Martin (1992: 370):
The approach to lexical relations developed here represents one of two major extensions of the analysis of lexical cohesion as it was outlined in Halliday and Hasan (1976). The other has been developed by Hasan in her work on cohesive harmony (1984, 1985). The two approaches have different goals. The interpretation of lexical relations is an attempt to refine lexical cohesion analysis in the direction of the register variable field. Hasan on the other hand has been concerned with developing a measure of coherence across texts. In spite of these different goals there is considerable convergence across the two approaches, especially with respect to what were treated above as nuclear relations.
 Martin's 'discourse semantics' model of lexical cohesion is not a development of Halliday and Hasan's (1976) theory of lexical cohesion — it is a major misunderstanding of it, as so many of the analyses herein demonstrate. Most fundamentally, Martin misconstrues a resource of the textual metafunction as a system of experiential meaning. Within this misunderstanding, Martin confuses textually cohesive lexical relations with the notion of (experiential) lexis as most delicate grammar. Moreover, Martin's discourse semantic model of experiential meaning consists of experiential units that are logically and/or interpersonally related to other experiential units. See previous posts for detailed verification.
 In SFL theory, field is not a register variable. Field is the ideational dimension of context, which is more abstract than language, whereas register is a functional variety of language itself. Each register realises a contextual situation type whose metafunctional dimensions are subpotentials of field, tenor and mode systems.