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I have a screenshot from my textbook here (Sudkamp, 3e), and I am trying to understand how macros are used with the Turing Machine. I am having a hard time grasping it, especially since I have never learned about macros before. If anyone can help with an explanation here, I would really appreciate it.
The only thing I really understand is that the CPY just copies the input, and then there ends up being 3 n’s. Otherwise, I don't really get how to come to that conclusion. I can try to be more specific if I am being too vague, let me know.
For the specific problem: yes, via CPY you get three times n. For computing f(n) = 3n the machine then computes n+n+n = 3n via the addition A.
About macros in general: they do not really work in the way suggested by the diagram. You cannot just put a machine for copying in a "place" in the computation of another machine. Adaptions for alphabet, start state etc. are necessary. The problem is that with TMs programs become very big, many states transition etc. and unreadable. So we suppose that these little adaptions can be done in principle. Now we do not specify complex machines in detail anymore, but use such macros for tasks that have been shown to be computable by a TM (like copying and adding). The resulting description is more understandable. A bit like a higher-level programming language, where you can use complex constructs and data structures without caring about their assembler implementation.
I'm learning Coq and the book I'm learning from, (CPDT) makes heavy use of auto in proofs.
Since I'm learning I think it might be helpful for me to see exactly what auto is doing under the hood (the less magic early on the better). Is there any way to force it to display exactly what tactics or techniques it's using to compute the proof?
If not, is there a place which details exactly what auto does?
There are multiple ways to get a glance at what is going on under the hood.
TLDR: Put info before your tactic, or use Show Proof. before and after calling the tactic and spot the differences.
To see what a particular tactic invocation has been doing, you can prefix is with info, so as to show the particular proof steps it has taken.
(This might be broken with Coq 8.4, I see that they provide info_ versions of some tactics, read the error message if you need to.)
This is probably what you want at a beginner level, it can already be quite terse.
Another way to see what is currently going on within a proof is to use the command Show Proof.. It will show you the currently built term with holes, and show you which hole each of your current goals is supposed to fill.
This is probably more advanced, especially if you use tactic such as induction or inversion, as the term being built is going to be fairly involved, and will require you to understand the underlying nature of induction schemes or dependent pattern-matching (which CPDT should teach you soon enough).
Once you have finished a proof with Qed. (or Defined.), you can also ask to look at the term that was built by using Print term. where term is the name of the theorem/term.
This will often be a big and ugly term, and it needs some training to be able to read these for involved terms. In particular, if the term has been built via the use of powerful tactics (such as omega, crush, etc.), it is probably going to be unreadable. You'd basically only use that to scan at some particular place of the term you're interested in. If it's more than 10 lines long, don't even bother reading it in such a crude format! :)
With all of the previous, you can use Set Printing All. beforehand, so that Coq prints the unfolded, explicit versions of everything. It is additionally verbose but can help when you wonder what the values of implicit parameters are.
These are all the ones I can think of on the top of my head, there might be more though.
As for what a tactic does, the usual best answer is found in the documentation:
http://coq.inria.fr/distrib/V8.4/refman/Reference-Manual011.html##tactic155
Basically, auto tries to use all the hints provided (depending on the database you use), and to solve your goal combining them up to some depth (that you can specify). By default, the database is core and the depth is 5.
More info on that can be found here:
http://coq.inria.fr/distrib/V8.4/refman/Reference-Manual011.html#Hints-databases
I've learned enough Common Lisp to be able to muddle my way through writing an application. I've read Seibel's Practical Common Lisp
What libraries or programs should I be reading to understand the idioms, the Tao, of Common Lisp?
CL-PPCRE is often cited as a good example, for good reason. Actually, probably any of Edi Weitz's libraries will make good reading, but CL-PPCRE is particularly clever and it's a useful and impressive library. Beyond that a lot of CL implementations are written mostly in CL. It can be pretty productive to pick some part of CL that's usually implemented in CL and compare how different implementations handle it. In particular, some of the best examples of large useful macro systems are implementations of things in the standard. Loop is an interesting read, or if you're really ambitious you could compare a few implementations of CLOS.
If there's some area of computing you are particularly interested in it might be worth mentioning that, so people can tailor recommendations to that.
It's another book, so it may not be precisely what you're looking for, but Peter Norvig's Paradigms in Artificial Intelligence Programming contains a lot of well-written, smallish Common Lisp programs. It's not perfectly natural code, especially in the the first few chapters, because, like code in Practical Common Lisp, it focuses on teaching you how to program in CL, but it's still very much worth a read. It also contains some excellent examples of ways you can build other languages on top of Common Lisp, and it has some valuable advice on how to improve the performance of CL programs.
The other recommendations (PAIP and CL-PPCRE) are excellent. I would also suggest becoming acquainted with Alexandria's code and also taking a look at GBBopen.
The Art of the Metaobject Protocol - is a book with the most beautiful code ever written.
LISP (Lisp In Small Pieces) is a neat book; shows clossette (small obect system) and
some compiler stuff. Without doubt, Norvig's book is awesome.
I really like "Building Problem Solvers" as well but the code is a bit rough. I'm not
used to binding dynamic-scoped variables in the parameter list. But it made for much fun
improvements trying to "pre-compile" the discrimination net. This book gives another
approaches to some of Norvig's code; I still think that Norvig's code
is much "neater and cleaner" code (easier to read and understand, and still creative).
"Building Problem Solvers" should come with a warning label like "you're gonna need some
aspiren (sp). It felt like a bolt of lightning struck me in the head when I finally
"understood" rms and Sussmans' dependency directed backtracking. Compiling the pdis
was also brilliant. Excellent stuff. I just wish I could remember it all ...
I like the SBCL code.
The only thing I would offer is to program. That is what I did.
I did two things. One I tackled a problem that i was familiar with, a unit testing framework and expanded it to include test suites. To get an understanding of macro writing.
The second thing I did was play around with basic objects in CL. Macros, closures, and style.
Also don't forget about getting feedback from Lispers about your code.
(defun ugly-lisp-code? () ())
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I picked up a LISP book at a garage sale the other day and was just wondering if it was worth spending some time on.
Yes. I'll stick to Common Lisp, here, though Scheme is also a superb language that has a lot to recommend it.
In Common Lisp, you have a largish multi-paradigm language that provides some things that either don't exist widely outside the Lisp family of languages, or are limited to CL and even more obscure/niche languages.
The first feature, which you can get in one way or another from CL, Scheme and quite a few other dialects, is a real macro system.
I say "real" because the system is much more complete, flexible and reliable than, say, C preprocessor macros. It's extremely difficult to get CPP macros to do even simple things (like swapping the values of two variables, or making a foreach construct) in a reliable fashion, but these are trivial with Lisp macros. This turns out to be a very powerful tool for introducing new abstractions and dispensing with "boilerplate" code.
The second feature, which is effectively limited to Common Lisp, is CLOS, the Common Lisp Object System. Despite the name, it's not a conventional OO system like that of Java with methods being part of a class's definition. Instead, it provides polymorphism through "generic functions" which are what methods are attached to, and by default allow you to do multiple dispatch.
I vastly prefer CLOS to the more usual approach to object orientation, as it makes a number of "patterns" (like the Visitor pattern) completely unneccessary and because extension of existing generic functions is so easy; others loathe it because it takes an extremely cavalier approach to encapsulation and because extension of generic functions becomes arguably too easy. Either way, CLOS is different enough that I think it's worth learning just for the different perspective it provides.
The third feature, which is available outside of Lisp but still fantastic if you've never experienced it before is dynamic, interactive programming. CL debuggers tend to be extremely powerful tools, and CL provides for dynamic definition and redefinition of functions, classes and methods, all of which dramatically improves one's ability to explore a problem, test solutions of that problem and its subproblems, and finally put together a program that works correctly and efficiently.
Lastly, for a lot of classes of problems, Lisp is a great practical language. It provides good performance (usually not as fast as C, but dramatically faster than most "scripting languages"), safety, automatic memory management, a decent "standard library" of functions and tremendous opportnities for easy extension.
It is worth learning for "mind-expansion" purposes but not so popular for building apps these days.
However, it is powerful, and mature, and there are fast and free compilers out there. So there is no reason not to choose it for a program if you like.
The way in which Lisp treats data structures and program structures the same offers amazing power which is worth understanding.
Its history is fascinating and it has shaped the world of computer science.
Be sure to check out Ableson and Sussman's Structure and Interpretation of Computer Programs at MIT OpenCourseware
Clojure: a Lisp on .NET and Java VMs
GNU CLISP.
CMU Common Lisp
Depends on the book. Which book?
Common Lisp is worth learning today because it's one of the few languages that pretty much "does everything". If there's some mainstream or obscure programming idiom or technique, odds are Common Lisp has it already in some form. About the only thing CL lacks is continuations (many argue it doesn't need them, but that's not helpful if you want to explore them).
Anyone spending any serious time writing in Common Lisp will come out Changed in some way, typically for the better, IMHO.
Even if you can't carry all of the Lispy concepts you learn and use in to other environments, knowing about them and how they work is still useful.
Good programmers expose themselves to as many different programming paradigms as they can - not as many programming languages as they can.
The LISP family (there are several variants) is very worth while getting to know. Your objective should be getting your head wraped around functional programming and the lambda calculus - the paradigm that LISP is based on. Focus less on becomming an "ace" LISP programmer (that could take years).
If you find functional programming "flips your switch", try having a look at PROLOG too - here the paradigm is based on evaluation of Horn Clauses (predicate logic).
I may have spent the last 20 years earning a living as a COBOL programmer (OMG - they still have those!), but I think I am a better programmer because of the time spent learning what LISP, and a number of other programming languages were really all about.
Have a blast...
Here's a Google Tech talk worth watching about a company currently producing large, complex software for the airline industry in Common Lisp:
Lisp for High-Performance Transaction Processing (The video is now unavailable. Here's some note by Zach Beane.)
Other topics are mentioned in that video, including Clojure, a new variant of Lisp for the JVM (some work is now being done to develop Clojure for the CLR too, but that is not as far along), which is worth checking out for the way it addresses concurrency issues. See the Clojure site at:
http://clojure.org/
and, in particular at first, check out the link in the upper right on that page to some excellent Screencasts with overviews of the concurrency issues and Clojure features.
If you get interested in Lisp, and the book you found is not that great (I have an old one myself that didn't do much for me), Paul Graham's book On Lisp is available free at http://www.paulgraham.com/onlisp.html and is very good. The general Lisp idea is the same for Common Lisp or Scheme or Emacs Lisp or Clojure, but the specifics will be different - so keep that in mind if reading Graham's book, which focuses mostly on Common Lisp (with some mentions of Scheme specifics.) On Lisp is probably not the best beginner book, but it's worth going through it and just skimming over specifics you're not ready to follow in detail yet to see what is there, particularly with regard to macros, which On Lisp really explores.
One benefit of Lisp is that you develop an appreciation for prefix and wonder why everyone else in the world doesn't us it too (like with Latex or vim)
+ 1 2 3 4 5 6 7 8 9
is much easier to code/edit/paste than
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
See this question, and especially the third answer, the one that explains that Lisp is good for solving complicated problems, those problems that are hard to decompose into more manageable modules if you were to try to solve them in another language. In other words, if you are keen on exploring ways to solve convoluted problems, that involve, let's say Natural Language Processing, or Knowledge Aggregation... then, yes, Lisp might just be useful to you.
Learn lisp to learn about macros, and that code is data, and to learn that you can reach enlightenment w/o the self-flagellation of C++.
Learn Common Lisp to learn about reader macros and compiler macros. I don't know any other language that has them.
Learn scheme for continuations.
Learn Clojure because it's going to make Java obsolete :-)
It (Common Lisp) is still heavily used by academics working in Artificial Intelligence. Scheme is a Lisp-like language used by many (most?) CS departments as well. Personally I think learning Lisp is worthwhile whether or not you end up using it. It's a classic language that we've learned a great deal from over time.
Learning LISP is a good way to learn functional programming effectively, and is often used as an introductory language for undergraduate students. Many people feel that Structure and Interpretation of Computer Programs, which uses the Scheme dialect of Lisp, is a book that should be on every programmers shelf.
Paul Graham has been a big proponent of Lisp, and in his book, Hackers and Painters, he describes how he used the power of Lisp to dominate the competition in creating ViaWeb for Yahoo Stores.
Elsewhere, I've seen Lisp dialects used prominently in the aerospace industry, as scripting tools for integration frameworks like Comet, and AML. Lisp will always be tied to the early AI experiments in the 1950's.
As other have alluded to, Lisp isn't that popular anymore for general programming, and it definitely (IMO) has some major problems for writing real systems in, but of course others disagree (for instance much of ITA's software is written in Lisp, and they make crazy bank).
Even if you never write a 'real' program in Lisp, it is absolutely worth learning. There are many programming techniques originally pioneered in Lisp that, knowing them, will help you write better code in Python, Perl, Ruby, ML, Haskell, and even C++. For instance, check out Higher Order Perl, which shows how to do all kinds of amazing tricks in Perl; to quote the introduction "Instead of telling you how wonderful Lisp is, I will tell you how wonderful Perl is, and in the end you will not have to know any Lisp, but you will know a lot more about Perl. [...] Then you can stop writing C programs in Perl. I think you will find it to be a nice change. Perl is much better at being Perl than it is at being a slow version of C."
And there are some great books out there that use Lisp, and it will be easier to understand them if you know the language - SICP, Norvig's Paradigms of Artificial Intelligence Programming, and The Reasoned Schemer all come to mind as must-reads.
Some people here are recommending Clojure. While I would say that Lisp in general is good, I would caution against Clojure, at least for beginners. This is not out of any difficulty using Clojure, just in the fact that Clojure is gratuitously inconsistent with Common Lisp and Scheme. If you want JVM integration, use Armed Bear Common Lisp: https://common-lisp.net/project/armedbear/ , though for general use, I would recommend Steel Bank Common Lisp: http://www.sbcl.org/
This is like questioning if "it's worth to learn C these days of web programming?". Only you can decide if it's worth. What you have to ask yourself is: what am I trying to achieve reading the book?
Learning new languages sometimes aren't useful in the practical sense of things (maybe you're aren't going to use LISP ever in your life), but in the long term it's going to be useful because of the knowledge acquired by different paradigms you aren't too familiar with - and you could use some of you learned in what you already use today.
It's been awhile since university, but after I took a 3rd year CS course that required learning Lisp and writing Lisp programs, writing and thinking recursively was a snap. Not that I had problems with recursion before the course, but afterwards, it was 2nd nature. I also used CLOS in the course (University of Toronto), but it was so long ago, I barely remember what I did.
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It is well known that different people have different aptitudes regarding various programming paradigms (e.g. some people have trouble learning non-procedural, especially functional languages. Some people have trouble understanding pointers - see Joel Spolsky's blog for musings on that. Some people have trouble grasping recursion).
I was recently reading about a study that looked at how the grammar of someone's native language affected their speed of learning math. Can't find that article now but a quick googling found this reference.
That led me to wondering whether someone's native culture or first language might affect their aptitude towards various programming paradigms. I'm more curious about positive influences - e.g. some trait that make it easier/faster for someone to learn a particular paradigm, for example native language grammar being very recursion-oriented.
To be clear, I'm looking for how culture/language grammare may affect the difference between aptitude of the same person towards various paradigms as opposed to how it affects overall aptitude towards programming between different persons.
Important: the only answers I'm interested in are either references to scientific studies, or personal observations from someone intimately familiar with a particular culture/language, including from their own experience.
E.g. I'm not interested in your opinion of how Chinese being your first language affects anything unless you speak Chinese or worked with extremely large set of Chinese-native programmers extensively.
I'm OK with your guesstimates not based on scientific studies, but please be sure to supply your reasoning about plausible causes of your observation.
I'm not interested in culture-bashing (any such commends will be deleted or flagged for deletion).
I'm also not particularly interested in culture-building - we all know Linus is from Finland and Tetris was written in Russia and Larry Wall is an American. Any culture/nation can produce a brilliant mind in any discipline. I'm interested in averages.
Disclaimer: I was a Cultural Anthropologist before I got into programming, so you know I'm going to be on a high horse, here.
Obviously, a person's history will have an impact on their aptitude for any particular task, but I think this has less to do with the structure or grammar of a person's language than it does with the particular material conditions of the culture in which that language is spoken.
For example, a pair of Anthropologists in the 60's went to various African communities and tested people's susceptibility to various optical illusions. Here is a classic one:
In this illusion, the bottom line looks longer, because the angled lines connecting it make it appear to be off in the distance.
These Anthropologists found that in many African cultures, the illusion doesn't work at all - people consider the lines to be the same length. By refining their study, they found that the only people who were susceptible to the illusion were people who had grown up in an urban environment. They hypothesized that the illusion did not work on people from remote jungle environments, because these people had little or no experience with right angles and seeing things at very long distances.
My point with this is that even if you successfully found a correlation between programmers' native languages and their abilities with certain aspects of programming, you couldn't be sure that the correlation wasn't spurious. For example, you might think that Asians tend to be bad drivers, and you might even be able to demonstrate this statistically. If you then concluded, however, that "bad driving" is some sort of fundamental characteristic of Asian-ness, you would be ignoring the fact that Asians are more likely to be from Asia, and thus to have had much less experience driving cars (or even being in cars) while growing up than Westerners (and especially Americans) have had.
With programming, we might think that a particular language inhibits programming ability, and not take note of the fact that the society in which that language is spoken has much less access to computers, and thus people growing up with that language appear to have less programming aptitude or ability to understand certain programming concepts.
In short, I wouldn't give much credence to the idea that language inhibits anyone's ability to understand anything in particular. The human mind is much too flexible and adaptable for that to be true.
This seems analogous to the Sapir-Whorf Hypothesis - that the facilities of a language affect the ease which which one can cogitate about certain subjects, or in the words of the Wikipedia article:
"The linguistic relativity principle (also known as the Sapir-Whorf Hypothesis) is the idea that the varying cultural concepts and categories inherent in different languages affect the cognitive classification of the experienced world in such a way that speakers of different languages think and behave differently because of it."
( http://en.wikipedia.org/wiki/Linguistic_relativity )
While there appears to be little definitive information here, the discussions appear to be relevant to the question, and perhaps worthy of further exploration.
Just a few random thoughts. I think the influence is generally very weak and can most of the time be neglected but they do exist and sometimes they can make us feel them.
In Chinese grammar, for example, we don't quite distinguish between plural and singular forms, but I wouldn't think we Chinese have any noticeable difficulty understanding the concepts of scalar and array in Perl. The reason might be this: although we generally don't need particular suffixes or changes in form to indicate whether something is singular or plural, we do have the concepts of plural and singular and we mostly depend upon the context to tell them apart. Grammar-wise, the context in Chinese may possibly be way more important than that in those languages belonging to indo-european family. We omit a lot of things sometimes when they have already been mentioned and sometimes when we just presume that these things can be implicitly well understood by the listener. In either case, we don't need those indefinite and definite articles (a, an, the) or those relative pronouns like, that, which and who, to indicate whether they're being mentioned for the first time or yet another time again. Maybe that's partially why I feel very comfortable with Perl's default variable "$". print; chomp; split; all act upon $, which has never ever been mentioned. But this is quite subjective.
I think the Chinese language is more characterized by implicitness and fuzziness than Indo-european languages. For example, We never ever pay attention to subject verb agreement and we never ever do verbal conjugation to denote tenses. This could mean that the Chinese are inclined use a not quite so logical mode of thinking. One of my teachers onced used an example to try to generalize (or maybe over-generalize)the difference between Chinese non-logical mode of thinking and American logical mode of thinking.
If the American version of quarrelling should be this:
“I can lick you.”
“No, you can’t.”
“Yes, I can.”
“No, you can’t.”
“I can.”
“you can’t.”
“Can!”
“Can’t!”
The Chinese version (translated in English) would be something like this:
I can lick you.
How dare you!
What if I dare?
Then you try.
Try? Hm, you wait and see.
Wait and see? I’m not afraid.
Not afraid? OK. You don’t run away.
Who runs away? Come on and lick
Well, I agree that there may be some differences between Chinese way of thinking and that of other countries but the example looks like a stereotype because the Chinese may easily switch to the use of the American version. Back to the question, I think the language and culture may indeed influence a programmer's learning process in one way or another but this influence is defninitely not decidingly noticeable. Maybe because of the culture you're exposed to makes you feel a little bit uncomfortable to get used to some notions in some programming language, recursion or whatever, but time will solve it.
I was recently reading about a study that looked at how the grammar of someone's native language affected their speed of learning math. ... Important: the only answers I'm interested in are either references to scientific studies, or personal observations from someone intimately familiar with a particular culture/language, including from their own experience.
I learned a lot of maths before I started programming (enough to count as "intimately familiar"), and IMO programming is relatively easy: more tangible.
Sometimes I've wondered whether it's beneficial to know more than one human language: if you only know one language, then you might think of the words "cat" and "dog" as being values, i.e. synonymous with cat and dog objects; but if you're fluent in more than one language, then "cat" and "dog" become pointers: because for example the French words "chat" and "chien" are referring/pointing to the same objects as "cat" and "dog", and so clearly there's a distinction between the word and the object.
It's disappointing that you post the question without linking to the article which inspired it. I thought of "reverse polish notation" and wondered whether that was at all the kind of differences in "grammar" that were considered in the original study.
The reference you cite seems to rest on the assumption that making it easier helps with learning. In my understanding, there is a countereffect: without enough challange, you're not learning enough.
There are theories/studies (anyone with a link?) that development of language created crucial pressure on expanding the cerebral cortex and thus "made us human". (in very darwinistic terms: more grey matter ==> better language capabilities ==> better teamwork ==> better survival as a group). So language complexity can't be all bad for learning.
(My only qualification is being an eager follower of The Frontal Cortex blog, so take this with a grain of salt.)
In german we have a strange ordering of numbers: 10^0 and 10^1 positions are switched, but others are normal, (e.g. 25 is 'five and twenty', 125 is 'one hundred five and twenty'). It's been claimed that this makes learning numbers harder, and thus german should adopt a more intuitive ordering.
I guess that it helps a lot with doing additions in your head - at least if you stay below 100 or 200 - You can first add the 10^0 position and already say it / write it down while taking any carry into account for the 10^1 position.
(That doesn't continue for 10^2, I guess that would be done in writing by the majority anyway)
Also: abstractions. There are languages where numbers aren't abstracted from objects, "two coconuts" and "two sabretooth tigers" don't share a common "two" word / concept. Such a language would probably be very bad for developing math skills. Here the abstraction (separating number and object) in language is important.
Generally, I'd say the language has a strong effect on shaping a developing mind, and I see no reason why this should not extend to culture.
Of course it's still open what would be the "right kind of complexity" - for what, and how particular language features affect general improvement vs. establishment of an elite (i.e. "sharpening the skills of the gifted, while hampering the rest").
Interesting Question, no doubt - looking forward to other replies.