Halliday & Matthiessen (1999: 129):
… the projecting figure represents symbolic processing, processing that brings another figure into symbolic existence. Figures of symbolic processing involve the symbolic process itself (thinking, saying etc) and a participant engaged in the symbolic processing, as in ‘Symboliser’: she + ‘Process’: said/thought —> that he had left. The projected symbolic content is either a proposition (she said/thought —> he had left) or a proposal (she asked him —> to leave; she wanted —> him to leave).