Martin (1992: 568-9):
Obviously much more work on these and related story genres is required before a workable approximation to their generic inter-relationships can be constructed. Three provisional systems are presented in Fig. 7.27 by way of encouraging this articulation. The first opposition distinguishes recount genres, which deal unproblematically with activity sequences, from other story genres which depend on counterexpectancy. Then narratives, which make use of counterexpectancy to frustrate the inclinations of key protagonists are separated from exemplums and anecdotes where what goes wrong is not predicted' in this way. The third system opposes anecdotes, which focus on reaction, to exemplums, which deal in judgements.
To be clear, from an SFL perspective, this is classifying text types (genres) "from roundabout", in terms of their semantics, instead of "from above", in terms of the the cultural (contextual) functions they serve. As a functional theory, SFL gives priority to the view "from above".
From Martin's perspective, where genre and register are misconceived, not as language, but as strata of context, this is classifying genres "from below" — either from the stratum immediately below (register: activity sequences), or from the second stratum below (discourse semantics: counter-expectancy).