diff --git a/examples/arithmetic.modal b/examples/arithmetic.modal
new file mode 100644
index 0000000..374274f
--- /dev/null
+++ b/examples/arithmetic.modal
@@ -0,0 +1,23 @@
+<> (add (s ?x) (s ?y)) ((s add ?x (s ?y)))
+<> (add (s ?y) (0)) ((s ?y))
+<> (add (0) (s ?y)) ((s ?y))
+<> (add (0) (0)) (0)
+
+<> (subtract (s ?x) (s ?y)) (subtract ?x ?y)
+<> (subtract (s ?x) (0)) (s ?x)
+<> (subtract (0) (s ?y)) (s ?y)
+<> (subtract (0) (0)) (0)
+
+<> (multiply (s ?x) (s ?y)) (add (s ?x) (multiply (s ?x) (subtract (s ?y) (s (0))))
+<> (multiply (s ?x) (s (0)) (s ?x)
+<> (multiply (s (0)) (s ?y) (s ?y)
+<> (multiply (s ?x) (0)) (0)
+<> (multiply (0) (s ?x)) (0)
+
+<> (?x + ?y) (add ?x ?y)
+<> (?x - ?y) (subtract ?x ?y)
+<> (?x * ?y) (multiply ?x ?y)
+<> (factorial (s (0))) ((s (0)))
+<> (factorial (s ?x)) ((s ?x) * factorial ((s ?x) - (s (0))))
+
+(s (0)) * (s (s (0)))
\ No newline at end of file
diff --git a/examples/test.modal b/examples/test.modal
index 310551e..374274f 100644
--- a/examples/test.modal
+++ b/examples/test.modal
@@ -1,3 +1,23 @@
-<> ((?x -> ?y)) (<> ?x ?y)
+<> (add (s ?x) (s ?y)) ((s add ?x (s ?y)))
+<> (add (s ?y) (0)) ((s ?y))
+<> (add (0) (s ?y)) ((s ?y))
+<> (add (0) (0)) (0)
 
-(foo -> bar) foo
\ No newline at end of file
+<> (subtract (s ?x) (s ?y)) (subtract ?x ?y)
+<> (subtract (s ?x) (0)) (s ?x)
+<> (subtract (0) (s ?y)) (s ?y)
+<> (subtract (0) (0)) (0)
+
+<> (multiply (s ?x) (s ?y)) (add (s ?x) (multiply (s ?x) (subtract (s ?y) (s (0))))
+<> (multiply (s ?x) (s (0)) (s ?x)
+<> (multiply (s (0)) (s ?y) (s ?y)
+<> (multiply (s ?x) (0)) (0)
+<> (multiply (0) (s ?x)) (0)
+
+<> (?x + ?y) (add ?x ?y)
+<> (?x - ?y) (subtract ?x ?y)
+<> (?x * ?y) (multiply ?x ?y)
+<> (factorial (s (0))) ((s (0)))
+<> (factorial (s ?x)) ((s ?x) * factorial ((s ?x) - (s (0))))
+
+(s (0)) * (s (s (0)))
\ No newline at end of file
diff --git a/src/modal.c b/src/modal.c
index 5e17697..a9f1b15 100644
--- a/src/modal.c
+++ b/src/modal.c
@@ -71,6 +71,10 @@ writereg(char r)
 {
 	int depth = 0;
 	char c, *s = regs[(int)r];
+	if(!s) {
+		printf("!! Reading from invalid register: ?%c\n", r);
+		return;
+	}
 	if(s[0] == '(') {
 		while((c = *s++)) {
 			if(c == '(') depth++;