Rebranding Halliday's 'Complex' Numeratives As The Authors' 'Re-counting' & 'Partitive' Subtypes Of Focus

 Martin, Matthiessen & Painter (2010: 170):

The Focus element can have a range of functions, which are outlined in Table 5.7 below.

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To be clear, the 're-counting' and 'partitive' subtypes of Focus are merely the authors' rebranding of Halliday's types of complex Numerative. Halliday (1985: 173-4; 1994: 195):

The 're-counting' subtype of Focus includes both quantitative Numeratives (cup, glass, jug, tank, pound, yard, metre, gallon, litre) and collective Numeratives (set, collection, group, crowd, school, herd, flock, gaggle, pod, swarm).

The 'partitive' subtype of Focus is just a rebranding of partitive Numeratives.