diff --git a/TODO.md b/TODO.md
index ecfd427..8869e5e 100644
--- a/TODO.md
+++ b/TODO.md
@@ -1,9 +1,6 @@
 TODO for leancheck.py
 =====================
 
-* add documentation to module and to all functions
-	- reorder functions if necessary
-
 * simplify code
 
 later
diff --git a/src/leancheck.py b/src/leancheck.py
index 201160f..8e9dfb4 100644
--- a/src/leancheck.py
+++ b/src/leancheck.py
@@ -236,6 +236,22 @@ class Enumerator:
     which can be registered using the `Enumerator.register()` method.
 
     This class supports computing sums and products of enumerations:
+
+    >>> print(Enumerator[int] + Enumerator[bool])
+    [0, False, True, 1, 2, 3, ...]
+
+    Use `*` to take the product of two enumerations:
+
+    >>> print(Enumerator[int] * Enumerator[bool])
+    [(0, False), (0, True), (1, False), (1, True), (2, False), (2, True), ...]
+    """
+
+    tiers: typing.Callable[[], typing.Generator]
+    """
+    Generate tiers of values.
+
+    >>> list(Enumerator[bool].tiers())
+    [[False, True]]
     """
 
     def __init__(self, tiers):
@@ -308,6 +324,9 @@ def __add__(self, other):
 
         >>> print(Enumerator[int] + Enumerator[bool])
         [0, False, True, 1, 2, 3, ...]
+
+        >>> Enumerator[int] + Enumerator[bool]
+        Enumerator(lambda: (xs for xs in [[0, False, True], [1], [2], [3], [4], [5], ...]))
         """
         return Enumerator(lambda: _zippend(self.tiers(), other.tiers()))
 
@@ -317,6 +336,9 @@ def __mul__(self, other):
 
         >>> print(Enumerator[int] * Enumerator[bool])
         [(0, False), (0, True), (1, False), (1, True), (2, False), (2, True), ...]
+
+        >>> Enumerator[int] * Enumerator[bool]
+        Enumerator(lambda: (xs for xs in [[(0, False), (0, True)], [(1, False), (1, True)], [(2, False), (2, True)], [(3, False), (3, True)], [(4, False), (4, True)], [(5, False), (5, True)], ...]))
         """
         return Enumerator(lambda: _pproduct(self.tiers(), other.tiers()))
 
@@ -335,6 +357,12 @@ def __str__(self):
         return "[" + ', '.join(xs) + "]"
 
     def map(self, f):
+        """
+        Applies a function to all values in the enumeration.
+
+        >>> Enumerator[int].map(lambda x: x*2)
+        Enumerator(lambda: (xs for xs in [[0], [2], [4], [6], [8], [10], ...]))
+        """
         return Enumerator(lambda: _mmap(f, self.tiers()))
 
     @classmethod
@@ -462,7 +490,7 @@ def _intercalate(generator1, generator2):
 
 
 def _zippend(*iiterables):
-    return itertools.starmap(itertools.chain,itertools.zip_longest(*iiterables, fillvalue=[]))
+    return map(list,itertools.starmap(itertools.chain,itertools.zip_longest(*iiterables, fillvalue=[])))
 
 
 def _pproduct(xss, yss, with_f=None):