Define XOR operator and move *valid-operators* to operators

This was been defined actually on parser.lisp. This doesn't
make any sense.

The XOR operator symbol mathematical is (+), but since this
add a ambiguity in Lisp, I would define as [+]. This should
works well.

Author: ryukinix

src/operators.lisp

@@ -4,6 +4,11 @@
 
 (in-package :lisp-inference)
 
+(eval-when (:compile-toplevel)
+  (defconstant F nil))
+
+(defparameter *valid-operators* '(~ ^ <=> => v [+]))
+
 ;; operators
 (defun ~ (p)
   "Not unary operator"
@@ -25,6 +30,10 @@
   "Biconditional binary operator"
   (^ (=> p q) (=> q p)))
 
+(defun [+] (p q)
+  "XOR operator or exclusive disjunction operator"
+  (^ (~ (^ p q))
+     (v p q)))
 
 
 ;; symbolic construction
@@ -42,3 +51,6 @@
 
 (defun make-biconditional (p q)
   (list '<=> p q))
+
+(defun make-xor (p q)
+  (list '[x] p q))

src/package.lisp

@@ -34,6 +34,7 @@
    :v
    :=>
    :<=>
+   :[+]
    :make-conjunction
    :make-negation
    :make-disjunction

src/parser.lisp

@@ -17,8 +17,6 @@
 (setf (symbol-function 'operator) #'car)
 (setf (symbol-function 'operands) #'cdr)
 
-(defparameter *valid-operators* '(~ ^ <=> => v))
-
 ;; operation checkers
 (defun operationp (exp op)
   "Based a 'op that can be a symbol, verify if the list