Wolfram Language

https://reference.wolfram.com/language

by lelf • 13 years ago

171 122 13 years ago

reference.wolfram.com

xradionut2• 13 years ago

The more interesting details aren't on this page. The license and the costs associated with the license.

trurl423• 13 years ago

So far it seems like the "Wolfram System" and the future "Mathematica 10.0" are the same thing (see: http://reference.wolfram.com/language/tutorial/WolframSystem... )

Licensing doesn't seem to have changed: http://reference.wolfram.com/language/guide/SystemAndLicense...

xradionut2• 13 years ago

So it's "A New Kind of Marketing" ?

tokipin10• 13 years ago

part of the problem Mathematica has is that people assume it's just for math, which isn't the case. it's a very general system. this renaming, while utterly dorky and aesthetically hamhanded, will at least help clear that misunderstanding

spitfire4• 13 years ago

Correct, it seems to be a repackaged Mathematica, with better deployment options.

xfax2• 13 years ago

Serious question - is Mathematica popular outside of academic circles? I remember being blown away in college but haven't used it since.

bhouston• 13 years ago

I've seen it used for prototyping, proving and equation simplification in the simulation space, but then those algorithms were converted to C++ for production use.

MATLAB can also be used in this fashion: http://www.mathworks.com/products/matlab/

kcorbitt• 13 years ago

I know an engineer at Boeing who leans on it heavily for his research. I'm not sure exactly what his department/responsibilities are, but there's one data point anyway.

stevenbedrick• 13 years ago

I know several industrial physicists who use it very heavily.

jwr3• 13 years ago

I use it for prototyping, analyzing data, and explorative research. When considering a new approach to a computational or machine learning problem, you can often try it out in Mathematica and see if it's the right direction at all.

tr• 13 years ago

I work at a biotech startup in the bay area and we use it heavily. Every piece of scientific data is parsed, analyzed, and shared in Mathematica.

msutherl2• 13 years ago

I built some utilities with it, like a Wheatstone Bridge calculator, that I use sometimes when I'm doing electronics.

gaius• 13 years ago

It and MATLAB are popular in finance.

hsmyers• 13 years ago

Excellent platform for fractal research. And trust me not all of those who search are academics :)

analog31• 13 years ago

From what I've observed, Matlab is more popular. There's a perception -- for whatever reason valid or invalid -- that Matlab is for numerical computation, and Mathematica is for symbolic or higher level math. And, that Matlab is easier.

However, I'm noticing a trend towards using mainstream programming languages and whatever free libraries are available, to do the same kind of work. I used Mathematica 15+ years ago, and for doing the same kind of work today, I now use Python and am quite happy with it.

berntb2• 13 years ago

To me this looks like a Lisp variant with a large set of utility libraries.

Am I missing something? Is the point the quality/volume of the support libraries?

jessriedel• 13 years ago

I don't know, but to me most of the power of Mathematica is basically the wide-ranging and compatible utilities. Not having to write my own basic math functions, nor spending hours trying to get some C++ package working, is huge.

berntb2• 13 years ago

Yeah, but wasn't this sold as something qualitatively new?

dagw• 13 years ago

Yes. The language in itself isn't that interesting, but the collection of libraries is vast and mostly world class.

Jtsummers4• 13 years ago

To me this looks like a Lisp variant with a large set of utility libraries.

I feel like I'm missing something because I read this a lot, but don't see it when I look at Mathematica. The language seems to be a higher-order, functional programming language with dynamic (?) typing. That part sounds like lisp, but syntactically it looks nothing like lisp to me. Is there a portion of the language that I'm overlooking?

brandonbloom2• 13 years ago

http://reference.wolfram.com/language/ref/FullForm.html

scrumper• 13 years ago

Technically the language is a Term Rewriting System[1]. You can use it as a TRS by directly manipulating transformation rules, in a functional way, in an imperative way, and of course as pure symbolic mathematics.

It does naturally suit functional thinking, so that becomes the default 'best' way of engaging with it.

[1] http://en.wikipedia.org/wiki/Rewriting#Term_rewriting_system...

JackFr2• 13 years ago

My experience was having used Mathematica years before I ever saw LISP, or really knew anything about programming beyond C & F77. A REPL, functional programming, lists, etc. -- it was pretty mind-blowing.

Now I know that none of those things were invented by Wolfram (the company or the man), but they were put into productive use, in a very slick and beautiful application with a slew of symbolic and numerical math libraries which were world class.

I guess to a large extent, you're not missing something, but the libraries are comprehensive, well designed, well documented, very consistent and reasonably intuitive.

discreteevent• 13 years ago

Similar experience here. I didn't do CS in college but used MMA a fair bit. Then ended up programming for a living in mainstream 90s languages. So when FP started to make a comeback recently it just hit me that "Hey this is just like Mathematica". But even then the Mathematica environment was better in ways than what you get with some FP languages now. I don't get all the retro fetish. I know my vi but I've no wish to use it over a good IDE. Hopefully Light table can do it for a functional language.

oleganza2• 13 years ago

When I was a student and working with Mathematica 5 and 6 a lot, I was always amazed about its simplicity and power. I had just two windows: typing in a white document window without any toolbars (only zoom control in the bottom) and having another window with documentation. And the documentation was great: you could evaluate examples right inside the doc page, play with parameters, like in your own document.

The design of the language, user interface and depth and clarity of documentation makes me think that Wolfram Research is even more design-obsessive than Apple. Stephen Wolfram takes credit for too many things (like Jobs), but he also delivers amazing stuff.

sampo• 13 years ago

a white document window without any toolbars

How did you set that up?

oleganza2• 13 years ago

I think it was a default. Or, at least, with one formatting toolbar which I simply disabled. I never used palettes of special symbols: it was easier to remember some common shortcuts via "escape" key (e.g. Euler constant is <escape> ee <escape>)

tokipin10• 13 years ago

you can do

    SetOptions[EvaluationNotebook[], DockedCells :> {}]

and there are options to remove the window frame, etc. but i think if you are using certain licenses the toolbar may not disappear. and the main toolbar never disappears, to my dismay

jcutrell• 13 years ago

Got really excited about Language Processing, then I saw what's on the page. https://reference.wolfram.com/language/guide/LanguageProcess...

I do look forward to what's next on this, especially because I have yet to buy a Pi.

klrr• 13 years ago

I like what they write about functional programming.

"Functional Programming

Long viewed as an important theoretical idea, functional programming finally became truly convenient and practical with the introduction of the Wolfram Language."

Not sure if anyone can take that seriously.

sudont2• 13 years ago

Seems more like mathematician ego rather that Wolfram's ego. I see the same attitude in xkcd, for example.

http://xkcd.com/435/

There was also a recent article on here about how programming is a dead-end, non-prestigious job in research circles. Sounds like a continuation of that sentiment.

scott_s5• 13 years ago

Randall Munroe is making fun of that attitude in xkcd, not supporting it. He was a physicist at NASA, but has done a decent amount of programming.

awef• 13 years ago

Would you mind linking said article?

xfax2• 13 years ago

Wow, don't know if they are delusional or just wrong.

scotth• 13 years ago

Clearly both.

JackFr2• 13 years ago

Those categories aren't exclusive.

scott_s5• 13 years ago

Back when he posted about trying to figure out what to name the language, I thought Ego would be perfect.

phaed• 13 years ago

Wolfram: Wolfram

jordigh4• 13 years ago

Not just that, he also seems to think that he invented Lisp's idea of code-as-data: "In most languages there’s a sharp distinction between programs, and data, and the output of programs. Not so in the Wolfram Language. It’s all completely fluid. Data becomes algorithmic. Algorithms become data. There’s no distinction needed between code and data." ( http://blog.wolfram.com/2013/11/13/something-very-big-is-com... )

Kinda funny considering how the Mathematica language is built on top of the M-expressions that lisp never bothered to implement.

lispm6• 13 years ago

Like RLISP, the implementation language of REDUCE?

msutherl2• 13 years ago

Note that this is marketing copy aimed at Mathematica users, mainly scientists and mathematicians, most of whom probably don't know what LISP or Haskell are.

taliesinb9• 13 years ago

To be fair, our brand of monotonicity is somewhat different from LISP's, as I've discussed before at length on HN.

taliesinb9• 13 years ago

Yeah that's pretty bad.

tokipin10• 13 years ago

i think that's a reference to the fact that Mathematica uses M-expressions and operator precedence. it doesn't look like lisp, but if you FullForm an expression you will see that it's all just M-expressions.

that said, i think it is lisp-like as a design choice. the Mathematica language itself is more raw than even lisp -- you can take the language in different design directions. Wolfram chose to include lisp aspects

xntrk• 13 years ago

Is there a PDF of this doc somewhere? I would like to scroll through it to see what is in there. but I don't think i'm going to click on 10000 links to see every language construct...

vseloved• 13 years ago

The better name would be Wolfram standard library

petercooper2• 13 years ago

I'm always struck by how slick and well produced everything related to Wolfram is. It's not what I've come to expect from most academically leaning companies at all. This goes for NKS which is a beautifully presented book whether or not you go along with its contents.

ThomPete• 13 years ago

Agree. And Wolfram surely is genius in some ways.

But ironically he is a much better entrepreneur than he is a scientist.

If only he was looking for praise in the former rather than the latter he would get all the recognition he seems to crave.

jordigh4• 13 years ago

It seems that whenever Wolfram makes these grandiose and dubious claims, there are always people cheering him on. The comments on his blog posts are always unending adulation. You sound just like those people.

I very much doubt that those of us who doubt just about all the marketing fluff that he exposes are just not understanding his genius. I have read parts of NKS, and I don't think it's all that fascinating other than "cellular automata produce pretty pictures, and there's no reason to try to understand why they do this." It's very cranky.

I think Stephen Wolfram is just a rare breed of socially successful crank. He scores high on the crackpot index, but not high enough to be completely discredited as a lunatic. His litigious nature and ability to wrangle the legal system in order to label everything "mine" is what keeps him in business.

JabavuAdams• 13 years ago

Wolfram made a really useful tool. This is independent of how you may feel about NKS.

Try to take yourself back to 1988. Macs are newish. Desktop publishing is new. There's this neat new program called Mathematica. You can type in equations, solve them, and even graph them in 3D. You can laser-print the notebooks and they look better than textbooks.

Wolfram may be an egomaniacal self-promoter, but it's not all empty hype.

hdevalence• 13 years ago

For those curious for more details about "He scores high on the crackpot index, but not high enough to be completely discredited as a lunatic. His litigious nature and ability to wrangle the legal system in order to label everything "mine" is what keeps him in business.", see this review of "A New Kind of Science", which begins:

Attention conservation notice: Once, I was one of the authors of a paper on cellular automata. Lawyers for Wolfram Research Inc. threatened to sue me, my co-authors and our employer, because one of our citations referred to a certain mathematical proof, and they claimed the existence of this proof was a trade secret of Wolfram Research. I am sorry to say that our employer knuckled under, and so did we, and we replaced that version of the paper with another, without the offending citation. I think my judgments on Wolfram and his works are accurate, but they're not disinterested.
With that out of the way: it is my considered, professional opinion that A New Kind of Science shows that Wolfram has become a crank in the classic mold, which is a shame, since he's a really bright man, and once upon a time did some good math, even if he has always been arrogant.

http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfra...

petercooper2• 13 years ago

I admire his (or his company's) high production values (I bet many would interpret my "slick" comment as a slur though!) but these certainly stand separate to his/their work's scientific merit which I'll sadly never be smart enough to judge ;-)

I suspect much of his/their success comes through his/their Jobsian eye for detail and ability in presentation and while this is at its best when applied to meritorious work, it's certainly a skill/asset in its own right too.

lispm6• 13 years ago

The language lacks a spec. For a language with mathematical background this is a joke. The descriptions of core features are just not existing - not even talking of a semantic definition, like Scheme has now since a few decades.

Maybe they want to prevent alternative implementations.

tokipin10• 13 years ago

the spec of the underlying language would be very simple. it's basically just repeated pattern matching. beyond that, knowing where to draw the line would be a bit weird. for example, does the function TextRecognize [1] need to be specified?

and by the way, Mathematica's documentation is enormous so i don't think a single spec would be necessary. maybe a few functions here or there would need some clarification in certain edge cases, but those would be higher-level functions like Plot

[1] http://reference.wolfram.com/mathematica/ref/TextRecognize.h...

lispm6• 13 years ago

Wrong. Just check the core language. It large and there is much more than repeated 'pattern matching'.

Xdes• 13 years ago

So how do I use this language? Do I need to buy Mathematica?

mcguire3• 13 years ago

Or get a Raspberry Pi: http://www.raspberrypi.org/archives/5282.

(Or get someone else to buy it, etc., etc.)

klausnrooster• 13 years ago

Searched for REBOL from Wolfram's site (hope that language can 'flatten' it's own nest of URLs, jeez...). Didn't find REBOL but interesting NLP blog post from 2010: http://blog.stephenwolfram.com/2010/11/programming-with-natu...

vph• 13 years ago

One has to take a grain of salt with Stephen Wolfram's claims of superiority.

Nevertheless, it appears that people have to pay to use "the Wolfram language" (although there might be scenarios that allow "free usage" for the purpose of attracting users who will eventually pay for using the language if they want to scale up their work). The concept of paying to use a language is troublesome in terms of common understanding of what a language is.

jwr3• 13 years ago

I find it amusing that many people (seemingly Hackers) concentrate on Wolfram's ego rather than on the actual thing at hand. I don't care about egos, lipstick color, or the pants the language creator wears. I care about the language, so let's talk about it now:

From a long-time Mathematica user: this is not a language I like. I use it, but there is little to no fun. Many things aren't immediately clear or become problematic if you stop using the language for a while. As an example, quick, what is the difference between Module[], Block[] and With[]? Even if you remember that With[] is a lexical scoping construct, Module[] and Block[] can be confusing.

It doesn't help that Mathematica is absolutely horrible for debugging code. I don't know why they put so little emphasis on their REPL, but it's way behind the times. Even mismatched parentheses can cause serious pain (and I hate the fact that things move around when I edit parentheses).

That said, I have a lot of respect for Mathematica as a complete system. It is incredibly useful, most mathematical tools you will ever need are there. It is also a great tool for explorative data analysis. Have a pile of data you'd like to see patterns in? Load it up, mash it into shape with high-level functions, then quickly produce great-looking graphics. Nothing even comes close to the flexibility of Mathematica here.

maaku4• 13 years ago

Because ego blinds one to effective criticism. And the criticism many of us have with Wolfram products is that while smart in limited domains, they can be blindingly stupid in others (your various examples providing evidence for this). If he listened to and respected our complaints, maybe we'd have a better product. But no.

taliesinb9• 13 years ago

Not really. Stephen knows how poor our debugging facilities are (and I regularly tell him how bad the situation is) -- we've just had limited bandwidth to actually fix it properly to our satisfaction.

Luckily I have a totally revamped debugging and logging system that will put us ahead of the curve here (imagine DTrace at a program level). Probably a point release of V10.

Same goes with multiple undo and retina support -- we know how embarrassing their absence is, and we've luckily been able to fix these for v10. I've been in design meetings where the multiple undo has bumped several other desirable features off our roadmap.

chaostheory• 13 years ago

If this thing is actually great, I feel that the license is important. If it's too restrictive, what's the point? We're not living in the 80s.

nswanberg• 13 years ago

Not sure if you just want commiseration and are just having trouble remembering which keyword is which, so I apologize if I'm explaining too much, but for me deciding which to use is more grappling with the difference between dynamic and lexical scoping rather than which concept maps to which keyword, and just as knowing more about a person seems to help me remember their name, so too does knowing more about the function help me remember its name.

What helped me straighten it out was to evaluate the examples here with Trace: http://reference.wolfram.com/mathematica/tutorial/BlocksComp...

  In[1]:= m=i^2
  Out[1]= i^2

  In[2]:= Block[{i=a},i+m]
  Out[2]= a+a^2

  In[3]:= Module[{i=a},i+m]
  Out[3]= a+i^2

  In[4]:= Block[{i=a},i + m] // Trace
  Out[4]= {Block[{i=a},i+m],{i=a,a},{{i,a},{m,i^2,{i,a},a^2},a+a^2},a+a^2}

  In[5]:= Module[{i=a},i+m]//Trace
  Out[5]= {Module[{i=a},i+m],{i$5592=a,a},{{i$5592,a},{m,i^2},a+i^2},a+i^2}

It's a bit dense to read through but with Block, "i" has been assigned the value "a", but still remains in the form "i" throughout the evaluation, and once "m" is replaced with "i^2", the "i" is seen and replaced with "a", acting as normal dynamic scoping.

In Module, however, "i" is replaced by a temporary variable with the form "i$5592", which does not have a definition anywhere in Mathematica, so when "m" is evaluated, "i" is left alone, which is how lexical scoping acts.

I dislike forgetting parts of languages in the ones I use. C# is full of things whose behavior I have to look up, as is javascript, python, and especially while I'm learning them: clojure and cljs.

But what's nice about this language is that these two concepts, Module and Block, while having different meaning, have the same form.

59nadir• 13 years ago

Correct me if I'm wrong, but the ego of the language creators seems to shine through in at least this[0] reference page, though. The most important bit I'd like to get some clarification on:

Long viewed as an important theoretical idea, functional programming finally became truly convenient and practical
with the introduction of the Wolfram Language. Treating expressions like as both symbolic data and the application
of a function provides a uniquely powerful way to integrate structure and function—and an efficient, elegant
representation of many common computations.

I see nothing on the reference page that could be said to make Wolfram's FP constructs more convenient or practical. They make it sound like FP was a long lost dream but then Wolfram came along and actually made it happen. They're seemingly using the exact same constructs as everyone else.

What you do actually get from the reference page, though, is that they went the Haskell route and decided the FP stuff shouldn't be readable by anyone who hasn't used the language before. This is all fine and dandy, really; it's a model as good as any other, since it at least gives writability where it loses readability... They aren't doing anything new, from the looks of it, though. They seem to be doing precisely the opposite... In exactly the same way.

[0] https://reference.wolfram.com/language/guide/FunctionalProgr...

ianbicking• 13 years ago

These comments would be a lot more interesting if people identified what was cool rather than just bitching about ego or syntax or licensing. I'm not going to be using the Wolfram Language, but I'd love to identify the best ideas from it. And it's a different enough language that I am confident there are interesting ideas in it.

My own contribution:

Idly looking about I come upon this page, which is not particularly notable: https://reference.wolfram.com/language/ref/Sow.html

What is notable is this example:

  In: Reap[Sow[a]; b; Sow[c]; Sow[d]; e]
  Out: {e, {{a, c, d}}}

Reap/Sow ss a funny language feature that I haven't imagined before, but that's not really the point. The point is that this is a runnable example – that's actually what is output. Typically when you run something like that you get "NameError: a is not defined". And "a" here is really a variable, of sorts – it's not a string or symbol (at least not a symbol in the sense that we know them in programming).

Given this, snippets of code are just as executable as entire programs. Every expression is like a function with the free variables as its parameters, and a sequence of expressions is a bit like function composition.

This is all natural from the perspective of mathematic notation. In a more traditional programming environment I think it's reminiscent of partial evaluation: https://en.wikipedia.org/wiki/Partial_evaluation – where you analyze a program and execute expressions opportunistically. It's really almost the same as partial evaluation, but the Wolfram Language knows a lot more about how you can execute different combinations of expressions than a typical language. A typical language does not really "believe" that (a+b) and (b+a) are equivalent. It doesn't know how to relate different operations. Nor do normal languages have a concept of simplification, so they can't speculatively try other arrangements (where none in isolation is clearly better or simpler than another) to see if simplifications are possible.

andolanra• 13 years ago

I know it's not the point of what you were mentioning, but I wanted to briefly mention that reap/sow are not unlike Haskell's so-called Writer Monad:

    newtype Farm a b = Farm (b, [a]) deriving (Eq,Show)

    instance Monad (Farm b) where
      return x = Farm (x, [])
      Farm (b, as) >>= f =
        let Farm (b', as') = f b in Farm(b', as ++ as')

    reap :: Farm a b -> (b, [a])
    reap (Farm x) = x

    sow :: a -> Farm a ()
    sow a = Farm ((), [a])

    -- prints ("e", ["a","c","d"])
    main = print (reap (do sow "a"
                           return "b"
                           sow "c"
                           sow "d"
                           return "e"))

(Reimplemented in a simple way here to show the underlying machinery; usually, instead of lists, a writer is parameterized by an arbitrary monoid.)

pr_fancycorn• 13 years ago

What you are getting at here is the fact that Mathematica is a symbolic language through-and-through.

In my webpage here: http://www.oftenpaper.net/sierpinski.htm I try to give passing mentions to how the Mathematica language and its infrastructure make various things easier.

As a programming language geek, I haven't found a language more powerful than Mathematica, and that's before considering the infrastructure it comes with.

sixbrx• 13 years ago

I've always found the repeated application of rules to simplify patterns in expressions until the expression stops changing to be pretty powerful when just playing around, especially with small problems. However, in my experience in bioinformatics, that flexible approach is so slow in the face of actual data as to be totally useless for use on real problems in my line of work.

I think an option to use a faster, less powerful, linear pattern matching algorithm more like in ML/Haskell would help a lot in this regard.

leoc• 13 years ago

So, it employs term-rewriting magics of some kind rather simple evaluate-the-subexpressions, doesn't it?

memracom• 13 years ago

Realistically, rather than work with the fussy syntax of this pseudo functional language, most people who work in data science would be better of using Python because of the IPython Notebook http://ipython.org/notebook.html which provides similar mixing of code and graphical results. The matplotlib, inspired by Mathematica, can produce a wide variety of graphical plots. Newer libraries like pandas have been bringing all the power of R into the Python world.

Five years ago, Wolfram may have been worthwhile, but today the wave has formed and it is converging on Python.

GuerraEarth• 13 years ago

The red fire truck russianed in a lot of Wolfram interest.

Wolfram Language

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