Notation as a Tool of Thought (1979)

http://www.jsoftware.com/papers/tot.htm

by ehudla • 10 years ago

106 25 10 years ago

Ah, yes. The paper that taught the world about the marvels of APL. Which is a pretty cool language, and definitely on my "to learn" list.

APL's unofficial slogan, by the way, is "and you thought Perl was executable linenoise." :-)

imglorp• 10 years ago

I took a numerical methods in APL class way back. Nothing we did took more than half a line, ever.

JosephHatfield• 10 years ago

[]pw <- 80?

gardano3• 10 years ago

Musician checking in. Reading music in the original notation I have found to be particularly enlightening.

Where the manuscript writer (or print publisher) chose to put bar lines, for instance, can give clues as to intent in performance. I'm thinking specifically about Venetian publishers in the 17th century -- but there are plenty of other examples.

Notation can be incredibly important when trying to discern intent in some disciplines.

gkya• 10 years ago

Would you mind to elaborate a bit more? Seems to be very interesting fact.

gardano3• 10 years ago

Picture a piece for 3 players -- 2 soprano instruments and Basso Continuo (a bass instrument + let's say, harpsichord). It's a piece with a recurring harmonic structure; say, Passamezzo or ciacona -- think Pachelbel Canon.

The BC in this particular instance might only have barlines every 8 measures. The soprano parts might have barlines every 8 measures too, but might also have them where a significant change to their melodies change. Like, when a flurry of 16th notes begin to crop up.

Now, this isn't always the case -- it's definitely inconsistent, but such things show up enough that those hints cannot be discounted at all, and seem to be enough of a performance hint to at least be noted and appreciated by the performer.

tnecniv• 10 years ago

Was bar placement not standardized to be at the end of every measure?

gardano3• 10 years ago

No, bars were not standardised at all!

One could interpret placement of barlines as something close to paragraph markers -- not all the time, but often enough that they seem to indicate specific intent.

kaoD• 10 years ago

Slightly unrelated: I often find myself in the browser console, exploring data scraped off webpages (often from Wikipedia tables). I think REPLs are another kind of "tool of thought". E.g.: I recently scraped my country's election results off Wikipedia to see how voting areas affected the distribution of seats. Very insightful.

Being tightly integrated to the browser offers the whole web as a data set. Unfortunately JavaScript does not lend itself very well to data analysis.

What is your tool of choice for interactive data exploration?

I've been looking for something similar for my phone, a sort of calculator-on-steroids even if not web-scraping ready. J for Android[0] fits the bill perfectly... except the language itself seems to get in the way with its short mnemonics, unrememberable verb train rules, function composition words and other weirdness in the construction of tacit phrases. I've (partially) learned and forgotten J three times already. Every single time I come back is like starting anew.

I tried Clojure too but the Android REPL[1] is stuck on Clojure 1.4.0 and the lack of an S-expression enabled keyboard/editor makes it a pain to code.

Any recommendations in this area?

[0] http://www.jsoftware.com/

[1] https://play.google.com/store/apps/details?id=com.sattvik.cl...

RodgerTheGreat• 10 years ago

It may not really be what you want, but I've been developing a mobile-friendly frontend for my K interpreter which makes it essentially a K-based graphing calculator:

http://johnearnest.github.io/ok/mobile.html

The browser security model severely limits potential for doing web scraping with it, but I have found it pleasant to use so far.

Docs can be found here: https://github.com/JohnEarnest/ok#mobile

dTal• 10 years ago

It's not Free Software, but Frink is my goto "calculator on steroids". Not sure if it's suited to what you have in mind.

https://frinklang.org/

carussell• 10 years ago

Side note:

I often find myself in the browser console, exploring data scraped off webpages (often from Wikipedia tables)

Are you aware of Wikidata? I don't have a lot of familiarity with it, only that some (a lot?) of the programmer types who were drawn to Wikipedia in its infancy have shifted their focus to Wikidata nowadays. As I understand it, Wikidata is meant to be the data source behind those tables that you're scraping.

(Forgive me if you're already involved with Wikidata and one of your primary uses for scraping is in pursuit of migrating content to Wikidata.)

qwertyuiop9243• 10 years ago

My goto tool for data analysis is AWK: it's not interactive, but it's succinct, and very good at handling DSV data.

As for handling non DSV data... I dunno. Lisp is pretty nice for this, but it's a pain to get the data into the system. TXR and its lisp dialect are pretty good with this, so that's an option.

But if you really want to handle tabular data interactively, doing manipulation and analysis on the fly... that's quite literally what Excel was designed for.

kazinator2• 10 years ago

Speaking of Awk and TXR, TXR Lisp has an awk macro (introduced in mid 2016), with which you can transliterate many kinds of Awk programs.

However, it's a lot slower than GNU Awk.

You don't get the duck typing of Awk (whereby strings that look like numbers can be treated arithmetically, and nonexistent or blank variables are zero, et cetera). To convert fields to numbers with reasonable succinctness, an "awk local macro" called fconv (field convert) is provided.

There is no function-for-function compatibility with the Awk or GNU Awk library, and regular expressions are TXR: that means no register capture, and ^ and $ done with functional combinators.

yummyfajitas3• 10 years ago

If anyone is interested in a more readable version of APL, I think python/numpy qualifies. Their first few examples can be expressed the same way in standard numpy:

    arange(6) # Same as ⍳5
    add.reduce(arange(6)) # Same as +/⍳5
    add.accumulate(arange(6)) # Same as +\⍳5

I've gone partway through this document (up to chapter 3, plus skimming other bits) and have not found any examples that don't translate into standard numpy code.

From what I can tell, the core learning one takes from J/K/etc is the concept of an array language and treating arrays as first class objects. And nowadays Python/R/Julia provide this same functionality in a more verbose/more readable/more mainstream package.

_mhr_• 10 years ago

It'd be a fun project to write a an APL-like that compiles down to NumPy. Would it be pointless? Another interesting project might be to make an APL-like for probabilistic programming.

yummyfajitas3• 10 years ago

My point is that it'd be pretty easy. The semantics are pretty close, it's only the syntax ("+/" -> "add.reduce") that varies.

3JPLW• 10 years ago

There's a start for this in Julia[0], where custom string literals mean that you can actually write APL in native Julia:

    julia> apl"ι5"
    1:5

    julia> apl"+/ι5"
    15

You can even just get the function that represents the `+/` operation and apply it to any Julia object:

    julia> apl"+/"(rand(100))
    52.17866879741195

0. https://github.com/shashi/APL.jl

beagle32• 10 years ago

From what I can tell, the core learning one takes from J/K/etc is the concept of an array language and treating arrays as first class objects. And nowadays Python/R/Julia provide this same functionality in a more verbose/more readable/more mainstream package.

That's just part of it. Other parts (by no means a complete list):

- Visual density puts the pattern matching engine in your brain to good use; e.g. the K idiom "|/0(0|+)+\" which implements maximum-subsequence-sum is a 10-character visually recognizable sequence recognizable to many K programmers, which is efficient and well specified; Similarly, ",//" flattens a list. I don't know of any other language family that has this feature.

- Arrays with equivalent indices work better than structures ("column major" captures some, but not all of it)

- A properly selected core set of concrete operations (in K's case, about 60 of them) makes the needed abstractions shallower and simpler than a properly selected set of abstraction constructs.

yummyfajitas3• 10 years ago

I agree that Python/R/Julia don't have the same visual density.

But your second point is definitely something that Python/R/Julia do - that's why data frames (e.g. Pandas) are so popular. Can you suggest something that K does beyond this?

By the way, I'm not asking to criticize K. I really want to know of there is something I'm missing. I've investigated J a bit, but never found the enlightenment that people say I'll find.

mayoff• 10 years ago

The year in the title should be 1979, not 2009. This was Ken Iverson's Turing Award lecture in 1979.

mcnamaratw• 10 years ago

Yep, here's a link http://delivery.acm.org/10.1145/1290000/1283935/a1979-iverso...

Notation as a Tool of Thought (1979)

Related Stories