Lecture_5

This lecture we are still going to study higher-order functions. The core of almost all programming languages.

We shall begin with an example:

def apply_twice(f, x):
    return f(f(x))

def square(x):
    return x * x

>>> apply_twice(square, 2)
16

Now let's examining a new kind of function:

{
def repeat(f, x):
    while f(x) != x
        x = f(x)
    return x

def g(y):
    return (y + 5) // 3
    
z = repeat(g, 7)
}

One shall examine and understand the above function completely.

Another example of nested functions:
{
def square(x):
    return x * x

def triple(x):
    return 3 * x

def compose(f, g):
    def h(x):
        return f(g(x))

>>> squiple = compose(square, triple)
>>> squiple(5) = 225