Higher-order function

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A higher-order function (HOF) is a function that is specialized by another function or that produces another function (i.e. it accepts a function as an argument and/or returns a function).

Background

Functions are data, so we can treat them like all other objects (e.g. numbers, strings, booleans, etc.) and use them as arguments or return values.

HOFs allow us to build abstractions by passing actions (functions) around. For example, a recurring pattern is applying a specific function to all the elements of a list. map abstracts away the details of this behavior, allowing us to apply any function that is passed in.

Examples

Functions as arguments

def map(f, iterable):
    return (f(x) for x in iterable)
def filter(f, iterable):
    return (x for x in iterable if f(x))

iterative improvement:

def iter_solve(guess, done, update):
    while not done(guess):
        guess = update(guess)
    return guess

Functions as return values

def make_adder(n):
  def adder(x):
    return x + n
  return adder
def countdown(n):
    def tick():
        nonlocal n
        n -= 1
        return n
    return tick
def rational(x, y):
    def dispatch(field)
        if field == 'numer':
            return x
        elif field == 'denom':
            return y
        else:
            return 'invalid field'
    return dispatch

Both

def make_doubler(f):
  def doubler(*args)
    f(f(*args))
  return doubler
curry = lambda f: lambda x: lambda y: f(x, y)

Sources