diff --git a/COPYING b/COPYING
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--- /dev/null
+++ b/COPYING
@@ -0,0 +1,25 @@
+Copyright (c) 2010 Conal Elliott
+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.
+3. The names of the authors may not be used to endorse or promote products
+   derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``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 AUTHORS 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
@@ -0,0 +1,3 @@
+#!/usr/bin/env runhaskell
+> import Distribution.Simple
+> main = defaultMain
diff --git a/src/Data/TotalMap.hs b/src/Data/TotalMap.hs
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--- /dev/null
+++ b/src/Data/TotalMap.hs
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+{-# LANGUAGE DeriveFunctor, GeneralizedNewtypeDeriving, TypeOperators #-}
+{-# OPTIONS_GHC -Wall #-}
+----------------------------------------------------------------------
+-- |
+-- Module      :  Data.TotalMap
+-- Copyright   :  (c) Conal Elliott 2012
+-- License     :  BSD3
+-- 
+-- Maintainer  :  conal@conal.net
+-- Stability   :  experimental
+-- 
+-- Finitely represented /total/ maps. Represented by as a partial map and
+-- a default value. Has Applicative and Monad instances (unlike "Data.Map").
+----------------------------------------------------------------------
+
+module Data.TotalMap (TMap,(!),tabulate,trim) where
+
+import Data.Monoid (Monoid(..))
+import Control.Applicative (Applicative(..),(<$>))
+import Data.Maybe (fromMaybe)
+
+import Data.Map (Map)
+import qualified Data.Map as M
+
+import Data.Set (Set)
+import qualified Data.Set as S
+
+-- | Total map
+data TMap k v = TMap v (Map k v) deriving Functor
+
+-- | Sample a total map. Semantic function.
+(!) :: Ord k => TMap k v -> k -> v
+TMap dflt m ! k = fromMaybe dflt (M.lookup k m)
+
+-- | Construct a total map, given a default value, a set of keys, and a
+-- function to sample over that set. You might want to 'trim' the result.
+tabulate :: Eq k => v -> Set k -> (k -> v) -> TMap k v
+tabulate dflt keys f = TMap dflt (f <$> idMap keys)
+
+-- | Optimize a 'TMap', weeding out any explicit default values.
+-- A semantic no-op, i.e., @(!) . trim == (!)@.
+trim :: (Ord k, Eq v) => TMap k v -> TMap k v
+trim (TMap dflt m) = TMap dflt (M.filter (/= dflt) m)
+
+{-
+-- Variation that weeds out values equal to the default. Requires Eq.
+tabulate' :: (Ord k, Eq v) => v -> Set k -> (k -> v) -> TMap k v
+tabulate' = (fmap.fmap.fmap) trim tabulate
+-}
+
+instance Ord k => Applicative (TMap k) where
+  pure v = TMap v mempty
+  fs@(TMap df mf) <*> xs@(TMap dx mx) = 
+    tabulate (df dx)
+             (M.keysSet mf `mappend` M.keysSet mx)
+             ((!) fs <*> (!) xs)
+
+-- Note: I'd like to 'trim' the tabulate result in <*>, but doing so would
+-- require the Eq constraint on values, which breaks Applicative.
+
+instance Ord k => Monad (TMap k) where
+  return  = pure
+  m >>= f = joinT (f <$> m)
+
+joinT :: Ord k => TMap k (TMap k v) -> TMap k v
+joinT (TMap (TMap dd dm) mtm) = 
+  TMap dd (M.mapWithKey (flip (!)) mtm `M.union` dm)
+
+{-
+joinT' :: (Ord k,Eq v) => TMap k (TMap k v) -> TMap k v
+joinT' = trim . joinT
+-}
+
+{-
+joinT (tt@(TMap (TMap (dd,dm),mtm))) = 
+  tabulate dd 
+           undefined
+           -- (join ((!) ((!) <$> tt)))
+           ((!) tt >>= (!))
+-}
+
+{-
+
+-- tt :: TMap k (TMap k v)
+-- fmap (!) tt :: TMap k (k -> v)
+-- (!) (fmap (!) tt) :: k -> (k -> v)
+
+tt :: TMap k (TMap k v)
+dd :: v
+dm :: Map k v
+mtm :: Map k (TMap k v)
+
+mapWithKey (flip (!)) mtm :: Map k v
+mapWithKey (flip (!)) mtm `union` dm :: Map k v
+
+TMap (dd,M.mapWithKey (flip (!)) mtm `M.union` dm) :: TMap k v
+
+spec:
+
+-}
+
+{--------------------------------------------------------------------
+    Misc
+--------------------------------------------------------------------}
+
+idMap :: Eq k => Set k -> Map k k
+idMap = M.fromAscList . map (\ k -> (k,k)) . S.toAscList
+
+-- or ... map (join (,)) ...
diff --git a/total-map.cabal b/total-map.cabal
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--- /dev/null
+++ b/total-map.cabal
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+Name:                total-map
+Version:             0.0.0
+Cabal-Version:       >= 1.6
+Synopsis:            Finitely represented /total/ maps
+Category:            
+Description:
+  Finitely represented /total/ maps. Represented by as a partial map and a default value.
+  Has Applicative and Monad instances (unlike Data.Map).
+Author:              Conal Elliott
+Maintainer:          conal@conal.net
+Copyright:           (c) 2012 by Conal Elliott
+License:             BSD3
+License-File:        COPYING
+Stability:           experimental
+build-type:          Simple
+
+-- Wait until Cabal 1.6 is more wide-spread and then add the following
+-- in place of the Package-Url field and bump Cabal-Version to >= 1.6.
+
+Source-Repository head
+    type:         git
+    location:     http://github.com/conal/total-map
+
+Library
+  hs-Source-Dirs:      src
+  Extensions:
+  Build-Depends:       base<5, containers
+  Exposed-Modules:     
+                       Data.TotalMap