If You Wish to Change the World, Start with Yourself: An Alternative Metaphor for Object Interaction

Published in TDAN.com July 2001


Abstract

During the past ten years, requirements on functionality of business applications have been slowly changing. This shift consists of moving from traditional command based applications to inherently
interactive applications of workflow and groupware type. For modeling new kind of business applications, the authors suggest an approach to defining interaction that is not based on explicit
communication. In this approach, interaction is realized via active relationships that can propagate changes from one object to another. Based on this idea, which comes from the previous research
work of the authors, the paper discusses the issues of introducing “harnesses” on the interactive behavior, finding the right place for the end-users in the model, and modeling distribution of
tasks between different users.


1. Introduction

1.1. Motivation – paradigm shift in business application development

During the past ten years, requirements on functionality of business applications have been slowly changing. This change may be described as moving from the traditional, “human-assisting”
systems, to a new generation of “human-assisted” systems.

A human-assisting system helps a human being only to perform certain activities, e.g. to write a letter, to print an invoice, to complete a transaction, etc. The relations between these activities,
and the aim of the whole process are beyond the understanding of the system, but are a prerogative of the human participant. In a human-assisted system, the roles are reversed, the system has a
complete picture of the process and is involved in all activities. Only when the system cannot perform some activity on its own, it will ask the human participant for assistance.

The difference between the old and new generations is essential, and it can be traced in all aspects of system development, including user-interface, as shown in figure 1. A human-assisting system
can be compared to a powerful tool set where the user should know exactly what tool to use and how to find it when it is needed. A human-assisted system functions like an assembly line conveyor
bringing the user a task that he/she is to complete and a tool to complete the task with, i.e. a word processor.

The difference between the generations affects also what kind of modeling techniques and languages are suitable for developing such systems. For the traditional “human-assisted system” the
following is true:

  1. The system is clearly separated from the user.
  2. There is only one user. Multiple users may be considered as mere repetition of the same user, with the exception of different users having different access rights. In a multi-user system, the
    users are not aware of each other, so the only complication for the systems development here is to solve conflicts when users access the common database.
  3. The system is purely reactive, the execution always starts on the user command.

 



 



Fig.1.Shift in functionality of business applications

These properties are reflected in the basic notions of the current modeling techniques and languages, like open system (the system knows nothing beyond its boundaries), use case (somebody is using
the system), message (a signal requesting some action), etc. The essence of such modeling is to model the software system rather than the whole business context where the system is only a part. The
technical focus of modeling is reflected in how the decomposition of the system in smaller units (e.g., objects, components, etc.) is done and how their behavior is described. For example:

The decomposition is driven by technical reasons, like geographical distribution of the system, users and information, reusability, etc.

The resulting units do not need to reflect the entities of the business reality. And if they do, their behavior do not need to correspond to the behavior of the entities of the real world. For
example, it is not uncommon that the employee object in the model has a method of calculating his/her own wages, which does not correspond to what the employee does in the business world.

The technical purposes of modeling determine also who should/could do the modeling work. Obviously, the modelers should be the technical people who understand the software systems architecture.

The properties of the “human-assisted” assisted systems are different:

There is no clear separation between the user and the system. Even after the system has been installed, some functions meant for the computer may be handed back to the user. And vice versa, some
functions meant for the human being may be handed to the computer.

Multiple users is an essential property. The system should know to which user to turn when requesting assistance of a certain kind (workflow problem). Furthermore, the users might be aware of
presence/absence of each other when they are engaged in collaborative work (groupware problem). Here, we have a situation of “distributed user” rather than a situation of “distributed users”
(in geographical sense). Term distributed user stresses that even when there is only one user, he/she is distributed between various tasks (e.g., playing a game with him/herself.) This view makes
the system independent of the number of users currently working with it, as long as there is somebody to get assistance from.

The system is both reactive and proactive. Not only the user can request an action from the system, but also the system can anticipate and request an action from the user.

The properties listed above create a different set of requirements for modeling techniques and languages than the one that can be derived from the properties of the traditional business
applications. First of all, the user becomes an integral part of the model. As the distribution of business tasks between the user and the system can change during the system’s lifetime, the
behavior of the user should be described in the same way as the behavior of other components of the model. Otherwise, redistribution of tasks will require rebuilding the model. Additionally, as the
system can request actions from the user, his/her representation can not differ much from representation of other components of the system.

Making the user part of the model moves us from the open system concept to the close system concept (on the difference see [9,15]), and thus from modeling software systems to modeling business
reality. Modeling the reality presumes that in the model, we reflect the entities that exist in the business world and their behavior. This is not the same as describing the behavior of the units
of technical decomposition. As business reality becomes the main subject of modeling, involvement of business people in the modeling process increases. This is impossible to do without “liberating
modeling from programming level abstractions”, the topic extensively covered in [8].

The greatest difference between the old and the new generations of business applications consists in that the systems of the new generation are much more interactive than the systems of the old
one. That puts the issue of modeling interactions in the center of discussion on which modeling techniques fit best the modern business application development.

1.2. Modeling interaction

The importance of interaction for software engineering is well understood in the computer science theory, see for example [15]. The most popular method of modeling the interactive behavior comes
from the field of object-oriented programming. In the “classical” object-oriented approach, the interactive behavior is described via methods encapsulated in objects and invoked by messages (see,
for example, [7]). This approach realizes the “signal-response” type of interaction. It proved to be useful for programming, specification and design of technical applications, and, moreover, for
specification of traditional (i.e. reactive) business applications. However, this method is not adequate for specification of human-assisted applications. It is not meant for modeling business
reality, and it does not consider the user to be an integral part of the model, i.e. on the same footing as other components.

The limitations of the classical object-oriented approach are well known in the computer science theory, see, for example, [9]. So called generalized object models, which allow several objects to
participate in the same action, where proposed in order to overcome part of those limitations, see, for example [6]. The notion of generalized object model has even been introduced in various
object-oriented standards, see, for example [12]. However, as justly reflected in [9], those ideas have not found the proper place in the software engineering practice.

The word interaction means that the state and/or behavior of one of the interacting entities (objects, components, etc.) affects the state and/or behavior of other entities that participate in the
interaction. The traditional object-oriented approach exploits explicit communication as a means of interaction (via objects sending messages to each other or themselves). This is not the only way
of achieving interactive behavior. An alternative approach can be derived from the well-known saying “If you wish to change the world, start with yourself.” This statement presumes that by
changing its own state or behavior, the entity may cause changes in other entities. Naturally, this is impossible if this entity is totally isolated from others; the saying presumes that:

  • >each entity has many relationships with other entities,
  • these relationships can propagate changes in one entity to the others without explicit communication (be it command-style, or negotiation-style communication).

Let us consider an example from figure 2 were two balls are connected by a spring. Suppose the centers of these balls are fixed and can’t be moved. Assume that the balls are made from some elastic
material, and each ball can change its shape and degree of elasticity. Presume that at some moment of time the first ball changed its shape as shown in figure 3, and became hard, while the second
ball remained to be elastic. Then the spring will force the second ball to change its shape, as shown in figure 4.

 



Fig. 2.Two balls connected by a spring.

 



Fig. 3.The first ball changed its shape and hardened.

 



Fig. 4.The spring adjusts the shape of the second ball.

The above example can be modeled as two objects connected via a computational device which we call a connector, see figure 5. The connector contains the text of a physical law that governs the
spring functionality. The connector watches the objects it hangs upon, i.e., their shapes and degrees of elasticity. As soon as it discovers some changes in one or both of the objects it adjusts
their shapes according to the spring law.

 



Fig. 5.A model of the spring-balls assembly.

The connector in figure 5 represents a way of modeling active relationships that exist in the real world. In the real world, the spring and the balls are not floating in an empty space, but are
part of some larger entity. The larger entity can also be modeled as an object in which body the spring connector with its operands (objects the connectors hangs on) is included, as shown in figure
6. The third object, O3, in its turn can have active relationships with other objects. The actions of these relationships can result, for example, in the spring-balls assembly being removed from
the body of O3.

 



Fig. 6.The connector with its operand is part of the object O3.

The connector that guards some law over its operands operates on the principle of localism. Namely, it knows nothing about the objects beyond its operands, and thus, neither can change them nor use
them in its work. Thus, the spring connector in figure 6 cannot remove itself from the body of object O3. This means that figure 6 does not cover the situation when the spring can break down as a
reaction on the balls becoming too large or too small. To cover this situation, the object O3 should become an operand of the spring connector as shown in Fig.7. The model in figure 7 allows the
spring connector to remove itself from the body of the object O3. If at this moment objects O1 and O2 has no other connection to object O3, or its other sub-objects, they disappear from O3
altogether.

 



Fig. 7.The model that covers the case when the spring can break down

We believe that the idea of active relationships and its realization through the concepts of law, object, and connector constitute a promising approach to modeling interactive behavior of
human-assisted business applications. The natural question arises: where is the user, is it a connector, or an object? The answer is that he/she is both.

The formal basics of the objects-connectors model hinted above are introduced in [3]. This paper is devoted to “almost” informal discussion of how to use this model to describe interactive
behavior. In several aspects the current paper goes further than [3]. This concerns the topics of distribution the users between various tasks, and making the texts of laws to be an integral part
of the model. The rest of the paper has the following structure. In section 2, we shortly overview the basic notions from [3], and in section 3, we illustrate these notions with examples. In
section 4, and 5 we discuss the place of the user in the model. In section 6, we compare our approach with other well-known metaphors of computer science. In section 7, the list of open problems is
presented that constitutes the directions of our future research.


2. Basic notions

In this section, we give a short overview of the basic notions of the objects-connectors model. Those notions generalize the example discussed in the previous section, and they are explained
informally with the help of another example in the next section.

The objects-connectors model from [3] describes the world as consisting of:

  • a set of typed atoms A,
  • a set of objects O,
  • a code of laws L, and
  • a set of connectors CON, each connector hanging on a group of objects that must obey a certain law.

Atoms represent the usual notion of elementary data types, like integers, floats, strings, etc. We assume that each atom from A is assigned a type t. By At, we will denote the set of all atoms of
the type t.

Atoms are the only elements of the model that can be described independently of other notions. All other notions are interconnected. The objects are used to represent complexly structured entities.
At each moment of time an object can be characterized by its state. The state is not more than a set of connectors from CON included in the body of the given object.

Let R(CON) be the powerset of CON (a set all subsets of connectors), and ^ be a special symbol that represents the embryo state of the object. A function

st: O -> R(CON) È {^},

that assigns each object o Î O its state is called a state function. A function w that maps the time axis T into the set of all possible state functions ST:

w: T -> ST

is called a world. The world determines the state w(t)(o) of any object o at any point of time t. For simplicity, we consider the discrete time axis with starting point, i.e. it consists of all
nonnegative integers called time ticks.

A law l is defined as a 5-tuple . The name assigns a name to the law. The arity is a positive integer n > 0 which defines the number of objects this particular law concerns. The law can be
unary, binary, etc. The type in the form t1 x t2 x … x tk, k ³ 0, where ti is an atomic type, defines how many atoms and of which types can be taken into consideration by the law.

Let l = be a law. Consider a world w at a moment of time t. Let v = be a k-tuple of atoms of the type type, and z = be an n-tuple of objects from O. Then the condition is a predicate that given v,
z, w, and t determines whether the law with parameters v holds for objects from z in world w at time t. The action provides the next state of objects from z for those points for which the law is
broken. In other words the action assigns a punishment for breaking the law. The simplest type of laws is a trivial law for which the condition is always true, and the action is always empty.

Finally, a connector is a triple c=, where l is an n-ary law with type t1 x t2 x … x tk, v = is a k-tuple of atoms, such that vi Î Ati, i = 1 ,…, k, and z = is an n-tuple of objects. If
the law is trivial, the connector just represents a passive relationship between its operands, eventually assigning some properties to the relationship with the help of its k atoms (if any). This
case corresponds to the usual notion of relationship from the ER model [4]. If the law is nontrivial, the connector forces the objects’ structure and behavior to be in sync with each other and,
possibly, with the properties of the relationship (if there are any atoms). This is the case of active relationship. If a connector’s law holds on its operands, we say that the connector is
satisfied, otherwise we say that it is unsatisfied.

The dynamics of the objects-connectors model can be defined by a machine in which a connector is regarded as a processing unit that monitors its operands. A connector

  • awakes when one of its operands has been changed,
  • checks whether the law still holds by reading the condition,
  • restores it when it has been broken,
  • falls asleep.

The machine has also a central unit that resolves conflicts when several connectors demand access to the same objects. For more details we refer to [3].


3. Analysis of example

In this section, we illustrate the basic notions from the previous section with the help of an example, and discuss some important features of the model while referring to this example.

We start with a simple promotion queue shown in figure 8. The queue consists of a number of cells, e.g., in a hospital. The cells are ordered according to the complexity of their equipment. Each
cell may have one inmate. Each inmate has a priority assigned to it. A new inmate can be placed in any empty cell. The queue should function in such a way that the inmates with higher priorities
are placed in the better-equipped cells.

 



Fig. 8.A promotion queue

Two laws are used for this model, priority, and promote. The priority law is trivial, it is meant just to assign a priority (atomic value) to the only operand of a connector, the atomic value is
considered to be an integer. The promote law is nontrivial, it has two operands and no atoms. It holds when a connector priority in its first operand assigns a lower priority to the inmate than a
similar connector in its second operand. Thus, in figure 8, the promote connector placed in cell1 is satisfied. If the connector is not satisfied, it swaps inmates between its first and second
operands. If the second cell is empty, it just moves the inmate from cell1 to cell2. Note that if the first cell is empty, the law is always satisfied.

The above example represents a kind of distributed search, and it is very similar to the distributed search algorithm from [1] expressed in Disco modeling language [5]. In the model from figure 8,
the evaluation of inmates is done by an external agent, and cannot be changed from inside the queue.

Let us make a more complicated example. Suppose each cell has a special measuring-device to which an inmate is connected. This device evaluates the state of the inmate and sets its priority. The
modified example is shown in figure 9. Instead of the trivial law priority, a new nontrivial law gauge is used. The gauge connector is satisfied if the overall state of the inmate is reflected by
the atomic value assigned to this connector. If the state of the inmate is not reflected by the atom, the atomic value should be changed. The legal way of changing an atom in the model is by
substituting the whole connector. Thus, when the gauge connector is not satisfied, it replaces itself with the same gauge connector but with another atomic value assigned to it. This situation
corresponds to the pointer changing its position on the dial of a real physical gauge.

An example in figure 9 illustrates how the decomposition is done in the objects-connectors model. The gauge connector is responsible for moving the pointer of the dial. He does it by watching the
state of his first operand and evaluating it. The promote connector knows nothing about the internal states of the inmates included in its operands. It watches only the gauges’ dials, which is
enough for this connector to decide on and complete the action. In other words, the promote law analyzes its operands only on the depth 1. It “sees” what connectors exist in its operands,
including the atomic values assigned to those connectors. Actually, the idea of reduced visibility is the reason why the dial of the gauge is modeled by an atom and not by an object.

 



Fig. 9.A promotion queue with own measuring-devices

The law in our model can take into account not only the current state of its operands, but their histories too. The promote law does not need any historical information, its condition and action
are based on the current readings of the gauges. The gauge itself, however, may take into account historic information. For example, if we evaluate the state of the patient in the hospital, his
absolute high temperature may not be enough to assign him a high priority; we need to know whether the temperature was rising, falling, or it remained the same for some time.

The objects-connectors model is state-oriented, i.e. the state is its basic notion. The example in figure 9 shows that state-orientation does not necessarily means the absence of encapsulation. The
idea of encapsulation is widely accepted, as it is not always possible or reasonable to know the state of an object in order to interact with it, the knowledge of the object’s behavior should be
enough. This idea is one of the grounds of the classical object-oriented programming. However, methods of the classical object-oriented programming are not the only approach to defining behavior.
Actually, to understand the behavior of an object without looking inside it, one needs to watch some wider area in which this object operates. In our example, the promote connector makes its
decisions based on watching the interaction between the inmate and the measuring-device inside the cell.


4. Where is the user?

The model described in the previous sections looks quite deterministic. The determinism would be justified if when modeling the reality, we could have the exact knowledge of all laws that act in
it. This is not true in practice where we always model only a part of the reality. There are two sources of non-determinism when modeling business reality. Firstly, the behavior of some elements of
business reality cannot be fully understood or controlled because they are external for the given business, for example, customers or suppliers (see the discussion on this topic in [15]). Secondly,
even the part of business reality that could be understood and controlled might be too complex to be described deterministically from the very beginning. Full understanding, if any, of this part of
reality could be reached long after the business application has been designed and introduced in the operational practice. Thus, a strategy of stepwise refinement of the model is required (see more
on this topic in [9]).

To express the idea of insufficient knowledge of reality, we exploit a notion of non-deterministic law. We differentiate two types of non-determinism: firing non-determinism, and action
non-determinism. For a law with firing non-determinism, an action can be defined even for those cases where the law holds. A connector that imposes such a law may be awoken even when none of its
(visible inside the model) operands has been changed. A law with action non-determinism can specify two different actions for the same behavior of its operands. A connector entrusted with such a
law appears to be taking different courses of action in the same situation. Of course, a law can have non-determinism of both types, firing, and action.

Connectors with non-deterministic laws, which we call boundary connectors, are our means of modeling interaction with the external world, e.g., people, or electronic devices. As part of the law is
known, the external world can’t function arbitrarily. The known part of the non-deterministic laws constitutes a harness (in terminology of [15]) on the external world behavior.

Now, the user’s role becomes clear, he/she is to help the connectors with non-deterministic laws. Such connector may be thought of as having a terminal where a human being can help the connector
to do its job. Let us assume that a connector’s law has action non-determinism. Then it is up to the connector in case when its operands have been changed, to request the human assistance via the
terminal by beeping, blinking, etc. After providing assistance, the human being may return to his other occupations, drinking coffee, for example, until the connector calls him again. Action
non-determinism may vary from allowing any possible structural changes in the connector’s operands to a selection from a list of predefined choices (menu).

Now, let a connector’s law have firing non-determinism. Such connector can be represented as a big button that the user presses from time to time based on observations that lie beyond the
boundaries of the computer system. Then it’s up to the connector to do the rest of the job. All other situations of non-determinism may be considered as a combination of these two cases.

Representing the user as a boundary connector insures flexibility in distribution of business tasks between the system and the user. In the initial introduction of the system, some connectors may
be defined as boundary, thus requiring user participation. After acquiring more knowledge on business laws, they may be substituted by totally deterministic connectors. Vice versa, some laws that
seemed to be totally deterministic may prove to need human assistance in the end. Switching between deterministic and non-deterministic laws will require adding/removing a user dialog script, which
is a minor problem comparing to changing the model (as normally is required in the traditional approaches).


5. How to distribute the user?

As was explained in the previous section, the role of the user is to assist boundary connectors. This idea would be enough for modeling purposes if there were only one user in the system. He/she
would be the only person to serve all the connectors that require human assistance. In the normal business reality, there are many users and they can be distributed between various business tasks
in many different ways. For example, suppose the gauge from the promotion queue in figure 9 cannot automatically evaluate the state of the inmate, and requires human assistance. The distribution of
human resources between different cells may vary from each cell having its own nurse (doctor) to the only person who serves all cells. The actual scheme, certainly, depends on the level of the
gauge’s intelligence. The more intelligent is the gauge, the less human resources it requires.

The distribution of users between various boundary connectors is not a simple task because the number of connectors and available users change in time. To cope with this task, we need to augment
the objects-connectors model described in the previous sections. First of all, we need to be able to differentiate one user from another. The natural way of doing this is by representing each user
as an object. Actually, the users are always part of business reality as they, normally, are employees of the company or organization whose business is to be modeled. And each employee should be
represented in the model as he/she has many business processes connected to it. For example, his/her salary should be calculated monthly, his/her professional level should be maintained via various
training programs, etc.

Secondly, we need a way of assigning an object that represents the user to the connector he/she is to assist to. This can be done by introducing in the model a set of assignment operators Q.
Different assignment operators serve to name various type of assistance the user can provide when helping a connector to do its job, e.g., head master, an assistant, etc. To each assignment
operator q from Q, we attach a type in the form t1 x t2 x … x tk, k ³ 0, where ti is an atomic type. The type defines the number and types of atoms that can be used to describe each
assignment. The atoms can be used, for example, to define an interval of time when a particular user is to assist a particular connector. This time may be absolute, or repetitive, e.g. each day
from 9 a.m. to 12 a.m.

Let q be an assignment operator of type t1 x t2 x … x tk, k ³ 0, v = be a k-tuple of atoms, such that vi Î Ati, i = 1 ,…, k, o be an object from O. Then the expression qv(o) is
called a resource allocation. By assigning each connector that exists in the world w at time t a set of resource allocations, we complete our model with the means to express resource assignments.
The assigned set can be empty, which is always the case with totally deterministic connectors. But it might be empty for boundary connectors too, which expresses the fact that human resources have
not been allocated to this connector yet.

Now, we need to understand who is to assign resources. This, naturally, is a connector, as it is the only element of our model that can perform actions. A new connector appears in our world only
when some other connector introduces it in the course of its action. If a new connector has a non-deterministic law, a human resource should be assigned to it. This may be done by a connector that
introduced the given one into the world. But it might be done by some other connector that serves as a resource manager. The latter watches the object were a new boundary connector has been
introduced, and as soon as he “sees” a connector without resource allocation, it performs resource assignment.

The two situations mentioned above have analogues in the management practice. The first case corresponds to a project manager that both defines the task, and assigns an available resource to it.
The second case corresponds to the matrix management, where the project manager just defines the task, and a separate resource manager finds appropriate resources to complete it. Note that both the
connector that creates a given boundary connector, and the one that assigns resources (if it is separated from the first one) can be boundary connectors themselves operated by the human project and
resource managers.

And finally, we need to understand how the assignments are done, which is the most difficult task. The simplest case of assigning resources is the assignment to “myself”, which means that the
creator of a new boundary connector assigns to it the same resource as it has itself. This case can be illustrated by en example where a user while editing some complex business object, decides to
edit another business object that is visible inside the first one, see figure 10. A new window is created to allow him to edit the new business object. This window is created on the same user
terminal as the initial one, thus the task of editing this new object is automatically handed to the same user as the one who edited the initial object, see figure 11.

 



Fig. 10.While editing the company object, the user decides that the person object that is visible inside the company object should be edied.

 



Fig. 11.The pesrson’s object window appears on the same terminal thus handing over the editing work to the same user.

When a task should be scheduled to somebody else, the assignment job becomes more complicated. So far we declared the law to be independent of objects it is meant to govern (see more on that in
[3]). The text of the law is external to the model, and the law condition and action do not depend on particular objects, only the object structure and behavior matter. However, when assigning
resources, we need to refer to particular objects. To cover the new challenge, additional modification of our model is required. At least some laws should become a part of the model. The natural
way to do this is by representing a law as an object. An example of such representation is shown in fig. 12.

 



Fig. 12.A law represented as an object

A law object in figure 12 is built with the help of three trivial laws LawText, LawArity, and LawResource. The unary connector LawText attaches the text of the law to the law object. The text of
the law is expressed with the help of an atom of some special type. This is a program written in a law programming language (more on the language issues see in [3]). The unary connector LawArity
defines the arity of the law represented by the law object. The arity is defined with the help of an integer atom. The LawResource connectors attach various resources to the given law, and assign
resource names with the help of string atoms. The text of the law does not refer to the actual objects. It refers only to the resource names. The LawResource connectors perform binding of the
resource names to the actual resources that exist in the model.

To make the law object work, we need to expand the definition of connector given in section 2. Now, we allow connectors to be defined as pairs c=, where o is an object from O, and z = is an n-tuple
of objects. We refer to this type of connectors as to compound connectors to differentiate them from the old-style connectors, which we call basic connectors.

As the law of the compound connector is an object, it can be changed by actions of other connectors. A change in the law object will force all connectors that impose this law to wake up, and check
whether the changed law still holds for their operands. This check concerns both the states of the connector’s operands, and the allocation of resources. Assume, for example, that the resource
binding of the law in figure 12 has been changed so that some user3 now functions as an Assistant resource instead of user2. Than all connectors that impose this law should adjust resource
assignments in their operands.

It is quite normal that there are several users that can do a particular type of job. When choosing the most appropriate one, the resource manager (i.e. a connector that serve as such) should take
into consideration other assignments of those users. It means that we need to reformulate the principle of localism mentioned in section 1.2. For resource assignment, the resource manager needs to
see all resource allocations made for the resources that are mentioned in its law object.

In conclusion, it is worthwhile to mention that direct binding of users to a law as in figure 12 was used only for demonstration purposes. While this method could be quite adequate for small
organizations, it might be too cumbersome for large organization. Actual binding can be done indirectly by referring to the user roles in law objects, and separately assigning those roles to the
users.


6. Related works

The idea of a device that guards some condition and performs some action when the condition is true is not new in the computer science theory and practice. It is expressed by such well known
metaphors as demons in AI and triggers in databases, and it is used in a number of modeling languages, see for example, [5]. Our notion of connector realizes this idea in a slightly different
fashion:

Normally, the condition is defined by a universal predicate, which means that the guard needs to observe the whole, or a large part of the database to find any place where the condition is true.
Our connector works locally, it guards only its own operands.

The connector is the only way of expressing relationships, be it passive or active relationships. Thus we use the same notion for describing both static data structures, and actions. The uniformity
allows treating actions in the same way as static links, i.e. we can add and delete actions in the same way as we add and delete static relationships during a database transaction.

Connectors are the only way to define actions. When a decomposition is required, the connector that guards the main law introduces connectors that guard some “local” laws between (part of) the
main connector’s operands. Then it is up to those local connectors to ensure that the local laws are satisfied. In case a local law is equal to the main one, we’ll get the recursive
decomposition. This idea was “borrowed” from the programming language Refal [14]. The recursive decomposition is illustrated in figure 13 that shows the decomposition done by the DeepMirrow law
(an analogue of the deep copy function or method).

We use the connector as the only way to model interaction with the external world.

 



Fig. 13.An example of recursive decomposition.

There are a number of other areas where our model has common features with other approaches. For example, the idea of representing the text of a program as data has its roots in the LISP
programming language. Resource allocation is one of the major themes of workflow literature, see for example [16]. Besides, the resource scheduling is a wide research and development area on its
own, see for example [11]. Concerning these fields, our research is not focused on finding new approaches to solving the problems that exist in them, but rather on how to incorporate the latest
results achieved in these fields into our objects-connectors model in the most natural way.

Note that our notion of connector differs from the similar notion used in the theory of architectural styles, see for example [13]. In [13], term connector is used to express “passive”
relationships between active components. In our model, this term is used to express active relationships between (relatively) “passive” objects. (More on the topic of active/passive
objects/relationships see in [3].)

As far as the concept of law-based programming is concerned, there is an interesting research on the law-governed architecture done by N.H. Minsky [10]. Though the basic idea of using the concept
of law for system definition and implementation is the same, the direction of its application is different. We apply the concept of law to describe local behavior, while in [10] laws are used to
describe global behavior. In our model the global behavior is determined by a number of global principles (see, [3]), where the principle of locality mentioned earlier is one of them.


7. Concluding remarks

The ideas presented in this paper come from our ongoing research and practical work. Our research is focused on developing a general framework for modeling discrete dynamic systems. Our practical
work is focused on business process analysis, and building business process support applications. The logical semantics of our theoretical framework is discussed in [3], the results of our
practical work are shortly reviewed in [2] (were the list of our other publications is presented).

In our practical work, we used the theoretical framework only as a methodology to check our practical decisions. For database design, we used only a reduced version of our theoretical model. As far
as connectors are concerned, they were programmed in an ad hoc fashion. With the current paper, we make a step towards developing a practical framework that can be used for modeling real business
situations. This step consisted of a detailed analysis of the role the user plays in our model. This analysis required a substantial extension of the model, e.g., introduction of allocation
operators, representing the users and the laws as objects, etc.

A lot of more work needs to be done to achieve the goal of converting our theoretical basis into a practical framework. The heaviest parts here are developing a practical system of modeling
notation, and designing a law programming language. Those are the main directions of our future work.


Acknowledgements

The work of the first author was partly supported by Stockholm foundation “TeknikBroStiftelsen”.

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This article was previously published in the
February, 2001 issue of the Journal of Conceptual Modeling (http://www.inconcept.com/JCM).

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