September 2017 Update

Task/Y-combinator/Haskell/y-combinator-1.hs

@@ -1,15 +1,27 @@
-newtype Mu a = Roll { unroll :: Mu a -> a }
+newtype Mu a = Roll
+  { unroll :: Mu a -> a }
 
 fix :: (a -> a) -> a
-fix = \f -> (\x -> f (unroll x x)) $ Roll (\x -> f (unroll x x))
+fix = g <*> (Roll . g)
+  where
+    g = (. (>>= id) unroll)
 
 fac :: Integer -> Integer
-fac = fix $ \f n -> if (n <= 0) then 1 else n * f (n-1)
+fac =
+  fix $
+  \f n ->
+     (if n <= 0
+        then 1
+        else n * f (n - 1))
 
 fibs :: [Integer]
-fibs = fix $ \fbs -> 0 : 1 : fix zipP fbs (tail fbs)
-  where zipP f (x:xs) (y:ys) = x+y : f xs ys
+fibs =
+  fix $ (0 :) . (1 :) . (fix (\f (x:xs) (y:ys) -> x + y : f xs ys) <*> tail)
 
-main = do
-  print $ map fac [1 .. 20]
-  print $ take 20 fibs
+main :: IO ()
+main =
+  mapM_
+    print
+    [ map fac [1 .. 20]
+    , take 20 fibs
+    ]

Task/Y-combinator/Haskell/y-combinator-2.hs

@@ -1,28 +1,36 @@
 fix :: (a -> a) -> a
-fix f = f (fix f)        -- _not_ the {fix f = x where x = f x}
+fix f = f (fix f) -- _not_ the {fix f = x where x = f x}
 
 fac :: Integer -> Integer
-fac_ f n | n <= 0    = 1
-         | otherwise = n * f (n-1)
-fac = fix fac_           -- fac_ (fac_ . fac_ . fac_ . fac_ . ...)
+fac_ f n
+  | n <= 0 = 1
+  | otherwise = n * f (n - 1)
+
+fac = fix fac_ -- fac_ (fac_ . fac_ . fac_ . fac_ . ...)
 
 -- a simple but wasteful exponential time definition:
 fib :: Integer -> Integer
 fib_ f 0 = 0
 fib_ f 1 = 1
-fib_ f n = f (n-1) + f (n-2)
+fib_ f n = f (n - 1) + f (n - 2)
+
 fib = fix fib_
 
 -- Or for far more efficiency, compute a lazy infinite list. This is
 -- a Y-combinator version of: fibs = 0:1:zipWith (+) fibs (tail fibs)
 fibs :: [Integer]
-fibs_ a = 0:1:(fix zipP a (tail a))
-    where
-      zipP f (x:xs) (y:ys) = x+y : f xs ys
+fibs_ a = 0 : 1 : fix zipP a (tail a)
+  where
+    zipP f (x:xs) (y:ys) = x + y : f xs ys
+
 fibs = fix fibs_
 
 -- This code shows how the functions can be used:
-main = do
-  print $ map fac [1 .. 20]
-  print $ map fib [0 .. 19]
-  print $ take 20 fibs
+main : IO ()
+main =
+  mapM_
+    print
+    [ map fac [1 .. 20]
+    , map fib [0 .. 19]
+    , take 20 fibs
+    ]