Haskell コード片鑑賞：「再帰」編 ref: http://qiita.com/nobsun/items/6c2fa63f294dbd98d5cb

file0.txt

factorial        ::  Integer -> Integer
factorial (n+1)  =   (n+1) * factorial n
factorial 0      =   1

file1.txt

append ::  [a] -> [a] -> [a]
append (x:xs) ys  =  x : append xs ys
append []     ys  =  ys

file10.txt

gappend :: ([a] -> [a] -> [a]) -> ([a] -> [a] -> [a])
gappend _ []     ys = ys
gappend f (x:xs) ys = x : f xs ys

append' :: [a] -> [a] -> [a]
append' = fix gappend

file11.txt

gfibs    ::  [Integer] -> [Integer]
gfibs f  =   0:1:zipWith (+) f (tail f)

fibs'  ::  [Integer]
fibs'  =   fix gfibs

file12.txt

gpascal :: [[Integer]] -> [[Integer]]
gpascal f = [1]:[ zipWith (+) ([0]++p) (p++[0]) | p <- f ]

pascal'  ::  [[Integer]]
pascal' = fix gpascal

file13.txt

undefined'  ::  a
undefined'  =   fix id

file2.txt

fix    ::  (a -> a) -> a
fix f  =   f (fix f)

file3.txt

fibs :: [Integer]
fibs = 0:1:zipWith (+) fibs (tail fibs)

file4.txt

pascal :: [[Integer]]
pascal = [1]:[ zipWith (+) ([0]++p) (p++[0]) | p <- pascal ]

file5.txt

undefined :: a
undefined =  undefined

file6.txt

gfactorial :: (Integer -> Integer) -> (Integer -> Integer)
gfactorial _ 0     = 1
gfactorial f (n+1) = (n+1) * f n

factorial' :: Integer -> Integer
factorial' = fix gfactorial

file7.txt

    factorial' 0
==> {- factorial' の定義 -}
    fix gfactorial 0
==> {- fix の定義 -}
    (let x = gfactorial x in x) 0
==> {- x を展開 -}
    gfactorial x 0
==> {- gfactorial の定義 -}
    1

file8.txt

    factorial' 1
==> {- factorial' の定義 -}
    fix gfactorial 1
==> {- fix の定義 -}
    (let x = gfactorial x in x) 0
==> {- let -}
    let x = gfactorial x in x 0
==> {- x = gfactorial x -}
    let x = gfactorial x in gfactorial x 1
==> {- x = gfactorial x -}
    let x = gfactorial x in gfactorial (gfactorial x) 1
==> {- gfactorial の定義 -}
    let x = gfactorial x in 1 * (gfactorial x 0)
==> {- gfactorial の定義 -}
    let x = gfactorial x in 1 * 1
==> {- 算術演算 -}
    1

file9.txt

    factorial' 2
==> {- factorial' の定義 -}
    fix gfactorial 2
==> {- fix の定義 -}
    (let x = gfactorial x in x) 2
==> {- let -}
    let x = gfactorial x in x 2
==> {- x = gfactorial x -}
    let x = gfactroial x in gfactorial x 2
==> {- x = gfactorial x -}
    let x = gfactorial x in gfactorial (gfactorial x) 2
==> {- gfactorial の定義 -}
    let x = gfactorial x in 2 * (gfactorial x 1)
==> {- x = gfactorial x -}
    let x = gfactorial x in 2 * (gfactorial (gfactorial x) 1)
==> {- gfactorial の定義 -}
    let x = gfactorial x in 2 * (1 * gfactorial x 0)
==> {- gfactorial の定義 -}
    let x = gfactorial x in 2 * (1 * 1)
==> {- 算術演算 -}
    2