From ff83c063ad5cdb1bf9476678a010aa0cfb782a8f Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 14 Oct 2012 14:04:31 -0400
Subject: [PATCH] Add a Vector class and make TwoTuple (and several base types)
 instances of it.

---
 src/TwoTuple.hs |  9 +++++++++
 src/Vector.hs   | 24 ++++++++++++++++++++++++
 2 files changed, 33 insertions(+)
 create mode 100644 src/Vector.hs

diff --git a/src/TwoTuple.hs b/src/TwoTuple.hs
index 8493114..daeb6e4 100644
--- a/src/TwoTuple.hs
+++ b/src/TwoTuple.hs
@@ -4,13 +4,22 @@
 module TwoTuple
 where
 
+import Vector
+
+
 data TwoTuple a = TwoTuple a a
   deriving (Eq, Show)
 
 instance Functor TwoTuple where
   f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)
 
+instance (RealFloat a) => Vector (TwoTuple a) where
+  -- The standard Euclidean 2-norm. We need RealFloat for the square
+  -- root.
+  norm (TwoTuple x1 y1) = fromRational $ toRational (sqrt(x1^2 + y1^2))
 
+-- | It's not correct to use Num here, but I really don't want to have
+--   to define my own addition and subtraction.
 instance Num a => Num (TwoTuple a) where
   -- Standard componentwise addition.
   (TwoTuple x1 y1) + (TwoTuple x2 y2) =
diff --git a/src/Vector.hs b/src/Vector.hs
new file mode 100644
index 0000000..e608a50
--- /dev/null
+++ b/src/Vector.hs
@@ -0,0 +1,24 @@
+{-# LANGUAGE FlexibleInstances #-}
+
+-- | The 'Vector' class represents elements of a normed vector
+--   space. We define instances for all common numeric types.
+module Vector
+where
+
+import Data.Number.BigFloat
+
+class Vector a where
+  norm :: RealFrac b => a -> b
+
+-- Define instances for common numeric types.
+instance Vector Integer where
+  norm = fromInteger
+
+instance Vector Rational where
+  norm = fromRational
+
+instance Epsilon e => Vector (BigFloat e) where
+  norm = fromRational . toRational
+
+instance Vector Double where
+  norm = fromRational . toRational
-- 
2.43.2