Is this use of Parallel.ForEach() thread safe?

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Yes; List<T> is not thread safe, so adding to it ad-hoc from arbitrary threads (quite possibly at the same time) is doomed. You should use a thread-safe list instead, or add locking manually. Or maybe there is a Parallel.ToList.

Also, if it matters: insertion order will not be guaranteed.

This version is safe, though:

var output = new string[data.Count];

Parallel.ForEach<String>(data, (line,state,index) =>
{
    String outputLine = index.ToString();
    // ** Do something with "line" and store result in "outputLine" **

    // Additionally, there are some this.Invoke statements for updating UI
    output[index] = outputLine;
});

here we are using index to update a different array index per parallel call.

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