Each is always singular. You are talking about how “each program is” doing one thing. Or how “each of these is” doing one thing. Both formulations are allowed, and in either case, it is singular. Only. That means that all of these are inadmissibly wrong — or alternately, each of these is inadmissibly wrong:
- each ∗programs ∗are
- each program ∗are
- each ∗programs is
- each of these programs ∗are
None of that is English.
Well, not correct English, that is. The OED says:
With reference to a sb. going before, or followed by of. Sometimes incorrectly with pl. vb.
All the citations of the incorrect use are also quite old.
No complex analysis is needed here: each, like every, is always singular, even when it is distributing a plural subject.
Also, “foo comprises of ” is also not English. It needs to be “foo comprises”. I know people who never, ever say comprise for fear of using it wrong, or worse, of being miscorrected. There might be betters words here, like consists of.