You can implement any of them in terms of the others, but only if you break convention and introduce side effects. Follow convention and try to implement (for example) reduce with map and you'll find that it's not possible.
This can't be right. forEach has no effects other than side effects. A convention that says not to use side effects prevents you from using forEach at all.
But that would make claims about the place of forEach in a hierarchy into meaningless nonsense.
> The forEach isn't returning it in your example, the line after it is returning.
That depends on your point of view. C has numerous functions which accept pointer parameters and return values in those parameters. That's just the normal way to return multiple values in C.
And by that standard, the forEach itself is returning the transformed list; that's where the transformation occurs. The following `return` line is only necessary if this is a snippet within a function whose purpose is to execute a for statement; you would actually do this inline, by just writing the for statement without needing a following `return`.
And without side-effects, a map can't implement a forEach.
Yes, it can, because without side effects, forEach is a NOP. That's not difficult to implement. As long as you don't do anything with the return value from map, you're there.
To make that untrue, you need to define very strict limits on what else your language can do.
(Sure, we produce a transformed list here through the use of side effects. But note that the original example sparking the claim that forEach can't do what map can was this:
Side effects are clearly allowed.)