Full Proposal Document - School of Computer Science

Carnegie Mellon University
Computer Science Department
Thesis Proposal
Doctor of Philosophy
Title:
Meld: A Logical Approach to Programming Ensembles
Date of Submission: ????
Submitted by:
Michael Ashley-Rollman
Supervisors:
Professor Seth Goldstein
School of Computer Science, Carnegie Mellon University
Professor Frank Pfenning
School of Computer Science, Carnegie Mellon University
Committee Members:
Professor David Andersen
School of Computer Science, Carnegie Mellon University
Professor Peter Lee
School of Computer Science, Carnegie Mellon University
Professor Radhika Nagpal
School of Engineering and Applied Sciences
& Wyss Institute for Bioinspired Engineering, Harvard University
Contents
1 Introduction
5
2 Meld by Example
7
2.1
Walk Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Routing Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3
Locality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4
Parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5
Fault Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Literature Review
7
16
3.1
Ensemble Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2
Other Concurrent Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Meld v1.0 Semantics: Language and Meaning
20
4.1
Structure of a Meld v1.0 Program
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2
Meaning of a Meld v1.0 Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5 Distributed Implementation of Meld v1.0 programs
25
5.1
Basic Distribution/Implementation Approach . . . . . . . . . . . . . . . . . . . . . . 25
5.2
Triggered Derivations
5.3
Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.4
Concerning Deletion and Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.5
X-Y Stratification
5.6
Implementation Targets of Meld v1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.6.1
DPRSim/DPRSim2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.6.2
Blinky Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2
5.6.3
Multi-core Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Analysis of Meld v1.0
33
6.1
Fault Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.2
Provability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.3
Messaging Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.4
Memory Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7 Shortcomings of Meld v1.0
38
8 Proposed New Research for Meld v2.0
40
9 Timeline
42
9.1
Already Done . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
9.2
Summer 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
9.3
Fall 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
9.4
Spring 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
10 Summary
43
3
Abstract
Concurrent systems are notoriously difficult to program. They suffer from such problems as race
conditions, deadlocks, and livelocks in addition to all the bugs encountered in sequential programs.
Better methods are necessary to write correct programs for concurrent systems. In this thesis I
will focus on a class of concurrent systems call ‘ensembles’. An ensemble is a massively distributed
system in which the topology varies over time. Modular robotic systems and sensor networks are
examples of ensembles.
I posit that the logic programming paradigm is a good match for programming ensembles. A
logic program is an inherently parallel representation. Each rule of a logic program expresses a
single unit of computation. Rules can be evaluated in any order that preserves the dependencies
between them. This implicit parallelism allows the programmer to focus on the program while the
compiler and run-time distribute it across an ensemble.
Thesis Statement: Logic programming is well-suited for ensemble programming. It permits
us to express algorithms in a way that can be executed efficiently and reasoned about easily.
In support of this thesis, I have designed and implemented Meld v1.0 [1], an expressive logic
programming language for concurrent systems. Meld programs are distributed across an ensemble
by the compiler and run-time, making use of the implicit parallelism in the logic programming
representation. Meld programs are concise and amenable to proof, as demonstrated in the proofs
of correctness of Dewey et al.’s meta-module planner [2], which showed the planner to be free of
race conditions, deadlocks, and livelocks. Meld v1.0 programs already run on multi-million-robot
simulations of Claytronics [3], Blinky Blocks [4], and multi-core machines.
In this thesis, I propose Meld v2.0 for programming ensembles. I will extend Meld v1.0 to be
more expressive (details in proposal document). I will explore the logical foundations of Meld,
providing a clear definition of Meld v2.0’s semantics and an understanding of Meld’s basis in logic.
I will prove correctness properties of other Meld programs. And I will analyze the fault tolerance
of Meld programs.
4
1
Introduction
Tremendous advances have been made in networks and distributed hardware. Personal computers
are no longer isolated devices, but now maintain a constant connection to other devices via local
area networks and the Internet. Other devices like cellular phones, televisions, and game consoles
are increasingly joining PCs on networks. Applications are being hosted in the cloud, permitting
people access to their documents from any computer. Cars and airplanes contain many computers
connected via an internal network. Sensor networks are being researched to gather and aggregate
data. Robots are being developed in a modular fashion to allow them to be reconfigured for different
applications and purposes. Taken to the extreme, they may form programmable matter [3], a
material that can be programmed to change it’s shape and color. Distributed systems, in various
forms, are becoming increasingly prevalent. Furthermore, multi-core systems, previously confined
to expensive machines for hosting servers and performing scientific computing are now common
place.
While concurrent systems have multiplied, our programming models for them have failed to keep
pace. Most programs are still written with the threading model for expressing parallel computation.
This model is fraught with peril as a programmer must be wary of such concurrency bugs as race
conditions, deadlock, and livelock. These concurrency bugs occur erratically depending upon the
particular order in which concurrent code happens to execute, making them notoriously difficult to
catch and eliminate. Any programming model that can alleviate or eliminate these sorts of errors
greatly simplifies the problem of programming distributed systems. Indeed, a variety of approaches
have been presented for some classes of problems, especially those of data-parallel algorithms. Some
of these models are discussed in §3.
One of the biggest problems with the threading model is that it requires explicit parallel constructs in an artificially sequentialized version of an algorithm. Typical imperative and functional
programming languages require that a set of instructions be given along with a precise ordering
for those instructions to execute. The threading model, along with many other proposed models,
provides a mechanism for teasing apart this sequential code into a set of independent sequential
blocks to be executed simultaneously. This works well only when the blocks are really independent,
such as for data-parallel algorithms. For other algorithms, when the data dependencies follow more
5
arbitrary graph structures, this approach deteriorates.
The logic programming paradigm, however, allows a programmer to easily specify parallelism in
the form of an arbitrary graph of data dependencies. Logic programs are specified as rules which
are small pieces of computation that can be run in arbitrary order so long as the implicit data
dependencies are satisfied. This mechanism is discussed in greater detail in §2, but the high level
point is that logic programs naturally express the parallelism present in a program and are adept
at handling arbitrary dependency graphs. They are not limited to largely independent threads of
control. Furthermore, the logic program representation is one that has been greatly studied and
can be reasoned about via the rules of logic. This allows us to show that particular individual logic
programs are correct, free of any of the concurrency bugs we discussed before.
The question, then, is if logic programs are the right representation to express parallel algorithms
and show that they are correct, can we efficiently make use of their parallelism? The answer to this
question turns out to be ’yes’, for a class of distributed systems called ’ensembles’. An ensemble
is a distributed system in which the network topology can change dynamically and the nodes are
relevant to the computation. Examples include sensor networks, modular robotic systems, and
Claytronics [3] (a particular modular robotic system containing millions of robots).
Thesis Statement: Logic programming is well-suited for ensemble programming. It permits
us to express algorithms in a way that can be run efficiently and reasoned about easily.
In the remainder of this document I discuss a logic programming language, Meld v2.0, which is
designed for this purpose. I provide examples of what logic programs for ensembles look like in §2.
In §4 I define the existing Meld v1.0 language and then explain how to implement it on an ensemble
in §5. Next I evaluate Meld v1.0, in §6, discussing both its successes and its shortcomings. In §8, I
propose a plan for addressing these shortcomings in Meld v2.0.
A point of clarification for the reader: there are two versions of Meld discussed throughout this
proposal. The term “Meld v1.0” is used in reference to the current published implementation of
Meld while “Meld v2.0” is used for the new version proposed here. “Meld” is reserved for statements
that apply equally to either version and do not need to be disambiguated.
6
Rule1:
dist(S,DS ):-
Rule3:
moveAround(S,T,P):-
at(S,P),
farther(S,T),
destination(Pd ),
vacant(T,P),
DS = |P - Pd |,
dist(S,DS ),
DS > module radius.
destination(Pd ),
DS > |P - Pd |.
Rule2:
farther(S,T):neighbor(S,T),
dist(S,DS ),
dist(T,DT ),
DS ≥ DT .
Figure 1: A first cut of the walk program.
2
Meld by Example
“Logic programming” is a broad term that can be used to describe any use of mathematical logic for
programming computers. There is a plethora of different logics that one might use, varying on such
components as what structural rules are permitted and rejected, what modalities are included,
etc. In logic programming this is further complicated by the potential addition of super-logical
operations (such as aggregation) and implementation details. Here I clarify what is meant by
“logic programming” in this context by first walking through a few examples. The full details and
semantics of the Meld v1.0 logic are discussed in §4.
2.1
Walk Example
The first example is Walk. Walk is a program for moving an ensemble of modular robots, such as
those envisioned by the Claytronics [3] project. The Claytronics model assumes that each module
is a sphere which is capable of rolling over or around an adjacent module. In this model, each
module is able to communicate directly with exactly those other modules it is in physical contact
with (modulo hardware failures).
A Meld program consists of a set of rules for generating new facts from an existing set of true
7
Initial facts:
Actions derived by Rule3
destination(<0,5>)
moveAround(s, t, <0,2>)
at(s, <0,0>)
moveAround(s, t, <1,1>)
at(t, <0,1>)
...
New initial facts after moveAround(s,t,<0,2>)
neighbor(s,t)
neighbor(t,s)
destination(<0,5>)
vacant(t, <0,2>)
at(s, <0,2>)
vacant(t, <1,1>)
at(t, <0,1>)
...
neighbor(s,t)
Facts derived by Rule1
neighbor(t,s)
dist(s, 5)
vacant(t, <1,1>)
dist(t, 4)
vacant(s, <0,3>)
Facts derived by Rule2
...
farther(s, t)
Figure 2: Initial facts and those derived as the first cut of Walk is run.
8
Rule1:
dist(S,DS ):-
Rule4:
vacantDist(S,P,D) :-
at(S,P),
vacant(S,P),
destination(Pd ),
destination(Pd ),
DS = |P - Pd |,
D = |P - Pd |.
DS > module radius.
Rule2:
Decl1:
type bestVacantDist(module, min <float>).
Rule5:
bestVacantDist(S,D) :-
farther(S,T):neighbor(S,T),
dist(S,DS ),
vacant(S,P,D).
dist(T,DT ),
DS ≥ DT .
Rule6:
bestVacant(S,P) :vacantDist(S,P,D),
Rule3:
moveAround(S,T,P):-
bestVacantDist(S,D).
farther(S,T),
bestVacant(T,P).
Figure 3: A second cut of the walk program.
facts. The set of facts is initially seeded based upon sensor data and program inputs. An example
set of initial facts for a two module ensemble is shown in Figure 2. In the Claytronics model,
neighbor(s,t) is defined to be true when the modules s and t are in physical contact and able
to communicate. Similarly, at(s,<0,0>) is defined to be true when the module s is at the point
<0,0> in space. Finally, vacant(t, <0,2>) indicates that the point <0,2> adjacent to module t
is available for another module to enter. A first cut of the Walk program, shown in Figure 1, uses
these facts along with an input destination(<0,5>) to derive instructions for a module to move
closer to the target point <0,5>. The program is then reset and run again to take an additional
step. This process repeats until the modules reach the destination.
There are two common approaches for executing logic programs. The first approach, top-down
execution, consists of a query for a particular fact and a proof search is carried out to look for
a derivation of that fact using the supplied rules and set of initial facts. This approach, used by
Prolog [5], is not a good match for ensemble programming because of the requirement for a specific
query. Instead we employ bottom-up execution, as used in Datalog [6], which takes the initial set of
9
Rule1:
dist(S,DS ):-
Rule4:
vacantDist(S,P,D) :-
at(S,P),
vacant(S, P),
destination(Pd ),
destination(Pd ),
DS = |P - Pd |,
D = |P - Pd |.
DS > module radius.
Rule2:
Decl1:
type bestVacantDist(module, min <float>).
Rule5:
bestVacantDist(S,D) :-
farther(S,T):neighbor(S,T),
dist(S,DS ),
vacant(S,P,D).
dist(T,DT ),
DS ≥ DT .
Rule6:
bestVacant(S,P) :vacantDist(S,P,D),
Rule3:
moveAround(S,T,P):-
bestVacantDist(S,D).
forall neighbor(S,U) [farther(S,U)],
neighbor(S,T).
bestVacant(T,P).
Figure 4: Final cut of the walk program.
facts and continuously derives whatever new facts can be derived using the rules until all derivable
facts have been found.
The Walk program works by determining the distance of each module from the destination,
determining which module is farther from the destination, and then instructing the farthest module
to move closer. These tasks are accomplished by Rule1, Rule2, and Rule3, respectively. Rule1
depends upon the at fact and the destination input to calculate the distance (dist) of a module
from the destination. dist is a new derived fact, created by the programmer to represent internal
program state, in this case the distance to the destination. The rule is written with variables so
it can match on any particular at and destination facts and produce a corresponding dist fact.
This produces dist(s,5) from destination(<0,5>) and at(s,<0,0>) and produces dist(t,4)
from destination(<0,5>) and at(t,<0,1>). These are the only pairs of facts that match the
rule, so these are all the facts that can be derived from this rule. These derived facts are shown in
Figure 2.
10
The second rule (Rule2) uses the dist facts derived by the Rule1 to determine which of two
adjacent modules is farther away from the destination. The usage of the neighbor fact restricts this
comparison to adjacent modules, so we will only be able to determine whether a module is farthest
amongst its immediate neighbors, not globally. Notice that when we start with neighbor(s,t) we
are able to derive farther(s,t) since the module s is farther from the destination than module
t, but would do nothing if module t were farther from the destination than module s. The reader
might think another rule is required to cover the second case where module t is farther. This,
however, is unnecessary. Observe that the neighbor fact is symmetric. That is, if neighbor(s,t)
is true then so is neighbor(t,s), just as in the initial facts in Figure 2. Rule2 covers both cases
for us as it can match whichever module happens to be farther away.
The third rule (Rule3) uses the farther fact derived by Rule2 along with the vacant fact
to determine which module should move and where it should move to. It uses the destination
input fact and the dist fact to make sure the location given by the vacant fact is closer to the
destination. This rule does not derive a new fact like the previous rules, but derives an action
instead. An action is a special predicate recognized by the system that causes something to occur.
In this case, the moveAround(s,t,<0,2>) action causes module s to move to the location <0,2>
by rotating around module t. Once this occurs, the program resets and is run again with a new
set of initial facts to determine the next step it needs to take. This process continues until the
modules reach the destination. If multiple actions are derivable, such as moveAround(s,t,<0,2>)
and moveAround(s,t,<1,1>) then one is arbitrarily chosen to be performed.
The first cut of the Walk program, as presented in Figure 1, illustrates the basic workings of the
Meld logic, but has two shortcomings that require us to refine the program using more advanced
features of the language. The first of these is that the program moves the farther away module to
some closer location adjacent to a closer module. This can be improved upon by selected the closest
location adjacent to the closer module. This is done in our second cut of the Walk program. The
second short-coming is that the group of modules may become disconnected if some middle module
moves closer. Disconnection is undesirable in the Claytronics model because the modules can only
communicate with directly connected neighbors, so a break in connectivity breaks the ensemble of
modules into two new independent ensembles. This problem will be addressed in the final version
of the Walk program.
11
The second cut of the Walk program (shown in Figure 3) makes use of the min aggregate to
select the closest vacancy to move into. An aggregate is a function that takes a list of values and
computes a single scalar from the list. In Meld we take the set of derivable facts that match on
all fields other than the one being aggregated over and then compute the aggregate of all values
derived for the aggregated field. To do this accurately Meld must derive all the facts that will be
aggregated together before calculating and using the aggregate value. Meld stages the firing of
the rules using stratification, discussed in §5.5. In this new version of the program, Rule1 and
Rule2 remain the same as in Figure 1, but Rule3 is updated to use a new bestVacant predicate
to choose a vacancy. To find the best vacancy, we calculate the distance of each vacancy to the
destination and select the one with the minimum distance.
Rule4 computes the distance of each vacancy from the destination just as Rule1 computed
the distance of each module from the destination. Rule5 makes use of an aggregate to select
the minimum distance from all of those introduced as vacantDist facts by Rule4. Observe
the typing declaration for bestVacantDist in Decl1. It declares that instead of producing all
possible bestVacantDist facts, we instead want only the one with the smallest second field for
each module. That is to say, we want only the bestVacantDist with the smallest distance for each
module. Rule6 then uses the bestVacantDist fact to pick out the actual vacant point that has
that distance which is closest to the destination. Meld supports a wide variety of aggregates, some
of which pick out a particular optimal value such as the minimum value or the maximum value and
others which combine the values such as a summation or an average. These are discussed further
in §4.
The second short-coming of the Walk program is addressed by adding additional constraints to
prevent a module from being left behind. In particular, a module will not be permitted to move
unless it is farther away from the destination than all neighboring modules.1 The features of the
language demonstrated so far are sufficient to add this constraint, but not in an intuitive manner.
Instead, we will make use of universal quantification. We update Rule3 in Figure 4 to check that
for every module u that is a neighbor of module s, module s is farther away than module u.
1
This is not sufficient to guarantee an ensemble will not become disconnected unless it starts in a ’good’ state. A
’good’ state is one in which the ensemble is tightly connected in a canonball packing. It is sufficient to maintain a
’good’ state once the invariant has been established.
12
Decl1:
type dist(module,module,min<int>).
Rule3:
?msg(U,T,M) :?msg(S,T,M),
Rule1:
dist(S,S,0).
dist(S,T,D),
neighbor(S,U),
Rule2:
dist(S,T,D+1) :-
dist(U,T,D-1).
neighbor(S,U),
dist(U,T,D).
Figure 5: A distance vector routing program.
2.2
Routing Example
The next example, shown in Figure 5, is an algorithm for sending messages between arbitrary nodes
in any type of connected ensemble. All we assume here is that a neighbor(s,t) fact exists for every
pair of connected modules s and t. These could be modular robots, sensor nodes, computers on a
network, etc. This program implements a distance vector routing protocol via the dist predicate.
A dist(s,t,d) fact means that module s is distance d from module t. This is seeded by Rule1
which sets the distance between any module and itself to 0. This rule has no preconditions and
contains an unbound variable, something disallowed in Datalog as it seemingly spawns an infinite
number of initial facts. The S here ranges over only the finite set modules in the ensemble and is
implicitly bound as discussed in §2.3, allowing us to support this rule. Rule2 then builds up the
distances via routing through all possible neighbors and uses the minimum aggregate to select the
shortest route.
Once the routes are populated, Rule3 can be used to forward messages between nodes. Rule3
the linear facts from Linear Logic [7] to represent messages. Linear facts, denoted with a question
mark in Meld v2.0, have the property that they can only be used once. Their usage here implies
that a message is to be deleted after it has been forwarded along to the next node on the route.
Without the use of linearity, these facts would accumulate at each node along the route.
13
2.3
Locality
A particularly astute reader may have observed that the first field of every fact is a module. In
the distributed setting, the facts are spread throughout the ensemble with each fact located at the
module referenced in the first field. An investigation of our examples shows that this is exactly
where we would expect these facts to be located. Initial facts like at(s,p) and neighbor(s,t) are
observed by s and stored at s. Derived facts like ?msg(s,t,d) are stored at s, fitting with the model
that s currently has a message that is destined for t. Derived actions like moveAround(s,t,p) are
located at s, the module which needs to perform the action.
A consequence of this method of localizing the facts is that a rule like Rule1 from the routing
example can be implemented. Each module in the ensemble can add an instance of the fact
dist(S,S,0) to its local database with its own identity substituted for S. Thus, S is implicitly
bound in this rule to the identities of each of the modules in the ensemble. Note that the rule
dist(S,T,0). is not supported as T remains ungrounded.
2.4
Parallelism
The logic programming paradigm provides a natural way to express the parallelism present in an
algorithm. Recall the final Walk program (shown in Figure 4). The program does not specify
any particular serial ordering in which the rules must be executed. The only ordering information
provided are the dependencies between the rules. Rule1 and Rule4 can be run in any order or
even simultaneously for a single module. They can be run in different orders for different modules.
Rule1 and Rule4 can be run simultaneously for different modules. Since there is no dependency
between them, the order in which they are run is irrelevant. On the other hand, Rule3 can only
be run for a particular module after Rule2 has been run for all adjacent neighbors and Rule6 has
been run for some adjacent neighbor.
Many methods of expressing algorithms require that the programmer produce a serialization of
the algorithm or use explicit parallel constructs to express some subset of the available parallelism.
The logic programming paradigm permits the programmer to implicitly specify the parallelism
inherent in the algorithm and provides the compiler/runtime with the opportunity to take advantage
of that parallelism without needing to reconstruct it from some arbitrary serialization. As a result,
14
it is trivial to extract parallelism from a logic program and distribute it across an ensemble. The
tricky part comes in finding the right way to assign computation to processors such that the
performance of the system is good and the program state is distributed.
Various techniques can be used to group and assign computation to the various processors, three
of which are discussed here:
1. A work list can be maintained, letting each processor pull work off the queue.
2. Rules can be partitioned, giving each processor the responsibility of performing some of the
rules. Data is distributed accordingly.
3. Data can be partitioned, making each processor responsibly for some of the data. Rules are
distributed accordingly.
The first approach of maintaining a common work queue between the different processors might
seem promissing at first, but the size of a single computation is so tiny that a means of combining the
computations would be required in order to make the resulting system efficient. Furthermore, each
processor would seem to require arbitrary pieces of memory, requiring a shared memory machine.
This is an impractical requirement for ensembles.
The other two approachs are two different ways of looking at the same idea - namely partitioning
the database and the computation on the database into sets and making each processor responsible
for a given set. Approach (2) is a computation-centric view on this idea while approach (3) is
data-centric. In either case the idea could work well, provided a good partitioning is used. But how
can we find a good partitioning? In an ensemble there is a natural partitioning and assignment
of the data and rules to the processors! The input data is already distributed to the different
nodes in the system and derived data is associated with the existing nodes. Thus the database can
be partitioned such that the data about a node is stored on that node. The partitioning of the
rules follows such that each processor is running instances of all of the rules with some variables
preassigned to the name of the processor they are running on.
In this way, a program’s state and execution are distributed across the nodes that make up the
ensemble. Each node in the ensemble runs its local rules and implicitly communicates with other
nodes in the ensemble when rules transcend multiple modules. These rules can be automatically
15
split into multiple pieces with explicit communication between them. Thus the programmer is not
required to write any explicit communication as it is implied by the distribution method. This
approach specifies a means to run a logic program on an ensemble.
2.5
Fault Tolerance
The way in which logic programs are expressed provides enough information to allow a limited kind
of fault tolerance. In the case of the routing example, for instance, if a module in the system or a
link between modules should fail the dist facts can be discarded and recomputed to create a new
set of dist facts that are representative of the new ensemble without the failed module or link.
This approach can be improved upon to remove only the affected dist facts from the database
while leaving all other routes intact. This is discussed further in §5.3.
3
Literature Review
A plethora of programming languages have been developed over the years, exploring various methods of expressing and executing programs and applying these ideas to different domains. Here I
discuss languages targeted to towards ensembles as well as those targeted towards more general
distributed systems. Afterwards, I discuss much of the work on logic programming which is the
base upon which Meld is built.
3.1
Ensemble Languages
One of the most interesting abstractions explored for ensemble programming language is that
of folding paper as demonstrated in Origami Shape Language [8] (OSL). OSL is designed for
programming an ensemble of smart paper to fold itself into some particular shape. The neat part
about OSL is that a program is writen to think about lines, creases, and points and not about the
modules that make up the physical system. In this way it truly provides an abstraction where one
writes a program for a piece of paper and the cells that make up that piece of paper implement
it. The programmer need never think about the actual cells or even be aware that they exist. The
success of this approach is inspiring, but, unfortunately, it’s not clear how it could be adapted for
16
general ensembles.
Regiment [9] is another high level programming language, targeted towards ensembles of sensor
networks. Regiment is geared for the common sensor network task of aggregating data across an
ensemble to a particular destination. The language allows one to create groups (such as k-nearest
neighbors) and talk about aggregate data over such a group. The data can also be easily forwarded
to some control system that is connected to the sensor network. The abstraction used provides
no mechanism to talk about individual modules or particular locations. This approach works very
well for aggregating data, but leaves no clear means to add features such as locomation for modular
robots, keeping it in the domain of sensor networks and not general ensembles.
Hood [10] is similarly based upon the idea that programs are written around neighborhoods,
with each module communicating via broadcast to all nearby modules. As a nesC library it is lower
level than Regiment, but targets providing a similar type of abstraction. Hood presents a simple
approach to simplifying programs by allowing a node to advertise a value to its neighbors and
permitting the neighbors to filter incoming values and cache them as desired. They show that this
simplifies the implementation of a variety of sensor network programs and appears to be a valuable
contribution on top of nesC. While Hood is successful in reducing the amount of code required
to implement many sensor network algorithms, it adds no benefit on top of traditional message
passing when individual communication is required and it does nothing to facilitate distributing
the program across many nodes.
Proto [11] is another high level language following the functional programming paradigm. It
permits one to write programs for sensor networks or similar systems. Proto abstracts away the
exact system and lets nodes interact with other nodes only via a foldl like command. This
abstraction could likely be abused to provide direct neighbor communication, but doing so would
be expensive on some systems as each message sent would go to all neighbors, only to be ignored
by most of them. The same functional program is executed at each node in the system and while
the authors make a big deal about 3 levels of abstraction, the ’Amorphous Medium’, and the idea
that one should be able to talk about a chunk of the system, they get no closer to this goal than
other languages. Finally, they treat all data as time-sychronized streams and require some external
entity to maintain a clock. It’s not clear how one would adapt this to a modular robotic system like
Claytronics, particular given the requirement for a time oracle. The stream approach to variable
17
values is would likely result in limitations on state, similar to those of DataLog like languages.
Protoswarm [12] is an attempt to adapt Proto to devices that actuate, but it is not particularly
useful for systems like Claytronics. There are serious problems in using the language for this
purpose which are not addressed by Protoswarm. In particular, the lack of direct communication
makes it extremely challenging (impossible?) to produce a spanning tree, implement any known
method for maintaining connectivity, or implement any known method for localization.
Pleiades [13], another low-level language, is an imperative programming language based on C
with the addition of a concurrent for loop that iterates over various nodes and lets each node
perform the body of the loop in parallel. It is much like an OpenMP [14] implementation, but
distributed over a sensor network and with only a particular node able to run each iteration of the
loop. It additionally provides extra consistency guarantees that the result of execution is equivalent
to some serial ordering of the loop. This is a convenient way of writing some programs (particularly
for wireless networks) as one can easily do tasks like computing aggregates over the values at the
different nodes. Attempting to write a shape change algorithm for module robots is awkward and
challenging, probably even harder from this perspective of a global sequential system than from
the perspective of individual nodes.
TinyDB [15] provides an SQL-like interface for extracting data from an ensemble, treating it
as a database. It is designed for extracting and aggregating data via resolving SQL queries. The
query is sent out through the ensemble, data is gathered and aggregated to form a response. This
approach presumes an external entity exists to formulate the queries. This is an effective means of
using a sensor network as a sorce of data, but is not applicable to general ensemble programming.
LDP [16] is another high level language for programming ensembles, targeted at modular robots.
LDP expresses programs as a set of predicates which match on the configuration of modules and
the internal state of the system. The predicates can then change the internal state and/or perform
actions such as causing robots to move. This approach produces a similar expression of programs
to that of first order logic, with the exception that program state can be mutated resulting in
consistency problems. An attempt is made to address these problems by taking snapshots of state
at modules, but there is no guarantee that these snapshots are consistent beyond a single module,
sometimes producing unexpected behavior. Additionally, LDP requires active polling for matching
18
predicates. This may work well in a rapidly changing ensemble, but can create repetative queries in
a relatively static ensemble. These queries continually failing to match on the same criteria waste
message bandwidth, cpu cycles, and energy. The ideas behind this work are solid, but faithfully
following the logic programming model will allow Meld to resolve these consistency and performance
concerns while allowing similarly concise programs at a similar level of abstraction.
The work on Meld was inspired by the ensemble programming langues P2 [17] and SNLog [18]
for declarative networks and sensor networks, respectively. These works pioneered the idea of using
logic programming for distributed systems. They view the state of the system as a database with
the contents distributed across the nodes of the system. First order logic programs, a la DataLog,
can be used to query the database and generate new facts for it. This allows for programs to be
implicitly distributed across a number of nodes for execution, but suffers from the restrictions on
expressivity inherent in first order logic. These works form a basis for developing more expressiving
logic programming languages for use on ensembles such as the one I propose here.
3.2
Other Concurrent Languages
Looking beyond languages targeted at various ensembles, there are many languages designed around
concurrent programming. Perhaps the most famous among these is the π-Calculus [19] [20], which
expresses parallel programs via a set of concurrent processes. At any time any of these processes may
be evaluated a single step. The processes share channels through which they can send data between
them. The π-Calculus is a generalization of the λ-Calculus to support parallel processes. The πcalculus is primarily intended for describing concurrent computations rather than implemention.
Another well known, but more recent, language is Map-Reduce [21]. Map-Reduce provides a
very simple abstraction for parallelizing programs via defining a task for processing a chunk of
data and a means of aggregating the processed chunks once an entire set has been processed. This
simple mechanism has had a great impact on simplifying the amount of effort required to perform
data-parallel tasks, but its applicability to other tasks is minimal. While it is possible to encode
some graph algorithms in the Map-Reduce paradigm, doing so is awkward and clunky, producing
inefficient results.
Dryad [22] is a generalization of Map-Reduce that allows the programmer to create a DAG of
19
programs for processing the data. It focuses on data processing, but is useful because it allows the
programmer to divide up the work both as chunks of data and as chunks of computation and lets
the system worry about matching this up to the physical resources available. It is more general
than Map-Reduce because it allows arbitrary DAGs of computation. It is intended as a mechanism
for utilizing large clusters to perform computations on fixed datasets. Ultimately, it is still limited
to data-parallel applications.
The Spider Calculus [23] is a functional programming language for creating and reasoning about
graphs. The idea consists of having an initial graph (called a web) with one or more computational
threads. Each thread (called a spider) runs some program (which may not be related to what the
other threads are running) and can both move about and modify the graph. This results in an
interesting method of creating, modifying, and computing on graphs. This approach has interesting
potential, although it is not clear how it relates to ensemble programming and whether it might be
adapted to work with modular robotics or sensor networks,
ML5 [24] is an ML-like language extended with a type system based on modal logic. This allows
ML5’s type system to understand where different computations occur and to produce appropriate
error messages at compile time if a given node in the system doesn’t provide the necessary features.
This allows for a system where different nodes have different capabilities which the programmer can
take advantage of rather than writing separate programs for every type of node in the system. The
examples given are for writing webservers which have a very different set of capabilities than web
browsers. The ideas in ML5 are very interesting, but are orthogonal to what is being considered
here.
4
Meld v1.0 Semantics: Language and Meaning
A running Meld v1.0 program consists of a database of facts and a set of production rules for
operating on and generating new facts. A Meld v1.0 fact is a predicate and a tuple of values;
the predicate denotes a particular relation for which the tuple is an element. Facts represent the
state of the world based on observations and inputs (e.g., sensor readings, connectivity or topology
information, runtime parameters, etc.), or they reflect the internal state of the program. Starting
from an initial set of axioms, new facts are derived and added to the database as the program runs.
20
Known Facts
Γ ::=
·kΓ, f (t̂)
Facts
F ::=
f (x̂)
Accumulated Actions
Ψ ::=
·kΨ, a(t̂)
Constraints
C ::=
c(x̂)
Set of Rules
Σ ::=
·kΣ, R
Expression
E ::=
E ∧ EkF k∀F.EkC
Actions
A ::=
a(x̂)
Rule
R ::=
E ⇒ F kE ⇒ A
kagg(F, g, y) ⇒ F
Figure 6: Abstract syntax for Meld v1.0 programs
In addition to facts, actions are also generated. They are syntactically similar to facts but cause
side effects that change the state of the world rather than the derivations of new facts. In a robotics
application, for example, actions are used to initiate motion or control devices. Meld v1.0 rules can
use a variety of arithmetic, logical, and set-based expressions, as well as aggregation operations.
4.1
Structure of a Meld v1.0 Program
Figure 6 shows the abstract syntax for states, rules, expressions, and constraints in Meld v1.0. A
Meld v1.0 program consists of a set of production rules. A rule may contain variables, the scope
of which is the entire rule. Each rule has a head that specifies a fact to be generated and a body
of prerequisites to be satisfied. If all prerequisites are satisfied, then the new fact is added to the
database. Each prerequisite expression in the body of the rule can either match a fact or specify a
constraint. Matching is achieved by finding a consistent substitution for the rule’s variables such
that one or more facts in the database are matched. A constraint is a boolean expression evaluated
on facts in the database; these can use arithmetic, logical, and set-based subexpressions. Finally,
forall statements iterate over all matching facts in the database and ensure that for each one, a
specified expression is satisfied.
Meld v1.0 rules may also derive actions, rather than facts. Action rules have the same syntax as
rules, but have a different effect. When the body of this rule is proved true, its head is not inserted
into the database. Instead, it causes an action to be carried out in the physical world. The action,
much like a fact, has a predicate and a tuple, which can be assigned values by the expressions in
the rule.
An important concept in Meld v1.0 is the aggregate. The purpose of an aggregate is to define a
21
(a) type logical neighbor parent(module, first module).
(b) type maxTemp(module, max float).
(c) parent(A, A) :- root(A).
(d) parent(A, B) :- neighbor(A, B), parent(B, ).
(e) maxTemp(A, T) :- temperature(A, T).
(f) maxTemp(B, T) :- parent(A, B), maxTemp(A, T).
(g) type globalMax(module, float).
(h) globalMax(A, T) :- maxTemp(A, T), root(A).
(i) globalMax(B, T) :- neighbor(A, B), globalMax(A, T).
(j) type localMax(module).
(k) localMax(A) :- temperature(A, T),
forall neighbor(A, B) temperature(B, T’) T > T’.
Figure 7: A data aggregation example coded in Meld v1.0Ȧ spanning tree is built across the
ensemble and used to aggregate the max temperatures of all nodes to the root. The result is flood
broadcast back to all nodes. Each node also determines whether it is a local maximum.
22
type of predicate that combines the values in a collection of facts. As a simple example, consider
the program shown in Figure 7, for computing the maximum temperature across all the nodes in
an ensemble. The parent rules, (c) and (d), build a spanning tree across the ensemble, and then
the maxTemp rules, (e) and (f), use this tree to compute the maximum temperature. Considering
first the rules for calculating the maximum, rule (e) sets the base case; rule (f) then propagates
the maximum temperature (T) of the subtree rooted at one node (A) to its parent (B). Applied
across the ensemble, this has the effect of producing the maximum temperature at the root of the
tree. To accomplish this, the rule prototype given in (b) specifies that when maxTemp is matched,
the max function should be used to aggregate all values in the second field for those cases where
the first field matches. In the case of the parent rules, the prototype given in (a) indicates the use
of the first aggregate, limiting each node to a single parent. The first aggregate keeps only the
first value encountered in any match on the rest of the tuple. The meaning of logical neighbor
is explained in §5.1.
In general, aggregates may use arbitrary functions to calculate the aggregate value. In the
abstract syntax, this is given as a function g that calculates the value of the aggregate given all
of the individual values. The result of applying g is then substituted for y in F . In practice, as
described by LDL++[25], the programmer implements this as three functions: two to create an
aggregate and one to retrieve the final value. The first two functions consist of one to create an
aggregate from a single value and a second to update the value of an existing aggregate given
another value. The third function, which produces the final value of the aggregate, permits the
aggregate to keep additional state necessary to compute the aggregate. For example, an aggregate
to compute the average would keep around the sum of all values and the number of values seen.
When the final value of the aggregate is requested, the current value of sum is divided by the total
number of values seen to produce the requested average.
4.2
Meaning of a Meld v1.0 Program
The state of an ensemble running a Meld v1.0 program consists of two parts: derived facts and
derived actions. Γ is the set of facts that have been derived in the current world. Γ is a list of facts
that are known to be true. Initially, Γ is populated with observations that modules make about
the world. Ψ, is the set of actions derived in the current world. These are much like the derived
23
facts that make up Γ, except that they are intended to have an effect upon the ensemble rather
than be used to derive further facts.
As a Meld v1.0 program runs, new facts and actions are derived from existing facts which are
then added to Γ and Ψ. Once one or more actions have been derived, they can be applied to bring
about a change in the physical world. When the actions have been applied to the world, all derived
facts are discarded and replaced with a set of new observations about the world. The program then
restarts execution in the new world.
The evaluation rules for Meld v1.0 allow for significant uncertainty with respect to actions and
their effects. This underspecification has two purposes. First, it does not make assumptions about
the type of ensemble nor the kinds of actions which can be triggered by a Meld v1.0 program.
Second, it admits the possibility of noisy sensors and faulty actuators. In the case of modular
robotics, for instance, a derived action may request that a robot move to a particular location.
External constraints, however, may prevent the robot from moving to the desired location. It is,
therefore, important that Γ end up containing the actual position of the robot rather than the
location it desired to reach.
This result is achieved by discarding Γ when an action is applied and starting fresh. By doing
this, we erase all history from the system, removing any dependencies on the intended effect of the
action. This interpretation also accounts for the fact that sensors may fail, be noisy, and even in
the best case that observations of the real world that are known to the ensemble are only a subset
of those that are available in the real world. To account for changes that arise due to external
forces we also allow the program to restart even when Ψ is empty.
This interpretation permits us to give Meld v1.0 programs a well-defined meaning even when
actuators fail, external forces change the ensemble, or sensors are noisy. In turn, this imbues Meld
v1.0 with an inherent form of fault tolerance. The greatest limitation of this approach, however, is
in our ability to reason about programs. By allowing the ensemble to enter a state other than the
one intended by the action, we eliminate the ability to directly reason about what a program does.
To circumvent this, it is necessary to make assumptions about how likely an action is to go awry
and in what ways it’s possible for it to go awry. This is discussed further in §6.2.
24
original rule from the temperature example:
localMax(A) :- temperature(A, T),
forall neighbor(A, B)
[temperature(B, T’),
T > T’].
send rule after splitting:
remote LM(A, B, T’) :- neighbor(B, A),
A
temperature(B, T’).
local rule after splitting:
B1
...
Bn
localMax(A) :- temperature(A, T),
forall neighbor(A, B)
[ remote LM(A, B, T’),
T > T’].
Figure 8: Example of splitting a rule into its local and send parts. On the left, the spanning tree
for home nodes is shown. On the right is a rule from the program in Figure 7 along with the two
rules that result from localizing it.
5
Distributed Implementation of Meld v1.0 programs
In this section we describe how Meld v1.0 programs can be run as forward-chaining logic programs
across an ensemble. We first explain the basic ideas that make this possible. We then describe the
additional techniques of deletion and X-Y stratification that are required to make this feasible and
efficient.
5.1
Basic Distribution/Implementation Approach
Meld v1.0 is an ensemble programming language; efficient and scalable execution requires Meld
v1.0 programs to be distributed across the nodes of the ensemble. To facilitate this, we require
the first variable of a fact, called the home variable, to refer to the node where the fact will be
stored. This convention permits the compiler to distribute the facts in a Meld v1.0 program to the
correct nodes in the ensemble. It also permits the runtime to introduce facts representing the state
of the world at the right nodes, i.e., facts that result from local observations are available at the
25
corresponding module, e.g., A in the temperature predicate of Figure 7 refers to the temperature
observed at node A.
Just as the data is distributed to nodes in the ensemble, the rules need to be transformed to
run on individual modules. Extending a technique from the P2 compiler, the rules of a program
are localized — split into rules with local bodies — such that two kinds of rules exist. The first
of these are local rules in which every fact in the body and head of the rule share the same home
node. The second kind of rule is a send rule for which the entire body of the rule resides on one
module while the head of the rule is instantiated on another module.
To support communication for the send rules, the compiler requires a means of determining
what routes will be available at runtime. This is facilitated by special facts, called logical neighbor
facts, which indicate runtime connectivity between pairs of modules, and potentially multi-hop
routes between them. Among the axioms introduced by the runtime system are logical neighbor
facts called neighbor facts, which indicate a node’s direct communication partners. Beyond an
ability to communicate (assumed to be symmetric), any meaning attributed to these facts are
implementation-dependent (e.g. for Claytronics, these indicate physically neighboring modules; for
sensor networks, these indicate motes within wireless range). Additional logical neighbor facts (e.g.
parent) can be derived transitively from existing ones (e.g. two neighbor facts) with the route
automatically generated by concatenation. Symmetry is preserved automatically by the creation
of a new predicate to support the inverted version of the fact (which contains the reverse route at
runtime).
Using the connectivity relations guaranteed by logical neighbor facts, the compiler is able to
localize the rules and ensure that routes will be known for all send rules. The compiler considers
the graph of the home nodes for all facts involved in the a rule, using the connectivity relations
supplied by logical neighbor facts as edges. A spanning tree, rooted at the home node of the head
of the rule, is generated (as shown in Figure 8).
For each leaf in the tree, the compiler generates a new predicate (e.g.
remote LM), which will
reside on the parent node, and creates a send rule for deriving this predicate based on all of the
relevant facts that reside on the leaf node. The new predicate is added as a requirement in the
parent, replacing the facts from the leaf node, and the leaf node is removed from the graph. This
26
is repeated until only the root node remains at which point we are left with a local rule. Note
that this process may add dependencies on symmetric versions of logical neighbor facts, such as
neighbor(B, A) in Figure 8.
Constraints from the original rule can be placed in the local rule’s body to produce a correct
implementation of the program. A better, more efficient alternative, however, places the constraints
in the send rules. This way, if a constraint does not hold, then a message is not sent, effectively
short-circuiting the original rule’s evaluation. To this end, constraints are pushed as far down the
spanning tree as possible to short-circut the process as early as possible.
The techniques of assigning home nodes, generating logical neighbors for multi-hop communications, and automaticly tranforming rules into local and send parts allow Meld v1.0 to execute a
program on a distributed set of communicating nodes.
5.2
Triggered Derivations
A Meld v1.0 program, as a bottom-up logic, executes by deriving new facts from existing facts
via application of rules. Efficient execution requires applying rules that are likely to find new
derivations. Meld v1.0 accomplishes this by ensuring that a new fact is used in every attempt at
finding a derivation. Meld v1.0 maintains a message queue which contains all the new facts. As a
Meld v1.0 program executes, a fact is pulled out of the queue. Then, all the rules that use the fact in
their body are selected as candidates rules. For each candidate, the rest of its rule body is matched
against the database and, if the candidate can be proven, the head of the rule is instantiated and
added to the message queue. This triggered activation of rules by newly derived facts is essential
to make Meld v1.0 efficient.
5.3
Deletion
One of the largest hurdles to efficiently implementing Meld v1.0 is that whenever the world changes
we must discard all known facts and start the program over from the beginning, as described in
§4.2. Fortunately, we can more selectively handle such changes by borrowing the notion of deletion
from P2. P2 was designed for programming network overlays and uses deletion to correctly handle
occasional link failures. Although the ensembles we consider may experience more frequent changes
27
root(a)
root(a)
...
neighbor(a,b)
...
neighbor(a,b)
neighbor(b,a)
neighbor(b,a)
...
...
maxTemp(a, 50)
maxTemp(a, 50)
globalMax(a,50[,1])
globalMax(b,50[,2])
globalMax(b,50)
globalMax(a,50)
globalMax(a,50[,3])
(a)
(b)
Figure 9: Partial derivation graph for the program in Figure 7. The graph on the left shows the
derivation graph for this program using the simple reference counting approach. Note the cycle in
the graph which prevents this approach from working correctly. The graph on the right shows how
the cycle is eliminated through the usage of the derivation counting approach.
in their world, these can be handled effectively with a local, efficient implementation of deletion.
Deletion avoids the problem of simultaneously discarding every fact at every node and restarting
the program by carefully removing only those facts from the system which can no longer be derived.
Deletion works by considering a deleted fact and matching the rules in exactly the same way as
derivations are done to determine which other facts depend on the deleted one. Each of these facts
is then, in turn, deleted. Strictly following this approach will result in a “conservative” approach
that deletes too many facts, e.g., ones with alternative derivations that do not depend on the
previously deleted facts. This approach would be correct if at each step all possible derivations
were tried again, but produces a problem given our triggered application of rules. In other words,
a derivable fact that is “conservatively” deleted may never be re-derived, even though an alternate
derivation may exist. Therefore, it is necessary to have an exact solution to deletion in order to
use our triggered approach to derivation.
P2 addresses this issue by using reference counting techniques similar to those used in garbage
collection. Instead of keeping track of the number of objects that point to an object, it keeps track
of the number of derivations that can prove a particular fact. When a fact is deleted, this count
is decremented. If the count reaches zero, then the fact is removed from the database and facts
derived from it are recursively deleted. This approach works for simple cases, but suffers from the
cyclic “pointer” problem. In Meld v1.0 a fact is often used to derive another instance of itself,
28
(a) Initial facts with ref counts:
neighbor(a,b) (×1)
root(a) (×1)
neighbor(b,a) (×1)
maxTemp(a,50) (×1)
(b) Facts after application of rules with reference counts:
neighbor(a,b) (×1)
root(a) (×1)
globalMax(b,50) (×1)
neighbor(b,a) (×1)
maxTemp(a,50) (×1)
globalMax(a,50) (×2)
(c) Facts after deletion of maxTemp(a,50) using basic reference counts:
neighbor(a,b) (×1)
root(a) (×1)
globalMax(b,50) (×1)
neighbor(b,a) (×1)
globalMax(a,50) (×1)
(d) Facts after application of rules with reference counts with depths:
neighbor(a,b) (×1)
root(a) (×1)
globalMax(b,50)(×1@2)
neighbor(b,a) (×1)
globalMax(a,50) (×1@1; ×1@3)
(e) Facts after deletion of maxTemp(a,50) using reference counts with depths:
neighbor(a,b) (×1)
neighbor(b,a) (×1)
root(a) (×1)
Figure 10: Example of deletion with reference counts, and derivation counts with depth (counts
and depths shown in parentheses after each fact). Based on the program from Figure 7, the
globalMax(a,50) fact can be cyclically derived from itself through globalMax(b,50). Derivation
counts that consider depth allow deletions to occur correctly, while simple reference counts fail.
Facts leading up to maxTemp(a,50) are omitted for brevity and clarity.
29
leading to cyclic derivation graphs (shown in Figure 9(a)). In this case, simple reference counting
fails to properly delete the fact, as illustrated in parts a–c of Figure 10.
In the case of Meld v1.0, and unlike a reference counting garbage collector, we can resolve
this problem by tracking the depth of each derivation. For facts that can be involved in a cyclic
derivation, we keep a reference count for each existing derivation depth. When a fact with a
simple reference count is deleted, we proceed as before. When a fact with reference counts for each
derivation depth is deleted, we decrement the reference count for that derivation depth. If the
smallest derivation depth is decremented to zero, then we delete the fact and everything derived
from it. If one or more derivations still exist after this process completes, then we reinstantiate the
fact with the new derivation depth. This process serves to delete any other derivations of the fact
that depended upon the fact and eliminates the possibility of producing an infinite cyclic derivation
with no start. This solution is illustrated in Figure 9(b) and parts d–e of Figure 10.
5.4
Concerning Deletion and Actions
Since the message queue contains both newly derived facts and the deletion of facts, an opportunity
for optimization presents itself. If a new fact (F ) and the deletion of that fact (6F ) both exist in
the message queue, one might think that both F and F
6 can be silently removed from the queue as
they cancel one another out. This would be true if all derived rules had no side-effects. However,
the possibility of deriving an action requires caution.
The key difference between facts and actions is that for facts we need to know only whether it
is true or not, while for an action we must act each time it is derived. The semantics of Meld v1.0
require that deletions be completed “instantly,” taking priority over any derivations of new facts.
Thus, when F comes before F
6 , then silently removing both from the queue is safe since F
6 undoes
the derivation of any fact that might be derived from F .
If, however, F
6 comes before F , then canceling them is not safe. In this case, processing them in
the order required by the semantics could result in deleting and rederiving an action, causing it to
be correctly performed. Had we silently deleted both F and F
6 , the action would not occur. Thus,
this optimization breaks correctness when 6F occurs before F in the queue. As a result, we only
cancel out facts in the queue when the fact occurs before the deletion of the fact.
30
5.5
X-Y Stratification
A naı̈ve way to implement aggregates (and forall statements which require similar considerations)
is to assume that all values for the predicate are known, and calculate the aggregate accordingly.
If a new value arrives, one can delete the old value, recompute, and instantiate the new one. At
first glance, this appears to be a perfectly valid approach, though somewhat inefficient due to
the additional work to clean up and update aggregate values that were based on partial data.
Unfortunately, however, this is not the case, as the additional work may be arbitrarily expensive.
For example, an aggregate computed with partial data early in the program may cause the entire
program to execute with the wrong value; an update to the aggregate effectively entails discarding
and deleting all facts produced, and rerunning the program. As this can happen multiple, times, this
is clearly neither efficient nor scalable, particularly for aggregates that depend on other aggregates.
Finally, there is a potential for incorrect behavior—any actions based on the wrong aggregate values
may be incorrect and cannot be undone.
Rather than relying on deletion, we ensure the correctness and efficiency of aggregates by using
X-Y stratification. X-Y stratification, used by LDL++[25], is a method for ensuring that all of the
contributing values are known before calculating the value of an aggregate. This is done by imposing
a global ordering on the processing of facts to ensure that all possible derivations for the relevant
facts have been explored before applying an aggregate. This guarantees that the correct value of
an aggregate will be calculated and eliminates the need for expensive or impossible corrections via
deletion.
Unfortunately, ensuring a global ordering on facts for X-Y Stratification as described for LDL++
requires global synchronization, an expensive, inefficient process for an ensemble. We propose a
safe relaxation of X-Y Stratification that requires only local synchronization and leverages an
understanding of the communications paths in Meld v1.0 programs. Because Meld v1.0 has a
notion of local rules and send rules (described in §5.1), the compiler can determine whether a fact
derivation depends on facts from only the local module, the neighboring modules, or some module
far away in the ensemble. Aggregation of facts that originate locally can safely proceed once all
such facts have been derived locally. If a fact can come only from a neighboring module, then it is
sufficient to know that all of the neighboring modules have derived all such facts and will produce no
31
more. In these two cases, only local synchronization between a module and its immediate neighbors
is necessary to ensure stratification.
Therefore, locally on each node, we impose an ordering on fact derivations. This is precisely the
ordering that is provided via X-Y stratification, but it is only enforced within a node’s neighborhood,
i.e., between a single node and its direct neighbors. An aggregation of facts that can only be derived
locally on a single node is handled in the usual way. Aggregation of facts that might come from a
direct neighbor is deferred until each neighbor has promised not to send any additional facts of that
type. Thus, to ensure that all the facts contributing to an aggregate are derived beforehand, some
nodes are allowed to idle, even though they may be able to produce new facts based on aggregates
of partial sets of facts. For the rare program that aggregates facts which can originate from an
arbitrary module in the ensemble, it may be necessary to synchronize the entire ensemble. The
compiler, therefore, disallows aggregates that depend upon such facts. To date we have not needed
such an aggregate, but intend to investigate this further in the future.
5.6
Implementation Targets of Meld v1.0
The Meld v1.0 compiler produces byte codes which are interpretted by an virtual machine. Meld
v1.0 programs can run on various systems by implementing a virtual machine on a target system
and providing the Meld v1.0 compiler with a model for the system. The system model consists of
the axiom predicates and action predicates for the target system, allowing the compiler to perform
type-checking for the system and link the axioms and actions correctly with the runtime. The Meld
v1.0 virtual machine and runtime is currently implemented on the three different systems described
below.
5.6.1
DPRSim/DPRSim2
DPRSim [26] and DPRSim2 [27] are a pair of simulators which simulate programmable matter.
They simulate robots which are able to perform computation, store data locally, and locomote
around one another. DPRSim runs on a single machine and is capable of simulating tens of
thousands of robots. DPRSim2 runs across many nodes in a cluster and is capable of simulating
tens of millions of robots. These simulators are capable of running arbitrary code on each simulated
32
robot and, therefore, an implementation of the Meld v1.0 VM. Using this simulator demonstrates
the utility of Meld v1.0’s actions as well as the ability to create and execute Meld v1.0 programs
scaled across millions of modules.
5.6.2
Blinky Blocks
The Blinky Blocks are “human-actuated” modular robots. Each block has a small processor and
small amount of memory and is capable of communicating with adjacent robots. They feature
accelerometers, allowing them to determine the direction of gravity and to detect taps. They also
feature bright LEDs, permitting them to change color. The blocks are fault-prone, power-cycling
any time they are moved or bumped too violently. This platform demonstrates that Meld v1.0
programs can be run on resources-limited nodes and are tolerant of abundant faults.
5.6.3
Multi-core Machines
Finally, a version of the VM has been ported to multi-core machines, exploring the utility of Meld
v1.0 in this environment. As previously mentioned, much prior work has focused on implementing
concurrent versions of logic programming languages. These works focused on splitting queries to be
performed by multiple nodes whereas Meld v1.0 partitions the database, leading to a different level
of parallelism. Exploring multi-core will allow us to test this method of parallizing logic programs,
but is not a focus of this thesis.
6
Analysis of Meld v1.0
In this section we discuss some of the advantages and disadvantages of writing programs in Meld
v1.0. To facilitate this, we consider two real programs for modular robots that have been implemented in Meld v1.0 in addition to the temperature averaging program for sensor networks
shown in Figure 7. These programs implement a shape change algorithm as provided by Dewey
et. al. [2] (a simplified version is shown in Figure 11) and a localization algorithm provided by
Funiak et. al. [28]. The localization algorithm generates a coordinate system for an ensemble by
estimating node positions from local sensor data and then iteratively refining the estimation.
33
// Choose only best state:
// B is not a child of A
// FINAL=0, PATH=1, NEUTRAL=2
notChild(A, B) :-
type state(module, min int).
neighbor(A, B),
type parent(module, first module).
parent(B, C), A != C.
type notChild(module, module).
notChild(A, B) :// generate PATH state next to FINAL
neighbor(A, B),
state(B, PATH) :-
state(B, FINAL).
neighbor(A, B),
state(A, FINAL),
position(B, Spot),
// action to destroy A, give resources to B
0 = inTargetShape(Spot).
// can apply if A is a leaf in deletion tree
destroy(A, B) :-
// propagate PATH/FINAL state
state(A, PATH),
state(B, PATH) :-
neighbor(A, B),
neighbor(A, B),
resources(A, DESTROY),
state(A, PATH).
resources(B, DESTROY),
forall neighbor(A, N)
state(B, FINAL) :-
notChild(A, N).
neighbor(A, B),
state(A, FINAL),
position(B, Spot),
// action to transfer resource from A to B
1 = inTargetShape(Spot).
give(A, B) :neighbor(A, B),
// construct deletion tree from FINAL
resources(A, CREATE),
parent(B, A) :-
resources(B, DESTROY),
neighbor(A, B),
parent(A, B).
state(B, PATH),
state(A, FINAL).
// action to create new module
// extend deletion tree along PATH
create(A, Spot) :-
parent(B, A) :-
state(A, FINAL),
neighbor(A, B),
vacant(A, Spot),
state(B, PATH),
1 = inTargetShape(Spot),
parent(A, ).
resources(A, CREATE).
Figure 11:
A metamodule-based shape planner based on [2] implemented in Meld v1.0. It uses an abstraction that provides
metamodule creation, destruction, and resource transfer as basic operations. The code ensures the ensemble stays connected
by forming trees and deleting only leaf nodes. This code has been tested in simulations with up to 1 million metamodules,
demonstrating the scalability of the distributed Meld v1.0 implementation.
34
X
a)
b)
X
c)
X
d)
Figure 12: (The max temperature program (in Figure 7) (a) creates a tree. When (b) a node fails,
the Meld v1.0 runtime is able to (c) destroy the subtree rooted at the failed node via deletion and
(d) reconnect the tree.
The shape change algorithm is a motion planner for modular robots. Planning for individual modules is plagued by non-holomonic constraints, however planning can be done for groups,
called metamodules, with only holonomic constraints. Dewey’s algorithm runs on this metamodule
abstraction rather than on individual modules. These metamodules are not capable of motion
themselves. Instead they can be absorbed into (destroyed by) or extruded out of (created by) an
adjacent metamodule. An absorbed metamodule can be transfered from one metamodule to an
adjacent one, allowing it to travel throughout the ensemble as a resource. The planner makes local
decisions on where to create new metamodules, destroy existing ones, and how to move resources.
6.1
Fault Tolerance
As evident from the discussion in §5, Meld v1.0 inherently provides a degree of fault tolerance to
programs. The operational semantics of Meld v1.0 allows for arbitrary changes in the physical
world; any visible change causes removal of facts that are no longer supported by the derivation
rules. In the event that a module ceases to function (fail-dead), every fact that is derived from
axioms about that module is deleted. New axioms, representing the new state of the world, are
introduced and affected portions of the algorithm are rerun. This allows the program to run as
though the failed module had never been present, modulo actions that have already occurred. As
long as the program has no special dependence on this module, it continues to run and tolerates
the failure. Other failures can also be tolerated as long as the program can proceed without the
lost functionality.
For the temperature averaging program, this feature of Meld v1.0 is very effective. If, for instance, a module fails then a break occurs in the constructed tree. In a naı̈ve implementation in
35
another language, this could result in a failure to complete execution or a failure to include observations from the subtree rooted at the failed node. An implementation that can tolerate such a fault
and reconstruct the tree (assuming the ensemble is still connected) requires significant additional
code, foresight, and effort from the programmer. The Meld v1.0 implementation, however, requires
nothing additional. When a module fails, Meld v1.0 automatically deletes the subtree rooted at
the failed node and, if the network is still connected, adds these modules back into the tree, as
shown in Figure 12.
6.2
Provability
As Meld v1.0 is a logic programming language, Meld v1.0 programs are generally well-suited for use
in correctness proofs. In particular, the structure and semantics let one directly reason about and
apply proof methods to Meld v1.0 program implementations, rather than on just the specifications
or translated pseudo-code representations. Furthermore, Meld v1.0 code is amenable to mechanized
analysis via theorem checkers such as Twelf [29]. Twelf is designed for analyzing program logics,
but can be used for analyzing logic program implementations as well.
Proofs of correctness for programs involving actions, however, may need to make assumptions
about what happens when an action is attempted. For the planner example, a proof of correctness
has been carried out with the assumption that actions are always performed exactly as specified.
The planner has been proven to achieve a correct target shape in finite time while maintaining
the connectivity of the ensemble.2 These simplifying assumptions, however, prevent any formal
reasoning about fault tolerance, as discussed in §6.1. Although empirical evidence shows that the
Meld v1.0 implementation is indeed tolerant to some faults, a good fault model will be required to
formally analyze this aspect of the program.
6.3
Messaging Efficiency
The distributed implementation of Meld v1.0 is effective at propagating just the information needed
for making forward progress on the program. As a result, a Meld v1.0 program’s message complexity can be competitive with hand-crafted messaging written in other languages. This was
2
A sketch of the proofs is available in [2] and the full proofs on the Meld v1.0 source code are available in [30].
36
demonstrated in [31] for small programs and our enhancements carry this through for more complex programs that use aggregates. In particular, the use of aggregates can cause high message
complexity. Before adding X-Y stratification, aggregates that depend on data received from neighbors, such as those used in the iterative refinement steps of the localization algorithm, could cause
multiple re-evaluations of the aggregate as data trickled in. In the worst case, this could cause
an avalanche of facts with intermediate values to be sent throughout the ensemble, each of which
is then deleted and replaced with another partial result. For localization, this resulted in a lack
of progress due to an explosion of messages on all but trivially small examples in the original implementation of Meld v1.0. Our addition of X-Y-stratification to Meld v1.0 alleviates this issue:
the result of an aggregate is not generated or propagated until all supporting facts have been seen,
limiting both messaging and computation overheads. With X-Y stratification, localization has been
demonstrated on ensembles of up to 10,000 nodes, with a message complexity logarithmic in the
number of modules, exactly as one would expect from a high level description of the algorithm.
6.4
Memory Efficiency
Although the Meld v1.0 compiler is not fully optimized for memory, many Meld v1.0 programs
have small memory footprints and can, therefore, fit into the limited memory available on sensor
network motes and on modular robots. To test this, we measure the maximum memory used among
all the modules in an ensemble executing the example Meld v1.0 programs. Both the temperature
aggregation program and the shape change algorithm prove to have very small memory footprints,
requiring at most only 488 and 932 bytes per module, respectively. The aggregation program is
sensitive to neighborhood size; this was assumed to be 6, and the memory required grows by 38
bytes for each additional neighbor. Furthermore, these numbers assume 32-bit module identifiers
and temperature readings; 16-bit module identifiers and data would halve the maximum memory
footprint. Both of these programs fit comfortably into the memory available on a mote or a modular
robot.
The localization algorithm, on the other hand, requires tens to hundreds of kilobytes of memory
depending on the ensemble size. This is due to the lack of support within Meld v1.0 for dynamic
state. Because of this limitation, the localization algorithm is written such that it produces a
new (static) estimated position fact for each step of iterative refinement. Furthermore, as the old
37
estimates are used in the derivation of the new ones, these are not discarded and they quickly
accumulate. As the ensemble grows, more steps of iterative refinement are required, generating
even larger quantities of outdated facts that only serve to establish a long chain of derivation from
the axioms. Thus, programs that require dynamic state (such as algorithms involving iterative
refinement) can not currently be efficiently run in Meld v1.0.
7
Shortcomings of Meld v1.0
Meld v1.0 has proven to be effective for writing some algorithms, such as the meta-module shape
change algorithm depicted in Figure 11. Unfortunately, other algorithms are difficult or impossible
to present faithfully in Meld v1.0. Funiak et al.’s localization algorithm [28], for instance, runs into
two problems when implemented in Meld v1.0. The two problems appear to be different, but they
stem from the same source.
The localization algorithm described by Funiak et al. uses sensor readings between closely packed
modules to build an accurate coordinate system. The algorithm assumes that sensor readings
indicate physical contact between the modules in the system and that the reading provides a
direction to a module with some degree of inaccuracy. The algorithm proceeds by building small
groups of modules (chosen via normalized cut) and localizing each group. A gradient decent step
is performed on each group to minimize any errors. The groups are then combined to form larger
groups via a rigid transformation, followed by additional gradient decent in order to use the new
information present in the larger group to further minimize the error. This process repeats until
all the groups have been combined and the ensemble has a single coordinate system.
Two problems arise in implementing this algorithm in Meld v1.0 - one with ease of representation
and efficiency of running and the other with trying to accurately represent the algorithm. The first
shortcoming is highlighted by the gradient descent step. As the algorithm runs, it continually
produces better estimates as to the location of each module in the ensemble. In an imperative
language we might represent the location of a module with some particular variable which we
update continuously as the algorithm is run. In Meld v1.0 we lack the ability to change a value
once assigned. We cannot have some position fact which we continuously update as we run the
algorithm. Instead, we must keep every estimate of our position. This can be made to work by
38
tagging position facts with a version number, but this solution is unsatisfying. Firstly, it places
greater burden on the program and inhibits the programmer’s ability to correctly implement the
algorithm. In particular, it is necessary to devise a method of tagging the position facts in such a
way that the current value can be selected. This is non-trivial because there is no way to inspect
the facts to determine which tag is the best one, rather the algorithm must be able to determine a
priori which tag is appropriate for the step. This problem is certainly tractable (as evidenced by
the completed implementation of the localization algorithm), but unnecessarily creates extra work
and a greater mental burden on the programmer.
Secondly, this solution is unsatisfying because it is wildly inefficient. The algorithm passes
through hundreds of estimates for each module. Keeping all of these estimates requires hundreds of
times more memory than keeping just the current estimate. This is problematic, to say the least,
on a small embedded module with minimal resources. Furthermore, this potentially increases the
runtime of the algorithm as the database now contains extra facts that we might try to match
against using the various rules of our program. Successful or not, attempting to match these will
waste CPU cycles and power.
The other concern arises when we consider changes to the positions of modules after successfully
building a coordinate system. What should we do if a module is removed from the ensemble?
Nothing. The positions of all robots still present have not changed, so we should keep them. Meld
v1.0 will helpfully erase many or all of these positions as it goes through the deletion process and
then generate a new coordinate system for us. This is a time consuming, a waste of resources, and
potential wrong as the new coordinate system might be substantially different from the prior one
(perhaps a different module will be chosen for the origin). What should we do if a module is added
to the ensemble? It should receive a coordinate and then gradient decent should be performed
locally to minimize the error. Meld v1.0, however, will again go through the deletion process and
produce a new coordinate system. We would like to write the localization algorithm in two stages,
one where an initial coordinate system is generated and one where it goes into an update mode,
handling minor changes in topology. Unfortunately, this is not possible in Meld v1.0.
Thus we see that Meld v1.0 has two major shortcomings. First, there is no way for the programmer to remove old stale facts. Meld v1.0 determines when facts are stale based on whether they
are still derivable, but a particular algorithm may have no further use for them and they may be
39
in the way. Second, there is no way for the programmer to prevent Meld v1.0 from removing good
facts. Meld v1.0 removes facts because they are no longer derivable, but they may still be useful
for the algorithm. Therefore, Meld requires some principled means of allowing the programmer to
determine when some facts are stale.
8
Proposed New Research for Meld v2.0
As shown in §7, some algorithms cannot be expressed accurately and easily in Meld v1.0. Any
approach to addressing these expressivity problems will require an extension of the Meld v1.0
language. I express here the ideas for addressing these problems in Meld v2.0.
In Meld v1.0, the compiler and runtime are responsible for managing all facts, determining when
they are stale and removing them via deletion. In many instances this functionality is convenient
for the programmer, but in some cases it prevents a program, such as localization, from being easily
or correctly expressed in Meld v1.0. In Meld v2.0, I intend to address this issue by splitting facts
into two classes - those managed by the Meld v2.0 runtime and those managed by the programmer.
To this end I will extend Meld v1.0 with a modality for user-managed facts. To support allowing
the user to add, modify, and remove facts in a disciplined way modal facts may be linear (in the
sense of linear logic). When considering how Meld v1.0 programs execute, I observe that the
existing facts are automatically updated to accurately reflect the state of the ensemble at all times.
The user-managed modality will sustain no automatic changes when a module moves or fails or any
other change in observable state occurs. These linear facts can, however, be used and influenced
by the observable facts.
Linear facts are permitted to retain knowledge about the history of the ensemble rather than
just the current physical state. This would allow for simple representation of time-dependent
state, program status, etc., while eliminating the need for and problems with the aforementioned
embeddings. The biggest concern about this approach is that it may (partially) eliminate some of
the nice features of Meld v1.0, such as fault tolerance. It will be necessary to understand what
these consequences will be and whether there are ways in which we can ameliorate the impact on
fault tolerance.
40
To this end, I will produce a formal operational semantics for Meld v2.0, just as was done
for Meld v1.0. To show that these additions are principled, I will need to uncover the logical
foundations for Meld v2.0. In the event that they prove elusive, we will still have a formal semantics
for the language along with an explanation of the problems encountered in uncovering the logical
underpinnings. Regardless, I will use the formal semantics to prove correctness properties of a few
example programs, like those already done for the Meld v1.0 implementation of the meta-module
shape change algorithm.
Another necessary challenge will be producing an efficient implementation of Meld v2.0. Meld
v1.0 programs have been shown to execute within the hardware constraints of the Blinky Blocks
and with asymptotic runtime and memory requirements comparable to equivalent C programs. The
number and size of messages exchanged as a Meld v1.0 program executes is comparable to that
of equivalent C program execution. I anticipate that Meld v2.0 programs will be able to boast
similar performance claims. In particular, Meld v2.0 programs should be able to match theoretical
asymptotic runtime and memory usage and interesting programs should fit within the hardware
available on the Blinky Blocks. The goal here is to demonstrate that the language is usable, not
to produce an optimizing compiler.
Implementing this system in a distributed fashion will require some changes from the Meld
v1.0 compilation and execution model. The Meld v1.0 implementation localizes rules, breaking
them into sub-rules which run independently. As the execution of a rule in Meld v2.0 (potentially)
requires removing facts from the database in addition to inserting them, it will be necessary to
ensure that rules are executed atomically. It should be sufficient to augment the existing execution
model with the usage of transactions to atomically execute each original rule across the relevent
nodes of the system. A concern here is that the usage of transactions could have a substantial
negative impact on performance and may make performance more difficult to evaluate.
This new work will demonstrate my thesis. The new linear modality in Meld v2.0 shows sufficient
expressivity to write interesting programs for a variety of ensembles. The implementation of Meld
v2.0 will demonstrate efficient execution of these programs on various platforms. The operational
semantics and proofs of program properties will demonstrate that Meld v2.0 programs can be
reasoned about. Thus, this work will show that logic programming, as exemplified by Meld v2.0,
is well-suited for ensemble programming.
41
9
Timeline
9.1
Already Done
I have an implementation of the Meld v1.0 compiler and runtime. The runtime runs on three different systems - the blinky blocks and blinky block simulator, the DPRSim and DPRSim2 Claytronics
simulators, and a parallel machine. The global and local semantics for Meld v1.0 are formally defined in Twelf and I have shown that they are equivalent. I have also proven the correctness and
termination (assuming adequate resources) of Dewey et al.’s meta-module shape change algorithm
implemented in Meld v1.0 using Twelf.
The performance of some simple Meld v1.0 programs for Claytronics has been analyzed in
comparison to C programs, showing that Meld v1.0 programs are comparable in messages sent
and memory/cpu scaling, but lag behind by an order of magnitude in actual memory/cpu usage.
The programs evaluated are an order magnitude more concise than their C counterparts. This
performance data is obsolete and does not reflect the current version of Meld v1.0.
A preliminary implementation of Meld v2.0 exists and is running on all three systems.
9.2
Summer 2011
This summer I intend to focus on the Meld v2.0 semantics and understanding their logical underpinnings. Presently I have a draft version of the semantics, but the logic behind them is unclear at
this time as the choice of modalities is novel. The modalities in use have many similaties to those
of the linear and persistent modalities and those of necessitation and truth. This will primarily be
a matter of understanding exactly what the relation is between the Meld v2.0 managed facts and
the user managed facts and relating that to logic. The Meld v2.0 semantics will be formalized in
either Twelf or Celf as appropriate.
9.3
Fall 2011
The fall semester will be spent ensuring that the Meld v2.0 implementation is consistent with the
formal semantics and analyzing the implementation. This will include analyzing the performance
42
of various example programs as well as proving properties about some of these programs. These
programs are to including Dewey et al.’s meta-module shape change algorithm, Funiak et at.’s
localization algorithm as reimplemented in Meld v2.0, and Blinky Block games.
9.4
Spring 2012
The spring semester is reserved for writing the thesis document. I expect that all necessary research
will be completed by this time.
10
Summary
I propose to design and implement a language, Meld v2.0, for the purpose of programming ensembles. Preliminary work on Meld v1.0 has shown the logic programming paradigm to be a good
match for programming ensembles. I will enhance the expressivity of Meld v1.0, eliminating the
weaknesses that hinder its present use for some classes of applications. Meld v1.0 programs are
automatically distributed across an ensemble and are inherently fault tolerant. Meld v2.0 will continue to boast these features. Furthermore, I will demonstrate proving properties of Meldprograms,
ensuring that implementations behave as expected.
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