diff --git a/Data/Poset.hs b/Data/Poset.hs
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+++ b/Data/Poset.hs
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+{-
+ - Copyright (C) 2009 Nick Bowler.
+ -
+ - License BSD2:  2-clause BSD license.  See LICENSE for full terms.
+ - This is free software: you are free to change and redistribute it.
+ - There is NO WARRANTY, to the extent permitted by law.
+ -}
+
+-- | Partially ordered data types.  The standard 'Prelude.Ord' class is for
+-- total orders and therefore not suitable for floating point.  However, we can
+-- still define meaningful 'max' and 'sort' functions for these types.
+--
+-- We define a 'PosetOrd' class which extends 'Prelude.Ord' by adding
+-- a 'NComp' constructor representing that two elements are
+-- incomparable.
+module Data.Poset (
+    Poset(..), 
+    PosetOrd(..),
+    module Data.Poset
+) where
+
+import Data.Poset.Instances
+import Data.Poset.Internal
+
+import Data.Function
+import Data.Monoid
+
+instance Poset a => Poset (Maybe a) where
+    Just x  `leq` Just y = x `leq` y
+    Nothing `leq` _      = True
+    _       `leq` _      = False
+
+instance Poset a => Poset [a] where
+    posetCmp = (mconcat .) . zipWith posetCmp
+
+-- | Apply a function to values before comparing.
+comparing :: Poset b => (a -> b) -> a -> a -> PosetOrd
+comparing = on posetCmp
diff --git a/Data/Poset/Instances.hs b/Data/Poset/Instances.hs
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+++ b/Data/Poset/Instances.hs
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+{-
+ - Copyright (C) 2009-2010 Nick Bowler.
+ -
+ - License BSD2:  2-clause BSD license.  See LICENSE for full terms.
+ - This is free software: you are free to change and redistribute it.
+ - There is NO WARRANTY, to the extent permitted by law.
+ -}
+
+-- | 'Poset' for instances of 'Prelude.Ord'
+{-# LANGUAGE CPP #-}
+module Data.Poset.Instances where
+
+import qualified Data.Poset.Internal as Poset
+import Data.Poset.Internal (Poset, partialOrder)
+
+import Data.Ratio
+import Data.List
+import Data.Word
+import Data.Int
+
+#define POSET_ORD_INSTANCE(ctx, v) instance ctx Poset (v) where { \
+    posetCmp = (partialOrder .) . compare; \
+    (<==>)  = const $ const True; \
+    (</=>)  = const $ const False }
+
+POSET_ORD_INSTANCE(, Bool)
+POSET_ORD_INSTANCE(, Char)
+POSET_ORD_INSTANCE(, Int)
+POSET_ORD_INSTANCE(, Int8)
+POSET_ORD_INSTANCE(, Int16)
+POSET_ORD_INSTANCE(, Int32)
+POSET_ORD_INSTANCE(, Int64)
+POSET_ORD_INSTANCE(, Word)
+POSET_ORD_INSTANCE(, Word8)
+POSET_ORD_INSTANCE(, Word16)
+POSET_ORD_INSTANCE(, Word32)
+POSET_ORD_INSTANCE(, Word64)
+POSET_ORD_INSTANCE(, Integer)
+
+POSET_ORD_INSTANCE(Integral a =>, Ratio a)
diff --git a/Data/Poset/Internal.hs b/Data/Poset/Internal.hs
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+++ b/Data/Poset/Internal.hs
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+{-
+ - Copyright (C) 2009-2010 Nick Bowler.
+ -
+ - License BSD2:  2-clause BSD license.  See LICENSE for full terms.
+ - This is free software: you are free to change and redistribute it.
+ - There is NO WARRANTY, to the extent permitted by law.
+ -}
+
+module Data.Poset.Internal where
+
+import Data.Monoid
+
+-- | Are two elements of the underlying comparabale or not; if they
+-- are, then Ordering tell the relation between them.
+data PosetOrd = Comp Ordering | NComp
+    deriving (Eq, Show, Read)
+
+instance Bounded PosetOrd where
+    minBound = Comp $ minBound 
+    maxBound = NComp
+
+instance Enum PosetOrd where
+    toEnum n | n >= 0 && n < 3 = Comp $ toEnum n
+             | n == 3 = NComp
+             | otherwise = error "Data.Poset.toEnum: bad argument"
+
+    fromEnum (Comp c) = fromEnum c
+    fromEnum NComp = 3
+
+-- Lexicographic ordering.
+
+instance Monoid PosetOrd where
+    mempty = Comp EQ
+    mappend (Comp EQ) x = x
+    mappend NComp _ = NComp
+    mappend (Comp LT) _ = Comp LT
+    mappend (Comp GT) _ = Comp GT
+
+-- | Internal-use function to convert the ordinary Ordering to ours.
+partialOrder :: Ordering -> PosetOrd
+partialOrder = Comp
+
+-- | Class for partially ordered data types.  Instances should satisfy the
+-- following laws for all values a, b and c:
+--
+-- * @a `leq` a@.
+--
+-- * @a `leq` b@ and @b `leq` a@ implies @a == b@.
+--
+-- * @a `leq` b@ and @b `leq` c@ implies @a `leq` c@.
+--
+-- But note that the floating point instances don't satisfy the first rule.
+--
+-- Minimal definition: posetCmp or leq.
+class Eq a => Poset a where
+    posetCmp :: a -> a -> PosetOrd
+    -- | Is comparable to.
+    (<==>)  :: a -> a -> Bool
+    -- | Is not comparable to.
+    (</=>)  :: a -> a -> Bool
+    -- | Less than or equal.
+    leq :: a -> a -> Bool
+    -- | Greater than or equal.
+    geq :: a -> a -> Bool
+    -- | Strict less than.
+    lt :: a -> a -> Bool
+    -- | Strict greater than.
+    gt :: a -> a -> Bool
+
+    a `posetCmp` b
+        | a == b = Comp EQ
+        | a `leq` b = Comp LT
+        | b `leq` a = Comp GT
+        | otherwise = NComp
+
+    a <==> b = a `posetCmp` b /= NComp
+    a </=> b = a `posetCmp` b == NComp
+
+    a `lt` b = a `posetCmp` b == Comp LT
+    a `gt` b = a `posetCmp` b == Comp GT
+
+    a `leq` b | a <==> b = a `posetCmp` b /= Comp GT
+              | otherwise = False
+    a `geq` b | a <==> b = a `posetCmp` b /= Comp LT
+              | otherwise = False
+
+infixl 4 <==>,</=>
diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
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+Copyright (c) 2009 Nick Bowler
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice,
+   this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+   notice, this list of conditions and the following disclaimer in the
+   documentation and/or other materials provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.
diff --git a/Setup.lhs b/Setup.lhs
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--- /dev/null
+++ b/Setup.lhs
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+#!/usr/bin/env runhaskell
+
+> import Distribution.Simple
+> main = defaultMain
diff --git a/ordered.cabal b/ordered.cabal
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--- /dev/null
+++ b/ordered.cabal
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+Name:               ordered
+Version:            0.1
+License:            OtherLicense
+License-File:       LICENSE
+Cabal-Version:      >= 1.6
+Author:             Nick Bowler, Miguel Pagano
+Maintainer:         miguel.pagano@gmail.org
+Stability:          experimental
+Category:           Mathematics
+Build-Type:         Simple
+Synopsis:           A definition of Posets.
+Description:
+	A library defining the notion of Poset.
+
+
+Source-repository head
+  type:     git
+  location: http://github.com/miguelpagano/ordered
+
+Library
+    Build-Depends: base >= 4 && < 5
+    Include-Dirs: .
+    Exposed-Modules:
+        Data.Poset
+    Other-Modules:
+        Data.Poset.Internal,
+        Data.Poset.Instances