To Scheme, or Not to Scheme: Scheming Schemers and Non-Scheming Schemers, or Keeping the Fun in Scheme

Do you use the Scheme programming language? If so, do you program mainly in a serious mood to write applications, or in a crafty mood to have fun? In other words, do you consider yourself a non-Scheming Schemer, or a Scheming Schemer? I consider myself a Scheming Schemer: I program in Scheme mainly in a crafty mood just to have fun. To quote Alan Perlis from the dedication in SICP:

“I think that it’s extraordinarily important that we in computer science keep fun in computing. When it started out, it was an awful lot of fun. Of course, the paying customers got shafted every now and then, and after a while we began to take their complaints seriously. We began to feel as if we really were responsible for the successful, error-free perfect use of these machines. I don’t think we are. I think we’re responsible for stretching them, setting them off in new directions, and keeping fun in the house. I hope the field of computer science never loses its sense of fun. Above all, I hope we don’t become missionaries. Don’t feel as if you’re Bible salesmen. The world has too many of those already. What you know about computing other people will learn. Don’t feel as if the key to successful computing is only in your hands. What’s in your hands, I think and hope, is intelligence: the ability to see the machine as more than when you were first led up to it, that you can make it more.”

Alan J. Perlis (April 1, 1922-February 7, 1990)

Nevertheless, as many of you probably know, some recent developments in the evolution of the Scheme programming language have reduced the influence of the language. In particular, the R5RS vs. R6RS schism and the replacement of the 6.001 course at MIT, based on Scheme, with a 6.01 course, based on Python, are two events that have created much controversy.

Concerned over such events, recently, I posted a thread, entitled “Ideas for an SICP’?” on the comp.lang.scheme USENET newsgroup, asking for suggestions for an alternative to SICP with a similar content, as follows:

[W]ith Scheme replaced by Python at MIT, this special role of Scheme
as the vehicle for teaching sophisticated students of computer science
has been greatly diminished. Arguments against SICP as being too
difficult for an introductory textbook notwithstanding, the presence
and usage of that textbook contributed greatly to the significance of
Scheme as a tool in teaching introductory computer science.

It seems that SICP could use a replacement. What is needed is an
alternative textbook to use Scheme in a role that cannot be fulfilled
by such languages as Python, in order to foster creativity and
originality in programming for future freethinking hackers. In
addition, such an alternative textbook would need to be actively used
by leading educational institutions of introductory computer science
in raising a new generation of future Scheme hackers.

Does anybody have any suggestions for a plan that could lead to the
birth and growth of such an alternative leading textbook? Many
programmers tend to be strongly influenced by the first textbook that
they encounter in learning programming; whether that language is
Scheme or Python could have great effect on the future influence of
such languages. The SICP phenomenon has been done once; why not give
rise to a new SICP’ phenonemon?

There were several responses. In particular, one user, Ray, responded as follows:

[N]obody who’s grown up with the web, and who thinks of
computers as being primarily communications devices, will
believe that that makes a language anything other than a
crippled toy if you can’t interface with the hardware
capabilities of the machine, enabling you to do something
as “simple” as writing a web browser in it, managing network
connections, handling Graphical UI elements, and rendering
text and graphics on the screen.

[...]

Now, consider what Scheme’s got that Python doesn’t got.
It comes down to syntactic abstraction and continuations.
Courses based on SICP don’t use them, so MIT had nothing
to lose by going to Python.

Perhaps. But has Scheme really lost the essence of its appeal?

I disagree. Recently, I started reading a guide (albeit in Japanese, since I can read that language as well) by Shiro Kawai on the Gauche implementation of Scheme, and opened up a chapter on continuations. (For those of you who do not know, continuations are a control mechanism in Scheme which allows assignment of control flow to a variable, allowing a process to be “continued” (hence the name) from the point where the continuation was saved.) Since I had not yet fully understood continuations, I found the chapter extremely interesting, and could not stop reading. At one point, I encountered the following procedure which used a continuation, written in continuation-passing style (a.k.a. “CPS” style) (in which, rather than assigning the continuation directly to a variable, the continuation is explicitly passed as a parameter), to calculate the factorial function:

(define (fact/cps n cont)
  (if (= n 0)
      (cont 1)
      (fact/cps (- n 1) (lambda (a) (cont (* n a))))))

This procedure returns the same results as the following (much simpler) one (listed on the same page), which does not use a continuation:

(define (fact n)
  (if (= n 0)
      1
      (* n (fact (- n 1)))))

In particular, I started at the mysterious “(a)” variable in the following piece of code above, wondering what that variable represented:

(fact/cps (- n 1) (lambda (a) (cont (* n a))))

Suddenly, it dawned upon me: The “(a)” variable stored the parameter that was passed to the continuation (“(lambda (a) (cont (* n a)))”), which, in turn, captured the control state of the procedure at that point of execution, which was, in turn, passed back as a parameter to the enclosing procedure! In short, the continuation was a microcosm of the execution context of the procedure at that point in time, encapsulated in a lambda abstraction!

Here, “fact/cps” is the name of the procedure, which stands for “factorial in CPS (continuation-passing style) form.”

Suppose we call “fact/cps” in the most simple case:  a value of 0 for the first parameter, and a function that simply returns the parameter passed to it as a second parameter:

(fact/cps 0 (lambda (a) a))

Then, in “fact/cps”, “(= n 0)” is true in the if-statement, so “(cont 1)” is called, where “cont” is simply the second parameter of the enclosing “fact/cps” function, or “(lambda (a) a)” (the continuation), which returns the value of the parameter “a”, which is 1 in this case, so 1 is returned.

Let’s be a little bolder, and use a value of 1 for the first parameter:

(fact/cps 1 (lambda (a) a))

This time, “(= n 0)” is false in the if-statement, so the following recursive call is made (substituting 1 for n):

(fact/cps (- 1 1) (lambda (a) (cont (* 1 a))))

In the recursive call, (- 1 1) is substituted for the first parameter of “fact/cps”, and “(lambda (a) (cont (* 1 a))” is substituted for the second parameter of “fact/cps”.  This is the same as the following call (reducing the first parameter to a value):

(fact/cps 0 (lambda (a) (cont (* 1 a))))

However, since we had passed an identity function, “(lambda (a) a)” for “cont” in the enclosing function, this reduces to the following call (expanding “cont” to “(lambda (a) a)”):

(fact/cps 0 (lambda (a) ((lambda (a) a) (* 1 a))))

Here, the explicit continuation “(lambda (a) ((lambda (a) a) (* 1 a))))” first takes whatever is handed to it as the parameter “a”, and passes it to the inner function (lambda abstraction, actually, but we’ll dismiss that point here), so we reach “((lambda (a) a) (* 1 a))”.  But this is just the identity function on the inner “(* 1 a)”.  So this part just reduces to “‘(* 1 a)”, which is the same as just “a”, which is whatever value is passed to this continuation, so this continuation is just the identity function.

So when “fact/cps” is recursively called with 0 for the first parameter n and this identity value continuation “(lambda (a) ((lambda (a) a) (* 1 a))))” for the second parameter cont, we first reach “(= n 0)” as the condition in the if-statement, which is true.  This leads to evaluating the following:

(cont 1)

But “(cont 1)” is just this identity continuation called with 1, so it just returns the parameter 1.  So, “(fact/cps 1 (lambda (a) a))” is just the value passed to it:

1

Of course, we didn’t need to pass the identity function “(lambda (a) a)” as the second parameter to “fact/cps”.  We could have formatted the output, for example, by passing a formatting function, instead (to borrow the syntax of Gauche Scheme):

(lambda (a) (format #t "The factorial value is ~a." a))

Then we could have invoked “fact/cps” with that formatting function for the function to be passed as the continuation, as follows:

(fact/cps 3 (lambda (a) (format #t "The factorial value is ~a." a)))

This would have returned the following:

The factorial value is 6.#<undef>

Alternatively, we could have chosen to multiple whatever was returned by 2, just to screw up the function, as follows:

(fact/cps 3 (lambda (a) (* 2 a)))

This would have returned the following:

12

Hey, why not combine the two functions, and get Scheme to say something funny?

(fact/cps 3 (lambda (a) (format #t "I do solemnly swear that the factorial value is ~a." (* 2 a))))

Scheme then would have returned the following:

I do solemnly swear that the factorial value is 12.

Despite (or maybe because of?) all this exploratory monkey-business, in the “Aha!” moment described above, I felt an ecstasy of enlightenment that I do not often experience elsewhere (er, elsewhen, rather).

Such “Aha!” moments are crucial to appreciating the fun in computer science. They are commonly found whenever a deeper level of understanding is achieved by contemplating something which is not obvious at first. I have noticed that they are found more easily in Scheme than in some other programming languages, because of the flexibility that the language allows in even esoteric expressions.

In order to enjoy programming, one must appreciate the fun in programming, and it is difficult to appreciate this factor without experiencing an “Aha!” moment. The deeper the understanding, the more intense the exhilaration associated. Continuations and syntactic abstraction, in particular, are very abstruse (some may even say “arcane”) topics, especially when first encountered, and can require relatively deep understanding. Hence, by providing opportunities to learn such concepts, Scheme can provide an ideal opportunity to experience the fun of programming.  Thus, the continued need for Scheme.

Not all books that use Scheme adopt this approach.  An alternative approach is to structure the curriculum so that the learning becomes a linear process, rather than a series of leaps, so that all the parts fit together neatly like solving a jigsaw puzzle, rather than like climbing a mountain.

Not to be critical of this approach, but not everybody prefers it.  In one critique, José Antonio Ortega Ruiz, in his blog, “A Scheme bookshelf « programming musings,” contrasts one well-known textbook that uses this alternative approach, How to Design Programs (a.k.a. “HtDP”), with SICP, as follows:

The most cited alternative to SICP is How to Design Programs by Felleisen, Findler, Flatt and Krishnamurthi. Its authors have even published a rationale, The Structure and Interpretation of the Computer Science Curriculum, on why they think SICP is not well suited to teaching programming and how their book tries to fix the problems they’ve observed. I won’t try to argue against such eminent schemers, but, frankly, my feeling is that HtDP is a far, far cry from SICP. HtDP almost made me yawn, and there’s no magic to be seen.

Ortega-Ruiz is somewhat harsh in his critique of HtDP.  After all, according to the authors of the paper explaining the rationale behind the book, The Structure and Interpretation of the Computer Science Curriculum, HtDP was created in the first place to rectify two major perceived problems with SICP (page 9 of the paper):

… SICP doesn’t state how to program and how to manage the design
of a program. It leaves these things implicit and implies that students can discover a
discipline of design and programming on their own. The course presents the various
uses and roles of programming ideas with a series of examples. Some exercises then
ask students to modify this code basis, requiring students to read and study code;
others ask them to solve similar problems, which means they have to study the
construction and to change it to the best of their abilities. In short, SICP students
learn by copying and modifying code, which is barely an improvement over typical
programming text books.

SICP’s second major problem concerns its selection of examples and exercises. All
of these use complex domain knowledge….

While these topics are interesting to students who use computing in electrical
engineering and to those who already have significant experience of programming
and computing, they assume too much understanding from students who haven’t
understood programming yet and they assume too much domain knowledge from
any beginning student who needs to acquire program design skills. On the average,
beginners are not interested in mathematics and electrical engineering, and they do
not have ready access to the domain knowledge necessary for solving the domain
problems. As a result, SICP students must spend a considerable effort on the do-
main knowledge and often end up confusing domain knowledge and program design
knowledge. They may even come to the conclusion that programming is a shallow
activity and that what truly matters is an understanding of domain knowledge.

While these are all valid points, Ortega-Ruiz’s last clause, “there’s no magic to be seen,” actually describes the key conflict here.  What exactly is this “magic?”  To be experimentally borderline facetious, according to Arthur C. Clarke,

Any sufficiently advanced technology is indistinguishable from magic.

Arthur C. Clarke, “Profiles of The Future”, 1961 (Clarke’s third law)
English physicist & science fiction author (1917 – )

So maybe we’re actually referring to “any sufficiently advanced technology.”  What do we mean by “sufficiently advanced?”  I would suggest (to use a recursive definition), “sufficiently advanced to the point that deep understanding unachievable superficially is required to understand the material.”

Whether or not this “magic” is to be used in pedagogy actually relates to the fundamental design philosophy behind HtDP, as opposed to that behind SICP.  To quote the above-referenced paper explaining the rationale behind HtDP, “The Structure and Interpretation of the Computer Science Curriculum,” as follows (page 11):

The recipes also introduce a new distinction into program design: structural ver-
sus generative recursion. The structural design recipes in the first half of the book
match the structure of a function to the structure of a data definition. When the
data definition happens to be self-referential, the function is recursive; when there
is a group of definitions with mutual cross-references, there is a group of function
definitions with mutual references among the functions. In contrast, generative re-
cursion concerns the generation of new problem data in the middle of the problem
solving process and the re-use of the problem solving method.

Compare insort and kwik, two standard sort functions:

;; (listof X) -> (listof X)
(define (insort l )
  (cond
    [(empty? l ) empty]
    [else
      (place
        (first l )
        (insort (rest l )))]))

;; (listof X) -> (listof X)
(define (kwik l )
  (cond
    [(empty? l ) empty]
    [else
      (append (kwik (larger (first l ) l ))
                  (first l )
                  (kwik (smaller (first l ) l )))]))

The first function, insort , recurs on a structural portion of the given datum, namely,
(rest l ). The second function, kwik, recurs on data that are generated by some other
functions. To design a structurally recursive function is usually a straightforward
process. To design a generative recursive function, however, almost always requires
some ad hoc insight into the process. Often this insight is derived from some mathe-
matical idea. In addition, while structurally recursive functions naturally terminate
for all inputs, a generative recursive function may diverge. htdp therefore suggests
that students add a discussion about termination to the definition of generative
recursive functions.

HtDP takes pains to remove the requirement for this “ad hoc insight” into the problem-solving process.  The authors of the book then make the following claim (same page):

Distinguishing the two forms of recursion and focusing on the structural case
makes our approach scalable to the object-oriented (OO) world.

That may be so, but that contrasts sharply with the spirit of the original quotation by Alan Perlis above:

Of course, the paying customers got shafted every now and then, and after a while we began to take their complaints seriously. We began to feel as if we really were responsible for the successful, error-free perfect use of these machines. I don’t think we are. I think we’re responsible for stretching them, setting them off in new directions, and keeping fun in the house.

So we have two sharply contrasting approaches:  One to use Scheme for fun, and the other to use Scheme for scalability.  Again, this basically is a matter of taste.

In his above-mentioned post in the above-mentioned thread, Ray contrasted the advantages of Scheme vs. Python as follows:

[S]cheme still has no standard means of managing network connections
or rendering anything on the screen.  Python has these things.

Now, consider what Scheme’s got that Python doesn’t got.
It comes down to syntactic abstraction and continuations.
Courses based on SICP don’t use them, so MIT had nothing
to lose by going to Python.

SICP doesn’t use syntactic abstraction.  In the first
edition, this was because Scheme didn’t have them yet.
In the current edition …. well, here’s the footnote
about macros from the current edition, page 373:

Practical Lisp systems provide a mechanism that
allows users to add new derived expressions and
specify their implementation as syntactic
transformations without modifying the evaluator.
Such a user-defined transformation is called a
/macro/. Although it is easy to add an elementary
mechanism for defining macros, the resulting
language has subtle name-conflict problems. There
has been much research on mechnaisms for macro
definitions that do not cause these  difficulties.
See, for example, Kohlbecker 1986, Clinger and
Rees 1991, and Hanson 1991.

(Aside: “practical” lisp systems have them; the dialect
covered in the book does not.  Students can and do draw
the obvious conclusion….)

Granted, specific implementations do have these functions.  But there is no single main implementation of Scheme that everybody uses, and the libraries that implement these functions are not necessarily portable across implementations.  Therefore, Scheme as a language (as opposed to a specific implementation) does not have these functions.

But is that necessarily bad?  I don’t think so.  I think that the whole point of Scheme, as a language, is, to quote Alan Perlis above, that we are “[not] responsible for the successful, error-free perfect use of these machines, [but] for stretching them, setting them off in new directions, and keeping fun in the house.”

To sum, when I first approached SICP, I found it too challenging to digest.  I had to quit reading it repeatedly, and then return to it later, and I still have read only a portion of the book.  But I became entranced with the magic of computer science as demonstrated by such creatures as tail recursion in Scheme in SICP.  And it was precisely this magic that kept me returning to computer science in general, and to Scheme in particular.

On the other hand, books such as HtDP are very comforting and reassuring.  While SICP sometimes makes me wonder why I am such an idiot, HtDP makes me feel as if I am no longer an idiot.  I no longer need to think for hours and hours during my sleep about how to overcome a particular problem.  Books such as HtDP make the material very straightforward.  However, by doing so, they also remove all the magic, and break the spell.

I feel that an intermediate approach is better.  The magic is necessary, but the sorcery in SICP can be too much at first.  However, the jigsaw-puzzle approach of HtDP seems too straightforward.  There is not enough exploration to maintain interest after a certain level of reader sophistication.  Paradoxically, although I can read HtDP much, much faster than SICP, I also fall asleep reading it just as much faster, and actually haven’t read so far in it.  A gentler approach than that of SICP, which still offers more exploration than HtDP, would be a better compromise.

Also, I feel that the greatest strength of Scheme lies in its flexibility for exploratory programming.  Scheme shares one quality that is also shared by such addictive games as Tetris:  It is relatively simple to learn, yet extremely difficult to master.  Writing simple procedures to calculate such functions as the factorial function or the Fibonacci sequence is deceptively simple at first.  But when the student ventures into such deeper areas as tail recursion, continuations, and syntactic abstractions, the procedures can become tantalizingly complex.

To conclude, shouldn’t Scheme really be a language for scheming programmers to figure out mainly how to have fun?  I like to be a Scheming Schemer, always scheming plots for stretching the lambda abstractions to set them off in new directions, mainly just to have fun.  Are you a Scheming Schemer?

Conquering the Fear of Reading Research Papers: Computer Science Research Papers for Non-Computer Scientists

Any non-mathematician, non-computer scientist layperson who has approached programming languages originally spawned in academia, such as Haskell or Scheme, has no doubt been intimidated by the academic rigor and density of many research papers on such subjects. Even such papers labeled “gentle,” as “A Gentle Introduction to Haskell” [1], can turn out to be less “gentle” than expected for those not familiar with the field.

Although I myself do have a background in computer science, as a patent translator, and not a mathematician, computer scientist, or programmer, I tend to approach such papers as more of an amateur programming language theory hobbiest and writer. Having tried to read a number of such papers, I have discovered that although many of them can be difficult to approach, some tend to be more approachable than others.

In particular, most recently, I was rather surprised to encounter a rather lengthy research paper on the history of one such programming language, Simula, which, although detailed, nevertheless turned out to be surprising approachable in not assuming advanced technical knowledge of the field (although it still required great attention to detail): “Compiling SIMULA: A Historical Study of Technological Genesis” [2].

This paper, rather than focusing solely on the technical development of the language, conducts a sociotechnical analysis of the broader historical background surrounding the Simula project. There are no formulas or even code snippets; instead, even though the paper is a research paper published in the IEEE Annals of the History of Computing, it is written as a history paper which just happens to be about the historical background of a programming language. Even more surprising, according to the endnote of the paper, the author, Jan Rune Holmevik, at the time of publication, was a graduate student in history at the University of Trondheim, Norway, and the paper itself “was written as part of [his] dissertation thesis in history Hovudfag [3] at the University of Trondheim” (page 36). In other words, this is a detailed research paper on a programming language, published in an academic journal, which does not assume any ability to program.

Until reading this paper, I had assumed that rigorous research papers on computer science published in academic journals were either written by mathematicians or computer scientists, or at least assumed a background in either mathematics or computer science to read. While this paper is definitely thoroughly researched, documented, and described, and approaches its topic in excruciating detail, it does not assume any background in either mathematics or computer science.

In other words, one need not necessarily be a mathematician or a computer scientist to write, much less read, a research paper on computer science; in fact, there are even some very thorough and detailed research papers on computer science published in academic journals which do not assume any background in either mathematics or computer science, such as this paper.

This discovery came as a revelation.

If it is possible to write a research paper without a background in either mathematics or computer science, then it must definitely also be possible to read at least some such papers. Furthermore, this is most likely not the only such research paper.

In fact, so far, I have encountered a number of computer science research papers which similarly require no or very little background in mathematics or computer science. Here is a list of some other interesting, yet approachable, research papers which (1) are either devoid of, or substantially devoid of, mathematical formulae; (2) are either devoid of, or substantially devoid of, code snippets; and (3) are either devoid of, or substantially devoid of, technical content assuming a background in mathematics or computer science:

i) “The Structure and Interpretation of the Computer Science Curriculum” [4]. By Matthias Felleisen, Robert Bruce Findler, Matthew Flatt, Shriram Krishnamurthi.
Published in the Journal of Functional Programming in 2004, this paper discusses the motivation and design rationale for the book How to Design Programs [5] by comparision and contrast with the book Structure and Interpretation of Computer Programs [6].

ii) “Haskell: Batteries Included” [7]. By Duncan Coutts, Isaac Potoczny-Jones, and Don Stewart. Published in Proceedings of the first ACM SIGPLAN symposium on Haskell (2008).
This paper outlines the motivation for and structure of the Haskell Platform, a “Haskell for the masses” versioned packaging system of Haskell and included libraries. Although this paper does not specifically assume familiarity with mathematics or computer science, it does make use of such technical terminology as “libraries,” “packages,” “source code,” and “package description file.”

iii) “Teaching Programming Languages in a Post-Linnaean Age” [8]. By Shriram Krishnamurthi. Published in First SIGPLAN Workshop on Undergraduate Programming Language Curricula in 2008.
This paper claims that programming languages should be viewed as aggregations of features, rather than languages defined by taxonomies, and asserts that the term “paradigm” is ill-defined and should play no role in classifying programming languages. The book also addresses the issue of the split between textbooks that are “rich in mathematical rigor but low on accessibility, and those high on accessibility but lacking rigor (and, often, even wrong),” and offers an alternative.

iv) “The Early History of Smalltalk” [9]. By Alan C. Kay. Published in History of Programming Languages: The second ACM SIGPLAN conference on History of programming languages in 1993.
This paper describes the historical background behind the evolution of Smalltalk, a pure object-oriented language. It also, in part, describes the visit of Steve Jobs, Jeff Raskin, and others of then Apple, Inc. to the Xerox PARC laboratory, which led to the subsequent development of the Macintosh user interface, based on the Smalltalk user interface.

v) “Design Principles Behind Smalltalk” [10]. By Daniel H. H. Ingalls. Published in BYTE Magazine, August 1981.
This paper is a non-technical exposition of the design principles behind the Smalltalk-80 programming system. Illustrated with descriptive figures, the paper focuses not just on the programming language issues behind Smalltalk as a language of description, but also the user interface issues behind Smalltalk as a language of interaction. In particular, the paper describes how the research, in two- to four-year cycles, has paralleled the scientific method in repeatedly making an observation, formulating a theory, and making a prediction that can be tested, and summarizes key concepts as one- to two-sentence nutshell statements.

Lastly (but not leastly), the following paper, although containing a significant number of code snippets and assuming some background in computer science, is sufficiently interesting to be worthy of special mention; the first few sections of it can be safely read by a reader unfamiliar with the subject matter:

vi) “A History of Haskell: Being Lazy With Class” [11]. By Paul Hudak, John Hughes, Simon Peyton Jones, and Philip Wadler. Published in The Third ACM SIGPLAN History of Programming Languages Conference (HOPL-III) in 2007.
This paper provides a very interesting description of the motivation and historical background of the functional programming language Haskell. In particular, the paper describes the influence of a precursor to Haskell, Miranda (pages 3 to 4); mentions how Gerry Sussman and Guy L. Steele briefly considered the idea of introducing lazy evaluation in Scheme (page 3); provides a timeline of the development of Haskell (page 7), and then proceeds on to describe the syntax and semantics (pages 11 to 28), implementations and tools (pages 28 to 35), and applications and impact (pages 35 to 46). I sometimes return back to this paper when I feel frustrated with the dryness of many other papers on Haskell, since this is one of the few papers on the language which conveys a sense of the excitement surrounding the birth and early development of the language; many other papers on Haskell tend to focus solely on technical issues, without discussing the role of human beings in the context.

As pointed out in Holmevik [2], programming languages do not “evolve in a technical or scientific vacuum” (page 35). This point is often ignored in many other papers about Haskell; luckily, it is dealt with in depth in this paper.

In my experience, becoming accustomed to reading research papers is a gradual, rather than instantaneous, process: After reading a number of such papers, one tends to become used to reading them; to recognize that failure to understand the content is not necessarily the fault of the reader, but often that of a wolly exposition that either fails to describe prerequisites to the content, or does not describe them adequately; and that the best research papers are not necessarily those that describe the most difficult content, but those that offer the most readily understandable exposition of the material to the intended target audience.

One must understand that many research papers are not necessarily written to be easy to read, but to fulfill a specific need, such as a part of a requirement for a degree, and are hence qualitatively different from most textbooks, which tend to be written so as to be easy to understand for a broader audience. Hence, it is actually quite normal for a research paper of mediocre quality to be written in such a way as to expect the reader to fill in the prequisite content, which may be assumed but not stated. (Of course, the best research papers tend to fill in any prerequisite content.)

Often, the best researchers are not the best writers; many of them cannot understand why a topic which is of trivial difficulty to them can possibly be of non-trivial difficulty for another reader. A reader aware of this fact can often approach research papers with a better plan for mastering the content therein.

Lastly, if I might add a personal expectation, I tend to enjoy reading papers that acknowledge that a programming language is an artifact resulting from a complex interplay of many different human desires, needs, and expectations surrounding its birth, and does not develop in a social vacuum. Computers do not design programming languages; people do. Therefore, discussing a programming language as if it were merely a logical extension of prior developments in syntax and semantics ignores a significant factor in its evolution. I have found that the best research papers tend to be those that, while providing a rigorous treatment of the subject material, do not assume any prerequite material not normally possessed by the intended target audience; acknowledge that some readers may not be as intelligent as the author and may find certain points that seem trivial to the author to be non-trivial; provide sufficient elucidation to cope accordingly; and discuss the human issues surrounding the design and evolution of the language.

[1] Hudak, Paul. “A Gentle Introduction to Haskell, Version 98.” New York, NY: ACM SIGPLAN Notices 27:5 (1992): 1-52. <http://portal.acm.org/ft_gateway.cfm?id=130698&type=pdf&coll=GUIDE&dl=GUIDE&CFID=50053868&CFTOKEN=12610081>. An updated, free 1998 version is also available at <http://www.haskell.org/tutorial/>.

[2] Holmevik, Jan Rune. “Compiling SIMULA: A Historical Study of Technological Genesis.” Washington, D.C.: Annals of the History of Computing 16:4 (1994): 25-36. <http://www.idi.ntnu.no/grupper/su/publ/simula/holmevik-simula-ieeeannals94.pdf>.

[3] Regarding the term “Hovudfag,” Holmevik writes (page 36, footnote), “Hovudfag may be regarded as the Norwegian equivalent to a master’s degree, although it carries considerably more workload and normally takes two to three years to complete.”

[4] Felleisen, Matthias, Robert Bruce Findler, Matthew Flatt, and Shriram Krishnamurthi. “The Structure and Interpretation of the Computer Science Curriculum.” Cambridge: Journal of Functional Programming 14:4 (2004): 365-378. <http://www.cs.brown.edu/~sk/Publications/Papers/Published/fffk-htdp-vs-sicp-journal/>.

[5] Felleisen, Matthias, Robert Bruce Findler, Matthew Flatt, and Shriram Krishnamurthi. How to Design Programs. Cambridge, MA: The MIT Press, 2003. <http://www.htdp.org/>.

[6] Abelson, Harold and Gerald Jay Sussman with Julie Sussman. Structure and Interpretation of Computer Programs, Second Edition. Cambridge, MA: The MIT Press and New York: McGraw-Hill, 1996. <http://mitpress.mit.edu/sicp/full-text/book/book.html>.

[7] Coutts, Duncan, Isaac Potoczny-Jones, and Don Stewart. “Haskell: Batteries Included.” Victoria, BC, Canada: Proceedings of the first ACM SIGPLAN symposium on Haskell (2008): 125-126.<http://www.cse.unsw.edu.au/~dons/papers/haskell31-coutts.pdf>.

[8] Krishnamurthi, Shriram. “Teaching Programming Languages in a Post-Linnaean Age.” Cambridge, MA: First SIGPLAN Workshop on Undergraduate Programming Language Curricula (2008): 81-83. <http://www.cs.brown.edu/~sk/Publications/Papers/Published/sk-teach-pl-post-linnaean/>.

[9] Kay, Alan C. “The Early History of Smalltalk.” Cambridge, Massachusetts: History of Programming Languages: The second ACM SIGPLAN conference on History of programming languages (1993): 69-95. <http://portal.acm.org/citation.cfm?id=154766.155364&coll=GUIDE&dl=GUIDE&CFID=45415434&CFTOKEN=84716013>. Also available at <http://gagne.homedns.org/~tgagne/contrib/EarlyHistoryST.html>.

[10] Ingalls, Daniel H. H. “Design Principles Behind Smalltalk.” BYTE Magazine, August 1981. <http://www.fit.vutbr.cz/study/courses/OMP/public/software/sqcdrom2/Documents/DesignPrinciples/DesignPrinciples.html>.

[11] Hudak, Paul, John Hughes, Simon Peyton Jones, and Philip Wadler. “A History of Haskell: Being Lazy With Class.” San Diego, CA: The Third ACM SIGPLAN History of Programming Languages Conference (HOPL-III) (2007): 12-1 – 12-55, 2007. <http://research.microsoft.com/en-us/um/people/simonpj/papers/history-of-haskell/history.pdf>.

Thinking in Scheme and Checking a Patent Claim: A Cross-disciplinary Application of Scheme-based Reasoning

(This content of this post is based on the content of my post [1] entitled “Re: [semi-OT] possible benefits from training in Scheme programming in patent translation” on the USENET newsgroup comp.lang.scheme.)

As a follow-up to my previous post, “How Scheme Can Train the Mind: One Reason that MIT Should Reinstate Scheme and 6.001,” here is an example of an application of the Scheme-style pattern of thinking applied to checking a pattern claim.

Most readers of this blog do not read Japanese; therefore, this example assumes that another translator has already translated a patent claim from Japanese to English, and that I need to check the translation for accuracy. In order to do so, I need to break down the claim into its semantic components and determine whether the semantics of the translation and the original are equivalent. Here is a contrived example, assuming that somebody has developed an in vitro, as opposed to in vivo, remote control device and receptor that can be optionally mounted on the ear (similarly to the ear-mounted transmitter/receivers worn by Agents in the motion picture saga The Matrix) and used as a controller for a video gaming device; please note that since I am not actually writing a Scheme program, but only using thought patterns derived from writing S-expressions in Scheme programs, this is merely pseudo-Scheme, not actual Scheme:

What is claimed is:

1. An in vitro remote-control device, the device comprising:
        a mounting unit for mounting the remote-control device on a portion of the head of a user; 
        a transmitter unit, further comprising:
             a neurotransmitter unit transmitting neural impulses to a brain of the user; 
             a neuro-digital conversion unit converting neural impulses to digital signals; 
	a receiver unit, further comprising:
             a neuroreceptor unit receiving neural impulses from the brain;
             a digital-neuro conversion unit converting digital signals to neural impulses; and 
        a power source unit converting thermal radiation from brain cells into electricity, the electricity powering the remote-control device;
   wherein:
        the transmitter unit transmits digital signals in response to neural impulses; and
        the receiver unit transmits neural impulses in response to digital signals.

The above-mentioned claim translates roughly into my personal variety of pseudo-Scheme as follows (apologies for any deviations from the syntax or semantics of actual Scheme):

(claim-define (_in-vitro_-remote-control-device mounting-unit transmitter-unit receiver-unit power-source-unit)
              (claim-comprising
               (mounting-unit
                (lambda (head user)
                  (mount head user)))
               (transmitter-unit
                (lambda (neurotransmitter-unit neuro-digital-conversion-unit)
                  (claim-define (neutrotransmitter-unit neural-impulses brain)
                                (transmit neural-impulses brain user))
                  (claim-define (neuro-digital-conversion-unit neural-impulses digital-signals)
                                (convert (neural-impulses digital-signals))))
                (receiver-unit
                 (lambda (neuroreceptor-unit digital-neuro-conversion-unit)
                   (claim-define (neuroreceptor-unit neural-impulses brain)
                                 (receive neural-impulses brain))
                   (claim-define (digital-neuro-conversion-unit)
                                 (convert digital-signals neural-impulses))))
                (power-source-unit
                 (lambda (thermal-radiation brain-cells electricity)
                   (power-convert thermal-radiation electricity brain-cells)))))
                (claim-wherein
                 (transmitter-unit
                  (lambda (digital-signals neural-impulses)
                    (transmit digital-signals neural-impulses)))
                 (receiver-unit
                  (lambda (neural-impulses digital-signals)
                    (transmit neural-impulses digital-signals)))))

This pattern of thinking can greatly simplify verifying equivalence between an English translation of a claim having a complex structure and the original Japanese claim.

[1] Russell, Benjamin L. “Re: [semi-OT] possible benefits from training in Scheme programming in patent translation.” Online posting. 20 Aug. 2009. 24 Aug. 2009. <news://comp.lang.scheme>. Also available at <http://groups.google.co.jp/group/comp.lang.scheme/msg/871965c4090e127f>.

How Scheme Can Train the Mind: One Reason that MIT Should Reinstate Scheme and 6.001

(This content of this post is substantially identical to the content of my post [1] entitled “[semi-OT] possible benefits from training in Scheme programming in patent translation” on the USENET newsgroup comp.lang.scheme.)

Today, I came across an interesting phenomenon in which exposure to Scheme programming helped with technical translation of part of a patent specification.

Since the material is classified, I can only reveal the structure, and not the content, but basically, there was a document containing a “claim” (a sentence in a specification which specifies what is being claimed in the patent being applied for) which somebody had slightly mis-translated from English to Japanese, and which was being amended.

The original English clause in the claim had the following structure:

“… an A in communication with a plurality of B, said A configured to generate a C signal, configured to cause at least one of said plurality of B to output a said D, said C signal based at least in part on said E signal.”

Unfortunately, whoever translated that clause from English to Japanese apparently left out the “said A configured to generate a C signal” portion.

Then this mis-translated Japanese translation of the original English clause was amended, but was never translated back to English.

Then this amended Japanese clause was re-amended, and I was asked to “apply” the re-amendment to the English original. The re-amended Japanese clause then had the following structure (after I finally figured out the structure):

“… an A in communication with a plurality of B, said A configured to generate a C signal, configured to cause the C coupled to said F so that a positional relationship, for the E which has sent the E signal, corresponding similarly to a positional relationship between the E which has sent the E signal and the G of said plurality of B to output a said force associated with the strength detected by the E, said B signal based on said E signal.”

The first aspect that I noticed was that the previous amendment had never been translated, requiring me to fill in the details.

However, then I noticed that this previous amendment had itself been based on a mis-translated original.

In order to figure out which portion was missing from the translation of the original clause, I needed to map portions of the original English clause to their Japanese equivalents, but since the structure itself was not written to reflect the structure of the original English clause, I then needed to break up the original English clause into its structural components.

At first, this process seemed very tedious and difficult, until I noticed that treating these structural components in the clause as if they were S-expressions in a Scheme program, and then mapping equivalent components of the English clause to semi-corresponding components of the Japanese (mis-)translation speeded up and simplified this process greatly, even though the correspondence was not exact.

For some reason, I have discovered that this kind of mental equivalence seems to proceed much more smoothly between S-expressions in Scheme programs and claims in patent documents than between other kinds of expressions in other functional programming languages and the same claims in patent documents. For example, I have not had similar experiences with finding equivalences between expressions in even Haskell programs and the claims in patent documents; Haskell expressions seem to be more equivalent to mathematical equations than to claims in patent documents.

Therefore, it seems that exposure to the Scheme programming language, in particular, can help in training non-programmers to think structurally in analyzing expressions in natural language, which can have benefits in translating claims in patent documents in such a manner that they can be more easily and clearly amended.

Perhaps MIT should reinstate Scheme and 6.001, and get rid of Python and the new C1. Somehow I feel that MIT is risking creating a new generation of idiots by getting rid of Scheme and SICP from their curriculum just for the ostensible reason that the recursive style of programming does not reflect the way that programming is actually conducted in industry. Students do not learn programming just to program; learning programming also has important ramifications for the structural thought processes underlying other technical fields, even those that do not seem superficially related (such as patent translation), and it seems that watering down a core programming course for such ostensible reasons undermines the crucial patterns of thinking which are cross-applicable to such other technical fields as well.

[1] Russell, Benjamin L. “[semi-OT] possible benefits from training in Scheme programming in patent translation.” Online posting. 19 Aug. 2009. 19 Aug. 2009. <news://comp.lang.scheme>. Also available at <http://groups.google.com/group/comp.lang.scheme/browse_thread/thread/4590474ce458597c#>.

A Correction to “Too Much is Not Enough: The Revised^6 Report on the Algorithmic Language Scheme (R6RS)”

In my previous blog entry, I had listed Jacob Matthews and Robert Bruce Findler as having been on the list of authors for the Revised^6 Report on the Algorithmic Language Scheme, but last month, Robby Findler pointed out in a comment that neither of these two authors had been responsible for decision-making; rather, they had only been authors of the formal semantics thereof.

Therefore, I am removing them from the list of people responsible for decision-making for R6RS.

My apologies for the late correction.

Too Much is Not Enough: The Revised^6 Report on the Algorithmic Language Scheme (R6RS)

On September 26, 2007, the Revised^6 Report on the Algorithmic Language Scheme was released. Normally, a new standard for Scheme is greeted with applause, but this time, the revision sparked a great controversy. The Scheme community became divided between pro-R6RS and anti-R6Rs factions, and some members even decided to leave programming language theory completely at least partly because of this change. As Nils M. Holm has mentioned,

A lot has happened since the release of the previous edition of Sketchy LISP. The Six’th Revised Report on the Algorithmic Language Scheme (R⁶RS) was ratified and Scheme is no longer the language it used to be.

Why not? Consider this graph provided by Grant Rettke. Looking at the graph, it is remarkable how there is a sudden break in continuity between most of the members of the list of authors for R2RS – R5RS, and those for R6RS. Specifically, the following authors were in common between R2RS – R5RS, but suddenly disappeared in R6RS:

Chris Hanson
Chris Haynes
Dan Friedman
David Bartley
Don Oxley
Eugene Kohlbecker
Gary Brooks
Hal Abelson
Jonathan Rees
Kent Pitman
Mitchell Wand
Norman Adams (or Norman I Adams IV, assuming this name references the same author)
Robert Halstead
William Clinger

Instead, we suddenly see the appearance of the following authors for R6RS, who had never appeared in any of R2RS – R5RS:

Anton Van Straaten
Jacob Matthews
Matthew Flatt
Michael Sperber
Robert Bruce Findler

In fact, the only person common in the lists between R3RS – R5RS (according to the chart, he was not an author for R2RS) and R6RS is Kent Dybvig.

What happened to all the previous authors, and who are these new authors?

Apparently, at least some of the previous authors quit the board, possibly because of a disagreement over the new standard. As for the new authors, I know of both Matthew Flatt and Robert Bruce Findler from PLT Scheme. They are members of the PLT Research Group, and they regularly post on the plt-scheme mailing list. (They have both been very helpful on many occasions, so I have no qualms against them personally; I am just trying to analyze their motivations for R6RS.) They are both also among the authors for HtDP. They are also among the co-authors for the influential paper “The Structure and Interpretation of the Computer Science Curriculum.” According to that paper (see pp. 6-7, in section “3.1 Functional and object-oriented programming”), they write as follows:

Functional programming and object-oriented programming differ with respect to
the syntax and semantics of the underlying languages. The core of a functional lan-
guage is small. All a beginning programmer needs are function definition, function
application, variables, constants, a conditional form, and possibly a construct for
defining algebraic types. In contrast, using an object-oriented language for the same
purposes requires classes, fields, methods, inheritance in addition to everything that
a functional language needs….

Using a functional language followed by object-oriented language is thus the
natural choice. The functional language allows students to gain confidence with
program design principles. They learn to think about values and operations on
values. They can easily comprehend how the functions and operations work with
values. Better still, they can use the same rules to figure out why a program pro-
duces the wrong values, which it often will. Teaching an object-oriented language
in the second course is then a small shift of focus….

I.e., Flatt and Findler believe that teaching functional programming should be followed by teaching object-oriented programming. This concept, however, is not shared by all educators. In particular, Paul Hudak, one of the designers of the Haskell programming language, writes on the Haskell-Cafe mailing list as follows on a related issue (see “[Haskell-cafe] a regressive view of support for imperative programming in Haskell“:

All of the recent talk of support for imperative programming in Haskell
makes me really nervous. To be honest, I’ve always been a bit
uncomfortable even with monad syntax. Instead of:

do x <- cmd1
y <- cmd2
…
return e

I was always perfectly happy with:

cmd1 >>= \x->
cmd2 >>= \y->
…
return e

Functions are in my comfort zone; syntax that hides them takes me out of
my comfort zone.

In my opinion one of the key principles in the design of Haskell has
been the insistence on purity. It is arguably what led the Haskell
designers to “discover” the monadic solution to IO, and is more
generally what inspired many researchers to “discover” purely functional
solutions to many seemingly imperative problems. With references and
mutable data structures and IO and who-knows-what-else to support the
Imperative Way, this discovery process becomes stunted.

Well, you could argue, monad syntax is what really made Haskell become
more accepted by the masses, and you may be right (although perhaps
Simon’s extraordinary performance at OSCOM is more of what we need). On
the other hand, if we give imperative programmers the tools to do all
the things they are used to doing in C++, then we will be depriving them
of the joys of programming in the Functional Way. How many times have
we seen responses to newbie posts along the lines of, “That’s how you’d
do it in C++, but in Haskell here’s a better way…”.

While Hudak contrasts imperative vs. functional, as opposed to object-oriented vs. functional, the basic issue is the same: Should functional programming be treated as a separate paradigm by itself (as “the Functional Way” vs. “the Imperative Way” (or maybe even “the Object-oriented Way”)), or should it be combined with a different paradigm (be it imperative or object-oriented, the issue is the same). Or even (according to some educators), should there even be an issue of “paradigm” at all?

This is an issue of basic teaching philosophy. As an example of the third viewpoint, Shriram Krishnamurthi writes on the plt-scheme mailing list as follows (see “[plt-scheme] Re: More pedagogic stuff“:

Besides the simplistic
reasoning, I am opposed to the whole idea of programming languages (or
even much of programming) being organized around “paradigms”. Here is
a short and intentionally somewhat provocative article that I recently
wrote about this:

http://www.cs.brown.edu/~sk/Publications/Papers/Published/sk-teach-pl-post-linnaean/

In the referenced page, Krishnamurthi writes as follows:

Programming language “paradigms” are a moribund and tedious legacy of a
bygone age. Modern language designers pay them no respect, so why do our courses
slavishly adhere to them? This paper argues that we should abandon this method of
teaching languages, offers an alternative, reconciles an important split in programming
language education, and describes a textbook that explores these matters.

In the referenced paper (see “Teaching Programming Languages in a Post-Linnaean Age,” Krishnamurthi writes (see p. 1, third paragraph):

Most books
rigorously adhere to the sacred division of languages into “functional”, “imperative”, “object-oriented”,
and “logic” camps. I conjecture that this desire for taxonomy is an artifact of our science-envy from the
early days of our discipline: a misguided attempt to follow the practice of science rather than its spirit.
We are, however, a science of the artificial. What else to make of a language like Python, Ruby, or Perl?
Their designers have no patience for the niceties of these Linnaean hierarchies; they borrow features as they
wish, creating melanges that utterly defy characterization.

Ultimately, it seems that this issue boils down to a matter of taste.

This is usually not a problem, so long as this taste is confined to a particular implementation. The problem with R6RS is that it is not just an implementation; it is a standard that can affect all implementations. R6RS, compared to previous revisions, makes a dramatic number of changes to the Scheme standard. Each one, individually, is not such a big problem; it is the entirety of all these changes taken together without sufficient discussion that is the problem.

The members of the board had to vote for all the changes taken together, rather than each one separately. A standard usually should require a consensus; however, this consensus was not really achieved in the case of R6RS (read through the reasoning behind both the “yes” and “no” votes in the “R6RS Ratification Vote,” and you will see the scope of the division).

Some of the main points of this division seem to be the following (apologies to those whose votes are not listed below; I have listed only the votes of names that sounded familiar to me, but there were many other significant votes, which were omitted not because of lack of significance, but because of lack of space and time):

the module system (see votes by Chris Hanson and Taylor R Campbell)

SYNTAX-CASE (see the vote by Chris Hanson above)

the switch to case sensitivity (see the vote by Jonathan Rees)

defining too many features as part of the language, rather than on top of the language (see the vote by Nils M Holm)

lack of time to change the draft to meet the deadline of the ratification draft (see the vote by Shiro Kawai)

too long description of the specification (thrice the previous one); restrictions on implementation design that impede future development of the language in the areas of numbers, text manipulation & Unicode, and the module system; overreach of the module system’s definition (see the vote by Taylor R Campbell)

Even some of the “yes” votes list “imperfections” that “troubled” them:

apparent inflexibility of the library system, and absence of a facility analagous to Common Lisp’s reader macros (see the vote by Alexey Radul)

In sum, it seems that R6RS was at least partly motivated by a perceived need by at least some of the new authors for a standard of Scheme that would help ease the transition between the functional and object-oriented paradigms. Apparently, at least some of the authors perceived that adding more features to the core language, instead of defining a small core language and adding features on top of the language, would help with this transition.

Another problem was lack of time. R6RS seems rather rushed compared to previous specifications. There probably should have been more discussion before finalizing the specification. In particular, there should have been some means of voting on each potential feature separately, instead of on all of them together. It is quite possible for each feature alone to be quite useful, but for the combination of all of them put together suddenly at once to be quite problematic.

(This entry an adaptation of my post “Re: History of Scheme People,” dated “Thu, 26 Feb 2009 15:45:33 +0900,” on the USENET newsgroup comp.lang.scheme.)

“Good Luck!,” Typed Scheme, and Curried Typed Scheme

Word of a strange variant of PLT Scheme known as “Typed Scheme” is spreading around (see http://www.ccs.neu.edu/home/samth/typed-scheme/).  The idea is to add types to Scheme and make it more like Haskell.  Doing so is supposed to make it easier to debug procedures.

I couldn’t resist, so I decided to write up a sample Typed Scheme procedure.  Called “good-luck.ss” in regular PLT Scheme, it changes the output message depending on the input user name:

;; good-luck.ss
;; PLT-Scheme-specific program to wish a person good luck
;; 
;; Copyright(C) October 20, 2008, at 13:42, 
;; by Benjamin L. Russell

#lang scheme

(define (good-luck name)
  (if (string=? name "Nobody")
      (printf "You are ~a." name)
      (good-luck-helper name "Good Luck")))

(define (good-luck-helper a b)
  (printf "~a, ~a!" a b))

To run the Scheme source code above, simply type:

(good-luck "Benjamin")

You shall be rewarded with:

Benjamin, Good Luck!

Alternatively, typing

(good-luck "Nobody")

will result in:

You are Nobody.

Well, by itself, this isn’t any fun, so I then decided to translate this into a Typed Scheme procedure named “good-luck-typed.ss”:

;; good-luck-typed.ss
;; Typed Scheme version of good-luck.ss program to wish a person good luck
;; 
;; Copyright(C) October 20, 2008, at 13:46, 
;; by Benjamin L. Russell

#lang typed-scheme

(: good-luck-typed (String -> Void))
(define (good-luck-typed name)
  (if (string=? name "Nobody")
      (printf "You are ~a." name)
      (good-luck-helper-typed name "Good Luck")))

(: good-luck-helper-typed (String String -> Void))
(define (good-luck-helper-typed a b)
  (printf "~a, ~a!" a b))

Let’s see … the main changes are the places where “#lang typed-scheme” has been added, and where “(: good-luck-typed (String -> Void))” and “(: good-luck-helper-typed (String String -> Void))” have been inserted.

Let’s take a look at this piece of code.  The procedure “good-luck-typed” takes a parameter of type String, and returns nothing (i.e., it returns a value of type “Void”).  The procedure “good-luck-helper-typed” takes two parameters of type String, and also returns nothing (i.e., it also returns a value of type “Void”).

Let’s see what happens:

> (good-luck-typed "Benjamin")
Benjamin, Good Luck!
> (good-luck-typed "Nobody")
You are Nobody.
>

Yes, the results are identical.

Normally, I would start writing about the differences when errors arise, but I don’t have time today, so let’s do that next time.

Lastly, I became curious about whether currying (see http://en.wikipedia.org/wiki/Currying) was possible.  Let’s give it a try:

;; good-luck-curried.ss
;; Curried Typed Scheme version of good-luck.ss program to wish a person good luck
;; 
;; Copyright(C) October 20, 2008, at 17:44, 
;; by Benjamin L. Russell

#lang typed-scheme

(: good-luck-curried (String -> Void))
(define (good-luck-curried name)
  (if (string=? name "Nobody")
      (printf "You are ~a." name)
      ((good-luck-helper-curried name) "Good Luck")))

(: good-luck-helper-curried (String -> (String -> Void)))
(define ((good-luck-helper-curried a) b)
  (printf "~a, ~a!" a b))

Hmm … the main differences are the “(: good-luck-helper-curried (String -> (String -> Void)))” and “(define ((good-luck-helper-curried a) b).”  Indeed, our gourmet code looks curried.  ;-)  Still, I can’t help wondering why in “(: good-luck-helper-curried (String -> (String -> Void))),” the parentheses are folded to the right, while in “(define ((good-luck-helper-curried a) b),” they are folded to the left….

Moving on (there is no time left, so let’s worry about that next time), let’s see what happens:

> (good-luck-curried "Benjamin")
Benjamin, Good Luck!
> (good-luck-curried "Nobody")
You are Nobody.
>

Right, identical results again.

Let’s worry about the details next time.

How hot would you like your curried Typed Scheme?

Towers of Hanoi

Ladies and Gentlemen!  Welcome to DekuDekuplex’s Blog, the Never Never Land of amateur functional programming theory!

What is the value of a process that doesn’t terminate?

Allow me to present my introductory Scheme procedure, Towers of Hanoi:

;; Towers of Hanoi, plt1.1
;; PLT-Scheme-specific Version 1.1 of Towers of Hanoi
;; 
;; Copyright(C) April 02, 2008, at 19:38, 
;; by Benjamin L. Russell

(define (hanoi n)
  (hanoi-helper 'A 'B 'C n))

(define (hanoi-helper source using destination n)
  (cond ((= n 1)
         (printf "Moving from disc ~a to ~a.\n" source destination))
        (else
         (hanoi-helper source destination using (- n 1))
         (hanoi-helper source using destination 1)
         (hanoi-helper using source destination (- n 1)))))

To run the Scheme source code above, simply type:

(hanoi 3)

You shall be rewarded with:

Moving from disc A to C.
Moving from disc A to B.
Moving from disc C to B.
Moving from disc A to C.
Moving from disc B to A.
Moving from disc B to C.
Moving from disc A to C.

Wonderful, isn’t it?

So much for now.  Until next time….

(lambda x.(x x))(lambda x.(x x))