Martin (1992: 388):
First, SUBSTITUTION and ELLIPSIS. Like the discourse semantics systems of IDENTIFICATION and CONJUNCTION, these systems can be used to presume information which is not grammatically related to presuming items. Substitutes and ellipses make explicit almost none of the experiential or interpersonal meaning they presume, treating it as redundant (thus the term redundancy phoricity, as opposed to reminding and relevance phoricity).
 In contradistinction, in SFL theory, substitution–&–ellipsis is a resource for setting up a relation that is lexicogrammatical. Halliday & Matthiessen (2004: 561-2, 563):
Another form of anaphoric cohesion in the text is achieved by ellipsis, where we presuppose something by means of what is left out. Like all cohesive agencies, ellipsis contributes to the semantic structure of the discourse. But unlike reference, which is itself a semantic relation, ellipsis sets up a relationship that is not semantic but lexicogrammatical — a relationship in the wording rather than directly in the meaning. … The substitute is phonologically non-salient and serves as a place-holding device, showing where something has been omitted and what its grammatical function would be;
 In SFL theory, the cohesive system of substitution–&–ellipsis is a resource for marking textual prominence. Halliday & Matthiessen (2004: 563):
Ellipsis marks the textual status of continuous information within a certain grammatical structure. At the same time, the non-ellipsed elements of that structure are given the status of being contrastive in the environment of continuous information. Ellipsis thus assigns differential prominence to the elements of a structure: if they are non-prominent (continuous), they are ellipsed; if they are prominent (contrastive), they are present. The absence of elements through ellipsis is an iconic realisation of their lack of prominence.