In Praise of APL (1977)

97 pointsposted 16 days ago
by tosh
(jsoftware.com)

61 Comments

JaumeGreen

16 days ago

One of my list of dream projects that I might never have time to do, and so feel free to "steal" the idea, would be a eink notepad in where you could code in APL or similar.

APL was born as a mathematical notation, pertaining to the blackboard, so it makes sense to write it using a writing implement. Its terseness would make it ideal for the handwriting world, it's REPL implementation would give quick feedback loops, you could move around input and output streams.

You could be in a sofa, writing the solution, expending most of your energy thinking, not writing, once you got used to the new way of thinking and the vocabulary.

If you haven't tested any array language I would recommend you try to solve things using one, and check existing solutions so you can see how to think differently. Some problems are naturally easier with this approach, some are harder.

mlajtos

15 days ago

You are exactly right that the original vision of APL was a handwritten, non-ambiguous, consistent, and executable math notation. This was never accomplished.

In 2021, I made a prototype calculator designed for iPad and Pencil and wrote four essays called "New Kind of Paper" describing this concept. The video demonstration of the prototype [Demo] sums up pretty well how it might be used.

In 2024, Apple released Math Notes, which implements this concept for standard math notation. My "review" of it is at [MathNotes]. In short, it is currently a preview of a damn great tool, but its future depends on notation and expressivity.

APL is a language from 2066, created in 1966. While its semantics make more sense now due to machine learning, syntactically it remains alien to most people. Backus' FP/FL and Iverson's J are more approachable to current programmers, but still not there. In New Kind of Paper, I created a tiny language called Fluent, which is nowhere near the ambition of any language mentioned, but it is intentionally designed to be handwritten. A week ago, I open-sourced it. [Fluent]

There is plenty of work left to do, but it is a good start.

[NKoP]: https://mlajtos.mu/posts/new-kind-of-paper

[MathNotes]: https://mlajtos.mu/posts/new-kind-of-paper-5

[Fluent]: https://news.ycombinator.com/item?id=46649223

[Demo]: https://youtu.be/y5Tpp_y2TBk

Thanks for coming to my TED talk.

bunderbunder

16 days ago

I would probably just go for an Android eink tablet like the ones made by Bigme and Onyx Boox.

It looks like there are a few APL implementations for Android out there, or you could use a remote editor or terminal app to access an APL implementation running elsewhere.

baruchel

16 days ago

I’ve practiced array languages extensively myself, including for code golfing, and I fully understand the intellectual joy they can provide. But as I’ve gotten older, I’ve come to see a deep mismatch between what these languages present as “elegant” and what I find truly elegant from a computer science perspective.

Sure, realizing that the foobar of x is nothing more than the transpose of the 15th foo of x, combined via an inner product with the 7th bar of x raised to the power of baz, can be an ineffable intellectual delight. But actually computing that, rather than writing a “boring” loop, feels horrible to me. To my eyes, a “boring” piece of code written by Dijkstra in some Algol-like language contains more beauty than all these dazzling sleights of hand that hide zillions of loops under the rug while pretending that the actual computation doesn’t matter.

bunderbunder

16 days ago

On the other hand, whenever I see Python code that does calculations over arrays of data with nested loops instead of using numpy, it always takes me a distressing amount of time to see what the code is actually doing and that the bug is because of a typo buried deep in that 100 lines of code that caused one of the inner products to be incorrect.

t-3

15 days ago

It's not like array languages don't do any optimizations... Denying the programmer the ability to be clever by manually writing loops makes some things easier and simpler for the compiler as well.

veqq

16 days ago

Array languages are more conceptually simple. What do you concretely mean to mock with:

> realizing that the foobar of x is nothing more than the transpose of the 15th foo of x, combined via an inner product with the 7th bar of x raised to the power of baz

i-blis

15 days ago

J is, within the APL family of languages, the one I have always found the most useful. I reach for it as I used to reach for my HP calculator in the past, to quickly compute or numerically model things. I always have it running in a terminal window.

Contrary to popular belief, its learning curve isn't steep. I once introduced it to high school freshmen who had no real experience with programming. I recommend the series of booklets by Kenneth Iverson himself: Arithmetic, Algebra, Calculus — there is even a Concrete Mathematics companion to accompany the book of the same name by Graham, Knuth et alii. They're all available for download on the site.

singularity2001

16 days ago

Should be the ultimate final incomprehensible programming language for code agents

ofalkaed

16 days ago

ChatGPT is pretty good at correcting my mistakes. Give it a snippet of not quite working code with no explanation and it almost always correctly identifies what I am trying to do and explains where I went wrong. Its corrected code almost never works but its explanation of why my code failed gets me my answer and that is what I really want. A year ago it could not help me in the slightest, it has improved quite a bit. The biggest issue with AI and APL seems to be that it does not quite understand the differences between the various versions of APL and seems to view APL2, Dyalog and GnuAPL as all the same language.

Edit: It probably would be useless to someone at all competent in APL and whose problems are more complex than their own failings.

user

16 days ago

[deleted]

adrian_b

16 days ago

True. Due to its lack of verbosity, APL is not at all forgiving for any substitution or transposition in its symbols, which can cause great differences in program output, so it is quite improbable for LLMs to generate a working program, unless it is identical with one from its training set.

What I have said matches exactly what another poster said about his experience in using a LLM with APL: "Its corrected code almost never works".

The LLM recognizes the problem that must be solved by the code, but it fails to generate the right APL symbol string.

I doubt that here a coding agent that attempts to verify the generated code by compiling it can help, because the LLM will generate eventually some syntactically-correct symbol string, but which will implement a different function than desired.

Only a complete feedback loop, with a battery of varied tests for the executable program produced by the generated code, which can verify if it really implements the desired functionality, can be used to filter the results for a working program.

APL is greatly superior to almost all programming languages that are popular today, for writing expressions involving arrays (this includes expressions that do not involve arrays in other languages, but which could be made simpler by using arrays in APL).

However, the original APL has defects, due mainly to the fact that it was an incomplete programming language, e.g. when compared to the other contemporaneous IBM language, i.e. PL/I.

What one needs is a programming language with modern program structures, data types and data type definition facilities, but also with an expression syntax matching the power of APL expressions.

The fact that in 2026 most programmers continue tho write "for" loops for handling arrays, instead of using array expressions like it was possible in 1966 in APL, 60 years ago, seems an aberration of history. Even in the 1966 PL/I one could use array expressions, even if only expressions that were much simpler than those of APL.

Using symbols instead of keywords, like in APL, is not cryptic for anyone who uses such a language regularly. It is cryptic for those who have not used them. The English-based keywords are somewhat less cryptic only for English speakers, and even for them they can be misleading before they learn their correct meanings.

skruger

16 days ago

Whilst LLMs still perform weakly in APL, the situation is improving at pace, and giving it a “skill” to evaluate code makes a dramatic difference. I gave a conference talk about it recently (video): https://youtu.be/H_wdKeJ8gt4

pavlov

16 days ago

> “it is quite improbable for LLMs to generate a working program, unless it is identical with one from its training set”

This is a fascinating result. In some sense it’s like APL is actually the most human programming language, despite being one of the most difficult for ordinarily trained human programmers to pick up.

ofalkaed

16 days ago

>it’s like APL is actually the most human programming language

As an incompetent programmer who is far more comfortable with even the most experimental and abstract literature than any of the "easy" programming languages, I agree with this.

Edit: I was going to fix that sentence, but it is a good example of what thinking about programming languages does to my brain. The idea of a context free human language is alien, thinking in such absolute and concrete terms is weirdly abstract.

kstrauser

16 days ago

I’d like to play with an array language because I’ve never used one. I don’t want to pay for it; this is just for fun and as an experiment. I also want to run it locally in a shell, writing it in a local editor, not working in a web UI. And while popularity isn’t everything, and none of these are exactly Python levels of widespread, I also don’t want to find myself learning a cool one along with 3 other people in the world and then find out all other array language programmers do things completely differently. (Analogy: I don’t want the equivalent experience of picking Haskell as my first ever PL.)

This topic tends to bring up a few, like APL itself, J, K, and BQN. Given those (soft!) constraints, what’s the one I want to start hacking around with?

gsinclair

15 days ago

I believe Uiua is an excellent one to look at first. It’s simpler than the others you mentioned without sacrificing any power (that I know of). You can type in meaningful words which then appear as cute glyphs, rather than learning new ways of entering things. Each glyph has only one meaning whereas APL (and I think the others) assign context-dependent meanings to some glyphs.

invalidOrTaken

16 days ago

I haven't tried the others, but J meets all those requirements.

RodgerTheGreat

16 days ago

Yep. J has a small userbase, but it isn't fragmented into dialects like K or even APL, J uses ASCII characters instead of requiring a custom font/keyboard layout, J is FOSS, J has extensive learning materials, and J is reasonably batteries-included and suitable for making practical nontrivial programs.

I like K better than J aesthetically, but it's harder to recommend to beginners due to the fragmentation of the ecosystem.

kstrauser

15 days ago

I keep getting nudged in that direction. I'll check it out, thanks!

vegabook

16 days ago

there's also a Forth-meets-APL project called uiua [https://www.uiua.org/]

kstrauser

15 days ago

That may require a little more mental bandwidth than I can summon right now. It looks incredibly cool, though.

runeks

16 days ago

I find APL very difficult to read. Incidentally, I am told (by stack overflow) that the APL expression "A B C" can have at least four different meanings depending on context[1]. I suspect there's a connection here.

[1] https://stackoverflow.com/a/75694187

skruger

16 days ago

Yes, it's either an array (if A, B and C are arrays), a function derived via the dyadic operator B, with operands A and C being either arrays or functions, a dyadic function call of the dyadic function B (A and C are arrays), or the sequential monadic application of functions A and B to array C, or a derived function as the tacit fork (A, B and C are functions). Did I miss anything?

abrudz

16 days ago

Yes, it can also a fork where A is an array while B and C are function and a tacit atop where either B is a monadic operator and A its array or function operand or A is a function and C is a monadic operator with B being its array or function operand. Finally, it can be a single derived function where B and C are monadic operators while A is B's array or function operand.

boxed

16 days ago

Do APL programmers think this is a good thing? It sounds a lot like how I feel about currying in language that have it (meaning it's terrible because code can't be reasoned about locally, only with a ton of surrounding context, the entire program in the worst case)

bunderbunder

16 days ago

It gets me thinking about the “high context / low context” distinction in natural languages. High context languages are one where the meaning of a symbol depends on the context in which it’s embedded.

It’s a continuum, so English is typically considered low context but it does have some examples. “Free as in freedom versus free as in beer,” is one that immediately comes to mind.

À high context language would be one like Chinese where, for example, the character 过 can be a grammatical marker for experiential aspect, a preposition equivalent to “over” “across” or “through” depending on context, a verb with more English equivalents than I care to try and enumerate, an affix similar to “super-“, etc.

When I was first starting to learn Chinese it seemed like this would be hopelessly confusing. But it turns out that human brains are incredibly well adapted to this sort of disambiguation task. So now that I’ve got some time using the language behind me it’s so automatic that I’m not really even aware of it anymore, except to sit here racking my brain for examples like this for the purpose of relating an anecdote.

I would bet that it’s a similar story for APL: initially seems weird if you aren’t used to it, but not actually a problem in practice.

skruger

16 days ago

It makes parsing tricky. But for the programmer it’s rarely an issue, as typically definitions are physically close. Some variants like BQN avoids this ambiguity by imposing a naming scheme (function names upper case, array names lower case or similar).

ofalkaed

16 days ago

I am not good enough with APL to be certain but I think you can generally avoid most of these sorts of ambiguities and the terseness of APL helps a great deal because the required context is never far away, generally don't even have to scroll. I have been following this thread to see what the more experienced have to say, decided to force the issue.

creata

16 days ago

Huh? Currying doesn't require any nonlocal reasoning. It's just the convention of preferring functions of type a -> (b -> c) to functions of type (a, b) -> c. (Most programming languages use the latter.)

boxed

16 days ago

Of course it requires non-local reasoning. You either get a function back or a value back depending on if you've passed all the arguments. With normal function calling in C-family languages you know that a function body is called when you do `foo(1, 2, 3)` or you get a compilation error or something. In a currying language you just get a new function back.

creata

16 days ago

Functions are just a different kind of value. Needing to know the type of the values you're using when you use them isn't "nonlocal reasoning".

And it's not like curried function application involves type-driven parsing or anything. (f x y) is just parsed and compiled as two function calls ((f x) y), regardless of the type of anything involved, just as (x * y * z) is parsed as ((x * y) * z) in mainstream languages. (Except for C, because C actually does have type-driven parsing for the asterisk.)

Another way to look at it: languages like Haskell only have functions with one argument, and function application is just written "f x" instead of "f(x)". Everything follows from there. Not a huge difference.

bunderbunder

15 days ago

It arguably depends on the syntax.

In an ML-like syntax where there aren’t any delimiters to surround function arguments, I agree it can get a little ambiguous because you need to know the full function signature to tell whether an application is partial.

But there are also languages like F# that tame this a bit with things like the forward application operator |> that, in my opinion, largely solve the readability problem.

And there are languages like Clojure that don’t curry functions by default and instead provide a partial application syntax that makes what’s happening a bit more obvious.

UncleEntity

15 days ago

>> Did I miss anything?

Derived operators?

And, 'A B C' as an array isn't valid (ISO) APL but an extension, the 'array syntax' only covers numbers and the parser is supposed to treat is as a single token.

Your useless information of the day...

yvdriess

16 days ago

And they could be 0- or 1- indexed? :P

kholis_ab

16 days ago

i love APL, but never ever tried it ... only watched videos of code_report

abrudz

16 days ago

I'll be happy to give you a live personalised intro in https://apl.chat or head over to https://challenge.dyalog.com/ for an automated guided introduction (with a chance of winning a prize).

kholis_ab

12 days ago

wow, thanks a lot! but my english is not good enough for a live "discussion" unfortunately :(

But maybe later, if you allow, I will contact you!

meken

16 days ago

I enjoyed the FBAPP acroymn. There should be a modern day equivalent.

misja111

16 days ago

> The virtues of APL that strike the programmer most sharply are its terseness — complicated acts can be described briefly, its flexibility — there are a large number of ways to state even moderately complicated tasks (the language provides choices that match divergent views of algorithm construction), and its composability

I had an introduction to APL in university and what I absolutely hated was this terseness. I guess when you're a mathematician APL is more natural but to me, as a programmer, I much prefer to have some extra verbosity to make my code more (human-)readable.

adrian_b

16 days ago

Terseness is easier to remove from a programming language than verbosity.

You can use a source preprocessor to enable you to write APL programs by using keywords instead of any symbols that you do not like. You can also use a source preprocessor to expand any traditional APL source, by converting symbols into keywords, so that it will be easier to read for you.

Using symbols instead of keywords is a minor feature of APL, which was inherited from the standard mathematical notation, from which APL was derived.

The important features of APL are the expression syntax and the set of available operators, not the symbols used for them.

Moreover, if you have difficulties in following complicated expressions, you can always break them in smaller subexpressions.

When someone presents an "incomprehensible" APL program, they show a huge expresion without comments.

A decent APL program, like in any other programming language, would need good comments, but here comments are frequently desirable at the level of subexpressions.

misja111

16 days ago

> A decent APL program, like in any other programming language, would need good comments, but here comments are frequently desirable at the level of subexpressions.

I guess that might be true for APL, for other programming languages that's not true at all. The ideal program is clear enough to be self explanatory. Of course there might be some implementation choices that need a comment. Or in some cases the problem is so difficult that this is not possible.

But readability should be the goal and most of the time this is feasible without comments. E.g. by using descriptive variable and function names. And by breaking up your program into logical and cohesive parts, using functions, objects, modules or whatever construct your language is offering.

creata

16 days ago

> The ideal program is clear enough to be self explanatory.

That depends on what you're doing and who you expect to be reading your code, doesn't it? Sometimes what the human needs and what the computer/runtime needs are too far apart.

gitonthescene

16 days ago

Serious question: Why is readability so important? For me consistency is far more important than anything as subjective as readability. I’d rather be able to reason about a code in its own logic than feel comfortable browsing code without much consistency. In the end all code needs to be understood for its internal logic and notation is secondary.

misja111

16 days ago

2 reasons:

- in a corporate environment, your code is going to be read by many other people than just you. Your team mates, the guy after you left etc.

- also, by making your code more readable, you're making your own life easier as well. You might have thought at first that your code was fine, but by structuring it properly and possibly removing some redundancy, you might find that you were overlooking some things.

gitonthescene

16 days ago

In my experience code reviews are generally cursory and the emphasis on “readability” is more about a culture that seeks to treat programmers as fungible. Also complaints about APL’s lack of readability are never about its lack of structure. So I took “readability” to mean something else as should be clear from my previous comment. Is your complaint about its lack of structure? If so would you mind elaborating?

gbacon

16 days ago

Jokesters quip “If a program was hard to write, it should be hard to read.”

adrian_b

16 days ago

What you say about readability is right, but it is something completely orthogonal to the syntax of APL expressions. All those things can be done in any language that uses the APL expression syntax.

For someone who knows the APL symbols, what an APL expression does is self-explanatory. Someone who does not like symbols can replace them with keywords, that does not change the APL syntax.

The only problem is that you can write a very complex APL expression, which may be equivalent with a page of text in other programming languages. In such cases it is still easy to see what the expression does, but its purpose may be completely obscure, e.g. because you are unfamiliar with the algorithm implemented there, so you need comments explaining why those operations are done.

In many cases you can do like you suggest, you can split a very big expression in many subexpressions and store intermediate results in temporary variables to which you give names that are suggestive for their purpose, instead of adding comments.

However, I see this solution as inferior to just providing short comments for the subexpressions, which give you the same information as the intermediate variable names, but without forcing the compiler to choose an expression evaluation strategy that may be suboptimal.

I completely agree that "The ideal program is clear enough to be self explanatory".

However, regardless of the programming language, it is very frequent to see programs where it is clear what is done, but you cannot understand why that is done. In most cases you already have precise expectations about what the program should do, but you see that it does something else, without any apparent reason. In many cases, the program does certain things because there are certain corner cases that are not at all obvious from the existing system documentation, or worse they are not documented at all anywhere, except for the presence of a mysterious program section that handles them. Even worse is when such mysterious program sections are present only because of some historical reasons, which are no longer true, and now the code is superfluous or even harmful.

These frequently encountered situations can be prevented only by adequate comments about the purpose of the code, regardless how self-explanatory is what it does.

t-3

15 days ago

> The ideal program is clear enough to be self explanatory.

If one doesn't know the programming language, no program will be clear, if they do know the language, any simple and well-written program will be clear. Clarity is a property partially of the reader and partially of the program, not the programming language.

Avshalom

16 days ago

>>The ideal program is clear enough to be self explanatory.

No one has ever written an "ideal program".

misja111

15 days ago

True, but that doesn't mean that you should stop trying getting close to it.

misja111

16 days ago

@creata:

yes I agree. In case of APL, if your readers are mathematicians, I guess it could well be the language of choice.

And yes like I already said, self explanatory code is not always possible but more often than not it is. It just takes a little extra care and thought.