Halliday & Matthiessen (1999: 442):
Although it has not been part of the central argument about particular distinctions in the meaning base, we have also referred to the relationship between semantics and context. Just as the meaning base has to be accountable lexicogrammatically, it also has to be accountable contextually. In our discussion, we emphasised register or functional variation as one of the keys to the relationship between semantics and context.
Don't repeat the sloppy mistake that incautious readers have made. This does not equate context with register. Registers are the varieties of linguistic content (semantics and lexicogrammar) that realise varieties of context (situation types).