diff --git a/docs/Types.ipynb b/docs/Types.ipynb
index 35e858f..a220b3f 100644
--- a/docs/Types.ipynb
+++ b/docs/Types.ipynb
@@ -499,6 +499,8 @@
     "        s[u] = v\n",
     "    elif isinstance(v, int):\n",
     "        s[v] = u\n",
+    "    else:\n",
+    "        s = False\n",
     "\n",
     "    return s"
    ]
@@ -884,6 +886,8 @@
     "        s = unify(a, c, s)\n",
     "        if s != False:\n",
     "            s = unify(b, d, s)\n",
+    "    else:\n",
+    "        s = False\n",
     "\n",
     "    return s"
    ]
diff --git a/docs/notebook_preamble.pyc b/docs/notebook_preamble.pyc
deleted file mode 100644
index 32b6331..0000000
Binary files a/docs/notebook_preamble.pyc and /dev/null differ
diff --git a/joy/library.py b/joy/library.py
index c3e00c7..13176c5 100644
--- a/joy/library.py
+++ b/joy/library.py
@@ -94,7 +94,6 @@ definitions = ('''\
 of == swap at
 product == 1 swap [*] step
 flatten == [] swap [concat] step
-unit == [] cons
 quoted == [unit] dip
 unquoted == [i] dip
 enstacken == stack [clear] dip
@@ -120,13 +119,14 @@ range_to_zero == unit [down_to_zero] infra
 anamorphism == [pop []] swap [dip swons] genrec
 range == [0 <=] [1 - dup] anamorphism
 while == swap [nullary] cons dup dipd concat loop
-dudipd == dup dipd
+dupdipd == dup dipd
 primrec == [i] genrec
 step_zero == 0 roll> step
 codireco == cons dip rest cons
 make_generator == [codireco] ccons
-ccons == cons cons
 '''
+##ccons == cons cons
+##unit == [] cons
 ##second == rest first
 ##third == rest rest first
 ##swons == swap cons
@@ -572,12 +572,12 @@ def clear(stack):
 ##  return second, (tos, stack)
 
 
-@inscribe
-@SimpleFunctionWrapper
-def swaack(stack):
-  '''swap stack'''
-  old_stack, stack = stack
-  return stack, old_stack
+##@inscribe
+##@SimpleFunctionWrapper
+##def swaack(stack):
+##  '''swap stack'''
+##  old_stack, stack = stack
+##  return stack, old_stack
 
 
 ##@inscribe
diff --git a/joy/utils/generated_library.py b/joy/utils/generated_library.py
index a6a2051..08c9285 100644
--- a/joy/utils/generated_library.py
+++ b/joy/utils/generated_library.py
@@ -5,55 +5,55 @@ def _Tree_add_Ee(stack):
   """
   ::
 
-    ([a3 a4 ...0] a2 a1 a0 -- [a1 a2 ...0])
+    ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
 
   """
-  (a0, (a1, (a2, ((a3, (a4, s0)), s1)))) = stack
-  return ((a1, (a2, s0)), s1)
+  (a1, (a2, (a3, ((a4, (a5, s1)), s2)))) = stack
+  return ((a2, (a3, s1)), s2)
 
 
 def _Tree_delete_R0(stack):
   """
   ::
 
-    ([a1 ...0] a0 -- [a1 ...0] a1 a0 a0)
+    ([a2 ...1] a1 -- [a2 ...1] a2 a1 a1)
 
   """
-  (a0, ((a1, s0), s1)) = stack
-  return (a0, (a0, (a1, ((a1, s0), s1))))
+  (a1, ((a2, s1), s2)) = stack
+  return (a1, (a1, (a2, ((a2, s1), s2))))
 
 
 def _Tree_delete_clear_stuff(stack):
   """
   ::
 
-    (a2 a1 [a0 ...0] -- [...0])
+    (a3 a2 [a1 ...1] -- [...1])
 
   """
-  ((a0, s0), (a1, (a2, s1))) = stack
-  return (s0, s1)
+  ((a1, s1), (a2, (a3, s2))) = stack
+  return (s1, s2)
 
 
 def _Tree_get_E(stack):
   """
   ::
 
-    ([a2 a3 ...0] a1 a0 -- a3)
+    ([a3 a4 ...1] a2 a1 -- a4)
 
   """
-  (a0, (a1, ((a2, (a3, s0)), s1))) = stack
-  return (a3, s1)
+  (a1, (a2, ((a3, (a4, s1)), s2))) = stack
+  return (a4, s2)
 
 
 def ccons(stack):
   """
   ::
 
-    (a1 a0 [...0] -- [a1 a0 ...0])
+    (a2 a1 [...1] -- [a2 a1 ...1])
 
   """
-  (s0, (a0, (a1, s1))) = stack
-  return ((a1, (a0, s0)), s1)
+  (s1, (a1, (a2, s2))) = stack
+  return ((a2, (a1, s1)), s2)
 
 
 def cons(stack):
@@ -115,22 +115,22 @@ def first_two(stack):
   """
   ::
 
-    ([a0 a1 ...0] -- a0 a1)
+    ([a1 a2 ...1] -- a1 a2)
 
   """
-  ((a0, (a1, s0)), s1) = stack
-  return (a1, (a0, s1))
+  ((a1, (a2, s1)), s2) = stack
+  return (a2, (a1, s2))
 
 
 def fourth(stack):
   """
   ::
 
-    ([a0 a1 a2 a3 ...0] -- a3)
+    ([a1 a2 a3 a4 ...1] -- a4)
 
   """
-  ((a0, (a1, (a2, (a3, s0)))), s1) = stack
-  return (a3, s1)
+  ((a1, (a2, (a3, (a4, s1)))), s2) = stack
+  return (a4, s2)
 
 
 def over(stack):
@@ -247,22 +247,22 @@ def rrest(stack):
   """
   ::
 
-    ([a0 a1 ...0] -- [...0])
+    ([a1 a2 ...1] -- [...1])
 
   """
-  ((a0, (a1, s0)), s1) = stack
-  return (s0, s1)
+  ((a1, (a2, s1)), s2) = stack
+  return (s1, s2)
 
 
 def second(stack):
   """
   ::
 
-    ([a0 a1 ...0] -- a1)
+    ([a1 a2 ...1] -- a2)
 
   """
-  ((a0, (a1, s0)), s1) = stack
-  return (a1, s1)
+  ((a1, (a2, s1)), s2) = stack
+  return (a2, s2)
 
 
 def stack(stack):
@@ -280,22 +280,33 @@ def stuncons(stack):
   """
   ::
 
-    (... a0 -- ... a0 a0 [...])
+    (... a1 -- ... a1 a1 [...])
 
   """
-  (a0, s0) = stack
-  return (s0, (a0, (a0, s0)))
+  (a1, s1) = stack
+  return (s1, (a1, (a1, s1)))
 
 
 def stununcons(stack):
   """
   ::
 
-    (... a1 a0 -- ... a1 a0 a0 a1 [...])
+    (... a2 a1 -- ... a2 a1 a1 a2 [...])
 
   """
-  (a0, (a1, s0)) = stack
-  return (s0, (a1, (a0, (a0, (a1, s0)))))
+  (a1, (a2, s1)) = stack
+  return (s1, (a2, (a1, (a1, (a2, s1)))))
+
+
+def swaack(stack):
+  """
+  ::
+
+    ([...1] -- [...0])
+
+  """
+  (s1, s0) = stack
+  return (s0, s1)
 
 
 def swap(stack):
@@ -313,22 +324,22 @@ def swons(stack):
   """
   ::
 
-    ([...0] a0 -- [a0 ...0])
+    ([...1] a1 -- [a1 ...1])
 
   """
-  (a0, (s0, s1)) = stack
-  return ((a0, s0), s1)
+  (a1, (s1, s2)) = stack
+  return ((a1, s1), s2)
 
 
 def third(stack):
   """
   ::
 
-    ([a0 a1 a2 ...0] -- a2)
+    ([a1 a2 a3 ...1] -- a3)
 
   """
-  ((a0, (a1, (a2, s0))), s1) = stack
-  return (a2, s1)
+  ((a1, (a2, (a3, s1))), s2) = stack
+  return (a3, s2)
 
 
 def tuck(stack):
@@ -353,13 +364,24 @@ def uncons(stack):
   return (s0, (a1, s23))
 
 
+def unit(stack):
+  """
+  ::
+
+    (a1 -- [a1 ])
+
+  """
+  (a1, s23) = stack
+  return ((a1, ()), s23)
+
+
 def unswons(stack):
   """
   ::
 
-    ([a0 ...0] -- [...0] a0)
+    ([a1 ...1] -- [...1] a1)
 
   """
-  ((a0, s0), s1) = stack
-  return (a0, (s0, s1))
+  ((a1, s1), s2) = stack
+  return (a1, (s1, s2))
 
diff --git a/joy/utils/polytypes.py b/joy/utils/polytypes.py
index d6df74d..beada70 100644
--- a/joy/utils/polytypes.py
+++ b/joy/utils/polytypes.py
@@ -256,8 +256,6 @@ def infer(e, F=ID):
 a0, a1, a2, a3, a4, a5, a6, a7, a8, a9 = A
 n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 = N
 s0, s1, s2, s3, s4, s5, s6, s7, s8, s9 = S
-f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = F = map(FloatJoyType, _R)
-i0, i1, i2, i3, i4, i5, i6, i7, i8, i9 = I = map(IntJoyType, _R)
 
 _R = range(1, 11)
 As = map(AnyStarJoyType, _R)
diff --git a/joy/utils/types.py b/joy/utils/types.py
index dc10c13..20f26a2 100644
--- a/joy/utils/types.py
+++ b/joy/utils/types.py
@@ -30,6 +30,7 @@ class AnyJoyType(object):
         return hash(repr(self))
 
 
+class BooleanJoyType(AnyJoyType): prefix = 'b'
 class NumberJoyType(AnyJoyType): prefix = 'n'
 class FloatJoyType(NumberJoyType): prefix = 'f'
 class IntJoyType(FloatJoyType): prefix = 'i'
@@ -41,12 +42,6 @@ class StackJoyType(AnyJoyType):
         return False
 
 
-_R = range(10)
-A = a0, a1, a2, a3, a4, a5, a6, a7, a8, a9 = map(AnyJoyType, _R)
-N = n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 = map(NumberJoyType, _R)
-S = s0, s1, s2, s3, s4, s5, s6, s7, s8, s9 = map(StackJoyType, _R)
-
-
 class JoyTypeError(Exception): pass
 
 
@@ -212,7 +207,7 @@ def _to_str(term, stack, switch):
         end = '' if term == () else '...'
         #end = '...'
     else:
-        end = '...%i' % term.number
+        end = '' if term == () else '...%i' % term.number
     a.append(end)
     return '[%s]' % ' '.join(a)
 
@@ -238,43 +233,62 @@ def __(*seq):
     return stack
 
 
+_R = range(10)
+A = a0, a1, a2, a3, a4, a5, a6, a7, a8, a9 = map(AnyJoyType, _R)
+B = b0, b1, b2, b3, b4, b5, b6, b7, b8, b9 = map(BooleanJoyType, _R)
+N = n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 = map(NumberJoyType, _R)
+S = s0, s1, s2, s3, s4, s5, s6, s7, s8, s9 = map(StackJoyType, _R)
+F = f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = F = map(FloatJoyType, _R)
+I = i0, i1, i2, i3, i4, i5, i6, i7, i8, i9 = I = map(IntJoyType, _R)
+
+
 def defs():
-    rolldown = __(a1, a2, a3), __(a2, a3, a1)
-    rollup = __(a1, a2, a3), __(a3, a1, a2)
-    pop = __(a1), __()
-    popop = __(a2, a1,), __()
-    popd = __(a2, a1,), __(a1)
-    popdd = __(a3, a2, a1,), __(a2, a1,)
-    popopd = __(a3, a2, a1,), __(a1)
-    popopdd = __(a4, a3, a2, a1,), __(a2, a1)
-    swap = __(a1, a2), __(a2, a1)
-    rest = __((a1, s0),), __(s0,)
-    rrest = C(rest, rest)
     cons = __(a1, s0), __((a1, s0),)
     ccons = C(cons, cons)
-    uncons = __((a1, s0),), __(a1, s0)
-    unswons = C(uncons, swap)
-    swons = C(swap, cons)
     dup = __(a1,), __(a1, a1)
     dupd = __(a2, a1), __(a2, a2, a1)
     dupdd = __(a3, a2, a1), __(a3, a3, a2, a1)
     first = __((a1, s1),), __(a1,)
-    second = C(rest, first)
-    third = C(rest, second)
-    fourth = C(rest, third)
-    tuck = __(a2, a1), __(a1, a2, a1)
     over = __(a2, a1), __(a2, a1, a2)
+    pop = __(a1), __()
+    popd = __(a2, a1,), __(a1)
+    popdd = __(a3, a2, a1,), __(a2, a1,)
+    popop = __(a2, a1,), __()
+    popopd = __(a3, a2, a1,), __(a1)
+    popopdd = __(a4, a3, a2, a1,), __(a2, a1)
+    rest = __((a1, s0),), __(s0,)
+    rolldown = __(a1, a2, a3), __(a2, a3, a1)
+    rollup = __(a1, a2, a3), __(a3, a1, a2)
+    rrest = C(rest, rest)
+    second = C(rest, first)
     stack = s0, (s0, s0)
     swaack = (s1, s0), (s0, s1)
+    swap = __(a1, a2), __(a2, a1)
+    swons = C(swap, cons)
+    third = C(rest, second)
+    tuck = __(a2, a1), __(a1, a2, a1)
+    uncons = __((a1, s0),), __(a1, s0)
+    unswons = C(uncons, swap)
     stuncons = C(stack, uncons)
     stununcons = C(stack, uncons, uncons)
-    first_two = C(uncons, uncons, pop)
+    unit = __(a1), __((a1, ()))
 
-    mul = __(n1, n2), __(n3,)
+    eq = ge = gt = le = lt = ne = __(n1, n2), __(b1)
+
+    and_ = __(b1, b2), __(b3)
+    bool_ = not_ = __(a1), __(b1)
+
+    
+
+    add = div = floordiv = modulus = mul = pow_ = sub = truediv = \
+          lshift = rshift = __(n1, n2), __(n3,)
     sqrt = C(dup, mul)
-    succ = pred = __(n1,), __(n2,)
+    succ = pred = neg = __(n1,), __(n2,)
     divmod_ = pm = __(n2, n1), __(n4, n3)
 
+    first_two = C(uncons, uncons, pop)
+    fourth = C(rest, third)
+
     _Tree_add_Ee = C(pop, swap, rolldown, rrest, ccons)
     _Tree_get_E = C(popop, second)
     _Tree_delete_clear_stuff = C(rollup, popop, rest)