Higher order functions

Higher order function is powerful concept, it takes one or more functions as an input(argument) and outputs a function as return. It can make some complex problem
become easy. Many languages support this concept and

also has some built-in functions like map and filter. They use these functions in a very well-defined way to accomplish specific behaviors. Higher-order functions allow to implement much more sophisticated
behaviors and can use it to write much more interesting programs. Have a try first.

In math higher-order functions are known as operators or functionals. Map a function to another function. Many functional languages has map funcion, it takes as
arguments function f and a list of elements, and apply each element of the list to f. In C and Java, some sorting functions take comparison function as a parameter, like standard functionqsort as an example.

Some python code of higher-order function for fun:

'''
Created on Jun 27, 2014

@author: will
'''

# Higher order functions.

def double(val):
return 2 * val

def square(val):
return val ** 2

print double(3)
print square(3)

def twice(func, val):
return func(func(val))

print twice(double, 3)
print twice(square, 3)

data = [1, 3, 6, 9, 18]
newdata = [double(item) for item in data]
print newdata

newdata2 = map(square ,data)
print newdata2

def even(val):
if val % 2:
return False
else:
return True

newdata3 = filter(even, data)
print newdata3

# Get the area of a curve, it is just approximate the result
def area(func, low, high, stepsize):
total = 0.0
loc = low
while loc < high:
total += func(loc) * stepsize
loc += stepsize

return total

def f(x):
return x

def g(x):
return x ** 2

def h(x):
if x < 3:
return x
elif x < 7:
return x ** 2
else:
return 7 * x - 4

print area(f, 0, 10, .01)
print area(g, 0, 10, .0001)
print area(h, 0, 10, .001)

C higher-order function to compute integral:

#include <stdio.h>

double integral(double f(double x), double a, double b, int n)
{
// Compute the integral of f() with the interval [a, b]
double sum = 0, dt = (b - a) / n;
int i;
for (i = 0; i < n; i++)
{
sum += f(a + (i + .5) * dt);
}
return sum * dt;
}

double f(double x)
{
return 3 * x * x;
}

int main()
{
double integ = integral(f, 0, 1, 100);
printf("The integral is: %g\n", integ);
return 0;
}

Reference:

http://en.wikipedia.org/wiki/Higher-order_function