So the actual structure is a nom gp
the days of auld lang syne
The Scottish National Dictionary gives multiple glosses for syne, including ‘ago’. In which case it’s an ellipsed embedded clause
the days [of old] [[long ago]]
(Qualifier probes are which days? and which days of old?)
Blogger Comments:
To be clear, Rose provides constituency and two functions, but no structural analysis. Returning to the original Scots wording, and applying the standard model of SFL Theory, lang syne is an adverbial group that elaborates the prepositional phrase of auld in a paratactic complex that serves as the Qualifier of days:
Both units of the Qualifier realise the meaning 'in the past', with the second elaborating the first, and the relation is paratactic, because neither depends on the other:
The days of auld (old)
The days lang syne (long ago)
However, on the model of Halliday (1994: 193):
the logical structure is: