How can I pass a C++ lambda to a C-callback that expects a function pointer and a context?

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The simple approach is to stick the lambda into a std::function<void()> which is kept somewhere. Potentially it is allocated on the heap and merely referenced by the void* registered with the entity taking the callback. The callback would then simply be a function like this:

extern "C" void invoke_function(void* ptr) {
    (*static_cast<std::function<void()>*>(ptr))();
}

Note that std::function<S> can hold function objects with state, e.g., lambda functions with a non-empty capture. You could register a callback like this:

register_callback(&invoke_function,
  new std::function<void()>([=](){ ... }));

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