MongoDB: Recreate documents with new Id (e.g. change Id type)

MigrateIds.cs

/// <summary>
/// For each document of a collection, remove it and add it again with a new
/// Id generated by a provided function.
/// </summary>
/// <param name="connectionString">MongoClient connection string.</param>
/// <param name="databaseName">The database name</param>
/// <param name="collectionName">The collection name.</param>
/// <param name="idFunction">The Id generation function.</param>
/// <returns>List of concern results.</returns>
public static IEnumerable<WriteConcernResult> MigrateIds(
    string connectionString, 
    string databaseName, 
    string collectionName,
    Func<BsonDocument, BsonValue> idFunction)
{
    MongoClient client = new MongoClient(connectionString);
    MongoServer server = client.GetServer();
    MongoDatabase database = server.GetDatabase(databaseName);
    MongoCollection<BsonDocument> entryCollection = database.GetCollection(collectionName);
    foreach (BsonDocument entry in entryCollection.FindAll())
    {
        yield return entryCollection.Remove(Query.EQ("_id", entry["_id"]));
        entry.Set("_id", idFunction(entry));
        yield return entryCollection.Save(entry);
    }
}