Re: A(n orthogonal) set of essential operations for CAS

Richard J. Fateman wrote:

> You can define any of these in terms of
> functional composition of higher-order functions, and
> construction of new objects. If you were using Lisp, you
> would have most of these items, as Albert points out, but
> if you didn't, all you would need is about 5 functions.
> car, cdr, cons, if, apply. Thus distribute is probably
> about the same as mapcar in Lisp. Mapcar built in, but if
> it weren't, you could define it approximately by
>
> (defun mapcar(f arglist)
> (if (null arglist)
> nil
> (cons (apply f (car arglist))
> (mapcar f (cdr arglist)))

I suspect there is something very close to Peano's system of axioms which
could serve as an orthogonal basis for a comprehensive CAS. I also suspect
that building pedantically upon these would lead to a very inefficient
system. That is to say, building the implementation of derived concepts
strictly in terms of the more primitive ones. Building the conceptual
model is a different matter.

> You might find it useful to look at Structure and Interpretation
> of Computer Programs by Abelson/Sussman. It's online, if you
> can't find it in a library or bookstore.

You are not the only person to recommend that text. Jamie Zawinski of
Mozilla infamy recommends it, and Roman Meader - a major contributor to the
design of Mathematica - mentions it in the bibliography of at least two of
his books. I'm pleased to find it on-line. Normaly I would purchase such
a book, but I'm having to limit myself these days.

I've attempted to learn Lisp a few times, but I believe I have a fairly
strong immunity to the language. You've persuaded me to have another go at
it. I'll thank you later. ;)
--
Nil conscire sibi
.

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