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diff --git a/Math/LinProg/Types.hs b/Math/LinProg/Types.hs
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+{-# LANGUAGE DeriveFunctor, FlexibleInstances, FlexibleContexts, UndecidableInstances #-}
+
+module Math.LinProg.Types (
+  LinExpr
+  ,var
+  ,vars
+  ,varTerms
+  ,getVar
+  ,split
+  ,LinProg
+  ,LinProg'(..)
+  ,obj
+  ,(<:)
+  ,(=:)
+  ,(>:)
+  ,eq
+  ,leq
+  ,geq
+) where
+
+import Data.Functor.Foldable
+import Control.Monad.Free
+import qualified Data.Map as M
+
+data LinExpr' t v a =
+  Lit t
+  | Var v
+  | Add a a
+  | Mul a a
+  | Negate a
+  deriving (Show, Eq, Functor)
+
+type LinExpr t v = Fix (LinExpr' t v)
+
+var = Fix . Var
+
+instance Num t => Num (LinExpr t v) where
+  a * b = Fix (Mul a b)
+  a + b = Fix (Add a b)
+  negate a = Fix (Negate a)
+  fromInteger a = Fix (Lit (fromInteger a))
+  abs = undefined
+  signum = undefined
+
+consts :: Num t => LinExpr t v -> t
+consts = cata consts' where
+  consts' (Negate a) = negate a
+  consts' (Lit a) = a
+  consts' (Var _) = 0
+  consts' (Add a b) = a + b
+  consts' (Mul a b) = a * b
+
+getVar :: (Num t, Eq v) => v -> LinExpr t v -> t
+getVar id x = cata getVar' x - consts x where
+  getVar' (Var x) | x == id = 1
+                  | otherwise = 0
+  getVar' (Lit a) = a
+  getVar' (Add a b) = a + b
+  getVar' (Mul a b) = a * b
+  getVar' (Negate a) = negate a
+
+vars :: LinExpr t v -> [v]
+vars = cata vars' where
+  vars' (Var x) = [x]
+  vars' (Add a b) = a ++ b
+  vars' (Mul a b) = a ++ b
+  vars' (Negate a) = a
+  vars' _ = []
+
+varTerms eq = go eq' where
+  go [t] = t
+  go (t:ts) = Fix (Add t (go ts))
+  go [] = Fix (Lit 0)
+
+  eq' = zipWith (\v w -> Fix (Mul (Fix (Lit w)) (Fix (Var v)))) vs ws
+  vs = vars eq
+  ws = map (`getVar` eq) vs
+
+split :: (Num t, Eq v) => LinExpr t v -> (LinExpr t v, t)
+split eq = (varTerms eq, consts eq)
+
+prettyPrint :: (Show t, Show v) => LinExpr t v -> String
+prettyPrint = cata prettyPrint' where
+  prettyPrint' (Lit a) = show a
+  prettyPrint' (Mul a b) = concat ["(", a, "×", b, ")"]
+  prettyPrint' (Add a b) = concat ["(", a, "+", b, ")"]
+  prettyPrint' (Var x) = show x
+
+-- Monad for linear programs
+
+data LinProg' t v a =
+  Objective (LinExpr t v) a
+  | EqConstraint (LinExpr t v) (LinExpr t v) a
+  | LeqConstraint (LinExpr t v) (LinExpr t v) a
+  deriving (Show, Eq, Functor)
+
+type LinProg t v = Free (LinProg' t v)
+
+obj a = liftF (Objective a ())
+eq a b = liftF (EqConstraint a b ())
+leq a b = liftF (LeqConstraint a b ())
+geq b a = liftF (LeqConstraint a b ())
+
+a =: b = eq a b
+a <: b = leq a b
+a >: b = geq a b