September Morn Update

Task/Happy-numbers/Python/happy-numbers-2.py

@@ -0,0 +1,79 @@
+'''Happy numbers'''
+
+from itertools import islice
+
+
+# main :: IO ()
+def main():
+    '''Test'''
+    print(
+        take(8)(
+            happyNumbers()
+        )
+    )
+
+
+# happyNumbers :: Gen [Int]
+def happyNumbers():
+    '''Generator :: non-finite stream of happy numbers.'''
+    x = 1
+    while True:
+        x = until(isHappy)(succ)(x)
+        yield x
+        x = succ(x)
+
+
+# isHappy :: Int -> Bool
+def isHappy(n):
+    '''Happy number sequence starting at n reaches 1 ?'''
+    seen = set()
+
+    # p :: Int -> Bool
+    def p(x):
+        if 1 == x or x in seen:
+            return True
+        else:
+            seen.add(x)
+            return False
+
+    # f :: Int -> Int
+    def f(x):
+        return sum(int(d)**2 for d in str(x))
+
+    return 1 == until(p)(f)(n)
+
+
+# GENERIC -------------------------------------------------
+
+# succ :: Int -> Int
+def succ(x):
+    '''The successor of an integer.'''
+    return 1 + x
+
+
+# take :: Int -> [a] -> [a]
+# take :: Int -> String -> String
+def take(n):
+    '''The prefix of xs of length n,
+       or xs itself if n > length xs.'''
+    return lambda xs: (
+        xs[0:n]
+        if isinstance(xs, list)
+        else list(islice(xs, n))
+    )
+
+
+# until :: (a -> Bool) -> (a -> a) -> a -> a
+def until(p):
+    '''The result of repeatedly applying f until p holds.
+       The initial seed value is x.'''
+    def go(f, x):
+        v = x
+        while not p(v):
+            v = f(v)
+        return v
+    return lambda f: lambda x: go(f, x)
+
+
+if __name__ == '__main__':
+    main()