"Programme" is rarely used in AmE.
I hadn't even realized that "programing" was a word. The usual English practice would be to double the 'm' to avoid the pronunciation of 'progrEIming'. Dam - Damming; Spam - Spamming; Ham - Hamming, etc. I haven't noticed much daming of rivers or spaming on the 'net.I am not a teacher.
I agree entirely with post #2.
As for the verb, I would add that even when the meaning can be compared to computer programing as in 'programming a person to behave in a particular way', in BrE it is still the version with two 'm's.
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