I've been very much of two minds in this debate: On the one hand, having these constraints is very practically useful. On the other, what we're doing here is very un-Haskellish, in that we're letting operational concerns leak into a declarative property (a function's type). The reason we're doing this is another un-Haskellish thing -- partiality -- but that ship has sailed.
So, may I propose a slightly different way forward?
Instead of adding a HasCallStack constraint on these functions, add an IsPartial constraint. For example:
> head :: IsPartial => [a] -> a
This is slightly awkward, still, because IsPartial is a class-constraint-like-thing, but it has no parameter. But it has a few very nice properties:
* IsPartial is declarative: it describes a property of the function without worrying about its operation.
* If we think about the way constraints propagate, IsPartial has the right semantics: the caller of a partial function would itself become partial.
I don't think this is true.
Clearly foo is total - it is defined for all of its inputs. That it uses a partial function in its body isn't observable. So it's a shame that IsPartial leaks out.