An Embedded Language Approach to Router Specification in Curry*

An Embedded Language Approach to Router Specification in Curry*
An Embedded Language Approach to
Router Specification in Curry⋆
J. Guadalupe Ramos1 , Josep Silva2 , and Germán Vidal2
1
Instituto Tecnológico de La Piedad
Av. Tecnológico 2000, Meseta los Laureles, La Piedad, Mich., México
[email protected]
2
DSIC, UPV, Camino de Vera s/n, E-46022 Valencia, Spain
{jsilva,gvidal}@dsic.upv.es
Abstract. The development of modern routers require a significant
effort to be designed, built, and verified. While hardware routers are
faster, they are difficult to configure and maintain. Software routers, on
the other hand, are slower but much more flexible, easier to configure
and maintain, less expensive, etc. Recently, a modular architecture and
toolkit for building software routers and other packet processors has been
introduced: the Click system. It includes a specification language with
features for declaring and connecting router elements and for designing
abstractions.
In this work, we introduce the domain-specific language Rose for the
specification of software routers. Rose is embedded in Curry, a modern
declarative multi-paradigm language. An advantage of this approach is
that we have available a framework where router specifications can be
transformed, optimized, verified, etc., by using a number of existing formal techniques already developed for Curry programs. Furthermore, we
show that the features of Curry are particularly useful to specify router
configurations with a high-level of abstraction. Our first experiments
point out that the proposed methodology is both useful and practical.
1
Introduction
In heterogeneous environments, special devices to interconnect different technologies are often required. Within Internet networks, the router is that device.
Basically, routers connect two or more networks and forward data packets between them. Thus, the primary function of a router is to determine the best
path in a complex network. Originally, routers have been developed entirely as
hardware components. However, there is a clear trend towards extending the set
of functions that network routers should support. These new functions include,
e.g., packet filtering, address translation, run proxies, performance monitoring,
etc. The flexibility required to cope with all these new functions motivated the
⋆
This work has been partially supported by CICYT TIC 2001-2705-C03-01, by the
Generalitat Valenciana under grant CTIDIA/2002/205, and by the MCYT under
grants HA2001-0059, HU2001-0019 and HI2000-0161.
definition of so called extensible routers [6], which support run-time customization of router functionality.
The most important approaches to extensible routers are Scout, Router Plugins, and Click. In Scout [14], the basic abstraction unit is the path: a linear flow
of data that starts at a source device and ends at a destination device. Each
path is composed by stages that are instances from a specific module, which
implements a well understood protocol (IP, TCP, etc). Scout provides tools to
create, modify, schedule, and control paths. Implemented in the NetBSD operating system, Router Plugins allows users to write (limited) extensions to an IP
router. These extensions can be placed at well known points—called gates—of
the router’s IP execution. Gates have been chosen to suit a wide variety of applications, like routing, packet scheduling, and security processing. Finally, Click
[11, 10] is based on composing many simple elements to produce a system that
implements the desired behavior. Each element may have multiple ports to connect it to other elements. These elements control every aspect of the behavior
of the router, from communicating with devices to packet modification to queuing, dropping policies and packet scheduling. New configurations can be built by
gluing elements together with a simple language (which is also called Click).
According to [6], Click is the most flexible of the three architectures above.
Its ability to form virtually any configuration from the set of elements gives the
programmer a high degree of freedom to modify routers incrementally and to
add new services. On the negative side, this flexibility also implies that Click
provides very little guidance on what constitutes a well-formed and meaningful configuration. For this purpose, Click already includes a set of tools which
help the user to deal with complex configurations. Nevertheless, the inclusion
of semantic aspects in Click (e.g., an abstract description of each element, with
the number of input and output ports, how it modifies the passing packets, etc)
would be very useful for the programmer.
In this paper we introduce Rose, a domain-specific language—which is based
on Click—for router specification. Rose is embedded in Curry [9], a declarative multi-paradigm language which integrates features from the most popular
declarative paradigms (namely, functional, logic and concurrent programming).
Therefore, router configurations are first-class objects in Curry, which allows
us to use the higher-level facilities of Curry, such as higher-order combinators,
constraints, laziness, logical variables, etc. Moreover, there already exists a number of tools for transforming, optimizing, and verifying Curry programs—with a
solid theoretical basis—that are also available to the programmer. Let us clarify
that we do not intend to compete with Click. Rather, our aim is to develop a
complementary approach. For instance, one can use Rose during the first design phases and, then, (automatically) translate the developed specification into
Click. One can also translate an existing Click configuration into Rose to perform
some transformation and analyses and, then, translate the result back into Click.
In other words, we do not plan to develop software routers in Curry (as Click
does), only their semantic specification. Consequently, Rose elements only contain high level information which is useful for analysis, simulation, verification,
etc. The main advantage of our proposal is that it provides an appropriate basis
to develop specific analysis and optimization tools (while only a few such tools
already exists for Click and, moreover, they have not been formally verified).
This paper is organized as follows. Section 2 introduces an overview of the
language Curry. In Section 3, we present our approach to router specification:
Section 3.1 reviews the Click language, Section 3.2 presents the specification
of Click elements in Rose, Section 3.3 defines some composition operators to
build larger components, and Section 3.4 briefly describes the implementation
of Rose. Finally, Section 4 discusses some related works and Section 5 concludes
and presents some directions for future work.
2
The Curry language
Curry [9] is a declarative multi-paradigm language which combines in a seamless way features from functional programming (nested expressions, higher-order
functions, lazy evaluation), logic programming (logical variables, partial data
structures, built-in search), and concurrent programming (concurrent evaluation of expressions with synchronization on logical variables). The development
of Curry is an international initiative intended to provide a common platform for
the research, teaching and application of integrated functional logic languages.
In Curry, functions are defined by a sequence of rules (or equations) of the
form
f t1 ...tn = e
where t1 , . . . , tn are constructor terms and the right-hand side e is an expression.
The left-hand side must not contain multiple occurrences of the same variable.
Constructor terms may contain variables and constructor symbols, i.e., symbols
which are not defined by the program rules. Functions can be also defined by
conditional equations which have the form
f t1 ...tn | c = e
where the condition (or guard ) c can be either a Boolean function or a constraint.
Elementary constraints are success, which is always satisfied, and equational
constraints e1 =:= e2 between two expressions. The latter is satisfied if both expressions are reducible to a same ground constructor term (i.e., the so-called
strict equality [13]). Operationally, an equational constraint e1 =:= e2 is solved
by evaluating e1 and e2 to unifiable constructor terms.
We can define non-deterministic functions either by providing several rules
with overlapping left-hand sides or by introducing free variables (i.e., variables
that do not occur in the left-hand side) in the condition or in the right-hand side
of the rules. For instance, the following function non-deterministically inserts
an element in a list (where [] denotes the empty list and x:xs a list with first
element x and tail xs):
insert x []
= [x]
insert x (y:ys) = x : y : ys
insert x (y:ys) = y : insert x ys
Local declarations can be defined by using the let or where constructs. The
following Curry function splits a list into two lists containing the smaller and
larger elements:
split e []
=
split e (x:xs) | e >= x =
| e < x
=
where (l,r)
([], [])
(x:l, r)
(l, x:r)
= split e xs
Higher-order features include partial function applications and lambda abstractions. Function application is denoted by juxtaposition of the function and its
argument. For instance, the well-known function map is defined in Curry by
map f []
= []
map f (x:xs) = f x : map f xs
Lambda abstractions—anonymous functions—are expressions of the following
form: \x1 . . .xn -> exp. The application of the above lambda abstraction to input arguments e1 , . . . , en produces the same result as the call “foo e1 . . . en ”,
where foo is defined by “foo x1 . . . xn = exp”. Curry also allows the use of
functions which are not defined in the user’s program, like arithmetic operators,
usual higher-order functions (map, foldr, etc.), basic input/output facilities, etc.
We refer the interested reader to the report on the Curry language [9] for a
detailed description of all the features of the multi-paradigm language Curry.
3
Specifying Click Routers
3.1
The Click Language
The Click programming language textually describes Click router configurations.
Click has only two basic constructs which are enough to describe any configuration graph [10]: declarations create (instances of) elements and connections
connect existing elements together. In order to build a router configuration, the
user chooses a collection of elements and connects them via ports into a directed
graph. For instance, the following graph shows several elements connected into
a simple router that counts incoming packets and, then, throws them all away:
In the Click language, this router is specified as follows:
// Declarations
src :: FromDevice(eth0);
ctr :: Counter;
sink :: Discard;
// Connections
src -> ctr;
ctr -> sink;
Basically, Click elements [10] fall into one of the following categories:
Packet sources. They spontaneously generate packets, either by reading them
from the network, reading them from a dump file, creating them from specified data, or creating them from random data. They have one output and
no inputs.
Packet sinks. They remove packets from the specified system, either by simply
dropping them, sending them to the network, writing their contents to a
dump file, or sending them to the Linux networking stack. They have one
input and no outputs.
Packet modifiers. They are used to change packet data. They have one input and
one (or two) outputs. Packets arriving on the input are modified and then
emitted on the first output (the second output, if present, is for erroneous
packets).
Routing elements. They choose where incoming packets should go based on a
packet-independent switching algorithm, general characteristics of packet
flow, or an examination of packet contents. For instance, a typical roundrobin switch pushes each arriving packet to one of the outputs; the next
packet will be pushed to the following output in round-robin order. They
have one input and two or more outputs.
Scheduling elements. They choose packets from one of several possible packet
sources. A Click packet scheduler is naturally implemented as an element
with two or more inputs and one output. For instance, this element could
react to requests for packets by choosing one of its inputs in turn until one
produces a packet, pulling a packet from it, and returning that packet. When
the next request is produced, it starts from the input after the one that last
produced a packet. This amounts to a round-robin scheduler.
3.2
The Specification Language Rose: Basic Elements
Designing a new programming language implies a considerable amount of work:
the definition of its syntax and semantics, the implementation of interpreters and
compilers, the development of a number of useful tools for analysis, debugging,
optimization, program manipulation, etc. An alternative approach is to define
an embedded language, i.e., to develop libraries in some existing language—the
host language—which allow us to define programs in the new language as objects
in the host language. In this way, we can reuse the syntax, language features and
tools of the host language.
In the following, we present the language Rose for the specification of Click
routers. Since we do not want to define yet another specification language, we
build Rose as an embedding in the multi-paradigm language Curry so that we
can reuse the features and tools of a powerful declarative language. We use
Curry because it has many useful properties for specification: the embedding is
easy,3 there are many features which are useful to describe routers (e.g., laziness,
guarded rules, and higher-order combinators), and it allows the use of logical
3
Indeed, Curry has already been used to embed other languages, e.g., a language for
distributed programming [7].
features (like logical variables, non-determinism and search), which can be useful
for simulation and testing (see below).
Let us summarize the main advantages of our approach and, in particular,
of embedding Rose in the multi-paradigm language Curry:
Data structures and recursion. We use Curry lists to describe elements that have
multiple inputs. Often such elements can be defined for any size, a property
that is called genericity in hardware description languages like VHDL. A
common way of defining and manipulating such elements is to use recursion.
Polymorphism. Some elements can accept as parameters different types in such
a way that they can be reused in many parts of the router with different
input data.
Higher-Order Functions. Higher-order facilities are essential in order to build a
router configuration by connecting or composing existing elements. The composition operators that will be described in Section 3.3 make extensive use
of higher-order functions.
Laziness. Curry follows a lazy evaluation model, which means that functions are
evaluated on demand. This is particularly useful to deal with infinite data
structures (like packet streams). For instance, we can define a router as a
function which generates an infinite stream of packets; however, if the user
only demands the visualization of the first 10 packets, the remaining packets
are not actually built.
Type System. Curry includes a standard type inference algorithm during compilation. Type errors can be very useful to detect errors in a router configuration, e.g., to detect that two incompatible elements have been erroneously
connected.
Logic Features. Current proposals, particularly Lava [3] and Hawk [12], are based
on pure functional languages (i.e., Haskell). In contrast, Curry provides logical features like non-deterministic functions, logical variables, built-in search,
etc. Although these features have not been exploited yet, they will be useful
to perform simulations with incomplete information (where the holes are
represented by logical variables), to define some kinds of analysis, etc. This
is subject of ongoing work and justifies our choice of Curry to embed the
specification language Rose.
Click elements are packet processors. Therefore, each element in the router configuration can be abstracted by a function which takes a number of packet
streams and returns a number of packet streams. In particular, each input port
receives a packet stream and each output port emits a packet stream. Packets
and streams are specified by means of the following types:
type Packet = [Int]
type Stream = [Packet]
A packet is regarded as a (finite) list of bytes, here encoded as integers, and
streams are (potentially infinite) lists of packets. Typically, a Click element has
the following type:
element :: [Conf] -> [Stream] -> [Stream]
i.e., it takes some configuration parameters (if any), a list of input streams
(which can be empty if the element is a packet source), and returns a list of
output streams (which can be empty if the element is a packet sink). Configuration parameters contain additional information to define the particular element
behaviour.
Now we show examples of the five kinds of elements we distinguished in the
previous section.
Packet sources. These elements are encoded as functions with no input streams
and only one output stream. For instance, the Click element FromDevice(eth)
is a packet source, where eth is a network device. It is specified in Rose by
fromDevice :: [Conf] -> [Stream] -> [Stream]
fromDevice [eth] [] = infiniteSource [eth] []
where the auxiliary function infiniteSource is similar to fromDevice but simulates the stream of packets coming from a given network address. Clearly,
there is no difference in Rose between the Click elements fromDevice and
infiniteSource, since we do not implement actual connections to the network.
Packet sinks. These elements are encoded as functions that return the input
streams with no modification (in contrast to Click packet sinks, which have no
output streams). The reason for this behavior is to allow the user to observe
the output of the router, which can be useful during the specification phase to
test the router behavior. For instance, the Click element ToDevice(eth) sends a
stream of packets to some network device. In Rose, we specify this element by4
toDevice [eth] [ps] = [aux ps]
where aux []
= []
aux (p:ps) = p : aux ps
Here, we discard the network device in the local function aux since we are not
interested in the network devices to which packets are sent. If more detailed
information would be needed, we could easily modify the above function in order
to return pairs (ethernet device, packet).
Packet modifiers. In contrast to Click, we consider packet modifiers with
one input stream and one output stream (i.e., we do not consider erroneous
packets). As an example of a packet modifier, we show the specification of the
Click element Strip(n), which deletes the first n bytes from each packet (e.g.,
to get rid of the Ethernet header). In Rose, it is encoded as follows:
strip [n] [ps] = [st n ps]
where st m []
= []
st m (q:qs) = drop m q : st m qs
where drop is a predefined Curry function—it is part of the Curry prelude—
which returns a suffix of a given list without the first n elements.
4
In the following, we do not show the type of elements since it always has the form
“[Conf] -> [Stream] -> [Stream]”.
Routing elements. These elements have only one input stream and two or
more output streams. As an example, in the following we consider the Click
element Classifier(pat1 ,...,patn ) which classifies packets according to their
contents. To be more precise, it takes a sequence of patterns pat1 ,. . . ,patn which
are pairs offset/value, compares each incoming packet data against the set of
patterns, and sends the packet to an output port corresponding to the first
pattern that matched. For instance, the Click declaration
Classifier(12/0806 20/0001,
12/0800,
-);
creates an element with three outputs intended to process Ethernet packets:
ARP requests (offset 12 has the hexadecimal value 0806 and offset 20 has the
hexadecimal value 0001) are sent to the first output, IP packets (offset 12 has
the hexadecimal value 0800) are sent to the second output and all other packets
(denoted by the special case “-”) are sent to the third output.
In Rose, we denote patterns by a list of expressions “Pat cons”, where cons
is a list with an odd number of integers and such that each pair of integers n, m
denotes the following condition: byte n of the packet must have value m. The
last integer denotes the output stream (starting from zero). Also, the special
case “-” (which matches every packet) is represented by a pattern with only
one element, the output stream. In this way, the above configuration string,
“12/0806 20/0001, 12/0800, -”, is specified in Rose as follows:
[Pat [12,8,13,6,20,0,21,1,0], Pat [12,8,13,0,1], Pat [2]]
Here, we denote each Click pair offset/value by several pairs byte,value; for
instance, the Click pattern 12/0800 is represented by the sequence 12, 8, 13, 0.
Now, the Rose specification of the element classifier can be given as follows:
classifier pats [p:ps] = add n p qs
where n = class pats p
qs = classifier pats [ps]
class (Pat pat : pats) p = let n = class pat p
in if n == (-1) then class pats p
else n
class [n] p = n
class (pos:val:es) p = if p!!pos == val then class es p
else -1
add n p qs = if n==0 then (p : qs!!0) : tail qs
else (qs!!0) : add (n-1) p (tail qs)
In general, a call of the form classifier pats (p:ps) returns a list of streams
[qs1 , ...,p:qsn ,...,qsk ], where [qs1 , ...,qsn ,...,qsk ] is the list returned
by classifier pats ps. Function classifier proceeds by first determining
the output stream n of the first input packet p—using the function class—and
then adding—using the function add—packet p on top of the n stream of the
result of applying classifier recursively to the remaining input packets ps.
Given a call of the form “ps!!n”, the predefined function !! returns the nth
element of the list ps, while a call of the form “tail ps” returns the tail of ps.
Scheduling elements. These elements have one output stream and two or
more input streams. They choose a packet from an input stream—according
to some scheduling policy—and send it to the output stream. Here, we assume
that there are always available packets in each input stream. For instance, the
following Rose function implements a trivial round-robin strategy:
roundRobin [] ss = [rr ss]
where rr []
= []
rr (s:ss) = if s==[] then rr ss
else (s!!0) : rr (ss++[tail s])
Function roundRobin takes a list of input streams and no configuration parameters. It returns the packet on top of the first input stream, moves the remaining
packets of this stream to the last position, and calls roundRobin recursively.
3.3
Composition Operators
Rose provides the user with a Curry library containing the specification of the
main Click elements. However, this is not enough to specify a router configuration. The programmer also needs simple ways to connect single elements in
order to build larger components. For this purpose, we also provide typical composition operators, which are defined by using the higher-order facilities of the
language Curry.
The simplest composition operator is used to combine a number of elements
in such a way that the output of one element is the input of the next one. This
operator is defined as follows:
seq :: [[Stream] -> [Stream]] -> [Stream] -> [Stream]
seq []
= id
seq (elem : es) = \input -> seq es (elem input)
where id is the identity function. Function seq takes a list of elements and
returns a new element whose input in the input of the first element in the list
and whose output is the output of the last element in the list. For instance, the
following function represents the router shown in Sect. 3.1:
simpleRouter = seq [fromDevice [Eth 0], Counter [], Discard []]
Another useful composition operator is mult, which is used to connect a routing
element (with multiple output streams) to several packet modifiers. The specification of mult is as follows:
mult :: ([Stream] -> [Stream]) -> [[Stream] -> [Stream]]
-> [Stream] -> [Stream]
mult elem es = \input -> mult es (elem input)
mult :: [[Stream] -> [Stream]] -> [Stream] -> [Stream]
mult es ss = concat (m es ss)
where m [] []
= []
m (e:es) (s:ss) = (e [s]) : m es ss
where concat is a predefined Curry function to concatenate a list of lists. Function mult takes an element with n output streams and a list of elements with
one input stream and connects them. It produces a new element whose input is
the input of the single element and whose output streams are the output streams
of the list of elements. For instance, the following function
classST = mult (classifier [Pat [12,8,13,6,20,0,21,1,0],
Pat [12,8,13,0,1],
Pat [2]])
[strip [I 14], checkIPHeader [], toDevice [Eth 0]]
creates a new component that takes an input stream and sends ARP requests
to element strip (which deletes the first 14 bytes from each packet), IP packets
to element checkIPHeader (which checks that the packet length is reasonable
and that the IP source address is a legal unicast address), and all other packets
to the packet sink toDevice [Eth 0].
There are more composition operators in Rose (e.g., to compose several
packet modifiers with a scheduling element) that are not shown here.
3.4
Implementation
We have implemented a Curry library to design router specifications in Rose.
This library contains
– a significant subset of the Click router elements,
– the basic composition operators, and
– some useful functions to test a router configuration.
Test functions have the following form:
test router n port = take n (router!!port)
In this way, one can obtain the first n packets sent to the output stream port by
the router specification router, thus avoiding an infinite loop if the input stream
is infinite. Predefined function take returns the n first elements of a given list.
Additionally, the library contains a number of auxiliary functions, like common
packet positions:
colAnnEth = 38
--color annotation in Ethernet packets
colAnnIP = colAnnEth - 14 --color annotation in IP packets
ttlIP
= 8
--TTL field position in IP packets
...
or useful functions to manipulate packet data, like the application of a function
to a given packet position. Moreover, in order to show the practicality of the
ideas presented so far, we have specified a typical IP router (from [10]) in Rose.
Preliminary experiments are encouraging and point out the usefulness of our
approach. More information is available at the following URL:
http://www.dsic.upv.es/~jsilva/routers/
4
Related Work
To the best of our knowledge, there is no previous approach for the specification of router configurations based on a well-established declarative language.
We find, however, similar approaches for the design and verification of hardware components based on a language embedded in the lazy functional language
Haskell [3, 12]. Clearly, our approach is inspired by these works in that we also
define an embedded language rather than a completely new language. We think
that this approach greatly simplifies the development of new domain-specific
languages. There are, however, some important differences:
– The base language is different. While [3, 12] embed their specification language in the lazy functional language Haskell, we embed Rose in the multiparadigm language Curry, which extends Haskell with logical features and
concurrent constraints. We think that these additional facilities can be useful
for future developments: simulation, verification, optimization, etc.
– The specified systems are different. While [3, 12] specify hardware circuits,
we deal with router configurations. Although they share some similarities,
the specification of routers has some particularities that are not present in
the specification of hardware circuits.
5
Conclusions
We have introduced the domain-specific language Rose for the description of
router configurations. It is embedded in the declarative multi-paradigm language
Curry, which means that we have available all existing Curry tools for analysis, optimization, program manipulation, etc. For instance, we can use a Curry
partial evaluator [1] to specialize generic router configurations, a fold/unfold
transformation system [2] to manipulate router configurations in a semanticspreserving way, or use the tracing facilities of the PAKCS environment [8] to
debug router specifications. We have shown how the basic Click elements are
specified in Rose and how the composition operators are used to build larger
configurations. In this way, Rose allows one to specify router configurations concisely, modularly and re-usably, while retaining its declarative nature.
There are many interesting topics for future work. On the one hand, we plan
to extend Rose in order to cover all the existing Click elements. Also, it would
be interesting to implement translators from Click into Rose and vice versa.
This will facilitate the interaction with Click so that Rose can be regarded as a
practical tool for the design and verification of Click router specifications. Finally,
we will investigate the definition of specific analyses for Rose specifications, e.g.,
by using well-established abstract interpretation techniques [4, 5].
Acknowledgments
We would like to thank Eddie Kohler for useful comments and suggestions.
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