Using Programming Language Concepts to Teach General ThinkingSkills

Martin RinardDepartment of Electrical Engineering and Computer Science

Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of Technology

Cambridge, MA 021139

1. IntroductionProgramming languages have traditionally been seen as ofinterest only to software developers (who need to use lan-guages to pursue their chosen profession). But the field hasdeveloped in response to an unprecedented situation in hu-man history — the need to communicate with entities (i.e.,computers) that are capable of carrying out very sophisti-cated computations involving prodigious amounts of infor-mation, but only if every aspect of the computation andinformation representation is specified explicitly and com-pletely. Because of the need to make everything explicit andprecise, concepts that arise in almost all human endeavorsare present with unique precision, sophistication, clarity, andtherefore accessibility. The availability of immediate, auto-mated feedback through appropriate interaction with a com-puter enhances the accessibility of the concepts and pro-motes a fully rigorous approach that makes it difficult fora student to slide by with only a partial understanding. Inthis white paper I focus on three fundamental concepts:

• Multiple Formal Perspectives: Each programming lan-guage embodies a particular perspective on computation.Researchers have developed a wide range of languages,each with its own perspective. Because these languagesare interactively explorable on a computer and have a pre-cise semantics, studying programming languages is theideal context in which to develop an understanding of1) how different perspectives are appropriate for differ-ent problems and 2) that the perspective one employs caninfluence or even determine the outcome of a particularendeavor.

• Automation and Translation: Computers provide anunprecedented potential to automate tasks. Advances inautomation correspond directly to advances in our abilityto effectively manage the activities of our society. Thedrive to automate also fosters new, more general, andmore productive ways of thinking about classes of prob-lems.

Much of the automation in programming languages dealswith the translation of computer programs from one lan-guage into another. Advances in programming languagesoften correspond directly to advances in the automationof tasks previously performed by programmers. Automa-tion and translation therefore provide an appropriate con-text for the exploration of which tasks should be auto-mated and which should be left to humans. Understand-ing translation also provides students with a much deeperunderstanding of computation and an important systemsbuilding tool.

• Abstraction: Programming languages has produced alarger, more precise, and more sophisticated range of ab-stractions than any other field. It is therefore the idealcontext in which to build an understanding of abstrac-tions. This understanding is a core prerequisite for a suc-cessful career in computer science. It can also be one ofthe keys to understanding unstated assumptions in otherfields, which in turn opens the door to new ways of con-ceptualizing and eliminating limitations in these fields.

In addition to providing reasoning skills and specific tech-niques that students will be able to draw on for their entirecareers, a solid understanding of and ability to appropriatelydraw on these concepts can dramatically increase a person’sability to conceptualize, understand, and reason about vari-ous aspects of the intellectual and physical world in whichwe all live. Acquiring this understanding can therefore bean important (and in some cases even critical) component ofthe education of virtually any student, whether that studentchooses to pursue a career involving any aspect of computertechnology or not. Indeed, developing an understanding andmastery of these concepts in a rigorous context (such as theone that programming languages provides) may be more im-portant for someone who pursues a career based largely onthe humanities than for a practicing scientist or engineer.Through his or her daily work activities, a scientist or en-gineer will acquire at least a rough working understandingof the capabilities and limitations of formal reasoning as ap-

plied to his or her area of specialization. But someone whofocuses exclusively on the humanities can easily fall into thetrap of failing to appreciate or even recognize the need for aformal and precise approach when it is appropriate. An ef-fective education can eliminate this shortcoming and enablethe student to bring a deeper and ultimately more produc-tive understanding to whatever endeavor he or she winds uppursuing.

2. Multiple Formal PerspectivesEach programming language provides a perspective — anidentification of basic concepts that people use to formulateand solve problems in a domain of interest. Programminglanguages are typically designed to specify computations ona digital computer and therefore (potentially in combinationwith their implementation) have a completely precise formalsemantics. Understanding that such a thing is possible andin some cases desirable is already an important intellectualleap. Students should acquire this understanding as part ofan introductory class in computer science when they writecomputer programs.

The additional contribution that a programming lan-guages class can make is understanding that there are multi-ple possible perspectives, and that the perspective one usescan make an enormous difference in the result one achieves.Specifically, the perspective affects and can even shape thefollowing activities:

• Problem Choice: Because the perspective provides away of thinking, it influences the problems one perceivesand attempts to solve.

• Problem Formulation: Once one has identified a prob-lem, the perspective plays an important role in how theproblem is formulated — which parts of the problem onepays attention to and develops, which parts one ignoresor even remains oblivious to.

• Problem Solution: There is a continuum of program-ming languages ranging from general-purpose languages(such as Java and C++) designed to support virtually anycomputation through to domain-specific languages de-signed to support only a very narrowly focused class ofcomputations. There are also general-purpose languages(such as Prolog, Scheme, or ML) whose basic conceptsand approaches differ significantly from other more pop-ular general-purpose languages. It is well known thatsome languages work much better for solving certainclasses of problems than others. When a language anda problem domain work well together, the solutions aremore compact, easier to understand, and (as discussedfurther below) more reliable. Indeed, a large enough mis-match can make it impossible to satisfactorily solve a theproblem.

• Errors: People working with a language and perspec-tive that matches the basic concepts of the problem do-

main make many fewer errors than people working witha language that is less well matched. The reason is thatworking through a translation from the concepts in theproblem domain to the concepts in the problem solutionimposes a cognitive burden. Errors are often the resultof this burden overwhelming the cognitive capacity ofthe person developing the solution. One of the reasonswhy programs written in general-purpose programminglanguages tend to have more errors than programs writ-ten in domain-specific languages is that general-purposelanguages almost always impose a more complex con-cept translation than domain-specific languages (whichideally impose no concept translation at all).

2.1 Intellectual ImportanceUnderstanding that perspectives can have such a powerfulimpact on results is an important realization. Most peo-ple adopt their perspectives unconsciously, to the point thatmuch of the time they are not explicitly aware that they havea perspective at all. Knowing that alternate and potentiallydifferent or better perspectives are always available is a keystage in one’s intellectual development. It helps people bet-ter understand the limitations of their reasoning, more read-ily listen to others that may have different perspectives, andintegrate a multiple perspective approach explicitly into theway they choose, formulate, and solve problems. A personwith this understanding can operate more effectively in arange of contexts that occur in all aspects of life, not justthe professional activities of a computer scientist.

Given that this is such an important and general conceptwith such broad applicability, why is it best taught in thecontext of a programming language class (or, for that matter,in the context of computer science at all)? The reason is thatthe combination of programming languages and automated,immediate feedback via execution on a computer helps tomake the concept precise, immediate, and accessible to stu-dents. For example, solving the same problem using two dif-ferent languages with different (mis)matches to the conceptsin the domain can make the importance of the perspectivepainfully obvious. This experience can prepare the studentto then better comprehend the concepts associated with thepresence of multiple perspectives when they are introducedas a topic of reflection after the exercise.

Activities in the humanities, in contrast, tend to be muchmore abstract, indirect, and imprecise. The feedback cycle islonger and the evaluation less clear cut. Because the evalua-tion is delayed and not automated, students can often cut cor-ners and miss key details with no immediate consequencesor feedback. The result is that students are less prepared tounderstand the significance of multiple perspectives, mustmake more of an intellectual leap to develop this understand-ing, and can more easily come away from the experiencewithout having grasped the concept. Other fields of com-puter science and engineering tend to come with one spe-cific perspective that works well in that field — indeed, one

of the primary purposes of education in that field is typi-cally to transmit that perspective to students. Programminglanguages is close to unique in its heavy emphasis on mul-tiple perspectives (as embodied precisely and concretely indifferent languages) as a central motif of the field. It is there-fore the ideal field in which to explore this broad and generalconcept.

2.2 Pragmatic ApplicationsUnderstanding the importance of perspectives on solutioneffectiveness will be central to the success of students whochoose to pursue careers in computer science or other areaswith a strong technical component. Many tasks now involvethe use of multiple programming languages, each with theirown strengths and weaknesses, and understanding how topartition the problem across the languages is crucial to de-veloping an effective solution. Even a problem as commonas building a database-backed web service may involve theuse of a scripting language, a database interface language,a traditional general-purpose programming language, and ahypertext preprocessor. Understanding how to operate effec-tively in these kinds of multilingual environments (and thepotentially even more complex multilingual environments ofthe more sophisticated systems our students will develop inthe future) will be crucial to the career success of our stu-dents.

One effective strategy is to organize the development ofa system around a set of domain-specific languages engi-neered for that purpose. This approach can be dramaticallymore productive than the standard approach of using off-the-shelf languages that may not be as well suited to the task.This approach, however, requires a very talented developers.It is not clear how many of our students can be educated tothis level of skill. There are two reasons why it is importantto expose all students to this approach. First, it helps to en-sure that students who do have the inherent potential to usethis approach become exposed to the ideas they need to real-ize this potential. And second, it helps students who do nothave this potential to be better able to work effectively insuch an environment.

3. Automation and TranslationThe emergence of automated systems with the capability, so-phistication, and scale of modern computers is a landmarkaccomplishment in technology. The result is a dramatic in-crease in the inherent range of accomplishment potentiallyavailable to our species. But to realize this potential, we mustunderstand which tasks to automate and which tasks are bet-ter left to humans. Note that this division will have a directimpact on our self-image as human beings and our concep-tion of our place in the universe. Societies have a need toidentify things that place humans apart. The discovery or de-velopment of other entities that can perform activities previ-ously believed to be the exclusive province of humans can

affect our perception of what it means to be human. Be-fore the development of calculators, for example, the abil-ity to do arithmetic quickly and accurately had great valueand was perceived as something that set humans apart fromother entities. A person could command respect in societybecause he or she had this ability. But as soon as a cheap au-tomated alternative was available, this ability was devaluedto the point that it was no longer considered to be a particu-larly valuable or distinctive human attribute at all.

3.1 Intellectual ImportanceThe development of every computer program has compo-nents that are today identified as human, valuable, and cre-ative (identifying the problem to solve, creating the design tosolve the problem, and building the solution) and others thatare identified as appropriate for automation (the tasks asso-ciated with compiling the program into a executable repre-sentation). Moreover, the development of programming lan-guages as a field has been driven in large part by the transferof activities from the human domain to the automated do-main. The emergence of high-level languages such as For-tran, for example, was predicated on the development of au-tomated techniques such as allocating values to machine reg-isters for computation and laying out data structures such asarrays in memory. Finally, there is an effective way to eval-uate whether or not a specific division of tasks between hu-mans and the automated system is productive — either theresulting system works or it doesn’t.

3.1.1 Obtaining AutomationProgramming languages therefore provides a rich context inwhich to explore questions relating to the division of tasksbetween automated systems and humans. The field supportshistorical approaches that look backward in time (how didcertain tasks become automated and what was the impact ofthe automation), speculative approaches that look forwardin time (what new programming language constructs canwe develop with automated support in the implementation),and integrated approaches that combine the two. The precisenature of programming languages and computer programsallows questions to be posed with great precision. Becauseeach language has an implementation, students can interactwith the computer to quickly gain a comprehensive under-standing of the automation and its value. Once students haveexplored questions related to the division of automation inprogramming languages, they are then prepared to see sim-ilar issues in other fields and work effectively to automateappropriate aspects of those fields.

3.1.2 Thinking Generally and ComprehensivelyAutomating various aspects of tasks also develops key think-ing skills. In most fields practitioners and researchers dealwith a single specific problem at a time. They therefore de-velop thinking skills oriented around obtaining insightfulpoint solutions for clearly defined problem instances. But

to develop an automated system, one must think more gen-erally and comprehensively to anticipate all of the impor-tant cases that can arise. This is a fundamentally differentway of thinking. Mastering this kind of thinking can providean enormous amplification effect as tasks that previouslyrequired human attention are shifted to an automated sys-tem. A common result is a dramatic increase in the scale ofprogress in the field — in some cases, it is possible to replaceyears of human effort with days or minutes of computing.Another advantage is the increased insight that comes fromobtaining a more general perspective on the field. This gen-eral perspective can lead to new breakthroughs as the sim-ilarities between different problems become apparent andsuggest new directions of understanding and exploration.

Programming languages is ideally placed as a field forexploring these issues. Existing languages provide the con-cepts and intellectual stimulation people need to automatevarious aspects. Moreover, the design of programming lan-guages is the ultimate in general thinking — one is not sim-ply using a building a system that automates some aspect of agiven problem, but instead building a general tool that peoplecan use to solve a variety of automation tasks. In this sense,the field of programming languages occupies a unique posi-tion within the entire field of human intellectual endeavor.

3.1.3 Planning Versus ImprovisationTranslation inherently involves questions of when activitiesshould happen. In almost every programming language im-plementation some activities take place before the programruns, which others take place only when the program runs.Understanding the tradeoffs involved in selecting where toplace each activity can provide great insight into the greaterissue of planning versus improvisation (two components ofalmost any human activity). Programming languages pro-vides a productive educational environment for exploringthis tradeoff, in part because it makes the trade-offs so obvi-ous and easily accessible. A comparison of the time requiredto interpret a program versus the time required to run a com-piled version provides an immediate and concrete illustra-tion of the power of planning and setting things up ahead oftime. On the other hand, understanding that other tasks sim-ply cannot be performed without information that is avail-able only when the program runs can also provide impor-tant insight. Finally, exploring the fluidity of moving tasksbetween compile time and run time (and the ramificationson programming language design) can provide insight intothe advantages and disadvantages of planning and improvi-sation.

Embracing translation also provides a qualitatively deeperunderstanding of how to organize computation. Instead ofsimply having a program that executes, students can appre-ciate the more general concept of sequencing computationin stages as information becomes available over time. Thewhole concept of meta-computation — programs that ma-nipulate other programs — introduces a new level of sophis-

tication and helps students understand a much wider rangeof system structuring possibilities and techniques. Program-ming languages is the field with the greatest development ofthese ideas and therefore the field that is best placed to teachthem.

3.2 Pragmatic ApplicationsEvery computer science professional uses a compiler or pre-processor. Studying translation provides the concepts re-quired to better understand and utilize the system in whichthe work takes place. Moreover, understanding how to writetranslators provides students with a powerful tool they canuse to build systems more efficiently and effectively. Forexample, it enables them to build preprocessors, domain-specific languages, consistency checkers, and other tools thatcan improve their productivity and help them eliminate er-rors. It is important to understand that approaching develop-ment in this way, instead of simply using existing general-purpose approaches, can transform the development process,the cost of development, and both the functionality and qual-ity of the resulting product.

4. AbstractionComputer systems are tremendously complicated, arguablythe most complex systems ever engineered. Abstraction (aprincipled discarding of detail) is therefore a central themein virtually every field of computer science. But abstractionhas developed most fully and completely in programminglanguages and is therefore most productively taught in thecontext of a course that focuses on programming languages.Consider the ways in which abstraction arises in program-ming languages:

• Language Design and Features: Most programminglanguages are abstractions of the underlying computingplatform. The abstraction is made precise and, at somelevel, accessible via the implementation of the language.

• Interfaces: Each interface is an abstraction of the encap-sulated functionality. Interfaces in general-purpose lan-guages often provide a way to preserve some of the struc-ture from the application domain in the final encoding ofconcepts from the domain in the program.

• Specifications: Specifications abstract the informationthat computations manipulate and the results and effectsthat the computation generates. Specifications are partic-ularly interesting because they make the distinction be-tween requirements and program behavior explicit andprecise.

• Types: Types abstract the computations and informa-tion that the computation manipulates. Strictly speaking,types are merely a specific form of partial specification.However, types seem to hit a sweet spot in the specifi-cation space — they are often intuitive for programmersto provide, are efficiently and modularly checkable, and

have become the focus of a large part of the field of pro-gramming languages.

• Program Analysis: Program analyses work with ab-stractions of the state and computation. This abstractionis necessary to make the analysis tractable and able tooperate without access to information that is availableonly when the program executes.

No other field comes close to providing abstractions withthis level of variety, sophistication, and precision. In com-parison with other fields, the precision of the abstractions isparticularly well developed in programming languages. Theconcrete and abstract domains are often formally specified,as are the mappings between the two domains.

4.1 Intellectual ImportanceAbstraction is a necessary process that most people engagein unconsciously. But an inappropriate abstraction can beproblematic — if one discards important information duringthe process of abstraction, they can limit their thinking,acquire blind spots, or come to the wrong conclusion.

The explicit, overt, and precise nature of abstraction inprogramming languages can help students develop a gen-eral framework that they can use to improve their reason-ing in other fields. This framework will help students per-ceive and understand both the need for abstraction and thepotential problems that are an inevitable consequence of itsuse. Building on their experience with abstraction in pro-gramming languages, they will also be more able to see, un-derstand, and criticize the implicit abstractions that they andothers make in other fields where the abstractions are muchless obvious and potentially even part of a standard and oth-erwise unquestioned approach. If students learn to apply aprocess of seeking out abstractions, understanding the result-ing limitations, then, when appropriate, developing new ab-stractions that remove inappropriate limitations, they will bebetter able to understand how to innovate around shortcom-ings and challenge ways of thinking that have, over time,become limited or even counterproductive. When applied bysomeone with a sufficient command of the process, it caneven become a mechanism for generating insights, creativ-ity, and productive new directions upon demand.

4.2 Pragmatic ApplicationsComputer science professionals must deal with abstractionson a daily basis. Knowledge of programming language ab-stractions and how to use them is a prerequisite for function-ing effectively in any professional environment. Moreover,many computer science professionals spend much of theirtime designing abstracts. A deeper understanding of abstrac-tions in general can help them design more effective abstrac-tions.

5. Potential Teaching ApproachesThe field of programming languages is rich enough to sup-port many productive teaching approaches. I outline twosuch approaches, but recognize that there are other ap-proaches that may be equally or even more productive.

Both of the approaches start with software developmentactivities. One advantage of this starting point is that it lever-ages the immediate feedback and precision that interactingwith a computer provides and requires, which makes theconcepts obvious and accessible. It is also possible to struc-ture the software development activities to emphasize spe-cific skills or approaches that students can immediately usein a professional software development career. It is also pos-sible to take a more theoretical approach that starts withmathematical modelling or analysis activities. In either case,however, the most important part of the educational experi-ence is reflecting on the concepts that the specific activitiesillustrate. This reflection is crucial to enabling students togeneralize the concepts to apply them productively in dif-ferent contexts, which is the most important and valuablelesson of the course. One way to incorporate this reflectioninto the course is to require students to perform additionalassignments (typically in essay form) that demonstrate theapplication of the acquired concepts to a field outside of pro-gramming languages.

5.1 A Domain-Specific LanguageThis approach would organize the course around designingand implementing a language for computations in a particu-lar domain. The course would be composed of several stages.The first would be to develop and understanding of the ba-sic concepts in the domain. The second would be to designa language that supported the concepts explicitly. The thirdwould be to implement the language. Finally, the studentswould implement several computations in the language.

Successfully developing the engineering artifacts wouldbe only part of the educational process. The arguably moreimportant part would be using the engineering experienceas a foundation for reflecting on the different concepts.To this end students would write essays focusing on howtheir experiences relate to multiple perspectives, automa-tion and translation, and abstraction in other contexts. Ide-ally, students would understand that the concepts in thedomain-specific language were different from the conceptsin general-purpose languages (the course would assume thatprevious introductory courses have already provided the stu-dents with knowledge of at least one such language) and thatproviding these concepts explicitly in the language providesa more productive perspective for computations in the do-main than the perspective from general-purpose languages.Students would also understand that making the domain con-cepts explicit in the language shapes how they formulate andsolve problems in the domain.

They would also understand how to generalize this ex-ample to understand that other perspectives would be usefulin other domains, and indeed that some domains would becomplex enough to justify the use of multiple perspectives.Finally, they would understand that it is possible (althoughpotentially not ideal) to explicitly adopt a given perspectiveduring the engineering of the system even though one mayuse a general-purpose language instead of a domain-specificlanguage.

Students would address the automation and translationconcepts as part of the implementation of the domain-specific language. They would understand that certain as-pects of the implementation were automated by the imple-mentation of the domain-specific language, and that theseaspects would instead be performed by the human developerif the system were built in a general-purpose language. Theywould also understand how to generalize the basic conceptsillustrated in this exercise to obtain an understanding of howautomating tasks can make people more productive, that au-tomation requires thinking about the general case as opposedto any specific single problem at hand, and that some tasksare still better left to humans. The implementation of thedomain-specific language would provide a concrete exam-ple of the power of translation in packaging automation foreffective use by developers. Ideally, students would be ableto build on this experience to become more aware of the po-tential benefits and drawbacks of automation, more able touse it effectively in their careers, and to better understandwhat kind of tasks are best automated and what kind of tasksshould be done by humans.

One way to address abstraction would be to develop atype system for the domain-specific language. Ideally, thestudents would formulate a formal connection between thesemantics of the full language and the abstract semanticsthat the type system induces. They would understand thepurposeful discarding of information involved in the abstrac-tion and the benefits and drawbacks of discarding the infor-mation. They would be able to generalize the experience toformulate frameworks for abstraction in other fields, be ableto understand the benefits and drawbacks of using abstrac-tions, and be prepared to identify (and if appropriate discard)otherwise implicit abstractions present in a variety of fields.

5.2 Different Language ParadigmInstead of developing a domain-specific language, one couldinstead start with an existing language whose basic approachand concepts differ substantially from those of conventionalprogramming languages. In this case, going through the ex-ercise would help students understand the importance of dif-ferent perspectives and how perspectives shape the under-standing and engineering process. The automation and trans-lation aspect could be covered by studying the implementa-tion of the logic programming language. One productive ap-proach could be to ask the students to implement a simplelanguage based on the core concepts of logic programming.

Developing an analysis for the language, either to supportefficient implementation or to check certain desirable prop-erties, could be an effective way to introduce the concept ofabstraction.

The important point here is not that logic programmingis necessarily valuable in and of itself or that students willnecessarily use the specific concepts in logic programmingin their careers. Rather, the use of logic programming in anappropriately structured course (like the use of other non-mainstream approaches) can illustrate general concepts andmake those concepts accessible to students in an immediateand concrete way.

6. ConclusionThe field of programming languages provides a uniquelyfavorable context for teaching certain fundamental conceptsthat arise in almost all modern human endeavors. Theseconcepts include:

• Understanding the central role that one’s perspectiveplays in the entire problem conceptualization, formula-tion, and solution process,

• Understanding that multiple perspectives are available,with different perspectives appropriate for different prob-lems,

• Understanding how automation can greatly improve hu-man productivity and that there is an appropriate divisionof tasks between automated systems and humans, and

• Understanding a precise notion of abstraction, that ab-straction is inevitably present in every activity, and thatdifferent abstractions are appropriate for different pur-poses and situations.

Most people will immediately accept these concepts; somewill even claim that they are obvious. But approaching theseconcepts through programming languages makes them pre-cise, explicit, and clear. Students can work with them in aninteractive setting that provides immediate feedback and re-quires completely precise thinking. This approach can there-fore provide part of the solid, foundational understandingthat all individuals, and not just computer scientists, needto think clearly and be truly effective in whatever endeavorthey choose to pursue.