diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,4 +1,4 @@
-Copyright (c) 2015-2016, Rudy Matela
+Copyright (c) 2015-2017, Rudy Matela
 
 All rights reserved.
 
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -134,7 +134,7 @@
 For an introduction to property-based testing
 and a step-by-step guide to LeanCheck, see the
 [tutorial on property-based testing with LeanCheck]
-(`doc/tutorial.md` in the source repository).
+\(`doc/tutorial.md` in the source repository).
 
 [LeanCheck's Haddock documentation]: https://hackage.haskell.org/package/leancheck/docs/Test-LeanCheck.html
 [tutorial on property-based testing with LeanCheck]: https://github.com/rudymatela/leancheck/blob/master/doc/tutorial.md
diff --git a/TODO.md b/TODO.md
--- a/TODO.md
+++ b/TODO.md
@@ -29,7 +29,13 @@
 * on data-invariant.md, write missing section;
 
 
-v0.6.1
+v0.6.2
+------
+
+* add copyright notices on modules using Haddock markup
+
+
+v0.6.3
 ------
 
 * implement stub `Test.LeanCheck.Function.*` modules;
diff --git a/leancheck.cabal b/leancheck.cabal
--- a/leancheck.cabal
+++ b/leancheck.cabal
@@ -11,7 +11,7 @@
 -- this cabal file too complicated.  -- Rudy
 
 name:                leancheck
-version:             0.6.0
+version:             0.6.1
 synopsis:            Cholesterol-free property-based testing
 description:
   LeanCheck is a simple enumerative property-based testing library.
@@ -50,7 +50,7 @@
 source-repository this
   type:            git
   location:        https://github.com/rudymatela/leancheck
-  tag:             v0.6.0
+  tag:             v0.6.1
 
 library
   exposed-modules: Test.LeanCheck
@@ -67,6 +67,7 @@
                  , Test.LeanCheck.Function
                  , Test.LeanCheck.Function.ListsOfPairs
                  , Test.LeanCheck.Function.CoListable
+                 , Test.LeanCheck.Function.Eq
                  , Test.LeanCheck.Function.Periodic
                  , Test.LeanCheck.Function.Show
                  , Test.LeanCheck.Function.ShowFunction
diff --git a/src/Test/LeanCheck/Core.hs b/src/Test/LeanCheck/Core.hs
--- a/src/Test/LeanCheck/Core.hs
+++ b/src/Test/LeanCheck/Core.hs
@@ -33,7 +33,7 @@
   , counterExamples
   , witness
   , witnesses
-  , Testable
+  , Testable(..)
 
   , results
 
diff --git a/src/Test/LeanCheck/Error.hs b/src/Test/LeanCheck/Error.hs
--- a/src/Test/LeanCheck/Error.hs
+++ b/src/Test/LeanCheck/Error.hs
@@ -15,6 +15,7 @@
   , witnesses
   , results
 
+  , fromError
   , errorToNothing
   , errorToFalse
   , errorToTrue
@@ -47,7 +48,7 @@
 
 import Control.Monad (liftM)
 import System.IO.Unsafe (unsafePerformIO)
-import Data.Maybe (listToMaybe)
+import Data.Maybe (listToMaybe, fromMaybe)
 import Control.Exception ( Exception
                          , SomeException
                          , ArithException
@@ -89,15 +90,13 @@
                                              return Nothing
 
 errorToFalse :: Bool -> Bool
-errorToFalse p = case errorToNothing p of
-                   Just p' -> p
-                   Nothing -> False
+errorToFalse = fromError False
 
 errorToTrue :: Bool -> Bool
-errorToTrue p = case errorToNothing p of
-                  Just p' -> p
-                  Nothing -> True
+errorToTrue = fromError True
 
+fromError :: a -> a -> a
+fromError x = fromMaybe x . errorToNothing
 
 holds,fails,exists :: Testable a => Int -> a -> Bool
 holds n = errorToFalse . C.holds n
diff --git a/src/Test/LeanCheck/Function/CoListable.hs b/src/Test/LeanCheck/Function/CoListable.hs
--- a/src/Test/LeanCheck/Function/CoListable.hs
+++ b/src/Test/LeanCheck/Function/CoListable.hs
@@ -8,6 +8,7 @@
 
 
 import Test.LeanCheck
+import Test.LeanCheck.Tiers
 import Data.Maybe (fromMaybe)
 
 
@@ -17,51 +18,59 @@
 
 
 class CoListable a where
-  coListing :: [[b]] -> [[a -> b]]
+  cotiers :: [[b]] -> [[a -> b]]
 
 
 instance CoListable () where
-  coListing rs = mapT (\r  () -> r) rs
+  cotiers rs = mapT (\r  () -> r) rs
 
 
 instance CoListable Bool where
-  coListing rs = productWith (\r1 r2  b -> if b then r1 else r2) rs rs
+  cotiers rs = productWith (\r1 r2  b -> if b then r1 else r2) rs rs
 
 
 instance CoListable a => CoListable (Maybe a) where
-  coListing rs = productWith (\z f  m -> case m of Nothing -> z
-                                                   Just x  -> f x) rs (coListing rs)
+  cotiers rs = productWith (\z f  m -> case m of
+                                         Nothing -> z
+                                         Just x  -> f x) rs (cotiers rs)
 
 
 instance (CoListable a, CoListable b) => CoListable (Either a b) where
-  coListing rs = productWith (\f g  e -> case e of Left x  -> f x
-                                                   Right x -> g x) (coListing rs) (coListing rs)
+  cotiers rs = productWith (\f g  e -> case e of
+                                         Left x  -> f x
+                                         Right x -> g x) (cotiers rs) (cotiers rs)
 
 
 instance (CoListable a) => CoListable [a] where
-  coListing rss = mapT const rss
-             \+:/ productWith (\y f  xs -> case xs of []      -> y
-                                                      (x:xs') -> f x xs') rss (coListing (coListing rss))
+  cotiers rss = mapT const rss
+           \+:/ productWith
+                  (\y f  xs -> case xs of
+                                 []      -> y
+                                 (x:xs') -> f x xs')
+                  rss
+                  (cotiers (cotiers rss))
 
 
+
+
 instance CoListable Int where
-  coListing rss = mapT const rss
-             \+:/ product3With (\f g z  i -> if i > 0 then f (i-1)
-                                        else if i < 0 then g (i+1)
-                                             else z) (coListing rss) (coListing rss) rss
+  cotiers rss = mapT const rss
+           \+:/ productWith
+                  (\f g  i -> if i >= 0 then f (i-1) else g (i+1))
+                  (cotiers rss) (cotiers rss)
 
 
 alts0 :: [[a]] -> [[a]]
 alts0 = id
 
 alts1 :: CoListable a => [[b]] -> [[a->b]]
-alts1 bs = coListing bs
+alts1 bs = cotiers bs
 
 alts2 :: (CoListable a, CoListable b) => [[c]] -> [[a->b->c]]
-alts2 cs = coListing (coListing cs)
+alts2 cs = cotiers (cotiers cs)
 
 alts3 :: (CoListable a, CoListable b, CoListable c) => [[d]] -> [[a->b->c->d]]
-alts3 ds = coListing (coListing (coListing ds))
+alts3 ds = cotiers (cotiers (cotiers ds))
 
-fListing :: (CoListable a, Listable b) => [[a->b]]
-fListing = coListing tiers
+ftiers :: (CoListable a, Listable b) => [[a->b]]
+ftiers = cotiers tiers
diff --git a/src/Test/LeanCheck/Function/Eq.hs b/src/Test/LeanCheck/Function/Eq.hs
new file mode 100644
--- /dev/null
+++ b/src/Test/LeanCheck/Function/Eq.hs
@@ -0,0 +1,7 @@
+-- A toy Eq instance for Functions.
+module Test.LeanCheck.Function.Eq () where
+
+import Test.LeanCheck.Core
+
+instance (Listable a, Eq b) => Eq (a -> b) where
+  f == g  =  and [f x == g x | x <- take 60 list]
diff --git a/src/Test/LeanCheck/Function/ShowFunction.hs b/src/Test/LeanCheck/Function/ShowFunction.hs
--- a/src/Test/LeanCheck/Function/ShowFunction.hs
+++ b/src/Test/LeanCheck/Function/ShowFunction.hs
@@ -27,6 +27,7 @@
 
 import Test.LeanCheck.Core
 import Test.LeanCheck.Error (errorToNothing)
+import Test.LeanCheck.Utils.Types
 import Data.List
 import Data.Maybe
 
@@ -63,15 +64,19 @@
 tBindingsShow :: Show a => a -> [[Binding]]
 tBindingsShow x = [[([],errorToNothing $ show x)]]
 
-instance ShowFunction ()   where tBindings = tBindingsShow
-instance ShowFunction Bool where tBindings = tBindingsShow
-instance ShowFunction Int  where tBindings = tBindingsShow
-instance ShowFunction Char where tBindings = tBindingsShow
+instance ShowFunction ()       where tBindings = tBindingsShow
+instance ShowFunction Bool     where tBindings = tBindingsShow
+instance ShowFunction Int      where tBindings = tBindingsShow
+instance ShowFunction Integer  where tBindings = tBindingsShow
+instance ShowFunction Char     where tBindings = tBindingsShow
+instance ShowFunction Float    where tBindings = tBindingsShow
+instance ShowFunction Double   where tBindings = tBindingsShow
+instance ShowFunction Ordering where tBindings = tBindingsShow
 instance Show a => ShowFunction [a]       where tBindings = tBindingsShow
 instance Show a => ShowFunction (Maybe a) where tBindings = tBindingsShow
+instance (Show a, Show b) => ShowFunction (Either a b) where tBindings = tBindingsShow
 instance (Show a, Show b) => ShowFunction (a,b) where tBindings = tBindingsShow
 
-
 -- instance for functional value type --
 instance (Show a, Listable a, ShowFunction b) => ShowFunction (a->b) where
   tBindings f = concatMapT tBindingsFor tiers
@@ -158,7 +163,7 @@
                 then "undefined"
                 else casePat ++ sep ++ cases
 
--- instances for further tuples --
+-- instances for further tuple arities --
 instance (Show a, Show b, Show c)
       => ShowFunction (a,b,c) where tBindings = tBindingsShow
 instance (Show a, Show b, Show c, Show d)
@@ -171,3 +176,21 @@
       => ShowFunction (a,b,c,d,e,f,g) where tBindings = tBindingsShow
 instance (Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h)
       => ShowFunction (a,b,c,d,e,f,g,h) where tBindings = tBindingsShow
+
+-- instance for types from Test.LeanCheck.Utils.Types
+instance ShowFunction Nat   where tBindings = tBindingsShow
+instance ShowFunction Nat1  where tBindings = tBindingsShow
+instance ShowFunction Nat2  where tBindings = tBindingsShow
+instance ShowFunction Nat3  where tBindings = tBindingsShow
+instance ShowFunction Nat4  where tBindings = tBindingsShow
+instance ShowFunction Nat5  where tBindings = tBindingsShow
+instance ShowFunction Nat6  where tBindings = tBindingsShow
+instance ShowFunction Nat7  where tBindings = tBindingsShow
+instance ShowFunction Int1  where tBindings = tBindingsShow
+instance ShowFunction Int2  where tBindings = tBindingsShow
+instance ShowFunction Int3  where tBindings = tBindingsShow
+instance ShowFunction Int4  where tBindings = tBindingsShow
+instance ShowFunction Word1 where tBindings = tBindingsShow
+instance ShowFunction Word2 where tBindings = tBindingsShow
+instance ShowFunction Word3 where tBindings = tBindingsShow
+instance ShowFunction Word4 where tBindings = tBindingsShow
diff --git a/src/Test/LeanCheck/Tiers.hs b/src/Test/LeanCheck/Tiers.hs
--- a/src/Test/LeanCheck/Tiers.hs
+++ b/src/Test/LeanCheck/Tiers.hs
@@ -14,6 +14,10 @@
   , bagCons
   , noDupListCons
 
+  , maybeCons0
+  , maybeCons1
+  , maybeCons2
+
   -- * Products of tiers
   , product3
   , product3With
@@ -37,6 +41,8 @@
 
   , deleteT
   , normalizeT
+  , catMaybesT
+  , mapMaybeT
 
   -- * Tiers of choices
   , choices
@@ -87,8 +93,18 @@
 -- | Given a constructor that takes a list with no duplicate elements,
 --   return tiers of applications of this constructor.
 noDupListCons :: Listable a => ([a] -> b) -> [[b]]
-noDupListCons f = mapT f (noDupListsOf tiers)
+noDupListCons = (`mapT` noDupListsOf tiers)
 
+maybeCons0 :: Maybe b -> [[b]]
+maybeCons0 Nothing  = []
+maybeCons0 (Just x) = [[x]]
+
+maybeCons1 :: Listable a => (a -> Maybe b) -> [[b]]
+maybeCons1 f = mapMaybeT f tiers `addWeight` 1
+
+maybeCons2 :: (Listable a, Listable b) => (a -> b -> Maybe c) -> [[c]]
+maybeCons2 f = mapMaybeT (uncurry f) tiers `addWeight` 1
+
 -- | Like '><', but over 3 lists of tiers.
 product3 :: [[a]] -> [[b]]-> [[c]] -> [[(a,b,c)]]
 product3 = product3With (\x y z -> (x,y,z))
@@ -221,6 +237,13 @@
 normalizeT [] = []
 normalizeT [[]] = []
 normalizeT (xs:xss) = xs:normalizeT xss
+
+-- | Concatenate tiers of maybes
+catMaybesT :: [[Maybe a]] -> [[a]]
+catMaybesT = map catMaybes
+
+mapMaybeT :: (a -> Maybe b) -> [[a]] -> [[b]]
+mapMaybeT f = catMaybesT . mapT f
 
 -- | Takes as argument tiers of element values;
 --   returns tiers of lists with no repeated elements.
diff --git a/src/Test/LeanCheck/Utils/Types.hs b/src/Test/LeanCheck/Utils/Types.hs
--- a/src/Test/LeanCheck/Utils/Types.hs
+++ b/src/Test/LeanCheck/Utils/Types.hs
@@ -18,22 +18,22 @@
   -- > read "2"          = -2 :: Int2
   -- > abs minBound      = minBound
   -- > negate n          = 2^N - n :: WordN
-    Int1
-  , Int2
-  , Int3
-  , Int4
-  , Word1
-  , Word2
-  , Word3
-  , Word4
-  , Nat
-  , Nat1
-  , Nat2
-  , Nat3
-  , Nat4
-  , Nat5
-  , Nat6
-  , Nat7
+    Int1 (..)
+  , Int2 (..)
+  , Int3 (..)
+  , Int4 (..)
+  , Word1 (..)
+  , Word2 (..)
+  , Word3 (..)
+  , Word4 (..)
+  , Nat (..)
+  , Nat1 (..)
+  , Nat2 (..)
+  , Nat3 (..)
+  , Nat4 (..)
+  , Nat5 (..)
+  , Nat6 (..)
+  , Nat7 (..)
 
   -- * Aliases to word types (deprecated)
   , UInt1