Understanding nested lambda function behaviour in python

Question

I'm trying to learn pure functional programming. But this code is puzzling me particularly the second line. I do not understand how the value 2 is passed to the variable x. Can somebody explain this nested lambda behaviour?

>>> square_func = lambda x: x**2
>>> function_product = lambda F, m: lambda x: F(x)*m
>>> square_func(2)
4
>>> function_product(square_func, 3)(2)
12

Answer 1

The inner lambda creates a function when the outer lambda is called. The outer lambda returns this function. This function is then called with the argument 2.

Answer 2

A good place to start would be to apply type to your definitions and see if it clarifies things. Also, I can't help but remark that something like Haskell would be a nicer place to start if you are interested in functional programming, even if you do not plan on using the language. That being said, here is what you get:

In [13]: type(square_func)
Out[13]: function

In [14]: type(function_product)
Out[14]: function

In [15]: type(square_func(2))
Out[15]: int

In [16]: type(function_product(square_func, 3))
Out[16]: function

In [17]: type(function_product(square_func, 3)(2))
Out[17]: int

So the puzzling part is the return type of function_product(square_func, 3), which is a function itself, one that is presumably intended to take a single number and return a single number. You could write it as:

f = function_product(square_func, 3)
f(2)