It is surprisingly difficult to separate form from function. In common speech, we refer to form with function words. Try describing a paper coffee cup, a pencil, or a spiral notebook without any reference to function. If you used the words “handle,” “eraser,” and “binding,” you were using words rooted in a function. To stay entirely in the form domain, we might use “flat cardboard half-circle,” “rubber cylinder,” and “metal spiral.” One objective of this chapter is to clearly distinguish form from function.

Form is what has been or is eventually implemented. Form is eventually built, written, composed, manufactured, or assembled. Form is about existence. As indicated by the definition in Box 4.1, the first test for form is that it exists. Form is what the system is. It is the concrete and often visible manifestation of the system. The clause “for some period of time” is included in the definition to enable us to discuss the form of things that have existed in the past (analysis of historical systems) or will exist in the future (analysis of system designs).

The second test for form is that it is instrumental in the execution of function. For this function to occur, there usually needs to be some instrument to facilitate the function, or to “carry” the function. Form is what is eventually operated to deliver function and value.

Consider the beach house shown in Figure 4.1. What is the form? The form can be interpreted as the spaces in the house—the grand room, the kitchen, and so on. The kitchen space exists and facilitates food preparation and conversation (function). In the emergency instructions shown in Figure 4.2, the structure is that some of the individual pictures are in sequence (reinforced by the numbering), and then, at a higher level, some of the sequenced pictures are prefaced by other, smaller pictures or letters.

Form includes the sum of the entities, which are the elements or chunks of form. These are elements of the whole, and this is the whole–part relationship for form. Form also includes the relationship among the entities of form, which is often called the structure. Form is the entities of form plus the structure.

In the case of the beach house, the formal relationships are easily represented by the floor plan, which shows the spatial relationships among the spaces. In the emergency instructions, the structure is that some of the individual pictures are in sequence (reinforced by the numbering), and then, at a higher level, some of the sequenced pictures are prefaced by other, smaller pictures and are in blocks indicated by horizontal rules.

Form is a system attribute; it is an independent way in which to view or characterize the system. Form is also part of the solution that the architect is proposing.

Each discipline has developed its own shorthand for representing form. Form was first represented by words, such as the way national constitutions describe the form of government. Next, representational maps and drawings were developed: illustrations, schematics, drawings, three-dimensional views, and perspective diagrams. These attempt to represent some sub-scale yet realistic image of the system. Later, symbolic representations were developed: equations, pseudocode, circuit diagrams, and the like. The symbols used in these diagrams have only ­abstract meaning.

We seek a way to represent the form of any system—natural, evolved, built, mechanical, electrical, biological, or informational—with the same set of semantically exact representations. These facilitate analysis, communication across disciplines, and the capture of knowledge.

The representation we adopt in this text closely follows Dori’s Object Process Methodology (Chapter 3). Dori determined that systems can be represented with only two classes of ­abstractions: objects and processes (hence the name). “Together, objects and processes faithfully describe the system’s structure, function and behavior in a single, coherent model in virtually any domain.” ^[1]

The definition of an object in Box 4.2 was deliberately phrased in such a way that it closely reflects the first part of the definition of form, so that objects could be used to represent form. However, the definition of form (Box 4.1) contains the additional criteria that the form must be instrumental of function and must exist before function. Objects that do not meet these additional criteria are operands, as discussed in Chapter 5. Generally, the names of objects are nouns.

Figure 4.1 shows a beach house that is an object, which is both physical and tangible. The rooms of the house are also objects. In Figure 4.2, the instructional drawings are objects, as are the smaller drawings to the upper left of the boxes.

Objects can also be informational. Dori defines an informational object as anything that can be comprehended intellectually, which implies that it exists. Informational objects include ideas, thoughts, arguments, instructions, conditions, and data. Domains such as control systems, software, mathematics, and policy make extensive use of informational objects.

One of the defining characteristics of objects is that they have characteristics or attributes that describe the object. An object can have physical, electrical, or logical attributes. Some of these attributes can be considered as states, in which an object can exist for some duration of time. A process can change an object’s state. The combination of all states describes the possible configuration of state of the object.

When our beach house is being built, its state of construction goes from “not built” to “built.” When people arrive, its state of occupancy goes from “unoccupied” to “occupied.” When the furnace runs, its state of temperature goes from “cooler” to “warmer.” In this example, the attributes and corresponding states are construction (unbuilt/built), occupancy (unoccupied/occupied), and temperature (cool/warm).

The graphical representations for an object are adopted from Object Process Methodology (OPM), where objects are denoted with rectangles (Figure 4.3). The representation on the left simply defines an object, and the one in the center shows possible states of the object. On the right, the “double triangle” on the line from the object to the attribute is read as the relationship “is characterized by.” The lower box lists the attribute and possible states.

Note that objects in SysML have different representations, depending on whether they are physical objects, human operators or users, or something else.

Decomposing entities into appropriate abstractions was discussed in Section 3.3. Decomposing form comes naturally to architects. Form is concrete, it decomposes easily, and the aggregation of form traces the decomposition in a simple way.

Decomposition is represented in OPM by a graphical tree diagram, as shown in Figure 4.4. The black triangle is used to indicate decomposition. This diagram shows that System 0 (the object at Level 0) decomposes into the objects at Level 1, which correspondingly aggregate into System 0.

In summary:

• Form is a system attribute that includes the elements that exist and are instrumental in the execution of function. Form is implemented and eventually operated.

• Form will be modeled as objects of form, plus the formal structure among them.

• Objects are static entities that exist and have attributes; among these are states that can be changed by a process.

• Form can be decomposed into smaller entities of form, which in turn aggregate into larger entities of form.