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RE: [Axiom-developer] documentation and the crystal

From: Bill Page
Subject: RE: [Axiom-developer] documentation and the crystal
Date: Sun, 28 Dec 2003 22:06:41 -0500


Well, I have often used the time between christmas and
new years for thinking what I hope are radical and
forward looking thoughts. It sounds to me like you share
this tradition!

We had a pleasant christmas but work stress and "holiday
stress" combined to give Faye a serious case of pneumonia.
She has been confined to bed for the last three days (but
improving) so that has significantly dampened our enjoyment
of the extraordinarily mild weather ... I trust that in
your case things went a little better. :)

I have also been thinking about Axiom documentation. I
definitely agree that the book (or even the "IBM library")
metaphor is not adequate for a system as complex as Axiom.
I realize that you are probably writing in an online
"brainstorming" style, but have to admit that your "crystal"
metaphor also tends to leave me feeling a little cold.
However, when you said "semantic network" this connected!

There is a large and growing literature on the "semantic

"Definition: The Semantic Web is the representation of
data on the World Wide Web. It is a collaborative effort
led by W3C with participation from a large number of
researchers and industrial partners. It is based on the
Resource Description Framework (RDF), which integrates a
variety of applications using XML for syntax and URIs for

In fact, NAG (Mike Dewar) has been one of the leading
organizations promoting the concept of mathematics in
the context of the semantic web.

See especially Mike's presentation on Monet


So rather than "crystal", I am inclined to think of
the Axiom documentation (and programs) as a "web". In
fact, the Axiom web could fundamentally reside on a
web application server such as

Zope provides a high level object-oriented environment
using tools that are not so different than Axiom itself

Using these tools together with some of the standards
discussed by Mike Dewar, I could imagine configuring Axiom
(and in the longer term, the network of Axiom developers)
into a dynamic distributed active environment for
mathematics ... [Ok, that's as far as I go with the hype.]

But seriously, as strange as it might sound at first,
what more suits the multidimensional network structure
of Axiom itself better than the "web". And the further we
look into your "thirty year" time horizon, the more sense
this makes to me.

Bill Page.

> -----Original Message-----
> From: 
> address@hidden 
> [mailto:address@hidden
> .org] On Behalf Of root
> Sent: Sunday, December 28, 2003 3:06 PM
> To: address@hidden
> Cc: address@hidden; address@hidden; 
> address@hidden; address@hidden
> Subject: [Axiom-developer] documentation and the crystal 
> Bill,
> per our long-lost prior discussion i've been documenting 
> axiom. the idea of documenting a system like axiom has 
> several facets as i've come to discover. what it means to 
> document axiom has a lot to do with why you are looking at 
> the documentation. so in some way the documentation has to be 
> structured into something like a large crystal egg with many 
> facets. somehow we've got to design a documentation structure 
> that will allow the same basic information to be used in 
> dozens of different ways depending on why you're looking at 
> it. consider that axiom needs documenting:
> of the internal structure of the system
>   the data structures
>   the logical layers (c, lisp, boot, spad)
>   the functional separation (compiler, interpreter, browser)
>   the system-dependent (sockets) vs independent (lisp)
> of the external structure
>   the interpreter
>   the compiler
>   the graphics
>   the hyperdoc
>   the openmath
>   the documentation
> of the algebra structure
>   the packages
>   the domains
>   the categories
> of the mathematical structure
>   the subjects covered
>   the theory underlying the subjects
>   categories
> of the computational mathematics structure
>   intermediate expression swell
>   simplification
>   math types vs computational types
> of the user structure (the book)
>   the commands for naviation
>   the commands for documentation
>   the available math functions
> of the programming language
>   the compiler syntax
>   the compiler semantics
>   sequencing, conditionals, looping, file i/o
>   domain construction
>   categorical tests/constraints
> of the testing structure
>   the mathematics underlying the tests (CATS, computer 
> algebra test suite)
>   the actual tests
>   boundary conditions
> of the literature
>   published algorithms
>   published theory
>   thesis work
> of the program proofs
>   underlying theorems and lemmas
>   program proof books
> i'm currently mucking around in the algebra structure. in 
> particular i've catted all of the algebra together into one 
> file and am "reducing" it to it's primitive structure. this 
> alone is a daunting task as it starts out with about a 
> quarter million lines which i've slowly reduced to about 100k 
> lines so far. i'm doing a topological sort of the algebra to 
> uncover the actual type hierarchy with the idea that it can 
> be reduced to a lattice. as you recall this problem was done 
> once before in order to get axiom to compile from scratch.
> getting down to this level of detail for documenting makes it 
> clear that current systems of documenting are hopelessly 
> weak. somehow we need to take advantage of the computer to 
> leverage and reuse documentation in creative ways. if we 
> don't we'll just drown in endless documents. ibm was famous 
> for delivering shelves worth of documentation which was never 
> used. barnes and noble has whole bookcases of documents on 
> linux. that way lies madness.
> in fact, documentation is probably the wrong idea. we need 
> somehow to be able to automatically generate information from 
> some core that represents the axiom system itself. 
> so i'm thinking about a "crystal browser", that is, a browser 
> where you can gaze into a crystal that surrounds axiom. each 
> facet represents a generated view of the whole system. 
> trivially we could have a facet that shows algebra source 
> code. we could also have a facet that shows the type 
> hierarchy, etc. so it is clear we can create automatic facets 
> with just the existing code and programs that do structure analysis.
> more generally we could construct facets that walk into the 
> pamphlets. one facet could walk the biblio references, 
> another could extract the tex, a third could walk index terms 
> to find all references to a single term (e.g. ideal). 
> particularly interesting would be facets that walk the 
> semantic structure of the system so you could pick out 
> particular kinds of ideals or proofs using ideals, etc. 
> certain facets could be used to impose order by certain 
> metrics (like rainbows in real 
> crystals). such rainbow facets could show the type lattice 
> ordered by layer (ala the structure in the 
> src/algebra/makefile). yet more 
> generally is that "literate programs" need to have sufficient 
> structure 
> to support the crystal.
> in particular, we need to look at some technology that will 
> do some automated work for us. one that leaps to mind is a 
> semantic network. new code would be automatically classified 
> into the system based on several factors (some hand supplied, 
> some derived from the code).
> the idea that it is "just documentation" and "just a browser" is 
> a weak notion but a good start. in general one would like to 
> use facets to CONSTRUCT new algebra, new booklets, new 
> proofs, etc. so both "documentation" and "browser" are the 
> wrong words.
> in 30 year computational mathematicians will need to be able 
> to deal with the complexity of all of the facets of 
> documentation i mentioned above. we need to construct tools 
> which help organize the system in ways that a mathematician 
> can effectively use to do research work.
> the general "visual image" is of a large crystal which you 
> can rotate. every facet gives a different view of the whole 
> of the axiom system. thus, a "crystal" surrounding axiom.
> hope your christmas went well.
> t
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