Halliday & Matthiessen (2014: 484):
Verbal conjunctions are derived from the imperative or from the present/active or past/passive participle + (optionally) that: provided (that), seeing (that/how), suppose/supposing (that), granted (that), say (that). In origin these are projections; their function as expanding conjunction reflects the semantic overlap between expansion and projection in the realm of ‘irrealis’: ‘let us say/think that ... ’ = ‘if ... ’, as in say they can’t mend it, shall I just throw it away?