition relations. It is commonly used in workflow engines, state machines, and project planning tools to reason about possible future states from a given point.

Etymology and scope: The word combines "stages," referring to discrete steps in a process, with "from," indicating origin. In practice, stagesfrom can be applied to any directed graph where nodes represent stages and edges represent permissible transitions, and it may be implemented with varying traversal rules and constraints.

Definition and behavior: If G=(V,E) is a directed graph and s ∈ V is a starting stage, stagesfrom(G,s) returns the subset or sequence of vertices reachable from s via directed paths. Implementations may include s in the result, and may provide different traversal modes (breadth-first or depth-first) and options such as maximum depth or filtering by attributes. Some variants return an ordered list, while others return a set.

Applications: Used to determine reachable workflow steps, to plan contingencies, to detect cycles or dead ends, and to generate visualizations of possible progressions in software design, manufacturing, or research pipelines.

Example: In a simple pipeline A → B → C, stagesfrom(G,A) might yield {A,B,C} with inclusive traversal or [A,B,C] as an ordered result, depending on the chosen method.

See also: state machine, graph traversal, topological sort, workflow, pipeline.