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Essential libraries for the Protelis language
There is a newer version: 17.6.0
module protelis:coord:meta:timereplication
import org.apache.commons.math3.util.FastMath.max
import org.apache.commons.math3.util.FastMath.pow
import org.apache.commons.math3.util.FastMath.floor
import org.apache.commons.math3.util.FastMath.min
import protelis:coord:sharedtimer
import protelis:coord:spreading
import java.lang.Double.POSITIVE_INFINITY

/*
 * This function should return false if the clock is out of date
 * (namely: no device in the network is still on that clock).
 */
def isCurrent(currentClock, clock, k) {
    currentClock - clock < k
}

def isNewClock(processes, clock) {
    processes
        .map(self, process -> {process.get(0)})
        .filter(self, pid -> {clock == pid})
        .isEmpty()
}

def clock(tuple) {
    tuple.get(0)
}

def emptyProcess(default) {
    rep (p <- [POSITIVE_INFINITY, () -> {"EMPTY"}, default]) {
        p
    }
}

def alignedExecution(processes, default) {
    alignedMap(
        nbr(processes.map(self, p -> { [p.get(0), p] } )),
        (pid, pField) -> { true },
        (pid, pField) -> {
            let p = hoodPlusSelf(
                (a, b) -> {if (a.compareTo(b) < 0) {a} else {b}},
                emptyProcess(default),
                pField
            );
            [p.get(0), p.get(1), p.get(1).apply()]
        },
        emptyProcess(default)
    ).map(self, tProc -> { tProc.get(1) } )
}

/**
 * Replicate a function over time.
 * 
 * p is inversely proportional to k.
 * p = (4 * d * self.getDeltaTime()) / (k - 1), where d is the network diameter.
 * @param process () -> T, function to be replicated
 * @param default T, default value
 * @param p       num, time to live of each replica
 * @param k       num, number of replicas
 * @return        T, execute the newest function or default
 */
public def timeReplicated(process, default, p, k) {
    let clock = sharedTimer(p, self.getDeltaTime());
    rep (processes <- []) {
        // Add process if the clock is new
        if (isNewClock(processes, clock)) {
            processes = processes.append([clock, process, default])
        };
        // Align on clock, execute process
        alignedExecution(processes.filter(self, process -> {clock - process.get(0) < p * k }), default)
    }
    .min(emptyProcess(default))
    .get(2)
}

/**
 * Replicate a function over time.
 * 
 * p is equal to (4 * d * self.getDeltaTime()) / (k - 1).
 * @param process () -> T, function to be replicated
 * @param default T, default value
 * @param d       num, network diameter
 * @param k       num, number of replicas. Must be greater than 1.
 * @return        T, execute the newest function or default
 */
public def timeReplicatedWithK(process, default, d, k) {
    timeReplicated(process, default, roundTripTime(d)/(k-1), k)
}