Representation trees and string-tree correspondences

The correspondence between a string of a language and its abstract representation, usually a (decorated) tree, is not straightforward. However, it is desirable to maintain it, for example to build structured editors for texts written in natural language. As such correspondences must be compositional, we call them "Structured String-Tree Correspondences" (SSTC). We argue that a SSTC is in fact composed of two interrelated correspondences, one between nodes and substrings, and the other between subtrees and substrings, the substrings being possibly discontinuous in both cases. We then proceed to show how to define a SSTC with a Structural Correspondence Static Grammar (SCSG), and which constraints to put on the rules of the SCSG to get a "natural" SSTC.