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arXiv:1507.07049v3 [] 16 Apr 2016

Ev

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Jedidiah McClurg

Hossein Hojjat

Nate Foster

CU Boulder, USA

Cornell University, USA

Cornell University, USA

CU Boulder, USA

hojjat@cornell.edu

jnfoster@cs.cornell.edu

pavol.cerny@colorado.edu

jedidiah.mcclurg@colorado.edu

Pavol Černý

execute on general-purpose machines. These programs react to events such as topology changes, traffic statistics,
receipt of packets, etc. by modifying sets of forwarding
rules installed on switches. SDN programs can implement
a wide range of advanced network functionality including
fine-grained access control [8], network virtualization [22],
traffic engineering [15, 16], and many others.
Although the basic SDN model is simple, building sophisticated applications is challenging in practice. Programmers must keep track of numerous low-level details
such as encoding configurations into prioritized forwarding
rules, processing concurrent events, managing asynchronous
events, dealing with unexpected failures, etc. To address
these challenges, a number of domain-specific network programming languages have been proposed [2, 10, 19, 21, 29,
31, 36, 37]. The details of these languages vary, but they all
offer higher-level abstractions for specifying behavior (e.g.,
using mathematical functions, boolean predicates, relational
operators, etc.), and rely on a compiler and run-time system
to generate and manage the underlying network state.
Unfortunately, the languages that have been proposed so
far lack critical features that are needed to implement dynamic, event-driven applications. Static languages such as
NetKAT [2] offer rich constructs for describing network configurations, but lack features for responding to events and
maintaining internal state. Instead, programmers must write
a stateful program in a general-purpose language that generates a stream of NetKAT programs. Dynamic languages such
as FlowLog and Kinetic [21, 31] offer stateful programming
models, but they do not specify how the network behaves
while it is being reconfigured in response to state changes.
Abstractions such as consistent updates provide strong guarantees during periods of reconfiguration [26, 33], but current realizations are limited to properties involving a single
packet (or set of related packets, such as a unidirectional
flow). To implement correct dynamic SDN applications today, the most effective option is often to use low-level APIs,
forgoing the benefits of higher-level languages entirely.

Abstract
Software-defined networking (SDN) programs must simultaneously describe static forwarding behavior and dynamic
updates in response to events. Event-driven updates are critical to get right, but difficult to implement correctly due to
the high degree of concurrency in networks. Existing SDN
platforms offer weak guarantees that can break application
invariants, leading to problems such as dropped packets,
degraded performance, security violations, etc. This paper
introduces event-driven consistent updates that are guaranteed to preserve well-defined behaviors when transitioning
between configurations in response to events. We propose
network event structures (NESs) to model constraints on
updates, such as which events can be enabled simultaneously and causal dependencies between events. We define
an extension of the NetKAT language with mutable state,
give semantics to stateful programs using NESs, and discuss
provably-correct strategies for implementing NESs in SDNs.
Finally, we evaluate our approach empirically, demonstrating that it gives well-defined consistency guarantees while
avoiding expensive synchronization and packet buffering.
Categories and Subject Descriptors C.2.3 [Computercommunication Networks]: Network Operations—Network
Management; D.3.2 [Programming Languages]: Language
Classifications—Specialized application languages; D.3.4
[Programming Languages]: Processors—Compilers
Keywords network update, consistent update, event structure, software-defined networking, SDN, NetKAT

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Event-Driven Network Programming

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Introduction

Software-defined networking (SDN) allows network behavior to be specified using logically-centralized programs that

Example: Stateful Firewall. To illustrate the challenges
that arise when implementing dynamic applications, consider a topology where an internal host H1 is connected to
switch s1 , an external host H4 is connected to a switch s4 ,
and switches s1 and s4 are connected to each other (see FigEvent-Driven Network Programming

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Existing Approaches. Experienced network operators may
be able to use existing tools/methods to correctly implement
event-driven configuration changes. However, as seen above,
this requires thinking carefully about the potential interleavings of events and updates, delegating atomic operations to
the controller (incurring a performance hit), etc.
As mentioned, there are stateful programming systems
that attempt to make this process easier for the programmer,
but update strategies in these systems either offer no consistency guarantees during dynamic updates, rely on expensive
processing via the controller, and/or require the programmer
to craft an update protocol by hand. In this paper, we group
these approaches together, using the term uncoordinated update to describe their lack of support for coordinating local
updates in a way that ensures global consistency.

Figure 1: Topology for simple Stateful Firewall.

ure 1). Suppose we wish to implement a stateful firewall: at
all times, host H1 is allowed to send packets to host H4 , but
H4 should only be allowed to send packets to H1 if H1 previously initiated a connection. Implementing even this simple application turns out to be difficult, because it involves
coordinating behavior across multiple devices and packets.
The basic idea is that upon receiving a packet from H1 at
s4 , the program will need to issue a command to install a
forwarding rule on s4 allowing traffic to flow from H4 back
to H1 . There are two straightforward (but incorrect) implementation strategies on current SDN controllers.
1. The outgoing request from H1 is diverted to the controller, which sets up flow tables for the incoming path
and also forwards the packet(s) to H4 . Reconfiguring
flow tables takes time, so H4 ’s response will likely be
processed by the default drop rule. Even worse, if the response is the SYN-ACK in a TCP handshake, normal retransmission mechanisms will not help—the client will
have to wait for a timeout and initiate another TCP connection. In practice, this greatly increases the latency of
setting up a connection, and potentially wreaks havoc on
application performance.
2. The outgoing request is buffered at the controller, which
sets up the flow tables for the incoming path but waits until the rules are installed before forwarding the packet(s).
This avoids the problem in (1), but places extra load
on the controller and also implements the firewall incorrectly, since incoming traffic is allowed before the outgoing request is delivered. Leaving the network unprotected
(even briefly) can be exploited by a malicious attacker.
Thus, while it is tempting to think that reliability mechanisms built into protocols such as TCP already prevent (or at
least reduce) these types of errors, this is not the case. While
it is true that some applications can tolerate long latencies,
dropped packets, and weak consistency, problems with updates do lead to serious problems in practice. As another
example, consider an intrusion detection system that monitors suspicious traffic—inadvertently dropping or allowing
even a few packets due to a reconfiguration would weaken
the protection it provides. The root of these problems is that
existing SDN frameworks do not provide strong guarantees
during periods of transition between configurations in response to events. An eventual guarantee is not strong enough
to implement the stateful firewall correctly, and even a consistent update [33] would not suffice, since consistent updates only dictate what must happen to individual packets.
Event-Driven Network Programming

Event-Driven Consistent Update. We propose a new semantic correctness condition with clear guarantees about updates triggered by events. This enables specification of how
the network should behave during updates, and enables precise formal reasoning about stateful network programs.
An event-driven consistent update is denoted as a triple
e
Ci −
→ Cf , where Ci and Cf are the initial and final configurations respectively, and e is an event. Intuitively, these
configurations describe the forwarding behaviors of the network before/after the update, while the event describes a
phenomenon, such as the receipt of a packet at a particular
switch, that triggers the update itself. Semantically, an eventtriggered consistent update ensures that for each packet:
1. the packet is forwarded consistently, i.e. it must be processed entirely by a single configuration Ci or Cf , and
2. the update does not happen too early, meaning that if
every switch traversed by the packet has not heard about
the event, then the packet must be processed by Ci , and
3. the update does not happen too late, meaning that if every
switch traversed by the packet has heard about the event,
then the packet must be processed by Cf .
The first criterion requires that updates are consistent, which
is analogous to a condition proposed previously by Reitblatt
et al. [33]. However, a consistent update alone would not
provide the necessary guarantees for the stateful firewall
example, as it applies only to a single packet, and not to
multiple packets in a bidirectional flow. The last two criteria
relate the packet-processing behavior on each switch to the
events it has “heard about.” Note that these criteria leave
substantial flexibility for implementations: packets that do
not satisfy the second or third condition can be processed by
either the preceding or following configuration. It remains to
define what it means for a switch s to have “heard about” an
event e that occurred at switch t (assuming s 6= t). We use
a causal model and say that s hears about e when a packet,
which was processed by t after e occurred, is received at s.
This can be formalized using a “happens-before” relation.
Returning to the stateful firewall, it is not hard to see that
the guarantees offered by event-driven consistent updates are
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sufficient to ensure correctness of the overall application.
e
Consider an update Ci −
→ Cf . In Ci , H1 can send packets
to H4 , but not vice-versa. In Cf , additionally H4 can send
packets to H1 . The event e is the arrival at s4 of a packet
from H1 to H4 . Before e occurs, can H4 send a packet to
H1 , as is possible in Cf ? No, since none of the switches
along the necessary path have heard about the event. Now,
imagine that the event e occurs, and H4 wants to send a
packet to H1 afterwards. Can s4 drop the new packet, as it
would have done in the initial configuration Ci ? No, because
the only switch the packet would traverse is s4 , and s4 has
heard about the event, meaning that the only possible correct
implementation should process this new packet in Cf .

The first defining aspect of our locality requirements involves the happens-before (“heard-about”) relation in eventdriven consistent update. For example, the receipt of a packet
in New York can not immediately affect the behavior of
switches in London. Intuitively, this makes sense: requiring
“immediate” reaction to remote events would force synchronization between switches and buffering of packets, leading
to unacceptable performance penalties. Event-driven consistent update only requires the switches in London to react
after they have heard about the event in New York.
The second defining aspect of our locality requirements
involves the compatibility constraints in NESs. Suppose that
New York sends packets to London and Paris, but the program requires transitioning to a different global state based
on who received a packet first. Clearly, it would be impossible to implement this behavior without significant coordination. However, suppose New York and Philadelphia are sending packets to London, and the program requires transitioning to a different global state based on whose packet was received first in London. This behavior is easily implementable
since the choice is local to London. We use NESs to rule out
non-local incompatible events—specifically, we require that
incompatible events must occur at the same switch.
Our approach gives consistency guarantees even when an
event occurs at a switch different from the one that will be
updated. The change will not happen “atomically” with the
event that triggered it, but (a) every packet is processed by
a single configuration, and (b) the configuration change occurs as dictated by event-driven consistent update (happensbefore) requirements. We show that these requirements can
be implemented with minimal performance penalty.
Locality issues are an instance of the tension between
consistency and availability in distributed systems, which
motivates existing SDN languages to favor availability
(avoiding expensive synchronization and packet buffering)
over consistency (offering strong guarantees when state
changes). We demonstrate that it is possible to provide the
same level of availability as existing systems, while providing a natural consistency condition that is powerful enough
to build many applications. We also show that weakening
the locality requirement forces us to weaken availability.
Overall, we present a new abstraction based on (i) a notion of causal consistency requiring that events are propagated between nodes, (ii) per-packet consistency governing
how packets are forwarded through the network, and (iii) locality requirements. We believe this is a powerful combination that is a natural fit for building many applications.

Event-Driven Transition Systems. To specify event-driven
network programs, we use labeled transition systems called
event-driven transition systems (ETSs). In an ETS, each
node is annotated with a network configuration and each
edge is annotated with an event. For example, the stateful
firewall application would be described as a two-state ETS,
one state representing the initial configuration before H1 has
sent a packet to H4 , and another representing the configuration after this communication has occurred. There would
be a transition between the states corresponding to receipt of
a packet from H1 to H4 at s4 . This model is similar to the
finite state machines used in Kinetic [21] and FAST [30].
However, whereas Kinetic uses uncoordinated updates, we
impose additional constraints on our ETSs which allow them
to be implemented correctly with respect to our consistency
property. For example, we extend event-triggered consistent
updates to sequences, requiring each sequence of transitions
in the ETS to satisfy the property. For simplicity, in this paper, we focus on finite state systems and events corresponding to packet delivery. However, these are not fundamental
assumptions—our design extends naturally to other notions
of events, as well as infinite-state systems.
Network Event Structures. The key challenge in implementing event-driven network programs stems from the fact
that at any time, the switches may have different views of
the global set of events that have occurred. Hence, for a given
ETS, several different updates may be enabled at a particular
moment of time, and we need a way to resolve conflicts. We
turn to the well-studied model of event structures [38], which
allows us to constrain transitions in two ways: (1) causal dependency, which requires that an event e1 happens before
another event e2 may occur, and (2) compatibility, which
forbids sets of events that are in some sense incompatible
with each other from occurring in the same execution. We
present an extension called network event structure (NES),
and show how an ETS can be encoded as an NES.

Implementing Network Programs. NESs also provide a
natural formalism for guiding an implementation technique
for stateful programs. Intuitively, we need switches that can
record the set of events that have been seen locally, make
decisions based on those events, and transmit events to other
switches. Fortunately, in the networking industry there is a
trend toward more programmable data planes: mutable state

Locality. While event-driven consistent updates require
immediate responses to local events (as in the firewall), they
do not require immediate reactions to events “at a distance.”
This is achieved by two aspects of our definitions.
Event-Driven Network Programming

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is already supported in most switch ASICs (e.g. MAC learning tables) and is also being exposed to SDN programmers in
next-generation platforms such as OpenState [5] and P4 [6].
Using these features, we can implement an NES as follows.
1. Encode the sets of events contained in the NES as flat tags
that can be carried by packets and tested on switches.
2. Compile the configurations contained in the NES to a
collection of forwarding tables.
3. Add “guards” to each configuration’s forwarding rules to
explicitly test for the tag enabling the configuration.
4. Add rules to “stamp” incoming packets with tags corresponding to the current set of events.
5. Add rules to “learn” which events have happened by
reading tags on incoming packets and adding the tags in
the local state to outgoing packets, as required to implement the happens-before relation.
In this paper, we prove that a system implemented in this
way correctly implements an NES.

• We propose a new semantic correctness condition for dy-

namic network programs called event-driven consistent
update that balances the need for immediate response
with the need to avoid costly synchronization and buffering of packets. Our consistency property generalizes the
guarantees offered by consistent updates, and is as strong
as possible without sacrificing availability.
• We propose network event structures to capture causal
dependencies and compatibility between events, and
show how to implement these using SDN functionality.
• We describe a compiler based on a stateful extension
of NetKAT, and present optimizations that reduce the
overhead of implementing such stateful programs.
• We conduct experiments showing that our approach gives
well-defined consistency guarantees, while avoiding expensive synchronization and packet buffering.
The rest of this paper is structured as follows: §2 formalizes
event-driven consistent updates; §3 defines event transition
systems, network event structures, and Stateful NetKAT; §4
describes our implementation; and §5 presents experiments.
We discuss related/future work in §6-7, and conclude in §8.

Evaluation. To evaluate our design, we built a prototype
of the system described in this paper.† We have used this to
build a number of event-driven network applications: (a) a
stateful firewall, which we have already described; (b) a
learning switch that floods packets going to unknown hosts
along a spanning tree, but uses point-to-point forwarding for
packets going to known hosts; (c) an authentication system
that initially blocks incoming traffic, but allows hosts to gain
access to the internal network by sending packet probes to a
predefined sequence of ports; (d) a bandwidth cap that disables access to an external network after seeing a certain
number of packets; and (e) an intrusion detection system that
allows all traffic until seeing a sequence of internal hosts
being contacted in a suspicious order. We have also built
a synthetic application that forwards packets around a ring
topology, to evaluate update scalability. We developed these
applications in an extended version of NetKAT which we
call Stateful NetKAT. Our experiments show that our implementation technique provides competitive performance on
several important metrics while ensuring important consistency properties. We draw several conclusions. (1) Eventdriven consistent update allow programmers to easily write
real-world network applications and get the correct behavior, whereas approaches relying only on uncoordinated consistency guarantees do not. (2) The performance overhead of
maintaining state and manipulating tags (measured in bandwidth) is within 6% of an implementation that uses only uncoordinated update. (3) There is an optimization that exploits
common structure in rules across states to reduce the number of rules installed on switches. In our experiments, a basic
heuristic version of this optimization resulted in a 32-37%
reduction in the number of rules required on average.
Summary.

2.

This section presents our new consistency model for stateful
network programs: event-driven consistent update.
Preliminaries. A packet pkt is a record of fields {f1 ; f2 ;
· · · ; fn }, where fields f represent properties such as source
and destination address, protocol type, etc. The (numeric)
values of fields are accessed via the notation pkt.f , and
field updates are denoted pkt[f ← n]. A switch sw is a
node in the network with one or more ports pt. A host is
a switch that can be a source or a sink of packets. A location
l is a switch-port pair n:m. Locations may be connected by
(unidirectional) physical links (lsrc , ldst ) in the topology.
Packet forwarding is dictated by a network configuration
C. A located packet lp = (pkt, sw , pt) is a tuple consisting
of a packet and a location sw :pt. We model C as a relation on located packets: if C(lp, lp 0 ), then the network maps
lp to lp 0 , possibly changing its location and rewriting some
of its fields. Since C is a relation, it allows multiple output
packets to be generated from a single input. In a real network, the configuration only forwards packets between ports
within each individual switch, but for convenience, we assume that our C also captures link behavior (forwarding between switches), i.e. C((pkt, n1 , m1 ), (pkt, n2 , m2 )) holds
for each link (n1 :m1 , n2 :m2 ). We refer to a sequence of located packets that starts at a host and can be produced by C
as a packet trace, using Traces(C) to denote the set of all
such packet traces. We let C be the set of all configurations.
Consider a tuple ntr = (lp 0 lp 1 · · · , T ), where the first
component is a sequence of located packets, and each t ∈ T
is an increasing sequence of indices corresponding to located
packets in the sequence. We call such a tuple a network trace
if and only if the following conditions hold:

Our main contributions are as follows.

† The PLDI 2016 Artifact Evaluation Committee (AEC) found that our
prototype system “met or exceeded expectations.”

Event-Driven Network Programming

Event-Driven Network Behavior

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1. for each lp j , we have j ∈ t for some t ∈ T , and
2. for each t = (k0 k1 · · · ) ∈ T , lp k0 is at a host, and
∃C ∈ C such that C(lp ki , lp ki+1 ) holds for all i, and
3. if we consider the graph G with nodes {k : (∃t ∈
T : k ∈ t)} and edges {(ki , ki+1 ) : (∃t ∈ T : t =
k0 k1 · · · ki ki+1 · · · )}, then G is a family of trees rooted
at K = {k0 : (∃t ∈ T : t = k0 · · · )}.
We will use ntr ↓k to denote the set {t ∈ T : k ∈ t}, and
when t = (k0 k1 · · · ) ∈ T , we can use similar notation ntr ↓t
to denote the packet trace lp k0 lp k1 · · · . Intuitively, we have
defined a network trace to be an interleaving of these packet
traces (the packet traces form the family of trees because,
as previously mentioned, the configuration allows multiple
output packets from a single input packet). Ultimately, we
will introduce a consistency definition that dictates which
interleavings of packet traces are correct.
We now define how the network changes its configuration
in response to events. An event e is a tuple (ϕ, sw , pt)eid ,
where eid is an (optional) event identifier and ϕ is a firstorder formula over fields. Events model the arrival of a
packet satisfying ϕ (denoted pkt |= ϕ) at location sw :pt.
Note that we could have other types of events—anything that
a switch can detect could be an event—but for simplicity, we
focus on packet events. We say that a located packet lp =
(pkt, sw 0 , pt 0 ) matches an event e = (ϕ, sw , pt) (denoted
by lp |= e) if and only if sw = sw 0 ∧ pt = pt 0 ∧ pkt |= ϕ.

Figure 2: Example topology with four switches and hosts.
• ∃t ∈ ntr ↓ki such that t is in Traces(Ci ) (intuitively, the

event ei can be triggered only by a packet processed in
the immediately preceding configuration).
If such a sequence exists, it is unique, and we denote it by
F O(ntr , U ), shorthand for “first occurrences.”

Definition 2 (Event-driven consistent update correctness). A
network trace ntr = (lp 0 lp 1 · · · , T ) is correct with respect
e1
e0
C1 −→
to an event-driven consistent update U = C0 −→
en
· · · −→ Cn+1 , if F O(ntr , U ) = k0 , · · · , kn exists, and for
all 0 ≤ i ≤ n, the following holds for each packet trace
ntr ↓t = lp 00 lp 01 · · · where t ∈ T :
• ntr ↓t is in Traces(C) for some C ∈ {C0 , · · · , Cn+1 }
(packet is processed entirely by one configuration), and
• if ∀j : lp 0j ≺ lp ki , then ntr ↓t is in Traces(C) for some
C ∈ {C0 , · · · , Ci } (the packet is processed entirely in a
preceding configuration), and
• if ∀j : lp ki ≺ lp 0j , then ntr ↓t is in Traces(C) for some
C ∈ {Ci+1 , · · · , Cn+1 } (the packet is processed entirely
in a following configuration).

Definition 1 (Happens-before relation ≺ntr ). Given a network trace ntr = (lp 0 lp 1 · · · , T ), the happens-before relation ≺ntr is the least partial order on located packets that
• respects the total order induced by ntr at switches, i.e.,
∀i, j : lp i ≺ lp j ⇐ i < j ∧ lp i = (pkt, sw , pt) ∧ lp j =
(pkt 0 , sw , pt 0 ), and
• respects the total order induced by ntr for each packet,
i.e., ∀i, j : lp i ≺ lp j ⇐ i < j ∧ ∃t ∈ T : i ∈ t ∧ j ∈ t.

To illustrate, consider Figure 2. We describe an update
e
Ci −
→ Cf . In the initial configuration Ci , the host H1
can send packets to H2 , but not vice-versa. In the final
configuration Cf , traffic from H2 to H1 is allowed. Event
e models the arrival to s4 of a packet from H1 (imagine
s4 is part of a distributed firewall). Assume that e occurs,
and immediately afterwards, H2 wants to send a packet to
s1 . Can s2 drop the packet (as it would do in configuration
Ci )? Event-driven consistent updates allow this, as otherwise
we would require s2 to react immediately to the event at s4 ,
which would be an example of action at a distance. Formally,
the occurrence of e is not in a happens-before relation with
the arrival of the new packet to s2 . On the other hand, if e.g.
s4 forwards some packets to s1 and s2 before the new packet
from H2 arrives, s1 and s2 would be required to change their
configurations, and the packet would be allowed to reach H1 .

Event-Driven Consistent Update. In Section 1, we informally defined an event-driven consistent update as a triple
e
Ci −
→ Cf consisting of an initial configuration Ci , event e,
and final configuration Cf . Here, we formalize that definition in a way that describes sequences of events and configurations (in the single-event case, this formal definition is
equivalent to the informal one). We denote an event-driven
consistent update as a pair (U, E), where U is a sequence
e0
e1
en
C0 −→
C1 −→
· · · −→
Cn+1 , and {e0 , · · · , en } ⊆ E.
Let ntr = (lp 0 lp 1 · · · , T ) be a network trace. Given an
event-driven consistent update (U, E), we need the indices
where the events from U first occurred. Specifically, we wish
to find the sequence k0 , · · · , kn where lp j does not match
any e ∈ E for any j > kn , and the following properties hold
for all 0 ≤ i ≤ n (assuming k(−1) = −1 for convenience):
• ki > ki−1 , and
• lp ki matches ei , and for all j, if ki−1 < j < ki then
lp j does not match ei (i.e., ki is the first occurrence of ei
after the index ki−1 ), and
Event-Driven Network Programming

Network Event Structures. As we have seen, event-driven
consistent updates specify how the network should behave
during a sequence of updates triggered by events, but additionally, we want the ability to capture constraints between
the events themselves. For example, we might wish to say
that e2 can only happen after e1 has occurred, or that e2 and
e3 cannot both occur in the same network trace.
To model such constraints, we turn to the event structures model introduced by Winskel [38]. Intuitively, an event
structure endows a set of events E with (a) a consistency
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predicate (con) specifying which events are allowed to occur
in the same sequence, and (b) an enabling relation (`) specifying a (partial) order in which events can occur. This is formalized in the following definition (note that we use ⊆fin to
mean “finite subset,” and Pfin (X) = {Y : Y ⊆fin P(X)}).

all proper subsets are not inconsistent. An NES N is called
locally-determined if and only if for each of its minimallyinconsistent sets E, all events in E happen at the same
switch (i.e., ∃sw ∀ei ∈ E : ei = (ϕi , sw , pt i )). To illustrate
the need for the locally-determined property, let us consider
the following two programs, P1 and P2 .
• Program P1 : Recall that two events are inconsistent if either of them can happen, but both cannot happen in the
same execution. Consider the topology shown in Figure 2
and suppose this program requires that H2 and H4 can
both receive packets from H1 , but only the first one to
receive a packet is allowed to respond. There will be two
events e1 and e2 , with e1 the arrival of a packet from H1
at s2 , and e2 the arrival of a packet from H1 at s4 . These
events are always enabled, but the set {e1 , e2 } is not
consistent, i.e. con({e1 , e2 }) does not hold. This models the fact that at most one of the events can take effect.
These events happen at different switches—making sure
that at most one of the events takes effect would necessitate information to be propagated instantaneously “at a
distance.” In implementations, this would require using
inefficient mechanisms (synchronization and/or packet
buffering). Our locality restriction is a clean condition
which ensures that the NES is efficiently implementable.
• Program P2 : Consider a different program where H2 can
send traffic to one of the two hosts H1 , H3 that sends it a
packet first. The two events (a packet from H1 arriving
at s2 , and a packet from H3 arriving at s2 ) are still
inconsistent, but inconsistency does not cause problems
in this case, because both events happen at the same
switch (the switch can determine which one was first).
In contrast to our approach, an uncoordinated update approach improperly handles locality issues, mainly because
it does not guarantee when the configuration change occurs.
Consider the program P1 again, and consider the (likely)
scenario where events e1 and e2 happen nearly simultaneously. In an uncoordinated approach, this could result in
switch s2 hearing about e1 , e2 (in that order), and s4 hearing about e2 , e1 (in that order), meaning the two switches
would have conflicting ideas of which event was “first” (i.e.
the switches would be in conflicting states, and this conflict
cannot be resolved). In our implementation, we would require e1 and e2 to occur at the same switch, guaranteeing
that we never see such a conflicting mix of states.

Definition 3 (Event structure). An event structure is a tuple
(E, con, `) where:
• E is a set of events,
• con : (Pfin (E) → Boolean) is a consistency predicate
that satisfies con(X) ∧ Y ⊆ X =⇒ con(Y ),
• ` : (P(E) × E → Boolean) is an enabling relation that
satisfies (X ` e) ∧ X ⊆ Y =⇒ (Y ` e).

An event structure can be seen as defining a transition system
whose states are subsets of E that are consistent and reachable via the enabling relation. We refer to such a subset an
as an event-set (called “configuration” in [38]).
Definition 4 (Event-set of an event structure). Given an
event structure N = (E, con, `), an event-set of N is any
subset X ⊆ E which is: (a) consistent: ∀Y ⊆fin X, con(Y )
holds, and (b) reachable via the enabling relation: for each
e ∈ X, there exists e0 , e1 , · · · , en ∈ X where en = e and
∅ ` {e0 } and {e0 , · · · , ei−1 } ` ei for all 1 ≤ i ≤ n.

We want to be able to specify which network configuration should be active at each event-set of the event structure.
Thus, we need the following extension of event structures.

Definition 5 (Network event structure (NES)). A network
event structure is a tuple (E, con, `, g) where (E, con, `) is
an event structure, and g : (P(E) → C) maps each event-set
of the event structure to a network configuration.
Correct Network Traces. We now define what it means for
a network trace ntr to be correct with respect to an NES
N = (E, con, `, g). We begin by constructing a sequence S
of events that is allowed by N . A sequence S = e0 e1 · · · en
is allowed by N , if ∅ ` {e0 } ∧ con({e0 }), and ∀1 ≤ i ≤ n :
({e0 , e1 , · · · , ei−1 } ` ei ∧ con({e0 , e1 , · · · , ei })).
Intuitively, we say that ntr is correct if there is a sequence
of events allowed by N which would cause ntr to satisfy the
event-driven consistent update condition.
Definition 6 (Correct network trace). Let S be the set of all
sequences allowed by N . Formally, a network trace ntr =
(lp 0 lp 1 · · · , T ) is correct with respect to N if
• no lp j matches any e ∈ E, and for all packet traces ntr ↓t
where t ∈ T , we have ntr ↓t is in Traces(g(∅)), or
• there exists some e0 e1 · · · en ∈ S such that ntr is correct
e0
with respect to event-driven consistent update (g(∅) −→
e1
en
g({e0 }) −→ · · · −→ g({e0 , · · · , en }), E).

Strengthening Consistency. We now show that strengthening the consistency conditions imposed by NESs would
lead to lower availability, as it would lead to the need for expensive synchronization, packet buffering, etc. First, we will
try to remove the locally-determined condition, and second,
we will try to obtain a strengthened consistency condition.
The proof of the following theorem is an adaptation of the
proof of the CAP theorem [7], as presented in [13]. The idea
is that in asynchronous network communication, a switch
might need to wait arbitrarily long to hear about an event.

Locality Restrictions for Incompatible Events. We now
show how NESs can be used to impose reasonable locality restrictions. A set of events E is called inconsistent
if and only if con(E) does not hold. We use the term
minimally-inconsistent to describe inconsistent sets where
Event-Driven Network Programming

6

2016/4/19

Lemma 1. In general, it is impossible to implement an NES
that does not have the locally-determined condition while
guaranteeing that switches process each packet within an a
priori given time bound.
Figure 3: Event-driven transition systems.

Proof Sketch. Consider a simple NES, with event sets ∅,
{e1 }, {e2 }, and where {e1 } and {e2 } are both enabled from
∅. Assume that con({e1 , e2 }) does not hold, and that e1 can
happen at switch A and e2 can happen at switch B (i.e., the
locally-determined condition does not hold).
Because the communication is asynchronous, there is no
a priori bound on how long the communication between
switches can take. When a packet p that matches e2 arrives
at the switch B, the switch must distinguish the following
two cases: (#1) event e1 has occurred at A (and thus p
does not cause e2 ), or (#2) event e1 has not occurred at
A (and thus p causes e2 ). No matter how long B waits, it
cannot distinguish these two cases, and hence, when a packet
that matches e2 arrives to B, the switch B cannot correctly
decide whether to continue as if e2 has happened. It has
the choice to either eventually decide (and risk the wrong
decision), or to buffer the packet that matches e2 .

and edges correspond to events. We also present a network
programming language based on NetKAT that provides a
compact notation for specifying both the transition system
and the configurations at the nodes.
3.1

Definition 7 (Event-driven Transition System). An eventdriven transition system (ETS) is a graph (V, D, v0 ), in
which V is a set of vertices, each labeled by a configuration;
D ⊆ V × V is a set of edges, each labeled by an event e;
and v0 is the initial vertex.
Consider the ETSs shown in Figure 3 (a-b). In (a), the
two events are intuitively compatible—they can happen in
any order, so we obtain a correct execution if both happen
in different parts of the network, and different switches can
have a different view of the order in which they happened.
In (b), the two events are intuitively incompatible—only one
of them can happen in any particular execution. Therefore,
even if they happen nearly simultaneously, only one of them
should take an effect. To implement this, we require the locality restriction—we need to check whether the two events
happen at the same switch. We thus need to distinguish between ETSs such as (a) and (b) in Figure 3, to determine
where locality restrictions must be imposed in the conversion from an ETS to an NES.

We now ask whether we can strengthen the event-driven
consistent update definition. We define strong update as an
e
update C1 −
→ C2 such that immediately after e occurred, the
network processes all incoming packets in C2 . We obtain the
following lemma by the same reasoning as the previous one.
Lemma 2. In general, it is impossible to implement strong
updates and guarantee that switches process each packet
within an a priori given time bound.
Proof Sketch. Let A be the switch where e can happen, and
let B be a switch on which the configurations C1 , C2 differ.
For A and B, the same argument as in the previous lemma
shows that B must either risk the wrong decision on whether
to process packets using C1 or C2 , or buffer packets.

3.

From ETSs to NESs. To convert an ETS to an NES, we
first form the event sets (Definition 4) and then construct the
enabling relation and consistency predicate. Given an ETS
T , consider the set W (T ) of sequences of events in T from
the initial node to any vertex (including the empty sequence).
For each sequence p ∈ W (T ), let E(p) be the set of events
collected along the sequence. The set F (T ) = {E(p) | p ∈
W (T )} is our candidate collection of event sets. We now
define conditions under which F (T ) gives rise to an NES.
1. We require that each set E in F (T ) must correspond to
exactly one network configuration. This holds if all paths
in W (T ) corresponding to E end at states labeled with
the same configuration.
2. We require that F (T ) is finite-complete, i.e. for any sets
E1 , E2 , · · · , En where each Ei ∈ F (T ), if there is a set
E 0 ∈ F (T ) which contains every Ei (an upper bound for
the sets Ei ), then the set Elub = ∪i Ei (the least upper
bound for the Ei ) must also be in F (T ). For example,
consider the ETS in Figure 3(c), which violates this condition since the event-sets E1 = {e1 } and E2 = {e3 } are
both subsets of {e1 , e4 , e3 }, but there is no event-set of
the form E1 ∪ E2 = {e1 , e3 }.

Programming with Events

The correctness condition we described in the previous section offers useful application-level guarantees to network
programmers. At a high level, the programmer is freed from
thinking about interleavings of packets/events and responses
to events (configuration updates). She can think in terms of
our consistency model—each packet is processed in a single
configuration, and packets entering “after” an event will be
processed in the new configuration (similar to causal consistency). An important consequence is that the response to an
event is immediate with respect to a given flow if the event
is handled at that flow’s ingress switch.
With this consistency model in mind, programmers can
proceed by specifying the desired event-driven program behavior using network event structures. This section introduces an intuitive method for building NESs using simple
transition systems where nodes correspond to configurations
Event-Driven Network Programming

Event-Driven Transition Systems

7

2016/4/19

In [38], such a collection F (T ) is called a family of configurations. Our condition (2) is condition (i) in Theorem 1.1.9
in [38] (conditions (ii)-(iii) are satisfied by construction).
Given an ETS T , it is not difficult to confirm the above
conditions statically. They can be checked using straightforward graph algorithms, and any problematic vertices or
edges in T can be indicated to the programmer. The development of efficient checking algorithms is left for future work.
We build the con and ` relations of an NES from the
family F (T ), using Theorem 1.1.12. of [38]. Specifically,
predicate con can be defined by declaring all sets in F (T ) as
consistent, and for `, we take the smallest relation satisfying
the constraints ∅ ` e ⇐⇒ {e} ∈ F (T ) and X 0 ` e ⇐⇒
(X 0 ∈ con) ∧ ((X 0 ∪ {e}) ∈ F (T ) ∨ (∃X ⊆ X 0 : X ` e)).
After obtaining an NES, deciding whether it satisfies
the locality restriction is easy: we check whether the NES
is locally determined (see Section 2), verifying for each
minimally-inconsistent set that the locality restriction holds.
Again, we leave the efficiency of this check for future work.

∈
∈
::=
::=
|
p, q ::=
|
f
n
x
a, b

Figure 4: Stateful NetKAT: syntax.

,

J(a:b) _ (c:d) _ hstate(m) ← niK~k

,

(
JtrueK~k
JfalseK~k

if ~k(m)=n
otherwise

J(a:b) _ (c:d)K~k

individual static configurations (though it is not a KAT itself), but also allows packets to affect processing of future
packets via assignments to (and tests of) a global state. The
syntax of Stateful NetKAT is shown in Figure 4. A Stateful
NetKAT program is a command, which can be:
• a test, which is a formula over packet header fields (there
are special fields sw and pt which test the switch- and
port-location of the packet respectively),
• a field assignment x←n, which modifies the (numeric)
value stored in a packet’s field,
• a union of commands p + q, which unions together the
packet-processing behavior of commands p and q,
• a command sequence p ; q, which runs packet-processing
program q on the result of p,
• an iteration p∗, which is equivalent to true + p + (p ; p) +
(p ; p ; p) + · · · ,
• or a link definition (n1 :m1 )_(n2 :m2 ), which forwards a
packet from port m1 at switch n1 across a physical link
to port m2 at switch n2 .
The functionality described above is also provided by standard NetKAT [35]. The key distinguishing feature of our
Stateful NetKAT is a special global vector-valued variable
called state, which allows the programmer to represent a collection of NetKAT programs. The function shown in Figure
5 gives the standard NetKAT program JpK~k corresponding
to each value ~k of the state vector (for conciseness, we only
show the non-trivial cases). We can use the NetKAT compiler [35] to generate forwarding tables (i.e. configurations)
corresponding to these, which we denote C(JpK~k ).

Stateful NetKAT

NetKAT [2] is a domain-specific language for specifying
network behavior. It has semantics based on Kleene Algebra with Tests (KAT), and a sound and complete equational theory that enables formal reasoning about programs.
Operationally, a NetKAT program behaves as a function
which takes as input a single packet, and uses tests, fieldassignments, sequencing, and union to produce a set of “histories” corresponding to the packet’s traces.
Standard NetKAT does not support mutable state. Each
packet is processed in isolation using the function described
by the program. In other words, we can use a standard
NetKAT program for specifying individual network configurations, but not event-driven configuration changes. We describe a stateful variant of NetKAT which allows us to compactly specify a collection of network configurations, as well
as the event-driven relationships between them (i.e. an ETS).
This variant preserves the existing equational theory of the
Event-Driven Network Programming

Jstate(m)=nK~k

Figure 5: Stateful NetKAT: extracting NetKAT Program (state ~k).

Loops in ETSs. If there are loops in the ETS T , the previous definition needs to be slightly modified, because we
need to “rename” events encountered multiple times in the
same execution. This gives rise to an NES where each eventset is finite, but the NES itself might be infinite (and thus
can only be computed lazily). If we have the ability to store
and communicate unbounded (but finite) event-sets in the
network runtime, then no modifications are needed to handle infinite NESs in the implementation (which is described
in Section 4). Otherwise, there are various correct overapproximations we could use, such as computing the stronglyconnected components (SCCs) of the ETS, enforcing the locality restriction on events in each (non-singleton) SCC, and
requiring the implementation to attach timestamps on occurrences of events in those SCCs. For simplicity of the presentation, we will consider only loop-free ETSs in this paper.
3.2

Field
(packet field name)
N
(numeric value)
f | pt
(modifiable field)
true | false | x = n | sw=n | state(n) = n
(test)
a ∨ b | a ∧ b | ¬a
a | x ← n | p + q | p ; q | p∗
(command)
(n:n) _ (n:n) | (n:n) _ (n:n) _ hstate(n) ← ni

3.3

Converting Stateful NetKAT Programs to ETSs

Now that we have the J · K~k function to extract the static configurations (NetKAT programs) corresponding to the vertices of an ETS, we define another function L · M~k , which
produces the event-edges (Figure 6). This collects (using parameter ϕ) the conjunction of all tests seen up to a given
8

2016/4/19

Lf = nM~k ϕ
Lsw = nM~k ϕ
Lport = nM~k ϕ

,
,
,

Lstate(m) = nM~k ϕ

,

({}, {ϕ ∧ f = n})
LtrueM~k ϕ
LtrueM~k ϕ
(
LtrueM~ ϕ if ~k(m) = n

,
,
,
,

({}, {(∃f : ϕ) ∧ f =n})
(LpM~k ϕ) t (LqM~k ϕ)
(LpM~k ‚ LqM~k ) ϕ
F j
~
j Fp (ϕ, k)

Lf ← nM~k
Lp + qM~k
Lp ; qM~k
Lp∗M~k

ϕ
ϕ
ϕ
ϕ

La ∧ bM~k
La ∨ bM~k
LtrueM~k
LfalseM~k
L¬trueM~k
L¬falseM~k
L¬(v = n)M~k
L¬¬aM~k
L¬(a ∧ b)M~k
L¬(a ∨ b)M~k

k

LfalseM~k ϕ

otherwise

L(s1 :p1 ) _ (s2 :p2 )M~k ϕ
L(s1 :p1 ) _ (s2 :p2 ) _ hstate(m) ← niM~k ϕ

,
,

ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ
ϕ

,
,
,
,
,
,
,
,
,
,

La ; bM~k ϕ
La + bM~k ϕ
({}, {ϕ})
({}, {})
LfalseM~k ϕ
LtrueM~k ϕ
Lv 6= nM~k ϕ
LaM~k ϕ
L¬a ∨ ¬bM~k ϕ
L¬a ∧ ¬bM~k ϕ

({}, {ϕ})
({(~k, (ϕ, s2 , p2 ), ~k[m 7→ n])}, {ϕ})

Figure 6: Stateful NetKAT: extracting event-edges from state ~k.

set upon ingress, and (iii) reads the tags carried by packets,
and updates the event-set at subsequent switches.

program location, and records a corresponding event-edge
when a state assignment command is encountered. The function returns a tuple (D, P ), where D is a set of event-edges,
and P is a set of updated conjunctions of tests. In the figure, the t operator denotes pointwise union of tuples, i.e.
(A1 , B1 , · · · ) t (A2 , B2 , · · · ) = (A1 ∪ A2 , B1 ∪ B2 , · · · ).
The ‚ operator
F denotes (pointwise) Kleisli composition, i.e.
(f ‚ g) , {g y : y ∈ f x}, and function F is as follows.
Fp0 (ϕ, ~k) ,
Fpj+1 (ϕ, ~k) ,

4.1

Static Configurations. The NES contains a set of network
configurations that need to be installed as flow tables on
switches. In addition, we must be able to transition to a new
configuration in response to a local event. We do this proactively, installing all of the needed rules on switches in advance, with each rule guarded by its configuration’s ID. This
has a disadvantage of being less efficient in terms of rulespace usage, but an advantage of allowing quick configuration changes. In Section 5.3, we discuss an approach for
addressing the space-usage issue by sharing rules between
configurations. Our implementation strategy encodes each
event-set in the NES as an integer, so a single unused packet
header field (or single register on switches) can be used. This
keeps the overhead low, even for very large programs.

({}, {ϕ})
(LpM~k ‚ Fpj ) ϕ

The symbol variable = is either equality “=” or inequality
“6=”, and 6= is the opposite symbol with respect to = . Given
any conjunction ϕ and a header field f , the formula (∃f : ϕ)
strips all predicates of the form (f = n) from ϕ.
Using fst to denote obtaining the first element of a tuple,
we can now produce the event-driven transition system for a
Stateful NetKAT program p with the initial state ~k0 :

Stateful Switches. Emerging data-plane languages such as
P4 [6] and OpenState [5] are beginning to feature advanced
functionality such as customizable parsing, stateful memories, etc. We assume that our switches support (1) modifying
a local register (e.g. an integer on a switch) appropriately
upon receipt of a packet, and (2) making packet forwarding
decisions based on the value of a register. This allows each
switch to maintain a local view of the global state. Specifically, the register records the set of events the device knows
have occurred. At any time, the device can receive a packet
(from the controller or another device) informing it of new
event occurrences, which are “unioned” into the local register (by performing a table lookup based on integer values).
Currently, P4 data planes support this type of functionality.
We also assume that the switch atomically processes each
packet in the order in which it was received. Such “atomic”
switch operations are proposed by the “Packet Transactions”
P4 extension [34]. Because the P4 switch platform is attracting considerable attention (even spawning its own highly-

ETS (p) , (V, D, v0 )
S
where V , ~k {(~k, C(JpK~k ))}
F
and D , fst
~
k LpM~
k true
and v0 , (~k0 , C(JpK~k0 ))

4.

Implementing Event-Driven Programs

Next, we show one method of implementing NESs in a real
SDN, and we prove that this approach is correct—i.e., all
traces followed by actual packets in the network are correct
with respect to Definition 6 in Section 2. At a high level, the
basic idea of our implementation strategy can be understood
as follows. We assume that the switches in the network
provide mutable state that can be read and written as packets
are processed. Given an NES, we assign a tag to each eventset and compile to a collection of configurations whose rules
are “guarded” by the appropriate tags. We then add logic
that (i) updates the mutable state to record local events, (ii)
stamps incoming packets with the tag for the current eventEvent-Driven Network Programming

Implementation Building Blocks

9

2016/4/19

Switch ID
Port ID
Host ID
Location

n
m
h
l

∈
∈
∈
::=

(h, n:m) ∈ L

0

Packet
Located Packet
Queue Map
Link
Links
Event
Event-set

N
N
N
n:m

pkt
lp
qm
lk
L
e
E

::=
::=
::=
::=
::=
::=
::=

{f1 ; · · · ; fk ; C; digest}
(pkt, l)
{n 7→ pkts, · · · }
(l, l)
{lk, · · · }
(ϕ, l)
{e, · · · }

S = S 0 ∪{(n, qm[m7→pkts], E, qm2 )}

(Q, R, S) −
→ (Q, R, S ∪{(n, qm[m7→pkts@[pkt[C←g(E)]]], E, qm2 )})

IN

(n:m, h) ∈ L

Configuration
Enabling Rel.
Consist. Pred.
Config. Map
Switch
Queue, Control.
Switches

C
`
con
g
sw
Q, R
S

::=
::=
::=
::=
::=
::=
::=

{(lp, lp), · · · }
{(E, e), · · · }
{E, · · · }
{E 7→ C, · · · }
(n, qm, E, qm)
E
{sw, · · · }

S = S 0 ∪{(n, q1 , E, qm[m7→pkt::pkts])}

(Q, R, S) −
→ (Q, R, S 0 ∪{(n, q1 , E, qm[m7→pkts])})

E 0 = {e : (E ∪ pkt.digest) ` e ∧ con(E ∪ pkt.digest ∪ {e}) ∧ (pkt, n:m) |= e}
{lp : pkt.C((pkt, n:m), lp)} = {(pkt 1 , n:m1 ), · · · } S = S 0 ∪ {(n, qm[m 7→ pkt::pkts], E, qm2 [m1 7→ pkts 1 , · · · ])}
(Q, R, S) −
→ (Q ∪ E 0 , R, S 0 ∪ {(n, qm[m 7→ pkts], E ∪ E 0 ∪ pkt.digest,
qm2 [m1 7→ pkts 1 @[pkt 1 [digest ← pkt 1 .digest ∪ E ∪ E 0 ]], · · · ])})

(n1 :m1 , n2 :m2 ) ∈ L

S = S 0 ∪ {(n1 , qm1 , E1 , qm2 [m1 7→ pkt::pkts]), (n2 , qm3 [m2 7→ pkts 0 ], E2 , qm4 )}

(Q, R, S) −
→ (Q, R, S 0 ∪ {(n1 , qm1 , E1 , qm2 [m1 7→ pkts]), (n2 , qm3 [m2 7→ pkts 0 @[pkt]], E2 , qm4 )})
Q = Q0 ∪ {e}
0

(Q, R, S) −
→ (Q , R ∪ {e}), S)

C TRL R ECV

R = R0 ∪ {e}

S = S 0 ∪ {(n, qm, E, qm2 )}

(Q, R, S) −
→ (Q, R, S 0 ∪ {(n, qm, E ∪ {e}, qm2 )})

O UT

S WITCH

L INK

C TRL S END

Figure 7: Implemented program semantics.

corresponding to its version number is denoted pkt.C. The
rules in Figure 7 can be summarized as follows.
• I N /O UT: move a packet between a host and edge port.
• S WITCH: process a packet by first adding new events
from the packet’s digest to the local state, then checking
if the packet’s arrival matches an event e enabled by the
NES and updating the state and packet digest if so, and
finally updating the digest with other local events.
• L INK: move a packet across a physical link.
• C TRL R ECV: bring an event from the controller queue
into the controller.
• C TRL S END: update the local state of the switches.

attended workshop), we feel that our assumptions are realistic for the current state-of-the-art in regards to switches.
Packet Processing. Each packet entering the network is
admitted from a host to a port on an edge switch. The
configuration ID j corresponding to the device’s view of
the global state is assigned to the packet’s version number
field. The packet will processed only by j-guarded rules
throughout its lifetime. Packets also carry a digest encoding
the set of events the packet has heard about so far (i.e.
the packet’s view of the global state). If the packet passes
through a device which has heard about additional events,
the packet’s digest is updated accordingly. Similarly, if the
packet’s digest contains events not yet heard about by the
device, the latter adds them to its view of the state. When a
packet triggers an event, that event is immediately added to
the packet’s digest, as well as to the state of the device where
the event was detected. The controller is then notified about
the event. Optionally (as an optimization), the controller
can periodically broadcast its view of the global state to all
switches, in order to speed up dissemination of the state.
4.2

4.3

We now prove the correctness of our implementation. Formally, we show that the operational semantics generates correct traces, as defined in Section 2.
Lemma 3 (Global Consistency). Given a locally-determined
network event structure N , for an execution of the implementation (Q1 , R1 , S1 )(Q2 , R2 , S2 ) · · · (Qm , Rm , Sm ), the
event-set Qi ∪ Ri is consistent for all 1 ≤ i ≤ m.

Operational Model

We formalize the above via operational semantics for the
global behavior of the network as it executes an NES. Each
state in Figure 7 has the form (Q, R, S), with a controller
queue Q, a controller R, and set of switches S. Both the controller queue and controller are a set of events, and initially,
R=Q=∅. Each switch s ∈ S is a tuple (n, qmin , E, qmout ),
where n is the switch ID, qmin , qmout are the input/output queue maps (mapping port IDs to packet queues). Map
updates are denoted qm[m 7→ pkts]. The event-set E represents a switch’s view of what events have occurred. A
packet’s digest is denoted pkt.digest, and the configuration
Event-Driven Network Programming

Correctness of the Implementation

Proof Sketch. We first show that if an inconsistent set Y
where |Y | > 1 satisfies the locality restriction (i.e. all of its
events are handled at the same switch), then Y ⊆ Ri ∪ Qi is
not possible for any i (the S WITCH rule ensures that multiple
events from Y could not have been sent to the controller).
We proceed by induction over m, the trace length, noting
that the base case Q0 ∪R0 = ∅ is consistent. Assume that the
implementation adds an e (via S WITCH) to some consistent
event-set Qm ∪ Rm , producing an inconsistent set. We look
at the minimally-inconsistent set Y ⊆ (Qm ∪Rm ∪{e}), and
notice that the locality restriction requires all events in Y to
10

2016/4/19

be detected at the same switch, so by the previous paragraph,
we must have |Y | ≤ 1. This generates a contradiction, since
it would mean that either Y = {e0 } or Y ⊆ Qm ∪ Rm ,
either of which would make Y consistent.

mance measurements on simple automatically-generated
programs. For the experiments, we assume that the programmer has first confirmed that the program satisfies the
conditions allowing proper compilation to an NES, and we
assume that the ETS has no loops. Our tool could be modified to perform these checks via basic algorithms operating
on the ETS, but they have not yet been implemented in the
current prototype (as mentioned in Section 3.1, developing
efficient algorithms for these checks is left for future work).
Our experimental platform was an Ubuntu machine with
20GB RAM and a quad-core Intel i5-4570 CPU (3.2 GHz).
To choose a representative set of realistic examples, we
first studied the examples addressed in other recent stateful network programming approaches, such as SNAP [3],
FlowLog [31], Kinetic [21], NetEgg [39], and FAST [30],
and categorized them into three main groups:
• Protocols/Security: accessing streaming media across
subnets, ARP proxy, firewall with authentication, FTP
monitoring, MAC learning, stateful firewall, TCP reassembly, Virtual Machine (VM) provisioning.
• Measurement/Performance: heavy hitter detection, bandwidth cap management (uCap), connection affinity in
load balancing, counting domains sharing the same IP
address, counting IP addresses under the same domain,
elephant flows detection, link failure recovery, load balancing, network information base (NIB), QoS in multimedia streaming, rate limiting, sampling based on flow
size, Snort flowbits, super spreader detection, tracking
flow-size distributions.
• Monitoring/Filtering: application detection, DNS amplification mitigation, DNS TTL change tracking, DNS
tunnel detection, intrusion detection system (IDS),
optimistic ACK attack detection, phishing/spam detection, selective packet dropping, sidejack attack detection,
stolen laptop detection, SYN flood detection, UDP flood
mitigation, walled garden.
As we will see in the following section, our current prototype
system is best suited for writing programs such as the ones in
the Protocols/Security category, since some of the Measurement/Performance programs require timers and/or integer
counters, and some of the Monitoring/Filtering programs require complex pattern matching of (and table lookups based
on) sequences of packets—functionality which we do not
(yet) natively support, Thus, we have selected three examples from the first category, and one from each of the latter
two, corresponding to the boldface applications in the list.
We believe that these applications are representative of the
basic types of behaviors seen in the other listed applications.

Traces of the Implementation. Note that we can readily
produce the network trace (Section 2) that corresponds to an
implementation trace, since a single packet pkt is processed
at each step of Figure 7. We now present the main result of
this section—executions of the implementation correspond
to correct network traces (Definition 6).
Theorem 1 (Implementation Correctness). For an NES N ,
and an execution (Q1 , R1 , S1 )(Q2 , R2 , S2 ) · · · (Qm , Rm ,
Sm ) of the implementation, the corresponding network trace
ntr is correct with respect to N .
Proof Sketch. The proof is by induction over the length m
of the execution. In the induction step, we show that (1)
the S WITCH rule can only produce consistent event-sets
(this follows directly from Lemma 3), and (2) when the I N
rule tags a packet pkt based on the local event-set E, that
E consists of exactly the events that happened before pkt
arrived (as ordered by the happens-before relation).

5.

Implementation and Evaluation

We built a full-featured prototype implementation in OCaml.
• We implemented the compiler described in Section 3.
This tool accepts a Stateful NetKAT program, and produces the corresponding NES, with a standard NetKAT
program representing the configuration at each node. We
interface with Frenetic’s NetKAT compiler to produce
flow-table rules for each of these NetKAT programs.
• We modified the OpenFlow 1.0 reference implementation
to support the custom switch/controller needed to realize
the runtime described in Section 4.
• We built tools to automatically generate custom Mininet
scripts to bring up the programmer-specified network
topology, using switches/controller running the compiled
NES. We can then realistically simulate the whole system
using real network traffic.
Research Questions. To evaluate our approach, we wanted
to obtain answers to the following questions.
1. How useful is our approach? Does it allow programmers
to easily write real-world network programs, and get the
behavior they want?
2. What is the performance of our tools (compiler, etc.)?
3. How much does our correctness guarantee help? For instance, how do the running network programs compare
with uncoordinated event-driven strategies?
4. How efficient are the implementations generated by our
approach? For instance, what about message overhead?
State-change convergence time? Number of rules used?
We address #1-3 through case studies on real-world programming examples, and #4 through quantitative perforEvent-Driven Network Programming

5.1

Case Studies

In the first set of experiments, we compare correct behavior (produced by our implementation strategy) with that of
an uncoordinated update strategy. We simulate an uncoordinated strategy in the following way: events are sent to the
controller, which pushes updates to the switches (in an un11

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(a, d)

(b)

(c, e)

Figure 8: Topologies: (a) Firewall, (b) Learning Switch, (c) Authentication, (d) Bandwidth Cap, (e) Intrusion Detection System.

(a)

(b)

(c)

(d)

(e)

pt=2 ∧ ip_dst=H4; pt←1; (state=[0];
(1:1)_(4:1)_hstate←[1]i + state6=[0];
(1:1)_(4:1)); pt←2
+ pt=2 ∧ ip_dst=H1; state=[1]; pt←1;
(4:1)_(1:1); pt←2

for each. We then plotted the total number of incorrectlydropped packets with respect to delay. The results are shown
in Figure 10. Note that even with a very small delay, the uncoordinated strategy still always drops at least one packet.

pt=2 ∧ ip_dst=H1; (pt←1; (4:1)_(1:1) +
state=[0]; pt←3; (4:3)_(2:1)); pt←2
+ pt=2 ∧ ip_dst=H4; pt←1; (1:1)_(4:1)_h
state←[1]i; pt←2
+ pt=2; pt←1; (2:1)_(4:3); pt←2

Stateful Firewall. The example in Figures 8-9(a) is a simplified stateful firewall. It always allows “outgoing” traffic
(from H1 to H4), but only allows “incoming” traffic (from
H4 to H1) after the outside network has been contacted, i.e.
“outgoing” traffic has been forwarded to H4.
Program p corresponds to configurations C[0] = JpK[0]
and C[1] = JpK[1] . In the former, only outgoing traffic is
allowed, and in the latter, both outgoing and incoming are

state=[0] ∧ pt=2 ∧ ip_dst=H1; pt←1;
(4:1)_(1:1)_hstate←[1]i; pt←2
+ state=[1] ∧ pt=2 ∧ ip_dst=H2; pt←3;
(4:3)_(2:1)_hstate←[2]i; pt←2
+ state=[2] ∧ pt=2 ∧ ip_dst=H3; pt←4;
(4:4)_(3:1); pt←2
+ pt=2; pt←1; ((1:1)_(4:1) + (2:1)_(4:3) +
(3:1)_(4:4)); pt←2

(dst=H4, 4:1)

allowed. The ETS has the form {h[0]i −−−−−−−−−→ h[1]i}.
The NES has the form {E0 =∅ → E1 ={(dst=H4, 4:1)}},
where the g is given by g(E0 ) = C[0] , g(E1 ) = C[1] .
The Stateful Firewall example took 0.013s to compile,
and produced a total of 18 flow-table rules. In Figure 11(a),
we show that the running firewall has the expected behavior.
We first try to ping H1 from H4 (the “H4-H1”/red points),
which fails. Then we ping H4 from H1 (the “H1-H4”/orange
points), which succeeds. Again we try H4-H1, and now this
succeeds, since the event-triggered state change occurred.
For the uncoordinated strategy, Figure 11(b) shows that
some of the H1-H4 pings get dropped (i.e. H1 does not hear
back from H4), meaning the state change did not behave as
if it was caused immediately upon arrival of a packet at S4.

pt=2 ∧ ip_dst=H4;
pt←1; (
state=[0]; (1:1)_(4:1)_hstate←[1]i
+ state=[1]; (1:1)_(4:1)_hstate←[2]i
+ state=[2]; (1:1)_(4:1)_hstate←[3]i
.
.
.
+ state=[10]; (1:1)_(4:1)_hstate←[11]i
+ state=[11]; (1:1)_(4:1)
); pt←2
+ pt=2 ∧ ip_dst=H1; state6=[11]; pt←1;
(4:1)_(1:1); pt←2
pt=2 ∧ ip_dst=H1; pt←1; (state=[0];
(4:1)_(1:1)_hstate←[1]i + state6=[0];
(4:1)_(1:1)); pt←2
+ pt=2 ∧ ip_dst=H2; pt←3; (state=[1];
(4:3)_(2:1)_hstate←[2]i + state6=[1];
(4:3)_(2:1)); pt←2
+ pt=2 ∧ ip_dst=H3; pt←4; state6=[2];
(4:4)_(3:1); pt←2
+ pt=2; pt←1; ((1:1)_(4:1) + (2:1)_(4:3) +
(3:1)_(4:4)); pt←2

Learning Switch. The example in Figures 8-9(b) is a simple learning switch. Traffic from H4 to H1 is flooded (sent
to both H1 and H2), until H4 receives a packet from H1, at
50
Total # dropped packets

Figure 9: Programs: (a) Firewall, (b) Learning Switch, (c) Authentication, (d) Bandwidth Cap, (e) Intrusion Detection System.

predictable order) after a few-seconds time delay. We believe
this delay is reasonable because heavily using the controller
and frequently updating switches can lead to delays between
operations of several seconds in practice (e.g. [17] reports up
to 10s for a single switch update).
To show that problems still arise for smaller delays, in the
firewall experiment described next, we varied the time delay in the uncoordinated strategy between 0ms and 5000ms
(in increments of 100ms), running the experiment 10 times
Event-Driven Network Programming

Incorrect
Correct

40
30
20
10
0

0

1000

2000
3000
Delay (ms)

4000

5000

Figure 10: Stateful Firewall: impact of delay.

12

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2

4

6

8

10 12
(a)
Time
(s)

14

16

18

Ping? (high=yes)

0

H4-H3
H4-H2
H4-H1

20

H4-H1
H1-H4

0
0

2

4

6

8

10 12
Time (s)

14

16

18

20

(b)

Figure 11: Stateful Firewall: (a) correct vs. (b) incorrect.

which point it “learns” the address of H1, and future traffic
from H4 to H1 is sent only to H1.
This program p corresponds to two configurations C[0] =
JpK[0] and C[1] = JpK[1] . In the former, flooding occurs from
H4, and in the latter, packets from H4 are forwarded directly

0

# Packets Sent
# Packets Sent

10
8
6
4
2
0

to H1
to H2

1

1

2

3

4
5
(a)
Time
(s)

6

7

8

9

2

3

4
5
Time (s)

6

7

8

9

20 25 30
(a)
Time
(s)

35

40

45

50

2

4

6
Time (s)

8

10

12

the state change (i.e. learning H1’s address), and all subsequent packets are sent only to H1. In Figure 12(b), however,
since the state change can be delayed, multiple packets are
sent to H2, even after H4 has seen a reply from H1.
Authentication. In this example, shown in Figures 8-9(c),
the untrusted host H4 wishes to contact H3, but can only do
so after contacting H1 and then H2, in that order.
This program p corresponds to three configurations:
C[0] = JpK[0] in which only H4-H1 traffic is enabled,
C[1] = JpK[1] in which only H4-H2 traffic is enabled,
and C[2] = JpK[2] which finally allows H4 to communi(dst=H1, 1:1)

cate with H3. The ETS has the form {h[0]i −−−−−−−−−→
(dst=H2, 2:1)

h[1]i −−−−−−−−−→ h[2]i}. The NES has the form {E0 =∅ →
E1 ={(dst=H1, 1:1)} → E2 ={(dst=H1, 1:1), (dst=H2,
2:1)}}, where the g function is given by g(E0 ) = C[0] ,
g(E1 ) = C[1] , g(E2 ) = C[2] .
The Authentication example took 0.017s to compile, and
produced a total of 72 flow-table rules. In Figure 13(a) we
demonstrate the correct behavior of the program, by first
trying (and failing) to ping H3 and H2 from H4, then successfully pinging H1, again failing to ping H3 (and H1), and
finally succeeding in pinging H3. The incorrect (uncoordinated) implementation in Figure 13(b) allows an incorrect
behavior where we can successfully ping H1 and then H2,
but then fail to ping H3 (at least temporarily).
Bandwidth Cap. The Figure 8-9(d) example is a simplified
bandwidth cap implementation. It allows “outgoing” traffic
(H1-H4), but only until the limit of n packets has been
reached, at which point the service provider replies with a

(b)

Figure 12: Learning Switch: (a) correct vs. (b) incorrect.

Event-Driven Network Programming

15

Figure 13: Authentication: (a) correct vs. (b) incorrect.

(dst=H4, 4:1)

to H1
to H2

10

(b)

to H1. The ETS has the form {h[0]i −−−−−−−−−→ h[1]i}.
The NES has the form {E0 =∅ → E1 ={(dst=H4, 4:1)}},
where the g is given by g(E0 ) = C[0] , g(E1 ) = C[1] .
This only allows learning for a single host (H1), but we
could easily add learning for H2 by using a different index
in the vector-valued state field: we could replace state in
Figure 9(b) with state(0), and union the program (using the
NetKAT “+” operator) with another instance of Figure 9(b)
which learns for H2 and uses state(1).
The Learning Switch example took 0.015s to compile,
and produced a total of 43 flow-table rules. We again compare the behavior of our correct implementation with that
of an implementation which uses an uncoordinated update
strategy. We first ping H1 from H4. Expected behavior is
shown in Figure 12(a), where the first packet is flooded to
both H1 and H2, but then H4 hears a reply from H1, causing

10
8
6
4
2
0

5
H4-H3
H4-H2
H4-H1

22
Ping? (high=yes)

Ping? (high=yes)
Ping? (high=yes)

H4-H1
H1-H4

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2

4

6

8

10 12
(a)
Time
(s)

14

16

18

20

Ping? (high=yes)

0

H4-H3
H4-H2
H4-H1

22

H1-H4

0
0

2

4

6

8

10 12
Time (s)

14

16

18

20

(b)

Figure 14: Bandwidth Cap: (a) correct vs. (b) incorrect.

notification message, and disallows the “incoming” path. In
this experiment, we use a bandwidth cap of n = 10 packets.
Program p corresponds to configurations C[0] =JpK[0] ,
· · · , C[n] =JpK[n] , which all allow incoming/outgoing traffic,
and a configuration C[n+1] =JpK[n+1] which disallows the

0

10

15

20
25
(a)
Time
(s)

30

4

6
Time (s)

8

35

40

45

2

10

12

(b)

Figure 15: Intrusion Detection System: (a) correct vs. (b) incorrect.

(dst=H4, 4:1)

incoming traffic. The ETS has the form {h[0]i −−−−−−−−−→
(dst=H4, 4:1)

5
H4-H3
H4-H2
H4-H1

22
Ping? (high=yes)

Ping? (high=yes)
Ping? (high=yes)

H1-H4

(dst=H4, 4:1)

h[1]i −−−−−−−−−→ · · · −−−−−−−−−→ h[n + 1]i}. The NES
has the form {E0 =∅ → E1 ={(dst=H4, 4:1)} → · · · →
En+1 ={(dst=H4, 4:1)0 , · · · , (dst=H4, 4:1)n }}, where
the g is given by g(E0 ) = C[0] , · · · , g(En+1 ) = C[n+1] .
Note that the subscripts on events in the NES event-sets
(e.g. the ones in En+1 ) indicate “renamed” copies of the
same event (as described in Section 3.1).
The Bandwidth Cap example took 0.023s to compile, and
produced a total of 158 flow-table rules. In Figure 14(a), we
show that the running example has the expected behavior.
We send pings from H1 to H4, of which exactly 10 succeed,
meaning we have reached the bandwidth cap. Using the
uncoordinated update strategy in Figure 14(b), we again
send pings from H1 to H4, but in this case, 15 are successful,
exceeding the bandwidth cap.

This IDS example took 0.021s to compile and produced
152 flow-table rules. In Figure 15(a), we demonstrate the
correct behavior of the program, by first successfully pinging H3, H2, H1, H3, H2, H1 (in that order) from H4. This
results in a situation where we have contacted H1 and then
H2, causing the third attempt to contact H3 to be blocked
(H4-H3 pings dropped). The incorrect (uncoordinated) implementation in Figure 15(b) allows a faulty behavior where
we can successfully ping H1 and then H2 (in that order), but
subsequent H4-H3 traffic is still enabled temporarily.
5.2

In this experiment, we automatically generated some eventdriven programs which specify that two hosts H1 and H2 are
connected to opposite sides of a ring of switches. Initially,
traffic is forwarded clockwise, but when a specific switch
detects a (packet) event, the configuration changes to forward counterclockwise. We increased the “diameter” of the
ring (distance from H1 to H2) up to 8, as shown in Figure
16, and performed the following two experiments.
1. We used iperf to measure H1-H2 TCP/UDP bandwidth, and compared the performance of our running
event-driven program, versus that of the initial (static)
configuration of the program running on un-modified
OpenFlow 1.0 reference switches/controller. Figure 16(a)
shows that our performance (solid line) is very close to
the performance of a system which does not do packet
tagging, event detection, etc. (dashed line)—we see
around 6% performance degradation on average (note
that the solid and dashed lines almost coincide).

Intrusion Detection System. In this example, shown in
Figures 8-9(e), the external host H4 is initially free to communicate with the internal hosts H1, H2, and H3. However,
if H4 begins engaging in some type of suspicious activity (in
this case, beginning to scan through the hosts, e.g. contacting H1 and then H2, in that order), the activity is thwarted
(in this case, by cutting off access to H3).
This program p corresponds to three configurations:
C[0] = JpK[0] and C[1] = JpK[1] , in which all traffic is
enabled, and C[2] = JpK[2] in which H4-H3 communica(dst=H1, 1:1)

tion is disabled. The ETS has the form {h[0]i −−−−−−−−−→
(dst=H2, 2:1)

h[1]i −−−−−−−−−→ h[2]i}. The NES has the form {E0 =∅ →
E1 ={(dst=H1, 1:1)} → E2 ={(dst=H1, 1:1), (dst=H2,
2:1)}}, where the g function is given by g(E0 ) = C[0] ,
g(E1 ) = C[1] , g(E2 ) = C[2] .
Event-Driven Network Programming

Quantitative Results

14

2016/4/19

Bandwidth (Mbit/sec)
Event Discovery Time (s)

100

∗,∅

1

0∗ , {r1 }

TCP perf.
UDP % loss
UDP perf.

10

2

3

00,

4
5
6
7
(a)
Network Diameter
(# switches)

8

10
3

4
5
6
7
8
Network Diameter (# switches)
(b)

# Original Rules

Figure 16: Circular Example: (a) bandwidth (solid line is ours,
dotted line is reference implementation) and (b) convergence.

500
x=y

400
300
280

300

320

340

Number of Rules w/ Heuristic

Figure 17: Heuristic: reducing the number of rules.

2. We measured maximum and average time needed for a
switch to learn about the event. The “Max.” and “Avg.”
bars in Figure 16(b) are these numbers when the controller does not assist in disseminating events (i.e. only
the packet digest is used), and the other columns are the
maximum and average when the controller does so.
5.3

Optimizations

When a configuration change occurs, the old and new configurations are often similar, differing only in a subset of flowtable rules. Tables are commonly stored in TCAM memory
on switches, which is limited/costly, so it is undesirable to
store duplicate rules. As mentioned in Section 4.1, each of
our rules is guarded by its configuration’s numeric ID. If the
same rule occurs in several configurations having IDs with
the same (binary) high-order bits, intuitively we can reduce
space usage by keeping a single copy of the rule, and guarding it with a configuration ID having the shared high-order
bits, and wildcarded low-order bits. For example, if rule r is
used in two different configurations having IDs 2 (binary 10)
and 3 (binary 11), we can wildcard the lowest bit (1∗), and
keep a single rule (1∗)r having this wildcarded guard, inEvent-Driven Network Programming

01,

10,

11,

0∗ , {r1 , r2 }
00,

01,

1∗ , {r3 }

10,

11,

{r1 , r2 }{r1 , r3 }{r2 , r3 }{r1 , r2 }

{r1 , r2 }{r1 , r2 }{r1 , r3 }{r2 , r3 }

(a)

(b)

stead of two copies of r, with the “10” and “11” guards. Ideally, we would like to (re)assign numeric IDs to the configurations, such that maximal sharing of this form is achieved.
We formalize the problem as follows. Assume there is a
set of all possible rules R. A configuration C is a subset
of these rules C ⊆ R. Assume there are k bits in a configuration ID. Without loss of generality we assume there
are exactly 2k configurations (if there are fewer, we can add
dummy configurations, each containing all rules in R). For
a given set of configurations, we construct a trie having all
of the configurations at the leaves. This trie is a complete
binary tree in which every node is marked with (1) a wildcarded mask that represents the configuration IDs of its children, and (2) the intersection of the rule-sets of its children.
Consider configurations C0 = {r1 , r2 }, C1 = {r1 , r3 },
C2 = {r2 , r3 }, C3 = {r1 , r2 }. Figure 18 shows two different assignments of configurations to the leaves of tries. The
number of rules for trie (a) is 6: (0∗)r1 , (00)r2 , (01)r3 ,
(1∗)r2 , (10)r3 , (11)r1 . The number of rules for trie (b) is 5:
(0∗)r1 , (0∗)r2 , (1∗)r3 , (10)r1 , (11)r2 . Intuitively, this is
because the trie (b) has larger sets in the interior. Our polynomial heuristic follows that basic intuition: it constructs the
trie from the leaves up, at each level pairing nodes in a way
that maximizes the sum of the cardinalities of their sets. This
does not always produce the global maximum rule sharing,
but we find that it produces good results in practice.
As indicated by the Figure 17 result (64 randomlygenerate configurations w/ 20 rules), on average, rule savings was about 32% of the original number of rules. We
also ran this on the previously-discussed Firewall, Learning
Switch, Authentication, Bandwidth Cap, and IDS examples,
and got rule reductions of 18 → 16, 43 → 27, 72 → 46,
158 → 101, and 152 → 133 respectively.

100

1

1∗ , {r2 }

Figure 18: Heuristic: two different tries for the same configurations.

Max.
Avg.
Max. w/ Controller
Avg. w/ Controller

1000

∗,∅

6.

Related Work

Network Updates, Verification, and Synthesis. We already
briefly mentioned an early approach known as consistent
updates [33]. This work was followed by update techniques
that respect other correctness properties [25] [17] [40] [26].
These approaches for expressing and verifying correctness
of network updates work in terms of individual packets.
In event-driven network programs, it is necessary to
check properties which describe interactions between multiple packets. There are several works which seek to perform
15

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network updates in the context of multi-packet properties
[12] [23]. There are also proposals for synthesizing SDN
controller programs from multi-packet examples [39] and
from first-order specifications [32]. Lopes et al. presented
techniques for verifying reachability in stateful network programs [24], using a variant of Datalog. This is a complimentary approach which could be used as a basis for verifying
reachability properties of our stateful programs.

interleavings of events and updates for each application, and
we show that our consistency model and implementation
technique work well in the context of SDN programs, but
we do not believe they are limited to that specific arena. Our
approach could also possibly be extended to other distributed
systems in which availability is prioritized, and consistency
can be relaxed in a well-defined way, as in our event-driven
consistent updates. Example domains include wireless sensor networks or other message-passing systems where the
nodes have basic stateful functionality.

Network Programming Languages. Network programs
can often be constructed using high-level languages. The
Frenetic project [10] [27] [11] allows higher-level specification of network policies. Other related projects like Merlin
[36] and NetKAT [35] [4] provide high-level languages/tools
to compile such programs to network configurations. Works
such as Maple [37] and FlowLog [31] seek to address the
dynamic aspect of network programming.
None of these systems and languages provide both (1)
event-based constructs, and (2) strong semantic guarantees
about consistency during updates, while our framework enables both. Concurrently with this paper, an approach called
SNAP [3] was developed, which enables event-driven programming, and allows the programmer to ensure consistency
via an atomic language construct. Their approach offers a
more expressive language than our Stateful NetKAT, but
in our approach, we enable correct-by-construction eventbased behavior and provide a dynamic correctness property,
showing (formally) that is strong enough for easy reasoning,
yet flexible enough to enable efficient implementations. We
also prove the correctness of our implementation technique.

Future Work. There are several directions for future work
which could address limitations of our current system.
1. We assume that the set of (potential) hosts is known in advance, and use this information to generate corresponding flow tables for each switch. This may not be the right
choice in settings where hosts join/leave. Our approach
could be extended to represent hosts symbolically.
2. We currently store all configurations on the switches, so
that they are immediately available during updates. Our
optimizations allow this to be done in a space-efficient
way, but there may be situations when it would be better
for the controller to reactively push new configurations to
switches. This is an interesting problem due to interleavings of events and controller commands.
3. It would be interesting to consider formal reasoning and
automated verification for Stateful NetKAT.
4. We provide a solution to the problem of performing multiple updates, and the dynamic implementations we produce are meant to “run” in the network indefinitely. However, there may be ways to update the running dynamic
program itself in some consistent way.

Routing. The consistency/availability trade-off is of interest in routing outside the SDN context as well. In [18], a
solution called consensus routing is presented, based on a
notion of causality between triggers (related to our events).
However, the solution is different in many aspects, e.g. it allows a transient phase without safety guarantees.

8.

This paper presents a full framework for correct event-driven
programming. Our approach provides a way of rigorously
defining correct event-driven behavior without the need for
specifying logical formulas. We detail a programming language and compiler which allow the user to write high-level
network programs and produce correct and efficient SDN
implementations, and we demonstrate the benefits of our approach using real-world examples. This paper considers the
challenging problem of distributing an event-based stateful
network program, and solves it in a principled way.

High-Level Network Functionality. Some recent work
has proposed building powerful high-level features into the
network itself, such as fabrics [9], intents [1], and other virtualization functionality [22]. Pyretic [28] and projects built
on top of it such as PyResonance [20], SDX [14], and Kinetic [21] provide high-level operations on which network
programs can be built. These projects do not guarantee consistency during updates, and thus could be profitably combined with an approach such as ours.

7.

Acknowledgments

Discussion and Future Work

Many thanks to the anonymous PLDI reviewers for offering
helpful and constructive comments, as well as Zach Tatlock
for shepherding our paper and providing useful feedback.
Our work is supported by the National Science Foundation
under grants CNS-1111698, CNS-1413972, CCF-1421752,
CCF-1422046, CCF-1253165, and CCF-1535952; the Office of Naval Research under grant N00014-15-1-2177; and
gifts from Cisco, Facebook, Fujitsu, Google, and Intel.

Generality of Our Approach. The event-driven SDN update problem considered in this paper is an instance of a
more general distributed-systems programming problem,
namely how to write correct and efficient programs for distributed systems. We provide a PL approach (consistency
property, programming language, and compiler/runtime)
which ensures that the programmer need not reason about

Event-Driven Network Programming

Conclusion

16

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[20] H. Kim, A. Gupta, M. Shahbaz, J. Reich, N. Feamster, and
R. Clark. Simpler Network Configuration with State-Based
Network Policies. Technical report, Georgia Tech, 2013.

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