Simple Matrix addition in Haskell.

MatrixDemo.hs

{-# LANGUAGE TemplateHaskell #-}
module MatrixDemo where

import Control.Lens

-- | Represents a matrix with the contents stored in row major order.
--   Note that we get equality, ability to read a Matrix from a stream
--   as well as write it to a stream for free by deriving (Eq,Read,Show).
data Matrix = Matrix { _numRows        :: Int
                     , _numColumns     :: Int
                     , _matrixContents :: [[Int]]
                     } deriving (Eq,Read,Show)
makeLenses ''Matrix

-- | Construct a Matrix from a list of rows.
toMatrix :: [[Int]] -> Matrix
toMatrix m = Matrix { _numRows = length m, _numColumns = length (head m), _matrixContents = m }

-- | Takes two matricies 'a' and 'b' and returns a new matrix obtained by taking
--   the matrix a and applying the function addCorresponding entries to it's contents.
--   The function addCorrespondingEntries simply overlays the two list of lists and
--   sums the corresponding elements.
add :: Matrix -> Matrix -> Matrix
add a b = a & over matrixContents addCorrespondingEntries
  where addCorrespondingEntries = (zipWith (zipWith (+)) (b^.matrixContents))

main = do
  let a = toMatrix [[1,2,3],[4,5,6]]
  let b = toMatrix [[1,1,1],[2,2,2]]
  print $ add a b