Hacker News Reader

Comment by radford-neal | Hacker News Reader

I wrote a tree editor for programs for my Master's thesis, in 1980. You can get it at https://www.cs.toronto.edu/~radford/MSc-thesis.abstract.html

The editor operates on the AST down to the lowest level, with careful design of keyboard input and cursor feedback to make that not too painful for things like infix operators. The language is described by a grammar, and there is an AST macro language.

My conclusion afterwards was that the shift at that time away from keyboard input towards editing with a mouse was negative for editing in terms of the AST (rather than text), since with AST editing there's a less direct connection between seeing and pointing and what you're editing. I got interested in other things.

But perhaps that was a premature conclusion.

View on HN

What do you think of TeXmacs, which uses a WYSIWYG tree editor for writing scientific/math documents?

(TeXmacs is not based on TeX nor emacs but is inspired by both.)

Math notation is hopelessly stuck in the 19th century and needs an update to the 20th. Polish notation with operators of known arity is an excellent way to ease natural scientists/mathematicians into a modern tree based grammar for mathematics without a soup of parenthesis, e.g. / 1 / 2 3 vs / / 1 2 3

A full s-expression based grammar for mathematics is unfortunately not something that you can write on paper and requires white space delineation to be readable. On a screen with something like emacs paredit both of those are a breeze however. The fact that higher order functions don't need a special notation is really freeing.

What value would Polish notation add over (largely) infix for the typical mathematician? Why do mathematicians need to be told what notation to use by non-mathematicians when their notations (note the plural) are in wide, and apparently successful, use today?

How would Polish notation help, for instance, with things like describing set membership or logical relations? How is this more readable (using ASCII):

  -> a b

Than the current approach:

  a -> b

Which provides a convention sense of the relationship that the former does not? The second one can be "read" in order: a implies b. The first cannot.

>Why do mathematicians need to be told what notation to use by non-mathematicians when their notations (note the plural) are in wide, and apparently successful, use today?

The same reason why geometers needed to be told to start using Arabic numerals by algebraists: mathematics is asking new questions and the old tools aren't good enough. That we even need to make a notational distinction between operators like addition and operators like high order partial derivatives should show that clearly enough.

>How would Polish notation help, for instance, with things like describing set membership or logical relations? How is this more readable (using ASCII):

Start working on longer expressions and the lack of parenthesis becomes a godsend.

-> -> a b c and -> a -> b c can be parsed in only one way, by comparison with infix notation you need miscellaneous parenthesis to show the way you want a -> b -> c to be parsed: (a -> b) -> c and a -> (b -> c). Or you need to memorize an arbitrary number of rules which increase exponentially with each new operator you add.

> Which provides a convention sense of the relationship that the former does not? The second one can be "read" in order: a implies b. The first cannot.

In English and only for binary operators, and even then you can just as easily understand "add 5 and 6" as you can "5 plus 6". How would you use infix notation to express a ternary or higher operator? The notation for the definite integral needs a super and sub script as well as a dummy variable for an operator that is fundamentally a ternary one. By comparison in prefix notation it becomes definite_integral upper_limit lower_limit function.

> The same reason why geometers needed to be told to start using Arabic numerals by algebraists. Mathematics is changing and the old tools aren't good enough to answer current questions.

At least those were other mathematicians who could understand the domain and the importance of notations for the work.

Hah, no, "-> -> a b c" is not easy to parse, except for a computer. going are people not to read easily. It's a silly argument that prefix is fundamentally easier for humans when it disrupts the flow even in your example.

Even using the words, "implies implies a b c", does not parse well as a reader, even if it can only be parsed one way. If you go to a higher arity operation, switch to function (which is prefix, like polish) notation if it makes sense. But even then, we have things like the integral which uses physical placement to take (typically) up to 3 arguments:

  b
  ∫ f(x) dx
  a

With other similar operations. And if order of operations is not clear from an expression, then yes, use parentheses. That's what they have been used for for quite a while.

>Hah, no, "-> -> a b c" is not easy to parse, except for a computer. going are people not to read easily. It's a silly argument that prefix is fundamentally easier for humans when it disrupts the flow even in your example.

The only argument I'm seeing here is that you can't parse prefix notation and won't put the effort into trying it, which is the same argument people used against Arabic numerals in the middle ages.

A prefix only language is fundamentally easier to read and write to anyone who hasn't spend two decades learning the mishmash of pre, in, post, and upside-down fix that mathematics currently uses.

>But even then, we have things like the integral which uses physical placement to take (typically) up to 3 arguments:

Using four variables. It's amazing to me people defend this type of mess as something meaningful instead of a terrible historical contingency which we should get rid of as quickly as we can. In prefix notation you can just use "integral upper lower function" to convey the same information in pure text without the need for inventing TeX and vector displays.

Try out your notation, which I will agree can be unambiguous in a technical sense, but will quickly become unreadable for actual human beings, on a few modest examples.

  = 1 + square sin x square cos x -- a trig identity

  / + - b √ - square b * * 4 a c * 2 a
      ^ oops, ambiguous, you need a new symbol for negation

Note as well, in that second example, the great distance between the division operation and the divisor. This does not lend itself to readability by people, they have to keep the entire stack of operations in their head. Ok, so you switch the notation to be more tree-like and use indentation (how I write complex Lisp math expressions):

      v still ambiguous, what alternate symbol can we use?
  / + - b
      √ - square b
           * * 4 a c
    * 2 a

Ok, somewhat clearer, but hardly "easy" to read for a person. At this point you may as well just put back the parentheses (and be back at Lisp s-exprs, which as you noted earlier is not well-suited to handwriting). The mathematical expression is clearer for people. It requires them to keep less in their head at any one point in the reading.

        _________
  -b + √b^2 - 4ac
  ---------------
        2a

I'm not saying this is perfect, there is room for improvement in this form, but it is going to be better for the average math literate person (by which I mean, someone who has at least covered high school algebra). Even if you taught prefix notation from the start, the user of that notation still has to keep more in their head as they try to parse it.

> Try out your notation, which I will agree can be unambiguous in a technical sense, but will quickly become unreadable for actual human beings, on a few modest examples.

It's perfectly legible to me and I use it daily in my (mathematical) work.

Again all you're saying is that you're not used to it and it must be a bad notation. Just like how people who were shown Arabic numerals defended Roman numerals.

I'd do you one better and point out that the example should be = 1 λ x square sin x square cos x since having unbound variables is poor form after someone invented lambda calculus.

And yes, you need a symbol for negation which is a step up since a-b is also ambiguous in the same sense.

For the second one you easily see why words are superior to symbols when you stop trying to use hieroglyphs and start using letters instead: div add neg b sqrt sub pow b 2 sub times 4 times a c times 2 a. I can define new functions with well known meaning without having to copy special characters or invent type setting systems.

So, you're a troll then, you can't even be consistent in your presentation.

+ and - are bad to use, but λ is ok to use? Words are the thing to use for "add" and "sub" and "div" (why not the whole word?), but not "equals" or "define function"? And the words you choose are strictly English, which makes your mathematical notation no longer mutually comprehensible across most of the globe? Those are all positives to you? That's how math notation will be dragged into the 20th century?

And, what, we now teach lambda calculus to elementary school kids once they start learning about variables? At least try to come up with a plausible argument.

> I use it daily in my (mathematical) work.

I find this highly unlikely, but sure, if you're not a troll, you've found a notation that (apparently) works for you (what kind of math?) and you think it's better but haven't bothered to think it though.

And you still haven't answered the question on the second example, you just made it more verbose. The reader still has to remember (with zero punctuation or other indicators in your example) that the dividend for the div is the next 14 tokens and the divisor the last 3. Because that's totally readable and comprehensible.

If you're not a troll, your idea isn't even half-baked.

Nice! One thing I thought ASTs weren't that good at was the initial writing of code - did you find that?

A big part of the design work was trying to get it to be good at that, while still being entirely tree based. But you'll have to judge yourself how successful I was.

Well, your judging that would be easier if you could use it, rather than just read about it... I still have the source code, but since it was designed to work with a vector graphics display attached to a PDP-11, getting it to work in a modern environment would take some work. We had only one vector graphics display, so there was no chance then to have a significant user community, which was another problem.

Reply on news.ycombinator.com