Halliday & Matthiessen (1999: 182-3):
We have already set up the general theory of participants, defining them in relation to ascriptive processes of being, being at, and having, in a process-participant configuration. There are three elements in such a configuration: the Process, intensive, possessive or circumstantial; the Attribute, which is being ascribed by one or other of these processes; and the Carrier. It is the role of Carrier which defines the concept of a participant. A participant, according to this theory, is that which may have assigned to it, in the discourse, properties, parts or circumstantial features. For example:
(a) properties (Process of 'being')some dishes are very tolerantthe grain looks orange and fulla kitchen should be a cheerful placethe swede is more nutritious than the turnip(b) parts (Process of 'having')it has branching stems covered with a green succulent fleshspinach has a decided flavour which some people dislikethey have a pleasant fresh flavour(c) circumstantial features (Process of 'being at')this plant is like chicorythese mangoes are from Mexicothe seeds will be inside long coffee-coloured podsthis effect might be because of over-heating
This analysis reveals two important aspects of a participant:
(i) that it is a thing that can 'carry' or be ascribed attributes, and(ii) that the ascription may be of different kinds — intensive (elaborating), possessive (extending), circumstantial (enhancing).