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Re: Axiom musings...

From: Tim Daly
Subject: Re: Axiom musings...
Date: Fri, 5 Feb 2021 15:22:50 -0500

I've worked hard to make Axiom depend on almost no other
tools so that it would not get caught by "code rot" of libraries.

However, I'm also trying to make the new SANE version much
easier to understand and debug.To that end I've been experimenting
with some ideas.

It should be possible to view source code, of course. But the source
code is not the only, nor possibly the best, representation of the ideas.
In particular, source code gets compiled into data structures. In Axiom
these data structures really are a graph of related structures.

For example, looking at the gcd function from NNI, there is the
representation of the gcd function itself. But there is also a structure
that is the REP (and, in the new system, is separate from the domain).

Further, there are associated specification and proof structures. Even
further, the domain inherits the category structures, and from those it
inherits logical axioms and definitions through the proof structure.

Clearly the gcd function is a node in a much larger graph structure.

When trying to decide why code won't compile it would be useful to
be able to see and walk these structures. I've thought about using the
browser but browsers are too weak. Either everything has to be "in a
single tab to show the graph" or "the nodes of the graph are in different
tabs". Plus, constructing dynamic graphs that change as the software
changes (e.g. by loading a new spad file or creating a new function)
represents the huge problem of keeping the browser "in sync with the
Axiom workspace". So something more dynamic and embedded is needed.

Axiom source gets compiled into CLOS data structures. Each of these
new SANE structures has an associated surface representation, so they
can be presented in user-friendly form.

Also, since Axiom is literate software, it should be possible to look at
the code in its literate form with the surrounding explanation.

Essentially we'd like to have the ability to "deep dive" into the Axiom
workspace, not only for debugging, but also for understanding what
functions are used, where they come from, what they inherit, and
how they are used in a computation.

To that end I'm looking at using McClim, a lisp windowing system.
Since the McClim windows would be part of the lisp image, they have
access to display (and modify) the Axiom workspace at all times.

The only hesitation is that McClim uses quicklisp and drags in a lot
of other subsystems. It's all lisp, of course.

These ideas aren't new. They were available on Symbolics machines,
a truly productive platform and one I sorely miss.


On 1/19/21, Tim Daly <> wrote:
> Also of interest is the talk
> "The Unreasonable Effectiveness of Dynamic Typing for Practical Programs"
> which questions whether static typing really has any benefit.
> Tim
> On 1/19/21, Tim Daly <> wrote:
>> Peter Naur wrote an article of interest:
>> In particular, it mirrors my notion that Axiom needs
>> to embrace literate programming so that the "theory
>> of the problem" is presented as well as the "theory
>> of the solution". I quote the introduction:
>> This article is, to my mind, the most accurate account
>> of what goes on in designing and coding a program.
>> I refer to it regularly when discussing how much
>> documentation to create, how to pass along tacit
>> knowledge, and the value of the XP's metaphor-setting
>> exercise. It also provides a way to examine a methodolgy's
>> economic structure.
>> In the article, which follows, note that the quality of the
>> designing programmer's work is related to the quality of
>> the match between his theory of the problem and his theory
>> of the solution. Note that the quality of a later programmer's
>> work is related to the match between his theories and the
>> previous programmer's theories.
>> Using Naur's ideas, the designer's job is not to pass along
>> "the design" but to pass along "the theories" driving the design.
>> The latter goal is more useful and more appropriate. It also
>> highlights that knowledge of the theory is tacit in the owning, and
>> so passing along the thoery requires passing along both explicit
>> and tacit knowledge.
>> Tim

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