Function

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A canonical function diagram that shows the input, output, and the function body. The name is visible, but the contents (the body) of the function are hidden.

A function is a piece of code that accomplishes a specific task. It usually takes in argument(s) as input, does some processing, and returns a result. Once a function is written, it can be called over and over again.

Motivation

Functions take advantage of abstraction: we don't care how the function carries out its task; we just care that it gives us a correct result.

In addition, functions allow us to reuse code instead of rewriting it to work with different values.

Pure function

A pure function produces no effects other than returning a value. Its return value depends only on the inputs. Given the same arguments, it always returns the same value.

Examples

  • add always returns the sum of the arguments and has no side effects.
  • square
def square(x):
    return x * x
  • A def statement is used to create the function with intrinsic name square and bind it to the name square in the current environment.
  • Following the intrinsic name is a list of formal parameters within the parentheses, the names that we will give the arguments to the function in a function call. In this case, we only have one formal parameter x.
  • Finally, we denote the expression whose value we output as the value of the function call using the return statement. In this example, the value of a function call to square will be the value of x * x evaluated in tho local frame created by that function call.
  • If a return statement is not present, a function will automatically output None.

Non-pure function

A non-pure function or impure function produces a side effect (e.g., mutation, printing to screen). Its return value may depend on external state; when called multiple times with the same arguments, it may return different values.

Examples

print

The print function displays a value on the screen and returns None.

Functions that modify a variable in another frame

The following get_a() function modifies the variable a in the global frame:

a = 0
def get_a():
    global a
    a += 1
    return a - 1

The following tick function modifies the variable n in the countdown frame:

def countdown(n):
    def tick():
        nonlocal n
        n -= 1
        return n
    return tick

Functions that mutate an object in another frame

The following add_square function mutates lst in the global frame:

lst = []
def append_square(n):
    lst.append(n*n)

randint

randint returns a random number in the provided range, so the same function call may return different values. Example:

>>> from random import randint
>>> randint(0, 10)
0
>>> randint(0, 10)
6
>>> randint(0, 10)
7
>>> randint(0, 10)
2
>>> randint(0, 10)
10

Higher-order function

Main article: Higher-order function

A higher-order function is a function that takes in functions as arguments and/or returns functions as output.

Sources