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What happens when a local object goes out of scope, and in what order?

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Its destructor runs at the closing brace of the enclosing block, automatically. That happens whether you fall off the end, hit a return, or throw.

Order is strictly the reverse of construction. Locals die newest first, which matters when a later object depends on an earlier one. Inside one object, the destructor body runs, then members in reverse declaration order, then base classes.

{
  Logger a;
  Connection b(a);
}  // ~b runs, then ~a

That reverse ordering is what keeps dependent resources safe. A connection that logs during shutdown can count on the logger still being alive. One caveat: only automatic-storage objects get this. A heap object made with new is untouched by scope exit; just the pointer dies.

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