Origin Tracking

In the framework of conditional, not necessarily orthogonal, term rewriting systems, we introduce the notion of an origin. Origins are relations between subterms of intermediate terms which occur during rewriting, and subterms of the initial term. Origin tracking is a method for incrementally computing origins during rewriting. Origins are a generalization of the well-known concept of residuals (also called descendants). We give a formal deenition of origins, and present a method for implementing them. Origin tracking is a highly versatile technique when applied to the prototyping of algebraic speciications of programming languages. For example, origin tracking allows program execution to be visualized in a semi-automatic way, given an algebraic speciication of the dynamic semantics of the programming language. Furthermore, various notions of breakpoints for generic debuggers can be deened without diiculty. Finally, given a speciication of the static semantics of a programming language, origin tracking enables, once an error (such as type-incompatibility) has been detected, to infer the position of the error in the source program automatically.