Chris Scott:
The HP side of the CFM56 is said to be based on the GE F101, which powered the (later cancelled) Rockwell B1A, although in the B1A it was reheated.
Quite right. But President Reagan revived the B-1 as a lower-cost machine (B-1B) and the F101 thus employed. Since then the F110 and F118 have been developed from the same core, and the CFM56-2 (military F108) powers the KC-135R.
There's a story that, during assembly of the first CFM56s at Villaroche (near Paris) in the early 1970s, the Snecma engineers were not permitted to see the interior of the requisite modules supplied by GE because the F101 was still classified.
It's more than a story; it was de rigueur for CFM development work for many months.