Control Flow

Programming is hard when we think simultaneously about several concepts. Good programming breaks down big problems into small problems and builds up small solutions into big solutions. By this practice the need for simultaneous thought is restricted to only a few elements at a time.

All modern languages provide mechanisms to build data into data structures and to build functions out of other functions. The third element of programming, besides data and functions, is control flow. Building complex control flow out of simple control flow presents deeper challenges.


Each element in a computer program is either

  • A variable or value literal like x, total, or 5
  • A function or computation like the + in x + 1, the function fib in fib(3), the method split in line.split(','), or the = in x = 0
  • Control flow like if, for, or return

Here is a piece of code; see if you can label each term as either variable/value, function/computation, or control flow

def fib(n):
    a, b = 0, 1
    for i in range(n):
        a, b = b, a + b
    return b

Programming is hard when we have to juggle many code elements of each type at the same time. Good programming is about managing these three elements so that the developer is only required to think about a handful of them at a time. For example we might collect many integer variables into a list of integers or build a big function out of smaller ones. While we have natural ways to manage data and functions, control flow presents more of a challenge.

We organize our data into data structures like lists, dictionaries, or objects in order to group related data together – this allows us to manipulate large collections of related data as if we were only manipulating a single entity.

We build large functions out of smaller ones; enabling us to break up a complex task like doing laundry into a sequence of simpler tasks.

def do_laundry(clothes):
    wet_clothes = wash(clothes, coins)
    dry_clothes = dry(wet_clothes, coins)
    return fold(dry_clothes)

Control flow is more challenging; how do we break down complex control flow into simpler pieces that fit in our brain? How do we encapsulate commonly recurring patterns?

Lets motivate this with an example of a common control structure, applying a function to each element in a list. Imagine we want to download the HTML source for a number of webpages.

from urllib import urlopen

urls = ['', '', '']
html_texts = []
for item in urls:
return html_texts

Or maybe we want to compute the Fibonacci numbers on a particular set of integers

integers = [1, 2, 3, 4, 5]
fib_integers = []
for item in integers:
return fib_integers

These two unrelated applications share an identical control flow pattern. They apply a function (urlopen or fib) onto each element of an input list (urls, or integers), appending the result onto an output list. Because this control flow pattern is so common we give it a name, map, and say that we map a function (like urlopen) onto a list (like urls).

Because Python can treat functions like variables we can encode this control pattern into a higher-order-function as follows:

def map(function, sequence):
    output = []
    for item in sequence:
    return output

This allows us to simplify our code above to the following, pithy solutions

html_texts = map(urlopen, urls)
fib_integers = map(fib, integers)

Experienced Python programmers know that this control pattern is so popular that it has been elevated to the status of syntax with the popular list comprehension

html_texts = [urlopen(url) for url in urls]


So maybe you already knew about map and don’t use it or maybe you just prefer list comprehensions. Why should you keep reading?

Managing Complexity

The higher order function map gives us a name to call a particular control pattern. Regardless of whether or not you use a for loop, a list comprehension, or map itself, it is useful to recognize the operation and to give it a name. Naming control patterns lets us tackle complex problems at larger scale without burdening our mind with rote details. It is just as important as bundling data into data structures or building complex functions out of simple ones.

Naming control flow patterns enables programmers to manipulate increasingly complex operations.

Other Patterns

The function map has friends. Advanced programmers may know about map’s siblings, filter and reduce. The filter control pattern is also handled by list comprehension syntax and reduce is often replaced by straight for loops, so if you don’t want to use them there is no immediately practical reason why you would care.

Most programmers however don’t know about the many cousins of map/filter/reduce. Consider for example the unsung heroine, groupby. A brief example grouping names by their length follows:

>>> names = ['Alice', 'Bob', 'Charlie', 'Dan', 'Edith', 'Frank']
>>> groupby(len, names)
{3: ['Bob', 'Dan'], 5: ['Alice', 'Edith', 'Frank'], 7: ['Charlie']}

Groupby collects each element of a list into sublists determined by the value of a function. Lets see groupby in action again, grouping numbers by evenness.

>>> def iseven(n):
...     return n % 2 == 0

>>> groupby(iseven, [1, 2, 3, 4, 5, 6, 7])
{True: [2, 4, 6], False: [1, 3, 5, 7]}

If we were to write this second operation out by hand it might look something like the following:

evens = []
odds = []
for item in numbers:
    if iseven(item):

Most programmers have written code exactly like this over and over again, just like they may have repeated the map control pattern. When we identify code as a groupby operation we mentally collapse the detailed manipulation into a single concept.

The Toolz library contains dozens of patterns like map and groupby. Learning a core set (maybe a dozen) covers the vast majority of common programming tasks often done by hand.

A rich vocabulary of core control functions conveys the following benefits:

  • You identify new patterns
  • You make fewer errors in rote coding
  • You can depend on well tested and benchmarked implementations

But this does not come for free. As in spoken language the use of a rich vocabulary can alienate new practitioners. Most functional languages have fallen into this trap and are seen as unapproachable and smug. Python maintains a low-brow reputation and benefits from it. Just as with spoken language the value of using just-the-right-word must be moderated with the comprehension of the intended audience.