RE: plain text math notation

All good issues and ones that should be solved before worrying about the language syntax.

I believe that the math structure should be bound to an interpretation that may be declared in the structure or held separately. Two mathematical structures may both contain an alpha but one binds it to some concept, variable, constant, or value and the other binds it some different one. When it is desired to calculate with the notation structure, it must be transformed into some other, computational structure based on the interpretation to which it is bound.

Of course, problems may occur when it is necessary to map the computational structure back to a notational structure. These mappings are not generally one-to-one. This can be a good thing as it is possible to change a given expression from one notational scheme to another, or one computational structure to another. But it is a bad thing because there are multiple representations that have non-trivial mappings between them.

Paul


From: Kevin Cheung [mailto:KEVINCHEUNG@CUNET.CARLETON.CA]
Sent: Thursday, September 22, 2016 3:02 PM
To: Paul Topping <pault@dessci.com>; Jos de Jong <wjosdejong@gmail.com>; Robin Berjon <robin@berjon.com>
Cc: Peter Krautzberger <peter.krautzberger@mathjax.org>; public-mathonw. <public-mathonwebpages@w3.org>
Subject: Re: plain text math notation


It will be nice if there is a math notation language that forces math writers to mean exactly what they write.  (Contrasting to what mathematicians sometimes do; they use the same LaTex symbols to mean different things in different contexts.)  With CAS, since the goal is to compute, you have no choice but to type what you mean.  Is the goal to come up with a universal CAS language?  If so, how would one go about dealing with really abstract math?

________________________________
From: Paul Topping <pault@dessci.com<mailto:pault@dessci.com>>
Sent: Thursday, September 22, 2016 3:17:56 PM
To: Jos de Jong; Robin Berjon
Cc: Peter Krautzberger; public-mathonw.
Subject: RE: plain text math notation

The goal of a single math language that describes standard math notation AND works well for computation and manipulation is a worthwhile and, IMHO, achievable goal. However, starting at the syntax is not going to work. Sure, it is fine to express preferences for one language or another but the place to start is the model that the language expresses. By model, I mean abstract data structure and its dynamic semantics.

MathML suffered from the too-many-cooks problem as well as not having a clear set of goals, IMHO. It also suffered from its association with XML but that's a whole other story.

I believe starting with the model is the only road to success but it is perhaps hard to convince people of that. Another advantage that might be more compelling is that, with well-designed model in hand, it should be possible to develop multiple syntaxes for expressing it, each useful in a different scenario: an XML syntax for the XML document world and, perhaps, for embedding in HTML, a JSON syntax for programmatic generation, manipulation, and consumption, a "plain-text math notation" for authors to type directly, etc.

BTW, I am not sure "plain text math notation" is well-defined. In a sense, all computer languages are plain text and, at the same time, all have a syntax. I'm guessing what is meant by this is a notation that humans feel comfortable typing. Computers like regular syntaxes and are not bothered by extra characters such as angle brackets. Humans like something that doesn't require too many keystrokes, hard to reach keys on the keyboard, doesn't get scrambled in email, and is easy for humans to read. If this is what is meant, perhaps "human math language" might work. Just a thought.

Paul Topping

Design Science, Inc.
"How Science Communicates"
Makers of MathType, MathFlow, MathPlayer, Equation Editor
http://www.dessci.com

From: Jos de Jong [mailto:wjosdejong@gmail.com]
Sent: Thursday, September 22, 2016 11:52 AM
To: Robin Berjon <robin@berjon.com<mailto:robin@berjon.com>>
Cc: Peter Krautzberger <peter.krautzberger@mathjax.org<mailto:peter.krautzberger@mathjax.org>>; public-mathonw. <public-mathonwebpages@w3.org<mailto:public-mathonwebpages@w3.org>>
Subject: Re: plain text math notation

@Robin can you elaborate a bit on your idea? Do you mean that it would be trivial to translate a math formula into plain JavaScript which then can be evaluated, or to SVG for rendering? Or both?... Do you have concrete use cases in mind?

Jos

On Thu, Sep 22, 2016 at 3:53 PM, Robin Berjon <robin@berjon.com<mailto:robin@berjon.com>> wrote:
On 22/09/2016 02:54 , Peter Krautzberger wrote:
> Jos has written up some notes on plain text math notations at [1].

This is IMHO a very promising area. I wonder if it may be interesting to
consider making it not too distant from the syntax of (modern) JS so
that it could easily be implemented as a BabelJS[0] plugin (like JSX[1]).

[0] http://babeljs.io/
[1] https://facebook.github.io/react/docs/jsx-in-depth.html

--
* Robin Berjon - http://berjon.com/ - @robinberjon
* http://science.ai/ - intelligent science publishing
*