Functions Are Values

In most languages a function is just a value — you can assign it to a variable, put it in a list, pass it to another function, and return it from a function. These are called higher-order functions (HOFs): functions that operate on other functions.

Terms used here (standalone):

• First-class function: a function that can be stored, passed, and returned like any other value.
• Higher-order function: a function that takes a function as an argument or returns one.
• compose(f, g)(x) returns f(g(x)) — g runs first, f runs second.

Read this code carefully and trace it by hand:

def make_adder(n):
    def add(x):
        return x + n
    return add

def make_multiplier(n):
    def multiply(x):
        return x * n
    return multiply

def compose(f, g):
    """h(x) == f(g(x)):  g runs first, f runs second."""
    def h(x):
        return f(g(x))
    return h

add5   = make_adder(5)
double = make_multiplier(2)
triple = make_multiplier(3)

steps    = [add5, double, triple]
pipeline = steps[0]
for step in steps[1:]:
    pipeline = compose(step, pipeline)

result = pipeline(2)

Trace pipeline after each iteration of the loop. What function does it represent?

Then apply it to 2.

The distractors are wrong for specific, traceable reasons — figure out which mistake each one corresponds to.