'Each' with plural or singular verb

Question

A source says that the word "each" should always be followed by a singular noun, but however I look at it in this sentence it just doesn't seem to fit:

foo comprises of multiple binary programs that each performs a single task.

Should it be "performs" or "perform"?

Answer 1

Each in phrases like each battery is singular; the verb you use in that cases is singular.

Each battery is in a separate compartment.

Vice versa, in sentences like the following the verb is plural.

They each have their own personality.
Foo comprises multiple binary programs that each perform a single task.

Subject and verb must agree in number; in multiple binary programs that each perform a single task, the subject is multiple binary programs, which is plural, and the verb needs to be plural too (perform).

Answer 2

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.

Answer 3

But the AHDEL does give a complex analysis of structures using each following a plural subject - and one that is in line with kiamlaluno's second example, and with which I agree. Admittedly there is not an example parallel to the original with the that-clause cited, but thesaurus.com has individually and each as synonyms in this usage, and obviously Foo comprises multiple binary programs that individually perform a single task needs plural verb concord. Whether the object should be singular or plural is a different matter.

I'd probably use:

Foo comprises multiple binary programs: each performs a single task.