circularreference

Circular reference is a situation in which two or more entities reference each other in a cycle, creating a loop that can prevent straightforward evaluation or cause infinite recursion. It can occur in software, data modeling, and document calculations, often complicating reasoning about dependencies and results.

In spreadsheets, a circular reference occurs when a cell's formula depends on itself directly or through a chain of dependencies. Example: A1 depends on B1, and B1 depends on A1. Most spreadsheet programs flag this as an error, though some allow iterative calculation that can produce a convergent result under certain conditions.

In programming and data structures, circular references arise with mutually recursive functions or objects that reference each other. This can lead to infinite recursive calls, stack overflows, or difficulties in memory management and serialization if ownership and lifecycle are not carefully handled.

Detection and consequences: Circular references can cause infinite loops, stack overflows, or inconsistent results when partial evaluations occur. They are often represented as cycles in dependency or call graphs, and may be detected by graph algorithms that seek cycles.

Resolution strategies include redesigning dependencies to break the cycle, introducing intermediate data, or applying lazy evaluation and controlled iteration. In memory-managed environments, using weak references or separating ownership can prevent leaks. In spreadsheets, removing a dependency or enabling well-understood iterative calculation can mitigate issues, while in graphs or data models, topological ordering or converting to a directed acyclic graph can avoid cycles.