On Referential Transparency in the Presence of Uniform Sharing

Factotum, a software system for implementing symbolic computing systems, provides an uniform subterm sharing facility based on congruence that automatically detects and imposes sharing of equivalent structures independantly of client code. In the presence of this automatic facility, the meaning of structure updates is dangerously ambiguous. We explain how we resolve this problem in the Factotum system by providing a formal distinction between global updates, which are immediate; and local updates, which are relative to a declared root and become available only after finalization. This distinction has interesting consequences for coupled traversals.