Lisp symbols without package bindings

Question

I've been working on some project. It should be able to do numerical and symbolic computing. But now I stuck on one problem and I don't really know how to resolve it. To be specific and short, let's say we are in package

(in-package #:brand-new-package)

Where we have symbol database

(defvar var-symbol-database (make-hash-table :test #'equal))

Reading and setting functions

(defun var-symbol (name)
  (get-hash name var-symbol-database))
(defun set-var-symbol (name value)
  (setf (get-hash name var-symbol-database) value))

 (set-var-symbol 'temperature 300) ;K
 (set-var-symbol 'f 200) ;Hz
 (set-var-symbol 'k 1.3806504e-23) ;J K^-1

and now in another file (but same package) I will try to evaluate this equation

  (eval '(+ 2 (var-symbol 'f)))

It won't work. Problem is that for some particular reason the value of key in hash table is.

    brand-new-package::f

I though that I will solve the problem defining function like this

  (set-var-symbol 1 '(var-symbol 'f)) ;Hz

But it is interpreted as

 (brand-new-package::var-symbol brand-new-package::f)

The problem is that program can create many different symbols. It will compute electronic circuit equations. Program first inspect device objects like capacitors, resistors and so. It create circuit tablo by MNA.

During it many new symbols representing node voltages and currents could be created

 (v1, v2, v3, i1, i2). 

I needed some method to hold count and names of variables presented in equation. Because they will be passed to symbolic derivator ie (diff '(* (+ 40 v1) u2 ...) 'v1)) I came with an idea, maybe wrong, to make them reachable by index to define them as a list

 '(v 1) '(v 2) '(v 3). 

To make them evaluable I added to begining var-variable funcall. So list becomed

 '(var-variable v 1) '(var-variable v 2) '(var-variable v 3) 

But as I have written, system changes it to

 '(brand-new-package::var-variable brand-new-package::v 1) '(brand-new-package::var-variable brand-new-package::v 2) '(brand-new-package::var-variable brand-new-package::v 3)

How to allow to users to acces these variables by typing (var-symbol 'v 1). I can imagine only one way. Instead of symbols use strings and export function (var-symbol). Then it will work this way

  '(var-variable "v" 1)

But it is a little bit confusing.

Answer 1

You are duplicating what Lisp already does. Symbols are already managed in tables, called packages. A symbol can have a value. Putting it into a package is INTERN. Finding it is FIND-SYMBOL or just using the Lisp READer.

If you want your own symbol index tables, hash tables are fine. If you don't want to deal with packages of those symbols, then just use keyword symbols. They have a single colon in front. :temperature would be an example. Keyword symbols are automagically in the package KEYWORD and they evaluate to themselves.

Answer 2

What you state to be a "problem" is as expected. The Common Lisp notation brand-new-package::var-symbol signifies that the symbol var-symbol is in the package brand-new-package, which was the current package at the time the symbol was read by the lisp.