Halliday & Matthiessen (1999: 95):
Construing a category thus includes locating it not only taxonomically and meronymically but also eco-functionally, as in the case of 'conscious being' just referred to. We noted above in connection with the cat example how the fact that a participant serves a participant role in a figure can be viewed either from the perspective of the figure or from the perspective of the participant (i.e. as a property of the participant). If cats kill mice, the ideation base accommodates the view from the angle of the figure: 'cats kill mice'; but it also accommodates the view from the angle of the participant: 'animals that kill mice'. Here the figure in which cats participate as actors has been construed as if it was a property, so that the category of cats might be construed within the system of the ideation base by means of the definition 'cats are animals that kill mice'. (In formal systems of representation, this can be expressed by means of lambda abstraction.)
There is a general semogenic strategy at work here. We referred to 'sequences', 'figures' and 'elements' as three orders of complexity in Section 2.1. The shift in perspective means that configurations of meanings that are of a particular order of complexity can be accessed through selection not only in their normal environment (within phenomena of the next higher order of complexity) but also within phenomena of lower orders of complexity. Through this semogenic strategy of opening up the possible domains of selection, a great deal of experiential complexity can be imported into the construal of a participant.