Martin McBride, 2019-09-28

Tags closure inner function function composition

Categories functional programming

*This article is part of a series on functional programming.*

Closures are a powerful and flexible way to create new functions out of existing functions. You can think of them as being *function factories*, that can create new functions according to a template and one or more parameters.

The Python implementation relies on *inner functions*.

An inner function is a function that is defined within the scope of another function, like this:

def add_3(v): n = 3 def f(x): return x + n return f(v) print(add_3(6)) # Prints 9

In this case our outer function `add_3`

adds 3 to the value of `x`

and returns the result.

The `add_3`

function contains:

- A local variable
`n`

that is set to 3. - An inner (or 'local') function
`f`

that adds`n`

to the supplied parameter`x`

It uses these to calculate the result of `v`

+ 3. Of course, you could write a much simpler function to do the same job, we are simply using it to illustrate the idea of inner functions.

The local variable `n`

cannot be accessed from outside the `print_add_3`

function. obviously, since it is a local variable. In a similar way, the inner function `f`

can't be accessed from outside the `print_add_3`

function either, it is also local. This makes sense, of course, the reason we use local variables and inner functions is to hide the inner workings of our function from the outside world. This is called encapsulation.

It is worth noting that the function `f`

is able to access the variable `n`

, because they are both within the scope of the outer function `print_add_3`

.

As an aside, though quite an important one, you may have heard it said that in Python everything is an object. Well that isn't just true of numbers, strings, lists etc, it is true of functions too! So:

print(min(1, 2))

calls the function `min`

, and prints the result. But without the brackets:

print(min)

will display `<built-in function min>`

, the function object for `min`

. You can even assign this function to a variable, and then call it using bracket notation:

a = min print(a(3, 2))

This will print 2, because `a`

references the `min`

function object, and `a(3, 2)`

calls it. We call this aliasing: `a`

is an alias of `min`

.

Now we will rearrange things a little:

def get_add_3(): n = 3 def f(x): return x + n return f add_3 = get_add_3() print(add_3(6)) # Prints 9

The first thing to notice here is that we `get_add_3`

returns `f`

. It doesn't call `f`

, it returns the function object `f`

.

So our new function `get_add_3`

doesn't add 3 to a number, instead it returns a function object `f`

that adds 3 to a number. This means that we need two steps to add 3 to a number:

- We call
`get_add_3`

, which returns a function object, which we store as`add_3`

. - We then call
`add_3(6)`

, which uses the function object to do the calculation.

Now you might have noticed something slightly odd here. `add_3`

is an alias of `f`

, and `f`

uses the value of `n`

, which is a local variable of `get_add_3`

. But `add_3`

is being called outside the context of `get_add_3`

, because we have already returned from the call.

Now `add_3`

obviously knows the value of `n`

, because it knows to add 3 to its arguments. So what is going on?

Well, when the function `f`

is returned, Python attaches extra information to the function object, storing the values of any free variables within the outer function.

In fact, this is a closure, it is just that at the moment it isn't a particularly useful closure.

The final step is to make this into something more useful:

def add_n(n): def f(x): return x + n return f add_4 = add_n(4) add_7 = add_n(7) print(add_4(6)) # Prints 10 print(add_7(5)) # Prints 12

This time, when we call `add_n`

, we actually pass in our required `n`

value. The function returns a closure of `f`

that includes the requested value of `n`

.

So `add_n(4)`

creates a function that adds 4 to a value. We can store this in a variable `add_4`

and then call `add_4()`

as a function - because that is exactly what it is. Likewise, we can create an `add_7`

function if we need one, or any `n`

we require.

Closures are basically function factories, and very useful ones at that.

You might wonder why we would go to all the trouble of creating a closure to add 4 to `x`

. Why not just do:

y = x + 4

Well, in functional programming you generally want to deal with functions rather than expressions. Of course we could do this:

def add_4(x) return x + 4

But that requires us to hand write a function, which could easily introduce bugs. Now assuming we have an `add_n`

closure already defined, and we trust it because it is part of a well tested library, we can just do this:

add_4 = add_n(4)

This is far more declarative - we are saying what we want rather than describing how to do it. It is both more readable and less error prone.

To summarise what we have done so far, a closure requires three things:

- An outer function that contains an inner function.
- The outer function has parameters and/or local variables.
- The outer function returns the inner function as a function object.

Suppose we wanted to take an object, convert it to a string, and find how long that string is. We could do it like this:

x = len(str(3*10)) # x = 2 because str(3*10) is '30' and len('30') is 2

That is all very well, but what if we wanted to apply this operation to a list of values using the map function. `map`

requires a function object and a list or other iterable. So we would have to create a special `lenstr`

functions:

def lenstr(x): return len(str(x)) map(lenstr, values)

This would work but is it a very procedural approach. Again, we are defining a special function, which is error prone.

Suppose instead we had a `compose`

closure, that takes two functions, `f`

and `g`

and returns a new function that finds `f(g(x))`

:

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

`compose`

is quite a general purpose function, available in several popular Python functional programming libraries. Now we can do this:

lenstr = compose(len, str)

This creates a `lenstr`

function without any procedural coding. Or we can just use `compose`

directly without storing the function:

map(compose(len, str), values)

Again, this is far more declarative. Rather than hand coding a special `lenstr`

function, we are simply declaring a function that is a composition of `len`

and `str`

. It is clearer and more reliable.

If you found this article useful you might be interested in my ebook Functional Programming in Python. It covers closures and composition in more depth.

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