diff --git a/src/graph/mod.rs b/src/graph/mod.rs
index 2b81879..6671c8a 100644
--- a/src/graph/mod.rs
+++ b/src/graph/mod.rs
@@ -384,17 +384,17 @@ mod tests {
         graph.set_output(Double(doubled));
         assert_eq!(graph.freeze().unwrap().evaluate(), 168);
     }
+    struct Inc(i32);
+    impl Rule<i32> for Inc {
+        fn visit_inputs(&mut self, _visitor: &mut impl InputVisitor) {}
+        fn evaluate(&mut self) -> i32 {
+            self.0 += 1;
+            return self.0;
+        }
+    }
 
     #[test]
     fn invalidatable_rule() {
-        struct Inc(i32);
-        impl Rule<i32> for Inc {
-            fn visit_inputs(&mut self, _visitor: &mut impl InputVisitor) {}
-            fn evaluate(&mut self) -> i32 {
-                self.0 += 1;
-                return self.0;
-            }
-        }
         let mut graph = Graph::new();
         let mut invalidate = None;
         let input = graph.add_invalidatable_rule(|inv| {
@@ -410,4 +410,78 @@ mod tests {
         invalidate.as_ref().unwrap().invalidate();
         assert_eq!(frozen.evaluate(), 6);
     }
+
+    struct Add(Input<i32>, Input<i32>);
+    impl Rule<i32> for Add {
+        fn visit_inputs(&mut self, visitor: &mut impl InputVisitor) {
+            visitor.visit(&mut self.0);
+            visitor.visit(&mut self.1);
+        }
+        fn evaluate(&mut self) -> i32 {
+            self.0.value() + self.1.value()
+        }
+    }
+
+    #[test]
+    fn rule_with_multiple_inputs() {
+        let mut graph = Graph::new();
+        let a = graph.add_value(2);
+        let b = graph.add_value(3);
+        graph.set_output(Add(a, b));
+        assert_eq!(graph.freeze().unwrap().evaluate(), 5);
+    }
+
+    #[test]
+    fn rule_with_invalidatable_inputs() {
+        let mut graph = Graph::new();
+        let mut invalidate = None;
+        let a = graph.add_invalidatable_rule(|inv| {
+            invalidate = Some(inv);
+            Inc(0)
+        });
+        let b = graph.add_rule(Inc(0));
+        graph.set_output(Add(a, b));
+        let mut frozen = graph.freeze().unwrap();
+        assert_eq!(frozen.evaluate(), 2);
+        invalidate.as_ref().unwrap().invalidate();
+        assert_eq!(frozen.evaluate(), 3);
+        assert_eq!(frozen.evaluate(), 3);
+    }
+
+    #[test]
+    fn cant_freeze_no_output() {
+        let graph = Graph::<i32>::new();
+        match graph.freeze() {
+            Err(GraphFreezeError::NoOutput) => (),
+            Err(e) => assert!(false, "unexpected error {:?}", e),
+            Ok(_) => assert!(false, "shouldn't have frozen graph"),
+        }
+    }
+
+    #[test]
+    fn cant_freeze_cycle() {
+        let mut graph = Graph::new();
+        struct DeferredInput(Rc<RefCell<Option<Input<i32>>>>);
+        impl Rule<i32> for DeferredInput {
+            fn visit_inputs(&mut self, visitor: &mut impl InputVisitor) {
+                let mut borrowed = self.0.borrow_mut();
+                let input = borrowed.as_mut().unwrap();
+                visitor.visit(input);
+            }
+            fn evaluate(&mut self) -> i32 {
+                0
+            }
+        }
+        let a_input = Rc::new(RefCell::new(None));
+        let a = graph.add_rule(DeferredInput(Rc::clone(&a_input)));
+        let b_input = Rc::new(RefCell::new(Some(a)));
+        let b = graph.add_rule(DeferredInput(b_input));
+        *a_input.borrow_mut() = Some(b);
+        graph.set_output(Inc(0));
+        match graph.freeze() {
+            Err(GraphFreezeError::Cyclic(_)) => (),
+            Err(e) => assert!(false, "unexpected error {:?}", e),
+            Ok(_) => assert!(false, "shouldn't have frozen graph"),
+        }
+    }
 }