Re: Layout syntax

<joachim.durchholz@web.de> wrote:


>In other words, mathematical objects are deeply nested, but
>mathematical formulae usually aren't. Actually, I'm hard pressed to
>remember having ever seen a mathematical formula that had more than
>three nesting levels.


Yes, this is what seems to happen: Mathematicians use a lot of
unnesting techniques, making the math nesting depth fairly flat. This
probably happens because it is written for human to parse. In fact,
when learning to write math papers, one also has to learn how to
unnest the math.


The question is what happens when math is written proof verification
system, as the computer can easily check any nesting: then manual
unnesting will no longer needed. So one will probably see more of such
nesting then.


I certainly admit nesting in my proof verification system: It is
declarative, and one can have local variables, just as in say C/C++
and most other modern declarative languages.


>That's exactly my point: mathematical syntax, designed for consumption
>by humans, isn't easily transferable to computer language syntax,
>designed for consumption by computers. In other words, drawing
>syntactical inspiration from actual mathematical usage may be helpful,
>but sooner or later one is going to run into trouble.


My development strategy is to wrestle a bit with the more common
popular syntactic features, such as sets, function definitions and the
like, to make them close to actual mathematical usage. Then, if I get
so far, added user math should use a less complicated syntax, perhaps
defined by some operator precedence.


> Which is just my point: mathematics isn't the best source of
>inspiration when it comes to syntax. (It's an excellent source of
>inspiration when considering semantics! At least if a precise
>semantics is desired.)


Quite on the contrary: Just because of these difficulties, math
becomes an important source if inspiration, because these apparent
syntactic quirks are in reality there so as to produce a syntax that
is efficient to humans. So, as computer languages can, in view of
better computers, become more adapted to humans, it is important to
have this input.


    Hans Aberg

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