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(定義1) map f [] = []
(定義2) map f (x:xs) = f x : map f xs
(定義3) (f . g) x = f (g x)



map f (map g xs) = map (f . g) xs
map f (map g []) = map (f . g) []
map f (map g []) = map (f . g) []
map f [] = []




(定義1) map f [] = []
map f (map g []) = map (f . g) []
map f [] = []
[] = []




(定義1) map f [] = []
(仮定1) map f (map g xs) = map (f . g) xs




map f (map g (x:xs)) = map (f . g) (x:xs)
map f (map g (x:xs)) = map (f . g) (x:xs)
map f (g x : map g xs) = (f . g) x : map (f . g) xs




(定義2) map f (x:xs) = f x : map f xs
map f (map g (x:xs)) = map (f . g) (x:xs)
map f (g x : map g xs) = (f . g) x : map (f . g) xs
f (g x) : map f (map g xs) = (f . g) x : map (f . g) xs




(定義2) map f (x:xs) = f x : map f xs
map f (map g (x:xs)) = map (f . g) (x:xs)
map f (g x : map g xs) = (f . g) x : map (f . g) xs
f (g x) : map f (map g xs) = (f . g) x : map (f . g) xs
f (g x) : map f (map g xs) = f (g x) : map (f . g) xs




(定義3) (f . g) x = f (g x)
map f (map g (x:xs)) = map (f . g) (x:xs)
map f (g x : map g xs) = (f . g) x : map (f . g) xs
f (g x) : map f (map g xs) = (f . g) x : map (f . g) xs
f (g x) : map f (map g xs) = f (g x) : map (f . g) xs
f (g x) : map (f . g) xs = f (g x) : map (f . g) xs




(仮定1) map f (map g xs) = map (f . g) xs
http://www.paraiso-lang.org/ikmsm/

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プログラミングHaskell 13章 問題7

  • 1.
  • 2. (定義1) map f [] = [] (定義2) map f (x:xs) = f x : map f xs (定義3) (f . g) x = f (g x) map f (map g xs) = map (f . g) xs
  • 3. map f (map g []) = map (f . g) []
  • 4. map f (map g []) = map (f . g) [] map f [] = [] (定義1) map f [] = []
  • 5. map f (map g []) = map (f . g) [] map f [] = [] [] = [] (定義1) map f [] = []
  • 6. (仮定1) map f (map g xs) = map (f . g) xs map f (map g (x:xs)) = map (f . g) (x:xs)
  • 7. map f (map g (x:xs)) = map (f . g) (x:xs) map f (g x : map g xs) = (f . g) x : map (f . g) xs (定義2) map f (x:xs) = f x : map f xs
  • 8. map f (map g (x:xs)) = map (f . g) (x:xs) map f (g x : map g xs) = (f . g) x : map (f . g) xs f (g x) : map f (map g xs) = (f . g) x : map (f . g) xs (定義2) map f (x:xs) = f x : map f xs
  • 9. map f (map g (x:xs)) = map (f . g) (x:xs) map f (g x : map g xs) = (f . g) x : map (f . g) xs f (g x) : map f (map g xs) = (f . g) x : map (f . g) xs f (g x) : map f (map g xs) = f (g x) : map (f . g) xs (定義3) (f . g) x = f (g x)
  • 10. map f (map g (x:xs)) = map (f . g) (x:xs) map f (g x : map g xs) = (f . g) x : map (f . g) xs f (g x) : map f (map g xs) = (f . g) x : map (f . g) xs f (g x) : map f (map g xs) = f (g x) : map (f . g) xs f (g x) : map (f . g) xs = f (g x) : map (f . g) xs (仮定1) map f (map g xs) = map (f . g) xs