[klibertp]

Wait, why? Could you elaborate? How is:

    + 1 2

fundamentally different from:

    1 2 +

? You just look for the operator on the other side of arguments.

I know both prefix, postfix and "crazy infix" (J, some APL) languages and I really don't see a qualitative difference. Of course, after you overcome the initial hurdle and get used to the notation.

EDIT: ok, J/K/APL are a special case and I shouldn't mention them.

[TazeTSchnitzel]

That's too trivial an example. When you get something more complex, the difference becomes clearer.

Can you parse the following easily?

c_z x * s_z y * s_y * c_y z * + c_x * c_z y * s_z x * - s_x * - d_z =

Compare that to the infix form:

d_z = c_x * (c_y * z + s_y * (s_z * y + c_z * x)) - s_x * (c_z * y - s_z * x)

With infix, the operator sits between its operands, so you can easily see what expression makes up the first operand, and which makes up the second: you just look to its left and its right. Postfix, however, requires you to read the entire expression, because the operator doesn't show which operands it has, they're just whatever the last two were, and those last two might themselves be complex expressions. This gets worse the longer the total length of the expression.

Postfix also suffers from not making it clear how many operands a given operator takes. With infix this is always clear.

I like postfix languages for their simplicity, but I refuse to pretend they are as easy to read as infix languages.

(example was taken from https://en.wikipedia.org/wiki/3D_projection#Perspective_proj...)

[klibertp]

Well, for me both examples are totally unreadable. I think math's is the most unreadable notation ever and even a cross between PERL and Brainfuck would be better. Mathematicians are masochists, and I refuse to follow their lead. I prefer meaningful variable names, good use of horizontal and vertical whitespace, context-free grammars, and the like. So maybe this is the difference and the reason for me perceiving the notations as more or less equivalent: I'm not biased, as most people, in favor of infix, but rather biased the other way.

Anyway, let's try doing something with your postfix example (I hope it displays alright; also, I think you made a mistake in your translation to postfix, but I left it as it is):

    c_z   x *
    s_z   y *
        s_y *
    c_y   z *
    +
        c_x *

    c_z   y *
    s_z   x *
    -
        s_x *
    -

        d_z =

Now, this is much more readable than unformatted infix version you give and that's before factoring this into smaller parts. I didn't read that much of Forth, but I'm 97% sure that it would be factored into 3 or 4 words, I think. And it also has an advantage that you read the operation in order they're going to be executed, while with infix you need to read the entire expression to know which computation occurs first.

Of course, it's only more readable for me, with my particular background knowledge and habits; I'm not saying this is or should be the same for anyone else. But, if there are people who see one form as more readable and people who see the other form as more readable, then I think that's a solid argument in favor of both forms not being drastically, qualitatively different.

The problems you point to are definitely real; it's true "the operator doesn't show which operands it has" by default (for example) and you need to go out of your way to show it. But infix notation has it's problems too, and you need to work around them as well. Like operator precedence, which is frankly a terrible idea.

> Postfix also suffers from not making it clear how many operands a given operator takes. With infix, this is always clear.

No, not always. J has words which take one argument on the left and, for example, two on the right. Or three. Or a variable number of arguments on the left (granted, they are `tied` with ` word, but still) and nothing on the right... And Ken Iverson says it's very readable! (To him, at least).

To summarize: I'm still not convinced that there is a major and unfixable difference in readability between the notations, and I still think you can make all 3 notations as readable as any other.

[kazinator]

It's not the direction, it's the lack of delimiting.

  ((1 2 +) (3 4 +) *)

is fundamentally different from

  1 2 3 4 + + *

Each word has a clear arity, and the arguments are delimited. We can follow the evaluation of the parenthesized expression in multiple orders and they come up with the same answer.

[klibertp]

If you take a look at my reply to TazeTSchnitzel you'll see that I "solved" (I think? at least tried to) this problem with indentation (generally whitespace. You can delimit expressions in many ways.

And in Forth case, you can very easily define your own delimiters:

    : [ ;
    : ] ;

which should make you able to write:

    [ [ 1 2 + ] [ 3 4 + ] * ] . 
    21  ok

(tested with gforth and works [EDIT: but of course breaks Forth! Both [ and ] are already defined, so in practice you'd rather choose another chars])

I mean, there is no rule saying that postfix notation cannot provide grouping constructs. I still fail to see a fundamental difference here :)

BTW, it's not going as fast as I'd like, but I managed to parse TXR man page and use it for displaying docs along auto-completion: https://github.com/piotrklibert/txr-mode/blob/master/screen....

I think I'll be able to find some time this weekend (or next weekend) to clean up the code and make it usable for others as well :)

[kazinator]

Whitespace that is not significant to the machine does nothing to help me convince myself that the code is correct. Indentation could be wrong.

If I already know that the code is correct and properly indented, then it helps the readability.

> And in Forth case, you can very easily define your own delimiters:

Those delimiters do nothing but occupy interpreter cycles. Hopefully they get recognized as noops and optimized away by a Forth compiler.

The machine will accept garbage like:

  ] 3 2 + [ 4 /

The fake syntax you've created is there is sort of like a cargo cult airplane made out of bamboo sticks and palm leaves. It has some value as an annotation of correct code, that is all. It could be a useful annotation tool in the process of verifying a piece of code and convincing myself that it's correct. Forth should have these markers built-in so they don't have to be defined as words, and it should check their pairing and nesting. (A syntax highlighting engine can be taught to do that, of course.)

[klibertp]

> Whitespace that is not significant to the machine does nothing to help me convince myself that the code is correct. Indentation could be wrong.

A sloppily written code is hard to understand correctly in every language (to different degrees, of course). You can easily mistake

    if (...)
       do1();
       do2();

for

    if (...) {
       do1();
       do2();
    }

right? This is C - an infix language - and it's arguably its fault for providing this stupid form, but you usually don't judge how readable infix notation is based on this.

> Those delimiters do nothing but occupy interpreter cycles. Hopefully they get recognized as noops and optimized away by a Forth compiler.

I'd expect so.

> The machine will accept garbage like: > ] 3 2 + [ 4 /

Yup. And by the way, this garbage is actually nearly correct J code. One possible fix would look like:

       ] 3 2 + [ 4 (+ /) [ 4

this gives `10 11` as an answer (and please don't ask me why...). ] and [ are left and right identity functions, they simply do nothing, so they may be inserted in many places, in many cases interchangeably.

> Forth should have these markers built-in so they don't have to be defined as words, and it should check their pairing and nesting.

That's unnecessary in Forth, I'm sure you can implement a "real" - with a semantic meaning - grouping in Forth yourself. Comments in Forth are enclosed in parens, and the parens are normal Forth words, defined in Forth. I mean, it's already a grouping syntax with a DROP semantics; you can probably define grouping syntax with other semantics as well.

Also, in Forth there are only words, and the syntax is that simple, but that isn't a property of all postfix languages. We're talking about postfix as a notation in general, not about it's particular brand practiced by Forth. This is why I keep mentioning J, again and again: it's an infix language. I could bash infix notation forever had I used J as an example! It's the same with postfix notation and Forth.