Comment by avmich | Hacker News Reader

Comment by avmich | Hacker News Reader

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> Do you think the APL family can exist without the terse syntax? Are there any aspects of the language that just wouldn't work well without it?

Considering the evolution of APL, yes.

Ken Iverson was teaching math in Harvard, when he was growing the - mathematical - notation to describe the subject formally. It was happening in late 1950's, and the computers were entering our life. At some point it became reasonable to use that evolved notation as A Programming Language - or APL, for short.

However, the idea was to make understanding easier - all along! Same idea which Alan Kay is pursuing with his works, same idea with many good technologies, when they are young - Java, JavaScript... Importance of notation - be it in math, or in formal-and-executable-math is the ideology of early APL. Now they say "it's hard to beat expressiveness of a whiteboard", but still attempt to use, say, an integral sign (and, similarly, one-letter variables), as one would do when showing the idea on a whiteboard. The history of hand-written math preferred terse notation - and that is carried on in APL as executable math.

So... yes, terseness is important, and APLers will also say that choice of symbols is important too. It's only to beginners that they feel strange - pretty soon programmer learns them, gets used to them and refuses to substitute them with more readable longer variants - even though that would make certain things better. You don't name variables on a whiteboard with long_names or camelCase - at best you use sub- and superscripts. Granted, you can have cups and power towers and other things, and they were really impractical with 1960's level technologies... yet at least you have a singular text direction for expressions, in editors or in print.

J makes certain things more logical, and switches to ASCII. May be we'll invent even better notation (to me, this - http://matt.might.net/articles/discrete-math-and-code/ - looks like a good start to think about basic building blocks), but so far, we have APL family languages as arguably closest thing to math notation. To some, it's the closest way they can imagine between making a solution in the head and explaining that to computer.

In agreement with @avmich above, and to turn the question around from above: > Do you think the APL family can exist without the terse syntax? Are there any aspects of the language that just wouldn't work well without it?

Do you think mathematics would exist or be shared and done as efficiently if it did away with the terseness of its symbols, Greek letters, etc...?

Yes, in J you can define average as:

  +/%#

so that,

  (+/%#) 2 3 4 5

returns 3.5

Or,

  avg=: +/%#

avg 2 3 4 5 returns 3.5

Or,

  sum =: +/
  divided_by =: %
  tally =: #

So, if you want to take baby steps into J you can:

avg=: sum divided_by tally

avg 2 3 4 5 returns 3.5

But, that defeats the purpose of being able to concisely manipulate abstractions to get work done for the sake of readability, and ONLY for those people who refuse to learn the symbols as in mathematics. Have you ever heard from an adult who has had basic mathematics say, 'I have to keep looking up that greek letter π'? It only takes me a very little while to review my concise code. I'd rather learn this sort of pattern recognition of short code when dealing with high abstractions to the spaghetti-like appearance, to me, of Java or C (I like C!). Strangely enough I find Lisp more clear to C-like langs. It may be more than just subjective preference, but order of reasoning in the syntax.

You are exactly right. My favourite is when resistance to APL-family languages comes from people who claim to be polyglots, and you ask them which languages and they list: C, C#, java, javascript, VB, ruby, python etc. Those are all really the same language with slightly different wording and details. Like german and english. APL-family is like Mandarin or Japanese. Lisp is like Latin (in fact lisp is really a mechanism to author your own language with s-exprs). Obviously, these languages won't be comprehensible to you until you put the effort into learning the abstractions... this isn't like transitioning from C++ to Java where you can broadly carry the same concepts over.

There is nothing difficult about reading these languages to people who use them, anymore than it is difficult for a musician to read sheet music. In fact, APL languages have less ambiguous parsing and precedence rules which I find make them easier to read.

> Those are all really the same language with slightly different wording and details. Like german and english.

I'd argue you only think that because they've opted for a familiar syntax. E.g. the object model (or lack of one) is vastly different between these languages and they employ drastically different type systems.

Ruby is closer to Smalltalk than C in most respects other than syntax, for example, and provides most of the abilities lisp gives you, including the ability to define domain-specific languages. The major aspect you're not getting from Ruby would be homoiconicity.

Here's and article comparing Lisp and Ruby[1].

I'm not saying learning languages outside of this group isn't important, but that a lot of the reason why languages like Lisp and APL are seen as so different has more to do with syntax than semantics. Most people don't know what the semantic differences even are, because getting past the alien syntax is too much effort. When you do, the differences aren't all that huge.

[1] http://www.randomhacks.net/2005/12/03/why-ruby-is-an-accepta...

Most adults give up on maths around the level where the amount of symbols start to grow, or slightly before (to be clear, I'm not claiming notation is the only cause of this - it certainly isn't, but it does mean we really don't know whether most people would manage to pick it up; personally I think it is a major factor in making people struggle with maths).

For my part, the notation was certainly part of it. It matters. I used to love maths but I started finding it impossible to read even as the concepts were still easy enough to understand. I'd write things out as programs instead to understand it without being hampered by the notation. I learned symbolic differentiation that way, for example.

But I quickly realised that this basically closed maths off to me as a viable subject, and I opted out of all optional maths courses other than boolean logic for my CS studies.

I get that for those who find mathematical notation easy to work with, it seems indispensable, but don't underestimate the amount of people for whom the notation is the barrier that basically makes mathematics inaccessible.

I've picked up quite a bit of maths since, but always by understanding the concepts through code rather than trying to parse mathematical notation.

I've had - and still have, to a degree - similar troubles with understanding math notation. Some 9 years ago a friend, solidly mathematician, gave a good advice to me - at least try to pronounce the math expression aloud. That forces you to pay attention to each symbol - instead of trying to immediately find word-like "phrases", failing that and missing the expression as a whole.

APLs are - as Arthur Whitney likes to employ - supposed to be read symbol-by-symbol, since each one represent a whole operation. That's why APL program are so dense - you may have plenty of work done in a short line (but many APL writers prefer to keep lines short, to help with understanding). A screenful of APL can be moderately sized program, without need for scrolling... When you write J, you might be tempted to add more and more operations to the left (APL and J work from right to left), until it's hard to "explain" what the whole expression does - because it does so much. With an alternative - short, understandable expressions - you have another problem, that of naming :) - trying to give a traditional, long-worded name to an intermediate result of expression doesn't fit well with the rest of the style... So a good sense of balance is very valuable.

Another saying which may help to understand APL's mindset is that APLers spend 5 minutes to write a program, then spend next 1 hour to write the same program better and cleaner. That's what I understand as refactoring; the idea is to make the code more readable, the expression more obvious, more obviously correct, more reuseable... Properly done, the expression is a pleasure to look at and well worth the efforts to decipher it symbol-by-symbol. And another great option is documentation - lots of comments, just as in good math texts, where the idea is explained in plain English and then succinctly put to code.

This way I better see the math background behind the problem. I certainly have an easier time to change something here and there - the changes required are so small. I also see similarities between different pieces of code, if they are put as similar expressions close to each other, on the same screen. Yes, the notation is terse... but it at least has good sides.

Musicians learn to read music. Yes, it is hard to learn it first, before playing or listening, but that is how it has been incorrectly taught. Same with mathematics. Learning mathematics by coding is perfectly fine, but when you start to go higher to the more abstract level, you need abstract symbols. That can, and should come later, I believe. But, I would rather deal with learning C=2πr as standing for the circumference of a circle, than writing it out longhand. Not to mention, diagrams are good too, to understand what a 'radius' or 'pi' is. The longhand version would be at least a paragraph. You just wouldn't write many pages of longhand to avoid symbols. Fear of mathematics is a result of poor teaching, not symbols.

> It's only to beginners that they feel strange - pretty soon programmer learns them, gets used to them and refuses to substitute them with more readable longer variants

That reminds me of how McCarthy always intended to replace S-expressions with M-expressions, but it never happened because programmers found they liked the S-expressions after all.

I believe Shen [1] creates m-expressions when certain expressions are passed through its compiler. Shen should appeal to Haskellers and Lispers I would believe. Deech has created a Shen port for elisp [2], and it exists on many other language platforms, because it runs on an enriched lambda calculus called Klambda implemented in a small set of functions.

  [1]  http://shenlanguage.org/
  [2]  https://github.com/deech/shen-elisp

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