Department numbers: Difference between revisions

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@@ Line 1,935: / Line 1,935: @@
 =={{header|Python}}==
+===Procedural===
 <lang python>from itertools import permutations
@@ Line 1,966: / Line 1,967: @@
 :   6     5       1     </pre>
+===Composition of pure functions===
-Or, expressing the options directly and declaratively in terms of '''reduce''' and '''add''', without importing permutations:
+Expressing the options directly and declaratively in terms of a ''bind'' operator, without importing ''permutations'':
+{{Works with|Python|3}}
+<lang python>'''Department numbers'''
-<lang python>from functools import (reduce)
+from itertools import (chain)
-from operator import (add)
+from operator import (ne)
 # options :: Int -> Int -> Int -> [(Int, Int, Int)]
 def options(lo, hi, total):
+    '''Eligible integer triples.'''
-    ds = range(lo, 1 + hi)
+    ds = enumFromTo(lo)(hi)
-    return bind(filter(lambda x: 0 == x % 2, ds))(
-        lambda x: bind(filter(lambda d: d != x, ds))(
+    return bind(filter(even, ds))(
+        lambda x: bind(filter(curry(ne)(x), ds))(
             lambda y: bind([total - (x + y)])(
                 lambda z: [(x, y, z)] if (
-                    z != y and z >= lo and z <= hi
+                    z != y and lo <= z <= hi
                 ) else []
             )
@@ Line 1,987: / Line 1,992: @@
 # TEST ----------------------------------------------------
 # main :: IO ()
 def main():
+    '''Test'''
     xs = options(1, 7, 12)
-    print (('Police', 'Sanitation', 'Fire'))
+    print(('Police', 'Sanitation', 'Fire'))
     for tpl in xs:
-        print (tpl)
+        print(tpl)
-    print ('\nNo. of options: ' + str(len(xs)))
+    print('\nNo. of options: ' + str(len(xs)))
-# GENERIC ABSTRACTION -------------------------------------
+# GENERIC ABSTRACTIONS ------------------------------------
 # bind (>>=) :: [a] -> (a -> [b]) -> [b]
 def bind(xs):
+    '''List monad injection operator.
-    return lambda f: reduce(add, map(f, xs), [])
+       Two computations sequentially composed,
+       with any value produced by the first
+       passed as an argument to the second.'''
+    return lambda f: list(
+        chain.from_iterable(
+            map(f, xs)
+        )
+    )
+# curry :: ((a, b) -> c) -> a -> b -> c
-main()</lang>
+def curry(f):
+    '''A curried function derived
+       from an uncurried function.'''
+    return lambda a: lambda b: f(a, b)
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+# even :: Int -> Bool
+def even(x):
+    '''True if x is an integer
+       multiple of two.'''
+    return 0 == x % 2
+if __name__ == '__main__':
+    main()</lang>
 {{Out}}
 <pre>('Police', 'Sanitation', 'Fire')