diff --git a/Makefile b/Makefile
new file mode 100644
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,24 @@
+# Haskell/Cabal Makefile
+# Requires GNU Make
+# The all target creates a default configuration if need be.
+
+PACKAGE = agum
+CONFIG	= dist/setup-config
+SETUP	= runhaskell Setup.hs
+
+all:	$(CONFIG)
+	$(SETUP) build
+
+Makefile:
+	@echo make $@
+
+$(PACKAGE).cabal:
+	@echo make $@
+
+$(CONFIG):	$(PACKAGE).cabal
+	$(SETUP) configure --ghc --user --prefix="${HOME}"
+
+%:	force
+	$(SETUP) $@
+
+.PHONY:	all force
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/agum.cabal b/agum.cabal
new file mode 100644
--- /dev/null
+++ b/agum.cabal
@@ -0,0 +1,34 @@
+Name:			agum
+Version:		1.0
+Maintainer:		ramsdell@mitre.org
+Cabal-Version:		>= 1.2
+License:		GPL
+License-File:		license.txt
+Synopsis:		Unification and Matching in an Abelian Group
+Description:            The unification problem is given the problem
+			statement t =? t\', find a most general
+			substitution s such that s(t) = s(t\') modulo
+			the axioms of an Abelian group.  The matching
+			problem is to find a most general substitution
+			s such that s(t) = t\' modulo the axioms.
+			Substitition s is more general than s\' if
+			there is a substitition s\" such that s\' =
+			s\" o s.
+Category:		Algebra.AbelianGroup
+Build-Type:		Simple
+Extra-Source-Files:	readme.txt Makefile
+
+Library
+  Build-Depends:	base <= 4.1.0.0, containers
+  Exposed-Modules:	Algebra.AbelianGroup.UnificationMatching
+  Hs-Source-Dirs:	src
+  GHC-Options:
+    -Wall -fno-warn-name-shadowing -fwarn-unused-imports
+
+Executable agum
+  Main-Is:		Algebra/AbelianGroup/Main.hs
+  Build-Depends:	base <= 4.1.0.0, containers
+  Other-Modules:	Algebra.AbelianGroup.UnificationMatching
+  Hs-Source-Dirs:	src
+  GHC-Options:
+    -Wall -fno-warn-name-shadowing -fwarn-unused-imports
diff --git a/license.txt b/license.txt
new file mode 100644
--- /dev/null
+++ b/license.txt
@@ -0,0 +1,675 @@
+
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+		       Version 3, 29 June 2007
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diff --git a/readme.txt b/readme.txt
new file mode 100644
--- /dev/null
+++ b/readme.txt
@@ -0,0 +1,21 @@
+This package contains a library for unification and matching in
+Abelian groups and a program that exercises the library.
+
+$ agum
+Abelian group unification and matching -- :? for help
+agum> 2x+y=3z
+Problem:   2x + y = 3z
+Unifier:   [x : g0,y : -2g0 + 3g2,z : g2]
+Matcher:   [x : g0,y : -2g0 + 3z]
+
+agum> 2x=x+y
+Problem:   2x = x + y
+Unifier:   [x : g1,y : g1]
+Matcher:   no solution
+
+agum> 64x-41y=a
+Problem:   64x - 41y = a
+Unifier:   [x : g0,y : g1,a : 64g0 - 41g1]
+Matcher:   [x : -16a - 41g6,y : -25]
+
+agum> :quit
diff --git a/src/Algebra/AbelianGroup/Main.hs b/src/Algebra/AbelianGroup/Main.hs
new file mode 100644
--- /dev/null
+++ b/src/Algebra/AbelianGroup/Main.hs
@@ -0,0 +1,111 @@
+-- A top-level loop for unification and matching in Abelian groups
+--
+-- Copyright (C) 2009 John D. Ramsdell
+--
+-- This program is free software: you can redistribute it and/or modify
+-- it under the terms of the GNU General Public License as published by
+-- the Free Software Foundation, either version 3 of the License, or
+-- (at your option) any later version.
+
+-- This program is distributed in the hope that it will be useful,
+-- but WITHOUT ANY WARRANTY; without even the implied warranty of
+-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+-- GNU General Public License for more details.
+
+-- You should have received a copy of the GNU General Public License
+-- along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+module Main (main, test) where
+
+import System.IO (isEOF, hFlush, stdout)
+import Algebra.AbelianGroup.UnificationMatching
+
+-- Test Routine
+
+-- Given an equation, display a unifier and a matcher.
+test :: String -> IO ()
+test prob =
+    case readM prob of
+      Err err -> putStrLn err
+      Ans (Equation (t0, t1)) ->
+          do
+            putStr "Problem:   "
+            print $ Equation (t0, t1)
+            subst <- unify $ Equation (t0, t1)
+            putStr "Unifier:   "
+            print subst
+            putStr "Matcher:   "
+            case match $ Equation (t0, t1) of
+              Err err -> putStrLn err
+              Ans subst -> print subst
+            putStrLn ""
+
+readM :: (Read a, Monad m) => String -> m a
+readM s =
+    case [ x | (x, t) <- reads s, ("", "") <- lex t ] of
+      [x] -> return x
+      [] -> fail "no parse"
+      _ -> fail "ambiguous parse"
+
+data AnsErr a
+    = Ans a
+    | Err String
+
+instance Monad AnsErr where
+    (Ans x) >>= k = k x
+    (Err s) >>= _ = Err s
+    return        = Ans
+    fail          = Err
+
+-- Main loop
+
+main :: IO ()
+main =
+    do
+      putStrLn "Abelian group unification and matching -- :? for help"
+      loop
+
+loop :: IO ()
+loop =
+    do
+      putStr "agum> "
+      hFlush stdout
+      done <- isEOF
+      case done of
+        True ->
+            do
+              putStrLn ""
+              return ()
+        False ->
+            do
+              line <- getLine
+              case () of
+                _ | line == ":?" || line == ":help" ->
+                      do
+                        help
+                        loop
+                  | line == ":quit" ->
+                      return ()
+                  | otherwise ->
+                      do
+                        test line
+                        loop
+
+help :: IO ()
+help =
+    mapM_ putStrLn mesg
+
+mesg :: [String]
+mesg =
+    [ "Pose a question as an equation such as",
+      "    2x + y = 3z, or",
+      "    2x = x + y, or",
+      "    64x - 41y = a.",
+      "The agum programs shows the result of unification and matching.",
+      "",
+      "The unification problem is given two terms t and t', find a most",
+      "general unifier s such that s(t) = s(t').  The matching problem",
+      "for terms t and t' is to find a most general matcher s such that",
+      "s(t) = t'.",
+      "",
+      ":quit quits the program, :? and :help print this message."]
diff --git a/src/Algebra/AbelianGroup/UnificationMatching.hs b/src/Algebra/AbelianGroup/UnificationMatching.hs
new file mode 100644
--- /dev/null
+++ b/src/Algebra/AbelianGroup/UnificationMatching.hs
@@ -0,0 +1,498 @@
+-- Unification and matching in Abelian groups
+--
+-- Copyright (C) 2009 John D. Ramsdell
+--
+-- This program is free software: you can redistribute it and/or modify
+-- it under the terms of the GNU General Public License as published by
+-- the Free Software Foundation, either version 3 of the License, or
+-- (at your option) any later version.
+
+-- This program is distributed in the hope that it will be useful,
+-- but WITHOUT ANY WARRANTY; without even the implied warranty of
+-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+-- GNU General Public License for more details.
+
+-- You should have received a copy of the GNU General Public License
+-- along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+-- |
+-- Module      : Algebra.AbelianGroup.UnificationMatching
+-- Copyright   : (C) 2009 John D. Ramsdell
+-- License     : GPL
+--
+-- This module provides unification and matching in an Abelian group.
+--
+-- In this module, an Abelian group is a free algebra over a signature
+-- with three function symbols:
+--
+--     * the binary symbol +, the group operator,
+--
+--     * a constant 0, the identity element, and
+--
+--     * the unary symbol -, the inverse operator.
+--
+-- The algebra is generated by a set of variables.  Syntactically, a
+-- variable is an identifer such as x and y (see 'isVar').
+--
+-- The axioms associated with the algebra are:
+--
+-- [Communtativity] x + y = y + x
+--
+-- [Associativity] (x + y) + z = x + (y + z)
+--
+-- [Group Identity] x + 0 = x
+--
+-- [Cancellation] x + -x = 0
+--
+-- A substitution maps variables to terms.  A substitution s is
+-- extended to a term as follows.
+--
+--      * s(0) = 0
+--
+--      * s(-t) = -s(t)
+--
+--      * s(t + t\') = s(t) + s(t\')
+--
+-- The unification problem is given the problem statement t =? t\',
+-- find a most general substitution s such that s(t) = s(t\') modulo
+-- the axioms of the algebra.  The matching problem is to find a most
+-- general substitution s such that s(t) = t\' modulo the axioms.
+-- Substitition s is more general than s\' if there is a substitition
+-- s\" such that s\' = s\" o s.
+
+module Algebra.AbelianGroup.UnificationMatching
+    (
+     -- * Terms
+     Term, ide, isVar, var, mul, add, assocs,
+     -- * Unification and Matching
+     Equation(..), Maplet(..), unify, match) where
+
+import Data.Char (isSpace, isAlpha, isAlphaNum, isDigit)
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+-- Chapter 8, Section 5 of the Handbook of Automated Reasoning by
+-- Franz Baader and Wayne Snyder describes unification and matching in
+-- communtative/monoidal theories.  This module refines the described
+-- algorithms for the special case of Abelian groups.
+
+-- In this module, an Abelian group is a free algebra over a signature
+-- with three function symbols:
+--
+-- * the binary symbol +, the group operator,
+-- * a constant 0, the identity element, and
+-- * the unary symbol -, the inverse operator.
+--
+-- The algebra is generated by a set of variables.  Syntactically, a
+-- variable is an identifer such as x and y.
+
+-- The axioms associated with the algebra are:
+--
+-- * x + y = y + x                 Commutativity
+-- * (x + y) + z = x + (y + z)     Associativity
+-- * x + 0 = x                     Group identity
+-- * x + -x = 0                    Cancellation
+
+-- A substitution maps variables to terms.  A substitution s is
+-- extended to a term as follows.
+--
+--     s(0) = 0
+--     s(-t) = -s(t)
+--     s(t + t') = s(t) + s(t')
+
+-- The unification problem is given the problem statement t =? t',
+-- find a most general substitution s such that s(t) = s(t') modulo
+-- the axioms of the algebra.  The matching problem is to find a most
+-- general substitution s such that s(t) = t' modulo the axioms.
+-- Substitition s is more general than s' if there is a substitition
+-- s" such that s' = s" o s.
+
+-- A term is represented by the group identity, or as the sum of
+-- factors.  A factor is the product of a non-zero integer coefficient
+-- and a variable.  In this representation, no variable occurs twice.
+-- Thus a term is represented by a finite map from variables to
+-- non-negative integers.
+
+-- | A term in an Abelian group is represented by the group identity
+-- element, or as the sum of factors.  A factor is the product of a
+-- non-zero integer coefficient and a variable.  No variable occurs
+-- twice in a term.  For the show and read methods, zero is the group
+-- identity, the plus sign is the group operation, and the minus sign
+-- is the group inverse.
+newtype Term = Term (Map String Int)
+
+-- Constructors
+
+-- | 'ide' represents the identity element (zero).
+ide :: Term
+ide = Term Map.empty
+
+-- | A variable is an alphabetic Unicode character followed by a
+-- sequence of alphabetic or numeric digit Unicode characters.  The
+-- show method for a term works correctly when variables satisfy
+-- the 'isVar' predicate.
+isVar :: String -> Bool
+isVar [] = False
+isVar (c:s) = isAlpha c && all isAlphaNum s
+
+-- | Return a term that consists of a single variable.
+var :: String -> Term
+var x = Term $ Map.singleton x 1
+
+-- | Multiply every coefficient in a term by an integer.
+mul :: Int -> Term -> Term
+mul 0 (Term _) = ide
+mul 1 t = t
+mul n (Term t) =
+    Term $ Map.map (* n) t
+
+-- Invert a term by negating its coefficients.  Same as multiplying
+-- a term by -1.
+neg :: Term -> Term
+neg (Term t) =
+    Term $ Map.map negate t
+
+-- | Add two terms.
+add :: Term -> Term -> Term
+add (Term t) (Term t') =
+    Term $ Map.foldWithKey f t' t -- Fold over the mappings in t
+    where
+      f x c t =                 -- Alter the mapping of
+          Map.alter (g c) x t   -- variable x in t
+      g c Nothing =             -- Variable x not currently mapped
+          Just c                -- so add a mapping
+      g c (Just c')             -- Variable x maps to c'
+          | c + c' == 0 = Nothing     -- Delete the mapping
+          | otherwise = Just $ c + c' -- Adjust the mapping
+
+-- | Return all variable-coefficient pairs in the term in ascending
+-- variable order.
+assocs :: Term -> [(String, Int)]
+assocs (Term t) = Map.assocs t
+
+-- | Convert a list of variable-coefficient pairs into a term.
+term :: [(String, Int)] -> Term
+term assoc =
+    foldr f ide assoc
+    where
+      f (x, c) t = add t $ mul c $ var x
+
+instance Eq Term where
+    Term t0 == Term t1 = t0 == t1
+
+-- Unification and Matching
+
+-- | An equation is a pair of terms.  For the show and read methods,
+-- the two terms are separated by an equal sign.
+newtype Equation = Equation (Term, Term) deriving Eq
+
+-- | A maplet maps one variable into a term.  For the show and read
+-- methods, the variable and the term are separated by a colon.  A
+-- list of maplets represents a substitution.
+newtype Maplet = Maplet (String, Term) deriving Eq
+
+-- | Given 'Equation' (t0, t1), return a most general substitution s
+-- such that s(t0) = s(t1) modulo the equational axioms of an Abelian
+-- group.
+unify :: Monad m => Equation -> m [Maplet]
+unify (Equation (t0, t1)) =
+    match $ Equation (add t0 (neg t1), ide)
+
+-- Matching in Abelian groups is performed by finding integer
+-- solutions to linear equations, and then using the solutions to
+-- construct a most general unifier.
+-- | Given 'Equation' (t0, t1), return a most general substitution s
+-- such that s(t0) = t1 modulo the equational axioms of an Abelian
+-- group.
+match :: Monad m => Equation -> m [Maplet]
+match (Equation (t0, t1)) =
+    case (assocs t0, assocs t1) of
+      ([], []) -> return []
+      ([], _) -> fail "no solution"
+      (t0, t1) ->
+          do
+            subst <- intLinEq (map snd t0) (map snd t1)
+            return $ mgu (map fst t0) (map fst t1) subst
+
+-- Construct a most general unifier from a solution to a linear
+-- equation.  The function adds the variables back into terms, and
+-- generates fresh variables as needed.
+mgu :: [String] -> [String] -> Subst -> [Maplet]
+mgu vars syms subst =
+    foldr f [] (zip vars [0..])
+    where
+      f (x, n) maplets =
+          case lookup n subst of
+            Just (factors, consts) ->
+                Maplet (x, g factors consts) : maplets
+            Nothing ->
+                Maplet (x, var $ genSyms !! n) : maplets
+      g factors consts =
+          term (zip genSyms factors ++ zip syms consts)
+      genSyms = genSymsAvoiding vars syms
+
+-- Generated variables start with this character.
+genChar :: Char
+genChar = 'g'
+
+-- Generated symbols are the gen start char followed by a number.
+genSym :: Int -> String
+genSym i = genChar : show i
+
+-- Produce a stream of generated identifiers avoiding what's in vars and syms.
+genSymsAvoiding :: [String] -> [String] -> [String]
+genSymsAvoiding vars syms =
+    genSymStream 0
+    where
+      seen = filter genStr (syms ++ vars)
+      genStr (c:_) = c == genChar
+      genStr _ = False
+      genSymStream n
+          | elem (genSym n) seen = genSymStream (n + 1)
+          | otherwise = genSym n : genSymStream (n + 1)
+
+-- So why solve linear equations?  Consider the matching problem
+--
+--     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] =?
+--         d[0]*a[0] + d[1]*a[1] + ... + d[m-1]*a[m-1]
+--
+-- with n variables and m constants.  We seek a most general unifier s
+-- such that
+--
+--     s(c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1]) =
+--         d[0]*a[0] + d[1]*a[1] + ... + d[m-1]*a[m-1]
+--
+-- which is the same as
+--
+--     c[0]*s(x[0]) + c[1]*s(x[1]) + ... + c[n-1]*s(x[n-1]) =
+--         d[0]*a[0] + d[1]*a[1] + ... + d[m-1]*a[m-1]
+--
+-- Notice that the number of occurrences of constant a[0] in s(x[0])
+-- plus s(x[1]) ... s(x[n-1]) must equal d[0].  Thus the mappings of
+-- the unifier that involve constant a[0] respect integer solutions of
+-- the following linear equation.
+--
+--     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = d[0]
+--
+-- To compute a most general unifier, a most general integer solution
+-- to a linear equation must be found.
+
+-- Integer Solutions of Linear Inhomogeneous Equations
+
+type LinEq = ([Int], [Int])
+
+-- A linear equation with integer coefficients is represented as a
+-- pair of lists of integers, the coefficients and the constants.  If
+-- there are no constants, the linear equation represented by (c, [])
+-- is the homogeneous equation:
+--
+--     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = 0
+--
+-- where n is the length of c.  Otherwise, (c, d) represents a
+-- sequence of inhomogeneous linear equations with the same
+-- left-hand-side:
+--
+--     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = d[0]
+--     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = d[1]
+--     ...
+--     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = d[m-1]
+--
+-- where m is the length of d.
+
+type Subst = [(Int, LinEq)]
+
+-- A solution is a partial map from variables to terms, and a term is
+-- a pair of lists of integers, the variable part of the term followed
+-- by the constant part.  The variable part may specify variables not
+-- in the input.  For example, the solution of
+--
+--     64x = 41y + 1
+--
+-- is x = -41z - 16 and y = -64z - 25.  The computed solution is read
+-- off the list returned as an answer.
+--
+-- intLinEq [64,-41] [1] =
+--     [(0,([0,0,0,0,0,0,-41],[-16])),
+--      (1,([0,0,0,0,0,0,-64],[-25]))]
+
+-- Find integer solutions to linear equations
+intLinEq :: Monad m => [Int] -> [Int] -> m Subst
+intLinEq coefficients constants =
+    intLinEqLoop (length coefficients) (coefficients, constants) []
+
+-- The algorithm used to find solutions is described in Vol. 2 of The
+-- Art of Computer Programming / Seminumerical Alorithms, 2nd Ed.,
+-- 1981, by Donald E. Knuth, pg. 327.
+
+-- On input, n is the number of variables in the original problem, c
+-- is the coefficients, d is the constants, and subst is a list of
+-- eliminated variables.
+intLinEqLoop :: Monad m => Int -> LinEq -> Subst -> m Subst
+intLinEqLoop n (c, d) subst =
+    -- Find the smallest non-zero coefficient in absolute value
+    let (i, ci) = smallest c in
+    case () of
+      _ | ci < 0 -> intLinEqLoop n (invert c, invert d) subst
+      --  Ensure the smallest coefficient is positive
+        | ci == 0 -> fail "bad problem"
+      --  Lack of non-zero coefficients is an error
+        | ci == 1 ->
+      --  A general solution of the following form has been found:
+      --    x[i] = sum[j] -c'[j]*x[j] + d[k] for all k
+      --  where c' is c with c'[i] = 0.
+            return $ eliminate n (i, (invert (zero i c), d)) subst
+        | divisible ci c ->
+      --  If all the coefficients are divisible by c[i], a solution is
+      --  immediate if all the constants are divisible by c[i],
+      --  otherwise there is no solution.
+            if divisible ci d then
+                let c' = divide ci c
+                    d' = divide ci d in
+                return $ eliminate n (i, (invert (zero i c'), d')) subst
+            else
+                fail "no solution"
+        | otherwise ->
+      --  Eliminate x[i] in favor of freshly created variable x[n],
+      --  where n is the length of c.
+      --    x[n] = sum[j] (c[j] div c[i] * x[j])
+      --  The new equation to be solved is:
+      --    c[i]*x[n] + sum[j] (c[j] mod c[i])*x[j] = d[k] for all k
+            intLinEqLoop n (map (\x -> mod x ci) c ++ [ci], d) subst'
+            where
+              subst' = eliminate n (i, (invert c' ++ [1], [])) subst
+              c' = divide ci (zero i c)
+
+-- Find the smallest non-zero coefficient in absolute value
+smallest :: [Int] -> (Int, Int)
+smallest xs =
+    foldl f (-1, 0) (zip [0..] xs)
+    where
+      f (i, n) (j, x)
+        | n == 0 = (j, x)
+        | x == 0 || abs n <= abs x = (i, n)
+        | otherwise = (j, x)
+
+invert :: [Int] -> [Int]
+invert t = map negate t
+
+-- Zero the ith position in a list
+zero :: Int -> [Int] -> [Int]
+zero _ [] = []
+zero 0 (_:xs) = 0 : xs
+zero i (x:xs) = x : zero (i - 1) xs
+
+-- Eliminate a variable from the existing substitution.  If the
+-- variable is in the original problem, add it to the substitution.
+eliminate :: Int -> (Int, LinEq) -> Subst -> Subst
+eliminate n m@(i, (c, d)) subst =
+    if i < n then
+        m : map f subst
+    else
+        map f subst
+    where
+      f m'@(i', (c', d')) =     -- Eliminate i in c' if it occurs in c'
+          case get i c' of
+            0 -> m'             -- i is not in c'
+            ci -> (i', (addmul ci (zero i c') c, addmul ci d' d))
+      -- Find ith coefficient
+      get _ [] = 0
+      get 0 (x:_) = x
+      get i (_:xs) = get (i - 1) xs
+      -- addnum n xs ys sums xs and ys after multiplying ys by n
+      addmul 1 [] ys = ys
+      addmul n [] ys = map (* n) ys
+      addmul _ xs [] = xs
+      addmul n (x:xs) (y:ys) = (x + n * y) : addmul n xs ys
+
+divisible :: Int -> [Int] -> Bool
+divisible small t =
+    all (\x -> mod x small == 0) t
+
+divide :: Int -> [Int] -> [Int]
+divide small t =
+    map (\x -> div x small) t
+
+-- Input and Output
+
+instance Show Term where
+    showsPrec _ t =
+        case assocs t of
+          [] -> showString "0"
+          (t:ts) -> showFactor t . showl ts
+        where
+          showFactor (x, 1) = showString x
+          showFactor (x, -1) = showChar '-' . showString x
+          showFactor (x, c) = shows c . showString x
+          showl [] = id
+          showl ((s,n):ts)
+              | n < 0 =
+                  showString " - " . showFactor (s, negate n) . showl ts
+          showl (t:ts) = showString " + " . showFactor t . showl ts
+
+instance Read Term where
+    readsPrec _ s0 =
+        [ (t1, s2)       | (t0, s1) <- readSummand s0,
+                           (t1, s2) <- readRest t0 s1 ]
+        where
+          readPrimary s0 =
+              [ (t0, s1) | (x, s1) <- scan s0, isVarToken x,
+                           let t0 = var x ] ++
+              [ (t0, s1) | ("0", s1) <- scan s0,
+                           let t0 = ide ] ++
+              [ (t0, s3) | ("(", s1) <- scan s0,
+                           (t0, s2) <- reads s1,
+                           (")", s3) <- scan s2 ]
+          readFactor s0 =
+              [ (t0, s1) | (t0, s1) <- readPrimary s0 ] ++
+              [ (t1, s2) | (n, s1) <- scan s0, isNumToken n,
+                           (t0, s2) <- readPrimary s1,
+                           let t1 = mul (read n) t0 ]
+          readSummand s0 =
+              [ (t0, s1) | (t0, s1) <- readFactor s0 ] ++
+              [ (t1, s2) | ("-", s1) <- scan s0,
+                           (t0, s2) <- readFactor s1,
+                           let t1 = neg t0 ]
+          readRest t0 s0 =
+              [ (t2, s3) | ("+", s1) <- scan s0,
+                           (t1, s2) <- readSummand s1,
+                           (t2, s3) <- readRest (add t0 t1) s2 ] ++
+              [ (t2, s3) | ("-", s1) <- scan s0,
+                           (t1, s2) <- readFactor s1,
+                           (t2, s3) <- readRest (add t0 (neg t1)) s2 ] ++
+              [ (t0, s0) | (s, _) <- scan s0, s /= "+" && s /= "-" ]
+
+isNumToken :: String -> Bool
+isNumToken (c:_) = isDigit c
+isNumToken _ = False
+
+isVarToken :: String -> Bool
+isVarToken (c:_) = isAlpha c
+isVarToken _ = False
+
+scan :: ReadS String
+scan "" = [("", "")]
+scan (c:s)
+    | isSpace c = scan s
+    | isAlpha c = [ (c:part, t) | (part,t) <- [span isAlphaNum s] ]
+    | isDigit c = [ (c:part, t) | (part,t) <- [span isDigit s] ]
+    | otherwise = [([c], s)]
+
+instance Show Equation where
+    showsPrec _ (Equation (t0, t1)) =
+        shows t0 . showString " = " . shows t1
+
+instance Read Equation where
+    readsPrec _ s0 =
+        [ (Equation (t0, t1), s3) | (t0, s1) <- reads s0,
+                                    ("=", s2) <- scan s1,
+                                    (t1, s3) <- reads s2 ]
+
+instance Show Maplet where
+    showsPrec _ (Maplet (x, t)) =
+        showString x . showString " : " . shows t
+
+instance Read Maplet where
+    readsPrec _ s0 =
+        [ (Maplet (x, t), s3) | (x, s1) <- scan s0, isVarToken x,
+                                (":", s2) <- scan s1,
+                                (t, s3) <- reads s2 ]