How do I write a function that returns another function?

In Python, I'd like to write a function make_cylinder_volume(r) which returns another function. That returned function should be callable with a parameter h, and return the volume of a cylinder with height h and radius r.

I know how to return values from functions in Python, but how do I return another function?

Try this, using Python:

import math
def make_cylinder_volume_func(r):
	def volume(h):
		return math.pi * r * r * h
	return volume

Use it like this, for example with radius=10 and height=5:

volume_radius_10 = make_cylinder_volume_func(10)
volume_radius_10(5)
=> 1570.7963267948967

Notice that returning a function was a simple matter of defining a new function inside the function, and returning it at the end - being careful to pass the appropriate parameters for each function. FYI, the technique of returning a function from another function is known as currying.

Using lambdas, also known as anonymous functions, you can abstract out the volume function inside the make_cylinder_volume_func to a single line. In no way different from Óscar López's answer, the solution using lambda is still in a sense 'more functional'.

This is how you can write the accepted answer using a lambda expression:

import math
def make_cylinder_volume_fun(r):
    return lambda h: math.pi * r * r * h

And then call as you'd any other curried function:

volume_radius_1 = make_cylinder_volume_fun(1)
volume_radius_1(1) 
=> 3.141592653589793

Just want to point out that you can do this with pymonad

 import pymonad 
 
 @pymonad.curry
 def add(a, b):
     return a + b
 
 add5 = add(5)
 add5(4)
 9

I know I am too late to the party, but I think you might find this solution interesting.

from math import pi
from functools import partial

def cylinder_volume(r, h):
	return pi * r * r * h

make_cylinder_with_radius_2 = partial(cylinder_volume, 2)
make_cylinder_with_height_3 = partial(cylinder_volume, h=3)

print(cylinder_volume(2, 3)) 			# 37.6991118431
print(make_cylinder_with_radius_2(3))	# 37.6991118431
print(make_cylinder_with_height_3(2))	# 37.6991118431

Here is documentation about how partial works.

Here is one massive example which covers many of single multiple argument cases in one function

def maths(var='NA'):
if var.lower() == 'add':
    def add(*args):
        return "Sum is : "+str(sum(args))
    return add
elif var.lower() == 'substract':
    def substract(a,b):
        if a>b:
            return "Difference is : "+str(a-b)
        else:
            return "Difference is : "+str(b-a)
    return substract
elif var.lower() == 'multiply':
    def multiply(*args):
        temp = 1
        for x in args:
            temp = temp*x
        return "multiplication is : "+str(temp)
    return multiply
elif var.lower() == 'divide':
    def divide(a,b):
        return "Division is : "+str(a/b)
    return divide
else:
    print("Please choose one of given operations: 'add','substract','multiply','divide'")

Here first call the maths function with the required operation and then use the returned function for the actual calculation