September Morn Update

Task/Ordered-Partitions/Python/ordered-partitions-3.py

@@ -0,0 +1,107 @@
+'''Ordered Partitions'''
+
+
+# partitions :: [Int] -> [[[Int]]]
+def partitions(xs):
+    '''Ordered partitions of xs.'''
+    n = sum(xs)
+
+    def go(s, n, ys):
+        return [
+            [l] + r
+            for (l, rest) in choose(s)(n)(ys[0])
+            for r in go(rest, n - ys[0], ys[1:])
+        ] if ys else [[]]
+    return go(enumFromTo(1)(n), n, xs)
+
+
+# choose :: [Int] -> Int -> Int -> [([Int], [Int])]
+def choose(xs):
+    '''(m items chosen from n items, the rest)'''
+    def go(xs, n, m):
+        f = cons(xs[0])
+        choice = choose(xs[1:])(n - 1)
+        return [([], xs)] if 0 == m else (
+            [(xs, [])] if n == m else (
+                [first(f)(x) for x in choice(m - 1)] +
+                [second(f)(x) for x in choice(m)]
+            )
+        )
+    return lambda n: lambda m: go(xs, n, m)
+
+
+# TEST ----------------------------------------------------
+# main :: IO ()
+def main():
+    '''Tests of the partitions function'''
+
+    f = partitions
+    print(
+        fTable(main.__doc__ + ':')(
+            lambda x: '\n' + f.__name__ + '(' + repr(x) + ')'
+        )(
+            lambda ps: '\n\n' + '\n'.join(
+                '    ' + repr(p) for p in ps
+            )
+        )(f)([
+            [2, 0, 2],
+            [1, 1, 1]
+        ])
+    )
+
+
+# DISPLAY -------------------------------------------------
+
+# fTable :: String -> (a -> String) ->
+#                     (b -> String) -> (a -> b) -> [a] -> String
+def fTable(s):
+    '''Heading -> x display function -> fx display function ->
+                     f -> xs -> tabular string.
+    '''
+    def go(xShow, fxShow, f, xs):
+        ys = [xShow(x) for x in xs]
+        w = max(map(len, ys))
+        return s + '\n' + '\n'.join(map(
+            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
+            xs, ys
+        ))
+    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
+        xShow, fxShow, f, xs
+    )
+
+
+# GENERIC -------------------------------------------------
+
+# cons :: a -> [a] -> [a]
+def cons(x):
+    '''Construction of a list from x as head,
+       and xs as tail.
+    '''
+    return lambda xs: [x] + xs
+
+
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+
+
+# first :: (a -> b) -> ((a, c) -> (b, c))
+def first(f):
+    '''A simple function lifted to a function over a tuple,
+       with f applied only the first of two values.
+    '''
+    return lambda xy: (f(xy[0]), xy[1])
+
+
+# second :: (a -> b) -> ((c, a) -> (c, b))
+def second(f):
+    '''A simple function lifted to a function over a tuple,
+       with f applied only the second of two values.
+    '''
+    return lambda xy: (xy[0], f(xy[1]))
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()