Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Functional programming, design and analysis of algorithms / 4 / a

Use the source's type Matrix a = [[a]]. For its nonempty rectangular matrices, the number of rows and the first row's length determine the dimensions:

dimensions :: Matrix a -> (Int,Int)
dimensions rows = (length rows, length (head rows))

addMat :: Num a => Matrix a -> Matrix a -> Matrix a
addMat a b
  | dimensions a /= dimensions b = error "addMat: incompatible sizes"
  | otherwise = [[x + y | (x,y) <- zip r s]
                         | (r,s) <- zip a b]

The outer list comprehension pairs corresponding rows; the inner one pairs corresponding entries. Checking both dimensions before using zip prevents silent truncation. Thus the result has entries $c_{ij} = a_{ij} + b_{ij}$ , the definition of matrix addition. The Num constraint supplies the addition operation.

ii

 0  0

Solution

 0  0

With dimensions as in part (i), the alternative definition is

addMat :: Num a => Matrix a -> Matrix a -> Matrix a
addMat a b
  | dimensions a /= dimensions b = error "addMat: incompatible sizes"
  | otherwise = zipWith (zipWith (+)) a b

The inner zipWith adds corresponding entries; the outer one applies that row operation to corresponding rows. This computes the same matrix addition, with the same rejection of unequal dimensions. Under the valid-input assumptions, either implementation takes