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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/functional-programming-design-and-analysis-of-algorithms/3/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Functional programming, design and analysis of algorithms / 3 / b / Solution by

Codex  0 2026-10-31

Normalize each word once by applying toLower to its characters. Maintain an association list whose keys are distinct normalized words and whose values are their frequencies:

import Data.Char (toLower)

type TextWord = String
type Text = [TextWord]
type Frequency = Integer
type Entry = (TextWord, Frequency)

count :: Text -> [Entry]
count = foldl addWord [] . map (map toLower)
  where
    -- Increment the unique matching key, or append a new key with count one.
    addWord :: [Entry] -> TextWord -> [Entry]
    addWord [] w = [(w, 1)]
    addWord ((v, n):rest) w
      | w == v    = (v, n + 1) : rest
      | otherwise = (v, n) : addWord rest w

After any input prefix, each normalized word seen so far occurs exactly once as a key, with its number of occurrences as value. This loop invariant holds initially for the empty association list. A step either increments the unique existing entry or introduces exactly one new entry, so mathematical induction proves

lookup w (count input) = Just (number of normalized occurrences of w)

(1)

for every word that occurs. In particular, Baa and baa contribute to the same key baa; the three frequency-two keys in the source example are baa, yes and sir.

The association list preserves first-occurrence order, although the specification allows any order here. For

t

input words and

d

distinct normalized words, it performs

O (t d)

key comparisons in the worst case. Character normalization costs the total input character count, and a string comparison can inspect multiple characters. Characterwise toLower supplies the intended case-insensitive comparison convention for the example; full Unicode case folding can require a different normalization policy.

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