public class DataStreamList {
    public DataStreamList(DataStream<?>... dataStreams) {...}

    // Returns the number of data streams in this list.
    public int size() {...}

    // Returns the data stream at the given index in this list.
    @SuppressWarnings("unchecked")
    public <T> DataStream<T> get(int index) {...}
}

@PublicEvolving
public interface IterationBody {
    /**
     * This method creates the graph for the iteration body.
     *
     * See Utils::iterate, Utils::iterateBoundedStreams and Utils::iterateAndReplayBoundedStreams for how the iteration
     * body can be executed and when execution of the corresponding graph should terminate.
     *
     * Required: the number of feedback variable streams returned by this method must equal the number of variable
     * streams given to this method.
     *
     * @param variableStreams the variable streams.
     * @param dataStreams the data streams.
     * @return a IterationBodyResult.
     */
    IterationBodyResult process(DataStreamList variableStreams, DataStreamList dataStreams);
}


/**
 * A helper class that contains the streams returned by the iteration body.
 */
class IterationBodyResult {
    /**
     * A list of feedback variable streams. These streams will only be used during the iteration execution and will
     * not be returned to the caller of the iteration body. It is assumed that the method which executes the
     * iteration body will feed the records of the feedback variable streams back to the corresponding input variable
     * streams.
     */
    DataStreamList feedbackVariableStreams;

    /**
     * A list of output streams. These streams will be returned to the caller of the methods that execute the
     * iteration body.
     */
    DataStreamList outputStreams;

    /**
     * An optional termination criteria stream. If this stream is not null, it will be used together with the
     * feedback variable streams to determine when the iteration should terminate.
     */
    Optional<DataStream<?>> terminationCriteria;
}


/**
 * The callbacks defined below will be invoked only if the operator instance which implements this interface is used
 * within an iteration body.
 */
@PublicEvolving
public interface IterationListener<T> {
    /**
     * This callback is invoked every time the epoch watermark increments. The initial epoch watermark is -1.
     *
     * The epochWatermark is the maximum integer that meets this requirement: every record that arrives at the operator
     * going forward should have an epoch larger than the epochWatermark. See Java docs in IterationUtils for how epoch
     * is determined for records ingested into the iteration body and for records emitted by operators within the
     * iteration body.
     *
     * If all inputs are bounded, the maximum epoch of all records ingested into this operator is used as the
     * epochWatermark by the last invocation of this callback.
     *
     * @param epochWatermark The incremented epoch watermark.
     * @param context A context that allows emitting side output. The context is only valid during the invocation of
     *                this method.
     * @param collector The collector for returning result values.
     */
    void onEpochWatermarkIncremented(int epochWatermark, Context context, Collector<T> collector);

    /**
     * This callback is invoked after the execution of the iteration body has terminated.
     *
     * See Java doc of methods in IterationUtils for the termination conditions.
     *
     * @param context A context that allows emitting side output. The context is only valid during the invocation of
     *                this method.
     * @param collector The collector for returning result values.
     */
    void onIterationTermination(Context context, Collector<T> collector);

    /**
     * Information available in an invocation of the callbacks defined in the IterationProgressListener.
     */
    interface Context {
        /**
         * Emits a record to the side output identified by the {@link OutputTag}.
         *
         * @param outputTag the {@code OutputTag} that identifies the side output to emit to.
         * @param value The record to emit.
         */
        <X> void output(OutputTag<X> outputTag, X value);
    }
}

/**
 * A helper class to apply {@link IterationBody} to data streams.
 */
@PublicEvolving
public class IterationUtils {
    /**
     * This method can use an iteration body to process records in unbounded data streams.
     *
     * This method invokes the iteration body with the following parameters:
     * 1) The 1st parameter is a list of input variable streams, which are created as the union of the initial variable
     * streams and the corresponding feedback variable streams (returned by the iteration body).
     * 2) The 2nd parameter is the data streams given to this method.
     *
     * The epoch values are determined as described below. See IterationListener for how the epoch values are used.
     * 1) All records in the initial variable streams has epoch=0.
     * 2) All records in the data streams has epoch=MAX_LONG. In this case, records in the data stream won't affect
     * any operator's low watermark.
     * 3) For any record emitted by this operator into a non-feedback stream, the epoch of this emitted record = the
     * epoch of the input record that triggers this emission. If this record is emitted by onEpochLWIncremented(), then
     * the epoch of this record = incrementedEpochLW - 1.
     * 4) For any record emitted by this operator into a feedback variable stream, the epoch of the emitted record =
     * min(the epoch of the input record that triggers this emission, MAX_LONG - 1) + 1. If this record is emitted by
     * onEpochLWIncremented(), then the epoch of this record = incrementedEpochLW.
     *
     * The execution of the graph created by the iteration body will not terminate by itself. This is because at least
     * one of its data streams is unbounded.
     *
     * Required:
     * 1) All the init variable streams must be bounded.
     * 2) There is at least one unbounded stream in the data streams list.
     * 3) The parallelism of any stream in the initial variable streams must equal the parallelism of the stream at the
     * same index of the feedback variable streams returned by the IterationBody.
     *
     * @param initVariableStreams The initial variable streams. These streams will be merged with the feedback variable
     *                            streams before being used as the 1st parameter to invoke the iteration body.
     * @param dataStreams The data streams. These streams will be used as the 2nd parameter to invoke the iteration
     *                    body.
     * @param body The computation logic which takes variable/data streams and returns variable/output streams.
     * @return The list of output streams returned by the iteration boy.
     */
    static DataStreamList iterateUnboundedStreams(DataStreamList initVariableStreams, DataStreamList dataStreams, IterationBody body) {...}

    /**
     * This method can use an iteration body to process records in some bounded data streams iteratively until a
     * termination criteria is reached (e.g. the given number of rounds is completed or no further variable update is
     * needed). Because this method does not replay records in the data streams, the iteration body needs to cache those
     * records in order to visit those records repeatedly.
     *
     * This method invokes the iteration body with the following parameters:
     * 1) The 1st parameter is a list of input variable streams, which are created as the union of the initial variable
     * streams and the corresponding feedback variable streams (returned by the iteration body).
     * 2) The 2nd parameter is the data streams given to this method.
     *
     * The epoch values are determined as described below. See IterationListener for how the epoch values are used.
     * 1) All records in the initial variable streams has epoch=0.
     * 2) All records in the data streams has epoch=0.
     * 3) For any record emitted by this operator into a non-feedback stream, the epoch of this emitted record = the
     * epoch of the input record that triggers this emission. If this record is emitted by onEpochLWIncremented(), then
     * the epoch of this record = incrementedEpochLW - 1.
     * 4) For any record emitted by this operator into a feedback variable stream, the epoch of the emitted record = the
     * epoch of the input record that triggers this emission + 1. If this record is emitted by onEpochLWIncremented(),
     * then the epoch of this record = incrementedEpochLW.
     *
     * Suppose there is a coordinator operator which takes all feedback variable streams (emitted by the iteration body)
     * and the termination criteria stream (if not null) as inputs. The execution of the graph created by the
     * iteration body will terminate when any of the following conditions is met:
     * 1) The termination criteria stream is not null. And the coordinator operator has not observed any new value from
     * the termination criteria stream between two consecutive onEpochLWIncremented invocations.
     * 2) The coordinator operator has not observed any new value from any feedback variable stream between two
     * consecutive onEpochLWIncremented invocations.
     *
     * Required:
     * 1) All the init variable streams and the data streams must be bounded.
     * 2) The parallelism of any stream in the initial variable streams must equal the parallelism of the stream at the
     * same index of the feedback variable streams returned by the IterationBody.
     *
     * @param initVariableStreams The initial variable streams. These streams will be merged with the feedback variable
     *                            streams before being used as the 1st parameter to invoke the iteration body.
     * @param dataStreams The data streams. These streams will be used as the 2nd parameter to invoke the iteration
     *                    body.
     * @param body The computation logic which takes variable/data streams and returns variable/output streams.
     * @return The list of output streams returned by the iteration boy.
     */
    static DataStreamList iterateBoundedStreamsUntilTermination(DataStreamList initVariableStreams, DataStreamList dataStreams, IterationBody body) {...}

    /**
     * This method can use an iteration body to process records in some bounded data streams iteratively until a
     * termination criteria is reached (e.g. the given number of rounds is completed or no further variable update is
     * needed). Because this method replays records in the data streams, the iteration body does not need to cache those
     * records to visit those records repeatedly.
     *
     * This method invokes the iteration body with the following parameters:
     * 1) The 1st parameter is a list of input variable streams, which are created as the union of the initial variable
     * streams and the corresponding feedback variable streams (returned by the iteration body).
     * 2) The 2nd parameter is a list of replayed data streams, which are created by replaying the initial data streams
     * round by round until the iteration terminates. The records in the Nth round will be emitted into the iteration
     * body only if the low watermark of the first operator in the iteration body >= N - 1.
     *
     * The epoch values are determined as described below. See IterationListener for how the epoch values are used.
     * 1) All records in the initial variable streams has epoch=0.
     * 2) The records from the initial data streams will be replayed round by round into the iteration body. The records
     * in the first round have epoch=0. And records in the Nth round have epoch = N - 1.
     * 3) For any record emitted by this operator into a non-feedback stream, the epoch of this emitted record = the
     * epoch of the input record that triggers this emission. If this record is emitted by onEpochLWIncremented(), then
     * the epoch of this record = incrementedEpochLW - 1.
     * 4) For any record emitted by this operator into a feedback stream, the epoch of the emitted record = the epoch
     * of the input record that triggers this emission + 1. If this record is emitted by onEpochLWIncremented(), then
     * the epoch of this record = incrementedEpochLW.
     *
     * Suppose there is a coordinator operator which takes all feedback variable streams (emitted by the iteration body)
     * and the termination criteria stream (if not null) as inputs. The execution of the graph created by the
     * iteration body will terminate when any of the following conditions is met:
     * 1) The termination criteria stream is not null. And the coordinator operator has not observed any new value from
     * the termination criteria stream between two consecutive onEpochLWIncremented invocations.
     * 2) The coordinator operator has not observed any new value from any feedback variable stream between two
     * consecutive onEpochLWIncremented invocations.
     *
     * Required:
     * 1) All the init variable streams and the data streams must be bounded.
     * 2) The parallelism of any stream in the initial variable streams must equal the parallelism of the stream at the
     * same index of the feedback variable streams returned by the IterationBody.
     *
     * @param initVariableStreams The initial variable streams. These streams will be merged with the feedback variable
     *                            streams before being used as the 1st parameter to invoke the iteration body.
     * @param initDataStreams The initial data streams. Records from these streams will be repeatedly replayed and used
     *                        as the 2nd parameter to invoke the iteration body.
     * @param body The computation logic which takes variable/data streams and returns variable/output streams.
     * @return The list of output streams returned by the iteration boy.
     */
    static DataStreamList iterateAndReplayBoundedStreamsUntilTermination(DataStreamList initVariableStreams, DataStreamList initDataStreams, IterationBody body) {...}

}