[exprla-devel] RE: [XPL] Hello, and a few comments.

[reid_spencer <ras...@re...>]

--- In xpl-dev@y..., "Richard Anthony Hein" <935551@i...> wrote:
I think maybe the problem is that there is doubt over the idea that 
you can
take something like MathML and generate programming logic from that 
MathML.
However, if you can generate MathML from an algorithm, then why can't 
you go
the other way?
  -----Original Message-----
  From: Alexander E. Gutman [mailto:gutman@m...]
  Sent: June 9, 2000 7:27 AM
  To: xpl@e...
  Subject: RE: [XPL] Hello, and a few comments.


  Richard Anthony Hein wrote:

  > I figure that it would be amazing to use MathML
  > as the markup that XSLT uses to build a function in XPL!

  What is "to build a function"? To produce a code for
  defining a function whose body is, in some sense,
  equivalent to the corresponding MathML expression?
  [Richard Anthony Hein]
  Yes!  Exactly.  We could build expressions and functions from 
MathML, that
take input parameters from MathML and return MathML.

  > Any mathematical expression that a mathematician can write
  > in MathML should be transformable into XPL!

  ANY mathematical expression? Hmm... If there is no integration
  operator in XPL's dictionary, how can we transform an expression
  that involves integration? Do you mean that XPL's dictionary
  must contain integration operator, etc.?
  [Richard Anthony Hein]
  Why not?  XPL is extensible ... so you can add strength to the
interpreter/complier that reads the MathML as the language grows.  If 
we can
instruct the complier how to handle the symbol - in this case 
integrate - we
could make it build an algorithm that will integrate according to the
MathML.  For cases of integration, we can actually use the proofs 
themselves
(which also happens to be written in MathML) to describe how to build 
the
XPL algorithm.

   > Algorithms in XPL should be able to be transformed into MathML.

  This seems reasonable. Alongside presentation considerations,
  any MathML-compliant software will thus be able to "understand" XPL.

  [Richard Anthony Hein]
  Right, but it is the other way that you don't think can work?  That 
is, if
we can transform XPL algorithms into MathML expressions, or physics 
(this is
something that would be needed to describe some systems ... I can 
picture
people making their own XPL extensions that describes the system 
optimally
... we should be able to go the other way as well.  Everything that 
happens
inside a computer and on the network can be described by mathematics,
therefore MathML is the bottom line.  If we describe functionality of 
a
microprocessor using MathML, which could be generated from XSLT that 
takes
design markup from chip manufacturers and makes it MathML, then we 
would
have a low level language that is described by the very markup that 
built
the chip!  That would free us from being restricted in chip 
architecture in
the future ... any hardware architecture could be described in MathML 
which
is interpreted into XPL  ... VIOLA you have a language specific to the
hardware that is extensible, and can be made into function libraries
immediately!  Yet it can all be XPL!  Does anyone see the 
possibilities?

  Any way, MathML's Content Markup is a very good example
  of how XPL expressions should look like.

  [Richard Anthony Hein]
  Yes it is!

  Richard A. Hein
  --
  Alexander E. Gutman


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