Initial data commit

Task/Evaluate-binomial-coefficients/Python/evaluate-binomial-coefficients-3.py

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+'''Evaluation of binomial coefficients'''
+
+from functools import reduce
+
+
+# binomialCoefficient :: Int -> Int -> Int
+def binomialCoefficient(n):
+    '''n choose k, expressed in terms of
+       product and factorial functions.
+    '''
+    return lambda k: product(
+        enumFromTo(1 + k)(n)
+    ) // factorial(n - k)
+
+
+# TEST ----------------------------------------------------
+# main :: IO()
+def main():
+    '''Tests'''
+
+    print(
+        binomialCoefficient(5)(3)
+    )
+
+    # k=0 to k=5, where n=5
+    print(
+        list(map(
+            binomialCoefficient(5),
+            enumFromTo(0)(5)
+        ))
+    )
+
+
+# GENERIC -------------------------------------------------
+
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+
+
+# factorial :: Int -> Int
+def factorial(x):
+    '''The factorial of x, where
+       x is a positive integer.
+    '''
+    return product(enumFromTo(1)(x))
+
+
+# product :: [Num] -> Num
+def product(xs):
+    '''The product of a list of
+       numeric values.
+    '''
+    return reduce(lambda a, b: a * b, xs, 1)
+
+
+# TESTS ---------------------------------------------------
+if __name__ == '__main__':
+    main()