Boolean Constraint Satisfaction System

In addition to simply building and evaluating an expression as in Arithmetica, you should allow the user a new command: to satisfy a boolean expression. 

Your program should recognize the following expressions:

expression	syntax	semantics	examples
Constant	<true/false>	a boolean constant	true T t
Variable	<any alpha-numeric string> [a-zA-z0-9]+	an expression represented by a word (other than keywords true or false) Note, the special symbol "current" refers to the current expression	a bugs q45
Assignment	var = expr	assigns an expression to a variable	a = false bugs = F || a a = bugs
Unary Operator	op expr	prefixes an expression  ~ // logical not	!a -(t && a || F) !F
Binary Operator	expr op expr	combines two expressions into a single expression (in precedence order) && // logical and || // logical or	a && b a || 2 a || T && c
Unary Functions	fun(expr)	a function that takes an expression as its single argument satisfy(expr) // return if it is possible for given expression to be true	satisfy(a) satisfy(a && F)
Parentheses	(expr)	raises an expression's precedence	(a && b) || 3 !(bugs && t)

Operators have the following precedence from left to right (listed from highest to lowest):

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