Thinking Functionally with Haskell勉強メモ: 第１章問題
Exercise A
右辺と左辺の等価性の「証明」
sum . map double = double .sum
分配法則 (distributative property)でc*a + c*b = c * (a + b)
sum . map sum = sum . concat
結合法則 (associative property)で(a+b)+(c+d) = (a+b+c+d)
sum . sort = sort
交換法則 (commutative property)でa+d+c+b = a+b+c+d
Exercise D
words . map toLowerが文字列を小文字化してから単語に分割する処理。
map (map toLower) . wordsが文字列を単語に分割してから、各単語を小文字化する処理。
Exercise E
0, [], idが和、リスト結合、関数合成の単位元(identity element)
Exercise F
整数nと単語リストwordListを受け取り、wordListの中のn文字の単語のアナグラムを列挙する文字列を出力する関数anagramsを大まかに定義する。
トップレベルの処理としては
anagrams :: Int -> [Word] -> String anagrams n = combineEntries . map showAnagramEntries . takeWordsOfLength n
個々の関数の型は：
takeWordsOfLength :: Int -> [Word] -> [Word] showAnagramEntries :: Word -> String combineEntries :: [String] -> String
最初の関数を少し詰めると：
takeWordsOfLength n = filter (isWordOfLength n) isWordOfLength :: Int -> Word -> Bool
という感じか。
Exercise G
(0<n<10)人の男が芝を刈りに行く歌を出力する関数songを定義する。
song :: Int -> String song 0 = "" song 1 = verse 1 song n = song (n-1) ++ "\n" ++ verse n verse n = line1 n ++ line2 n ++ line3 n ++ line4 n verse :: Int -> String line1 :: Int -> String line2 :: Int -> String line3 :: Int -> String line4 :: Int -> String line1 = capitalize . line1a line1a 0 = "" line1a 1 = "one man went to mow\n" line1a n = wordify n ++ " men went to mow\n" line2 n = "Went to mow a meadow\n" line3 = capitalize . line3a line3a 0 = "" line3a 1 = "one man and his dog\n" line3a n = wordify n ++ " men, " ++ line3a (n-1) line4 = line2 capitalize :: String -> String capitalize (c:cs) = toUpper c : cs wordify :: Int -> String wordify n = ["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine"] !! n
こんな感じか？
putStrLn (song 5)の出力：
One man went to mow Went to mow a meadow One man and his dog Went to mow a meadow Two men went to mow Went to mow a meadow Two men, one man and his dog Went to mow a meadow Three men went to mow Went to mow a meadow Three men, two men, one man and his dog Went to mow a meadow Four men went to mow Went to mow a meadow Four men, three men, two men, one man and his dog Went to mow a meadow Five men went to mow Went to mow a meadow Five men, four men, three men, two men, one man and his dog Went to mow a meadow
