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diff --git a/lambdacube-ir.haskell/src/LambdaCube/Linear.hs b/lambdacube-ir.haskell/src/LambdaCube/Linear.hs
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+++ b/lambdacube-ir.haskell/src/LambdaCube/Linear.hs
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+{-# LANGUAGE DeriveFunctor, OverloadedStrings #-}
+module LambdaCube.Linear where
+
+import Data.Int
+import Data.Word
+import Data.Map
+
+import Data.Text
+import Data.Aeson
+import Control.Monad
+
+data V2 a = V2 !a !a deriving (Eq,Ord,Show,Read,Functor)
+data V3 a = V3 !a !a !a deriving (Eq,Ord,Show,Read,Functor)
+data V4 a = V4 !a !a !a !a deriving (Eq,Ord,Show,Read,Functor)
+
+-- matrices are stored in column major order
+type M22F = V2 V2F
+type M23F = V3 V2F
+type M24F = V4 V2F
+type M32F = V2 V3F
+type M33F = V3 V3F
+type M34F = V4 V3F
+type M42F = V2 V4F
+type M43F = V3 V4F
+type M44F = V4 V4F
+
+type V2F = V2 Float
+type V3F = V3 Float
+type V4F = V4 Float
+type V2I = V2 Int32
+type V3I = V3 Int32
+type V4I = V4 Int32
+type V2U = V2 Word32
+type V3U = V3 Word32
+type V4U = V4 Word32
+type V2B = V2 Bool
+type V3B = V3 Bool
+type V4B = V4 Bool
+
+instance ToJSON a => ToJSON (V2 a) where
+  toJSON (V2 x y) = object ["x" .= x, "y" .= y]
+
+instance ToJSON a => ToJSON (V3 a) where
+  toJSON (V3 x y z) = object ["x" .= x, "y" .= y, "z" .= z]
+
+instance ToJSON a => ToJSON (V4 a) where
+  toJSON (V4 x y z w) = object ["x" .= x, "y" .= y, "z" .= z, "w" .= w]
+
+instance FromJSON a => FromJSON (V2 a) where
+  parseJSON (Object obj) = V2 <$> obj .: "x" <*> obj .: "y"
+  parseJSON _ = mzero
+
+instance FromJSON a => FromJSON (V3 a) where
+  parseJSON (Object obj) = V3 <$> obj .: "x" <*> obj .: "y" <*> obj .: "z"
+  parseJSON _ = mzero
+
+instance FromJSON a => FromJSON (V4 a) where
+  parseJSON (Object obj) = V4 <$> obj .: "x" <*> obj .: "y" <*> obj .: "z" <*> obj .: "w"
+  parseJSON _ = mzero
+