diff --git a/stl/test_utils.py b/stl/test_utils.py
index a2c78fc..ec96ec9 100644
--- a/stl/test_utils.py
+++ b/stl/test_utils.py
@@ -29,13 +29,16 @@ class TestSTLUtils(unittest.TestCase):
         self.assertEqual(set(map(str, stl.utils.param_lens(phi).get_all())), set())
         self.assertEqual(phi, phi2)
 
-    def test_walk(self):
-        raise NotImplementedError
-
-
-    def test_type_pred(self):
-        raise NotImplementedError
+    @params(("x > 5", 1), ("~(x)", 2), ("(F[0,1](x)) & (~(G[0, 2](y)))", 6))
+    def test_walk(self, phi_str, l):
+        self.assertEqual(l, len(list(stl.walk(stl.parse(phi_str)))))
 
+    @params(([], False, False),([int], True, False), ([int, bool], True, True))
+    def test_type_pred(self, types, b1, b2):
+        pred = stl.utils.type_pred(*types)
+        self.assertFalse(pred(None))
+        self.assertEqual(pred(1), b1)
+        self.assertEqual(pred(True), b2)
 
     def test_ast_lens(self):
         raise NotImplementedError
diff --git a/stl/utils.py b/stl/utils.py
index 0209c0a..6dbe234 100644
--- a/stl/utils.py
+++ b/stl/utils.py
@@ -12,11 +12,11 @@ from stl.ast import (LinEq, And, Or, NaryOpSTL, F, G, Interval, Neg,
                      AtomicPred)
 from stl.types import STL, STL_Generator, MTL
 
-def walk(phi:STL, bfs:bool=False) -> STL_Generator:
-    """Walks Ast. Defaults to DFS unless BFS flag is set."""
-    pop = deque.popleft if bfs else deque.pop
+def walk(phi:STL) -> STL_Generator:
+    """DSF walk of the AST."""
+    pop = deque.pop
     children = deque([phi])
-    while len(children) != 0:
+    while len(children) > 0:
         node = pop(children)
         yield node
         children.extend(node.children())