List of principles of Computer Science

5.4 Recurring Concepts

The discussion thus far has emphasized the division of computing into nine subject areas, three processes, and its social and professional context. However, certain fundamental concepts recur throughout the discipline and play an important role in the design of individual courses and whole curricula. Computing as a Discipline refers to some of these concepts as affinity groups or basic concerns throughout the discipline¹. The Take Force refers to these fundamental concepts as recurring concepts in this report.

Recurring concepts are significant ideas, concerns, principles and processes that help to unify an academic discipline at a deep level. An appreciation for the pervasiveness of these concepts and an ability to apply them in appropriate contexts is one indicator of a graduates maturity as a computer scientist or engineer. Clearly, in designing a particular curriculum, these recurring concepts must be communicated in an effective manner; it is important to note that the appropriate use of the recurring concepts is an essential element in the implementation of curricula and courses based upon the specifications given in this report. Additionally, these concepts can be used as underlying themes that help tie together curricular materials into cohesive courses.

Each recurring concept listed in this report

• Occurs throughout the discipline
• Has a variety of instantiations
• Has a high degree of technological independence

Thus, a recurring concept is any concept that pervades the discipline and is independent of any particular technology. A recurring concept is more fundamental than any of its instantiations. A recurring concept has established itself as fundamental and persistent over the history of computing and is likely to remain so for the foreseeable future.

In addition to the three characteristics given above, most recurring concepts

• Have instantiations at the levels of theory, abstraction and design
• Have instantiations in each of the nine subject areas
• Occur generally in mathematics, science and engineering

These additional points make a strong assertion concerning the pervasiveness and persistence of most of the recurring concepts. Not only do they recur throughout the discipline, they do so across the nine subject areas and across the levels of theory, abstraction and design. Furthermore, most are instances of even more general concepts that pervade mathematics, science and engineering.

Below is a list of twelve recurring concepts that we have identified as fundamental to computing. Each concept is followed by a brief description and a characterization in terms of concrete examples. In the remainder of the report, each is explicitly referenced whenever it appears within a curriculum element of the common requirements.

Binding: the processes of making an abstraction more concrete by associating additional properties with it. Examples include associating (assigning) a process with a processor, associating a type with a variable name, associating a library object program with a symbolic reference to a subprogram, instantiation in logic programming, associating a method with a message in an object-oriented language, creating concrete instances from abstract descriptions.

Complexity of large problems: the effects of the nonlinear increase in complexity as the size of a problem grows. This is an important factor in distinguishing and selecting methods that scale to different data sizes, problem spaces, and program sizes. In large programming projects, it is a factor in determining the organization of an implementation team.

Conceptual and formal models: various ways of formalizing, characterizing, visualizing and thinking about an idea or problem. Examples include formal models in logic, switching theory and the theory of computation, programming language paradigms based upon formal models, conceptual models such as abstract data types and semantic data models, and visual languages used in specifying and designing systems, such as data flow and entity-relationship diagrams.

Consistency and completeness: concrete realizations of the concepts of consistency and completeness in computing, including related concepts such as correctness, robustness, and reliability. Consistency includes the consistency of a set of axioms that serve as a formal specification, the consistency of theory to observed fact, and internal consistency of a language or interface design. Correctness can be viewed as the consistency of component or system behavior to stated specifications. Completeness includes the adequacy of a given set of axioms to capture all desired behaviors, functional adequacy of software and hardware systems, and the ability of a system to behave well under error conditions and unanticipated situations.

Efficiency: measures of cost relative to resources such as space, time, money and people. Examples include the theoretical assessment of the space and time complexity of an algorithm, feasibility, the efficiency with which a certain desirable result (such as the completion of a project or the manufacture of a component) can be achieved, and the efficiency of a given implementation relative to alternative implementations.

Evolution: the fact of change and its implications. The impact of change at all levels and the resiliency and adequacy of abstractions, techniques and systems in the face of change. Examples include the ability of formal models to represent aspects of systems that vary with time, and the ability of a design to withstand changing environmental demands and changing requirements, tools and facilities for configuration management.

Levels of Abstraction: the nature and use of abstraction in computing; the use of abstraction in managing complexity, structuring systems, hiding details, and capturing recurring patterns; the ability to represent an entity or system by abstractions having different levels of detail and specificity. Examples include levels of hardware description, levels of specificity within an object hierarchy, the notion of generics in programming languages, and the levels of detail provided in a problem solution from specifications though code.

Ordering in space: the concepts of locality and proximity in the discipline of computing. In addition to physical location, as in networks or memory, this includes organizational location (e.g., of processors, processes, type definitions, and associated operations) and conceptual location (e.g., software scoping, coupling, and cohesion).

Ordering in time: the concept of time in the ordering of events. This includes time as a parameter in formal models (e.g., in temporal logic), time as a means of synchronizing processes that are spread out over space, time as an essential element in the execution of algorithms.

Reuse: the ability of a particular technique, concept or systems to respond appropriately to be reused in a new context or situation. Examples include probability, the reuse of software libraries and hardware components, technologies that promote reuse of software components, and language abstractions that promote the development of reusable software modules.

Security: the ability of software and hardware systems to respond appropriately to and defend themselves against inappropriate and unanticipated requests; the ability of a computer installation to withstand catastrophic events (e.g., natural disasters and attempts at sabotage). Examples include type-checking and other concepts in programming languages that provide protection against misuse of data objects and functions, data encryption, granting and revoking of privileges by a database management system, features in user interfaces that minimize user errors, physical security measures at computer facilities, and security mechanisms at various levels in a system.

Tradeoffs and consequences: the phenomenon of trade-offs in computing and the consequences of such trade-offs. The technical, economic, cultural and other effects of selecting one design alternative over another. Trade-offs are a fundamental fact of life at all levels and in all subject areas. Examples include space-time trade-offs in the study of algorithms, trade-offs inherent in conflicting design objectives (e.g., ease of use versus completeness, flexibility versus simplicity, low cost versus high reliability and so forth), design trade-offs in hardware, and trade-offs implied in attempts to optimize computing power in the face of a variety of constraints.

In constructing curricula from the overall specifications of the Task Force, curriculum designers must be aware of the fundamental role played by recurring concepts. That is, a recurring concept (or a set of recurring concepts) can help to unify the design of a course, a lecture, or a laboratory exercise. From the instructors perspective (and also from the students perspective) a course is rarely satisfying unless there is some "big idea" that seems to hold disparate elements together. We see the use of recurring concepts as one method for unifying the material in a course.

At the level of the entire curriculum, the recurring concepts also play a unifying role. They can be used as threads that tie and bind different courses together. For example, in introducing the concept of consistency as applied to language design in a programming language course, the instructor might ask students to consider other contexts in which consistency played an important role, such as in a previous software engineering or user interfaces course. By pointing out and discussing the recurring concepts as they arise, the conscientious instructor can help portray computing as a coherent discipline rather than as a collection of unrelated topics.