Re: Axiom musings...

[Tim Daly]

A great deal of thought has gone into the representation
of functions in the SANE version.

It is important that a function lives within an environment.
There are no "stand alone" functions. Given a function
its environment contains the representation which itself
is a function type with accessor functions. Wrapped
around these is the domain type containing other
functions. The domain type lives within several
preorders of environments, some dictated by the
structure of group theory, some dictated by the structure
of the logic.

Lisp has the ability to construct arbitrary structures
which can be nested or non-nested, and even potentially
circular.

Even more interesting is that these structures can be
"self modified" so that one could have a domain (e.g.
genetic algorithms) that self-adapt, based on input.
Or "AI" domains, representated as weight matrices,
that self-adapt to input by changing weights.

Ultimately the goal of the representation should be that,
given a function, it should be possible to traverse the
whole of the environment using a small, well-defined
set of well-typed structure walkers.

All of this is easy to write down in Lisp.
The puzzle is how to reflect these ideas in Spad.

Currently the compiler translates all of the Spad
code to Lisp objects so the Spad->Lisp conversion
is easy. Lisp->Spad is also easy for things that have
a surface representation in Spad. But, in general,
Lisp->Spad is only a partial function, and somewhat
limited at that.

I suspect that the solution will allow some domains
to be pure Lisp and others will allow in-line Lisp.

Most of these ideas are nearly impossible to even
think about in other languages or, if attempted,
fall afoul of Greenspun's Tenth Rule, to wit:

  "Any sufficiently complicated C or Fortran program
   contains an ad hoc, informally-specified, bug-ridden,
   slow implementation of half of Common Lisp."

Fortunately Spad is only a domain specific language
on top of Lisp. Once past the syntax level it is Lisp
all the way down.

Tim