Capturing a lambda in another lambda can violate const qualifiers
I'll start by addressing your second question first. std::function type erases, and holds a copy of the functor it's initialized with. That means there's a layer of indirection between std::function::operator() and the actual functor's operator().
Envision if you will, holding something in your class by pointer. Then you may call a mutating operation on the pointee from a const member function of your class, because it doesn't affect (in a shallow view) the pointer that the class holds. This is a similar situation to what you observed.
As for your first question... "Always" is too strong a word. It depends on your goal.
If you want to support self mutating functors easily, then you should capture in a mutable lambda. But beware it may affect the library functions you may call now.
If you wish to favor non-mutating operations, then a non-mutable lambda. I say "favor" because as we observed, the type system can be "fooled" with an extra level of indirection. So the approach you prefer is only going to be easier to use, not impossible to go around. This is as the sage advice goes, make correct use of your API easy, and incorrect harder.
Does this mean that if I have a library function that accepts an arbitrary function argument and captures it in a lambda, I always need to make that lambda mutable, because I don't know what users can pass in?
That's a design decision for your library API. You can require client code to pass function objects with a const-qualified operator() (which is the case for non-mutable lambda expressions). If something different is passed, a compiler error is triggered. But if the context might require a function object argument that modifies its state, then yes, you have to make the internal lambda mutable.
An alternative would be to dispatch on the ability to invoke operator() on a const-qualified instance of the given function type. Something along those lines (note that this needs a fix for function objects with both const and non-const operator(), which results in an ambiguity):
template <class Fct>
auto wrap(Fct&& f) -> decltype(f(), void())
{
[fct = std::forward<Fct>(f)]() mutable { fct(); }();
}
template <class Fct>
auto wrap(Fct&& f) -> decltype(std::declval<const Fct&>()(), void())
{
[fct = std::forward<Fct>(f)]() { fct(); }();
}
Notably, wrapping f1 in std::function seems to resolve this problem (how?).
This is a bug in std::function due to its type-erasure and copy semantics. It allows non-const-qualified operator() to be invoked, which can be verified with such a snippet:
const std::function<void()> f = [i = 0]() mutable { ++i; };
f(); // Shouldn't be possible, but unfortunately, it is
This is a known issue, it's worth checking out Titus Winter's complaint on this.