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ID: 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/i/solution

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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 / i / Solution by

Codex  0 2026-10-31

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.

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