SYNTAX

Expression syntax
-----------------

1. Operators

	In decreasing priority:

	^ 		(exponentiation)
	- 		(negative sign)
	* /		
	+ -
	= 		(rule-equation)

	Exponentiation is right-associative, while all the other
	arithmetic operators are left-associative.

	Example: 1 + 2 * 3

2. Parentheses

	Example: (1 + 2) * 3

3. Variable names / symbols

	Example: bob

4. Functions

	Example: cos(x * x)
	Example: foo(A * (B + 1), asdf, clown, qwerty - fjds(bob * log(derp)))

Rule syntax
-----------

Rules are written as equations. Variable in the left-hand-side get matched
to expressions which are subsituted into the right-hand-side.

For example, the rule 'x + x = 2 * x' will turn the expression 
'cos(x) + cos(x)' into '2 * cos(x)'.

There are some "special" syntaxes:

e|x matches any expression e without any occurence of x in it
e:x matches any expression e with an occurence of x in it,
    including x itself.

e::x matches any expression e with an occurence of x in it,
     but not x itself.

e|'x matches anything that isn't literally the symbol x

[ Issue: x has to have been defined before (to the left) of the  ]
[ syntax for these syntaxes to work :(				 ]
[								 ]
[ So for example, expressions like "D(e|x, x)" are a problem	 ]
[ but "D(x, e|x)" will work. There might be a way to fix this... ]

?x matches a direct variable symbol x
#n matches a number n
$f matches a function f
@e matches an expression e which isn't a number
'e matches literally the symbol e

In the preloaded rule files ("rules" directory, comment-lines start
with '%' characters).