diff --git a/spherogram_src/graphs.py b/spherogram_src/graphs.py
index b5c3196..acc69b0 100644
--- a/spherogram_src/graphs.py
+++ b/spherogram_src/graphs.py
@@ -84,7 +84,7 @@ def __hash__(self):
     def incident_to(self):
         return list(self)
 
-    def is_loop(self):
+    def is_loop(self) -> bool:
         return self[0] is self[1]
 
 
@@ -374,7 +374,7 @@ def components(self, deleted_vertices=[]):
             result.append(frozenset(component))
         return result
 
-    def is_connected(self, deleted_vertices=[]):
+    def is_connected(self, deleted_vertices=[]) -> bool:
         """
         Determine whether the graph obtained by removing the
         deleted_vertices and incident edges is connected.
@@ -391,7 +391,7 @@ def reduced(self):
             R.add_edge(*e)
         return R
 
-    def is_planar(self):
+    def is_planar(self) -> bool:
         return self.reduced().is_planar()
 
     def merge(self, V1, V2):
@@ -478,7 +478,7 @@ def multi_valence(self, vertex):
         """
         return sum(e.multiplicity for e in self.incidence_dict[vertex])
 
-    def is_planar(self):
+    def is_planar(self) -> bool:
         """
         Return the planarity.
         """
@@ -697,14 +697,14 @@ def components(self):
         raise ValueError('Not meaningful for Digraphs.\n'
                          'Use weak_components() or strong_components()')
 
-    def is_weakly_connected(self):
+    def is_weakly_connected(self) -> bool:
         """
         A digraph is weakly connected if the associated undirected graph
         is connected.
         """
         return len(self.weak_components()) <= 1
 
-    def is_connected(self):
+    def is_connected(self) -> bool:
         """
         A digraph is connected if, for every pair of vertices v, w,
         there is either a directed path from v to w or a directed path
@@ -732,7 +732,7 @@ def strong_components(self):
         """
         return StrongConnector(self).components
 
-    def is_strongly_connected(self):
+    def is_strongly_connected(self) -> bool:
         """
         A digraph is strongly connected if, for every pair of vertices
         v, w, there is a directed path from v to w and a directed path
diff --git a/spherogram_src/links/bands/core.py b/spherogram_src/links/bands/core.py
index eae954a..e22c044 100644
--- a/spherogram_src/links/bands/core.py
+++ b/spherogram_src/links/bands/core.py
@@ -313,7 +313,7 @@ def __ge__(self, other):
     def __repr__(self):
         return f'Band{self._spec}'
 
-    def is_nonminimal(self, link=None):
+    def is_nonminimal(self, link=None) -> bool:
         """
         Do various tests to see if self is obviously equivalent to a
         band other with other < self.
diff --git a/spherogram_src/links/bands/search.py b/spherogram_src/links/bands/search.py
index b49e68d..d73f7f3 100644
--- a/spherogram_src/links/bands/search.py
+++ b/spherogram_src/links/bands/search.py
@@ -3,7 +3,7 @@
 from .core import Band, add_one_band, banded_links, normalize_crossing_labels
 
 
-def linking_nums_all_zero(link):
+def linking_nums_all_zero(link) -> bool:
     """
     >>> linking_nums_all_zero(Link('L2a1'))  # Hopf
     False
@@ -13,7 +13,7 @@ def linking_nums_all_zero(link):
     return all(x == 0 for row in link.linking_matrix() for x in row)
 
 
-def is_unlink_exterior(manifold):
+def is_unlink_exterior(manifold) -> bool:
     """
     If there is clearly a hyperbolic structure present, we don't even
     look at the fundamental group as it takes some time to compute and
@@ -24,7 +24,7 @@ def is_unlink_exterior(manifold):
     return manifold.fundamental_group().num_relators() == 0
 
 
-def could_be_strongly_slice(link):
+def could_be_strongly_slice(link) -> bool:
     """
     Checks several obstructions for a link L to be strongly slice,
     that is that all components of L simultaneously bound embedded
diff --git a/spherogram_src/links/exhaust.py b/spherogram_src/links/exhaust.py
index 84b604d..285a5a3 100644
--- a/spherogram_src/links/exhaust.py
+++ b/spherogram_src/links/exhaust.py
@@ -256,12 +256,14 @@ def _check(self):
         return sorted(self.int_to_set) == list(range(self.n))
 
 
-def is_range(L):
+def is_range(L) -> bool:
     """
     >>> is_range([2, 3, 4]), is_range([2, 3, 5])
     (True, False)
     """
-    return L == list(range(min(L), max(L) + 1))
+    if not L:
+        return False
+    return all(i == Li for i, Li in enumerate(L, start=L[0]))
 
 
 class Frontier(BiDict):
diff --git a/spherogram_src/links/jones.py b/spherogram_src/links/jones.py
index 9ebb272..d481452 100644
--- a/spherogram_src/links/jones.py
+++ b/spherogram_src/links/jones.py
@@ -160,8 +160,8 @@ def add_positive_crossing(self, i):
     def add_negative_crossing(self, i):
         return self.cap_then_cup(i) + (-q) * self
 
-    def is_multiple_of_empty_pairing(self):
-        return len(self.dict) == 1 and (PerfectMatching([]) in self.dict)
+    def is_multiple_of_empty_pairing(self) -> bool:
+        return len(self.dict) == 1 and PerfectMatching([]) in self.dict
 
 
 def kauffman_bracket(link):
diff --git a/spherogram_src/links/jones_old.py b/spherogram_src/links/jones_old.py
index 038a253..56af55d 100644
--- a/spherogram_src/links/jones_old.py
+++ b/spherogram_src/links/jones_old.py
@@ -32,7 +32,7 @@ def cut(G, T, e):
     return answer
 
 
-def is_internally_active(G, T, e):
+def is_internally_active(G, T, e) -> bool:
     """
     Input:
     --A graph G.
@@ -88,7 +88,7 @@ def cyc(G, T, e):
     return answer
 
 
-def is_externally_active(G, T, e):
+def is_externally_active(G, T, e) -> bool:
     """
     Input:
     --A graph G.
diff --git a/spherogram_src/links/links_base.py b/spherogram_src/links/links_base.py
index 006b7b7..d57fc6d 100644
--- a/spherogram_src/links/links_base.py
+++ b/spherogram_src/links/links_base.py
@@ -33,7 +33,7 @@ def __getitem__(self, n):
 # Helper function.
 
 
-def is_iterable(obj):
+def is_iterable(obj) -> bool:
     try:
         iter(obj)
         return True
@@ -149,13 +149,12 @@ def orient(self):
             self.rotate_by_180()
         self.sign = 1 if (3, 1) in self.directions else -1
 
-    def is_incoming(self, i):
+    def is_incoming(self, i) -> bool:
         if self.sign == 1:
             return i in (0, 3)
-        elif self.sign == -1:
+        if self.sign == -1:
             return i in (0, 1)
-        else:
-            raise ValueError('Crossing not oriented')
+        raise ValueError('Crossing not oriented')
 
     def __getitem__(self, i):
         return (self, i % 4)
@@ -281,10 +280,10 @@ def other(self):
         other = nonzero_entry_point if self.strand_index == 0 else 0
         return CrossingEntryPoint(self.crossing, other)
 
-    def is_under_crossing(self):
+    def is_under_crossing(self) -> bool:
         return self.strand_index == 0
 
-    def is_over_crossing(self):
+    def is_over_crossing(self) -> bool:
         return self.strand_index != 0
 
     def component(self):
@@ -362,7 +361,7 @@ def format_adjacent(a):
         print("<%s : %s>" %
               (self.label, [format_adjacent(a) for a in self.adjacent]))
 
-    def is_loop(self):
+    def is_loop(self) -> bool:
         return self == self.adjacent[0][0]
 
 
@@ -947,7 +946,7 @@ def digraph(self):
                 G.add_edge(cs0.crossing, cs1.crossing)
         return G
 
-    def is_planar(self):
+    def is_planar(self) -> bool:
         """
         Whether the 4-valent graph underlying the link projection is planar.
 
@@ -989,7 +988,7 @@ def is_planar(self):
         euler = -v + len(self.faces())
         return euler == 2 or v == 0
 
-    def is_alternating(self):
+    def is_alternating(self) -> bool:
         """
         Returns whether or not this link diagram is alternating.
 
@@ -1225,10 +1224,8 @@ def PD_code(self, KnotTheory=False, min_strand_index=0):
         >>> [len(c) for c in L_copy.link_components]
         [4, 4, 4, 6, 8]
         """
-        PD = []
-
-        for c in self.crossings:
-            PD.append([s + min_strand_index for s in c.strand_labels])
+        PD = [[s + min_strand_index for s in c.strand_labels]
+              for c in self.crossings]
         if KnotTheory:
             PD = "PD" + repr(PD).replace('[', 'X[')[1:]
         else:
diff --git a/spherogram_src/links/morse.py b/spherogram_src/links/morse.py
index 414f6ea..fe65aea 100644
--- a/spherogram_src/links/morse.py
+++ b/spherogram_src/links/morse.py
@@ -339,7 +339,7 @@ def pack_snakes(self):
 
         self.snakes_at_height = snakes_at_height
 
-    def is_bridge(self):
+    def is_bridge(self) -> bool:
         """
         Returns whether the link is in bridge position with respect to this
         height function.
@@ -431,5 +431,5 @@ def HF(self):
         import bohua_HF
         return bohua_HF.compute_HF(self.bohua_code())
 
-    def is_proper(self):
+    def is_proper(self) -> bool:
         return all(abs(a - b) < 2 for a, b in self.crossings)
diff --git a/spherogram_src/links/orthogonal.py b/spherogram_src/links/orthogonal.py
index b6df570..d08c9bb 100644
--- a/spherogram_src/links/orthogonal.py
+++ b/spherogram_src/links/orthogonal.py
@@ -156,7 +156,7 @@ def kitty_corner(self):
         if not self.exterior:
             return kitty_corner(self.turns)
 
-    def is_turn_regular(self):
+    def is_turn_regular(self) -> bool:
         return self.kitty_corner() is None
 
     def switches(self, swap_hor_edges):
@@ -416,11 +416,10 @@ def orient_edges(self, edge, orientation):
             dir = (dir + t) % 4
         return ans
 
-    def is_turn_regular(self):
+    def is_turn_regular(self) -> bool:
         if self.exterior:
             return True
-        else:
-            return kitty_corner(self.turns) is None
+        return kitty_corner(self.turns) is None
 
     def __repr__(self):
         ext = '*' if self.exterior else ''
diff --git a/spherogram_src/links/seifert.py b/spherogram_src/links/seifert.py
index 366d2be..b6821be 100644
--- a/spherogram_src/links/seifert.py
+++ b/spherogram_src/links/seifert.py
@@ -149,7 +149,7 @@ def isotope_to_braid(link):
         pass
 
 
-def is_chain(tree):
+def is_chain(tree) -> bool:
     tails = [e[0] for e in tree]
     heads = [e[1] for e in tree]
     return len(set(tails)) == len(tails) and len(set(heads)) == len(heads)