Halliday & Matthiessen (2014: 295-6):
Here the participants embody the notion of possession, one signifying property of the possessor, e.g. Peter’s, the other signifying the thing possessed, e.g. the piano. Thus in the piano is Peter’s, both the piano and Peter’s express ‘that which Peter possesses’, the relationship between them being simply one of identity. Note that here the piano is Token and Peter’s is Value.