add xor, adjust implies following Carl's comments

collects/racket/bool.rkt

@@ -3,7 +3,7 @@
 (provide true false false?
          boolean=?
          symbol=?
-         implies nand nor)
+         implies nand nor xor)
 (require (for-syntax racket/base))
 
 (define true #t)
@@ -24,9 +24,7 @@
 (define-syntax (implies stx)
   (syntax-case stx ()
     [(implies x y)
-     (syntax/loc stx (if x y #t))]
-    [(implies x y z w ...)
-     (syntax/loc stx (if x (implies y z w ...) #t))]))
+     (syntax/loc stx (if x y #t))]))
 
 (define-syntax (nor stx)
   (syntax-case stx ()
@@ -35,3 +33,10 @@
 (define-syntax (nand stx)
   (syntax-case stx ()
     [(_ expr ...) (syntax/loc stx (not (and expr ...)))]))
+
+(define (xor a b)
+  (if a
+      (if b
+          #f
+          a)
+      b))

collects/scribblings/reference/booleans.scrbl

@@ -268,17 +268,33 @@ Returns @racket[(not v)].}
           
 }
 
-@defform[(implies expr expr expr ...)]{
+@defform[(implies expr1 expr2)]{
   Checks to be sure that the first
-  expression implies the second, implies
-  the third, etc.
+  expression implies the second.
+  
+  Same as @racket[(if expr1 expr2 #f)].
   
   @examples[#:eval 
             bool-eval
             (implies #f #t)
             (implies #f #f)
-            (implies #f #f #t)
             (implies #t #f)
             (implies #f (error 'ack "we don't get here"))]
                                        
 }
+
+@defproc[(xor [b1 any/c] [b2 any/c]) any]{
+  Returns the exclusive or of @racket[b1] and @racket[b2].
+                              
+  If exactly one of @racket[b1] and @racket[b2] is
+  not @racket[#f], then return it. Otherwise, returns
+  @racket[#f].
+  
+  @examples[#:eval
+            bool-eval
+            (xor 11 #f)
+            (xor #f 22)
+            (xor 11 22)
+            (xor #f #f)]
+                                          
+}

collects/tests/racket/bool.rkt

@@ -20,9 +20,8 @@
 
 (for ([x (in-list '(#f #t))])
   (for ([y (in-list '(#f #t))])
-    (for ([z (in-list '(#f #t))])
-      (check-equal? (implies x y z)
-                    (or (not x) (or (not y) z))))))
+    (check-equal? (implies x y)
+                  (or (not x) y))))
 (check-equal? (implies #f (car 'x)) #t)
 
 
@@ -37,3 +36,8 @@
 (check-equal? (nor #f #t) #f)
 (check-equal? (nor #t #t) #f)
 (check-equal? (nor #t (car 'x)) #f)
+
+(check-equal? (xor 11 22) #f)
+(check-equal? (xor 11 #f) 11)
+(check-equal? (xor #f 22) 22)
+(check-equal? (xor #f #f) #f)