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# Pure function

In computer programming, a pure function is a function that has the following properties:[1][2]

1. the function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable reference arguments or input streams, i.e., referential transparency), and
2. the function has no side effects (no mutation of local static variables, non-local variables, mutable reference arguments or input/output streams).

## Examples

### Pure functions

The following examples of C++ functions are pure:

• `floor`, returning the floor of a number;
• `max`, returning the maximum of two values.
• the function f, defined as
```void f() {
static std::atomic<unsigned int> x = 0;
++x;
}
```
The value of `x` can be only observed inside other invocations of `f()`, and as `f()` does not communicate the value of `x` to its environment, it is indistinguishable from function `void f() {}` that does nothing. Note that `x` is `std::atomic` so that modifications from multiple threads executing `f()` concurrently do not result in a data race, which has undefined behavior in C and C++.

### Impure functions

The following C++ functions are impure as they lack the above property 1:

• because of return value variation with a static variable
```int f() {
static int x = 0;
++x;
return x;
}
```
• because of return value variation with a non-local variable
```int f() {
return x;
}
```
For the same reason, e.g. the C++ library function `sin()` is not pure, since its result depends on the IEEE rounding mode which can be changed at runtime.
• because of return value variation with a mutable reference argument
```int f(int* x) {
return *x;
}
```
• because of return value variation with an input stream
```int f() {
int x = 0;
std::cin >> x;
return x;
}
```

The following C++ functions are impure as they lack the above property 2:

• because of mutation of a local static variable
```void f() {
static int x = 0;
++x;
}
```
• because of mutation of a non-local variable
```void f() {
++x;
}
```
• because of mutation of a mutable reference argument
```void f(int* x) {
++*x;
}
```
• because of mutation of an output stream
```void f() {
std::cout << "Hello, world!" << std::endl;
}
```

The following C++ functions are impure as they lack both the above properties 1 and 2:

• because of return value variation with a local static variable and mutation of a local static variable
```int f() {
static int x = 0;
++x;
return x;
}
```
• because of return value variation with an input stream and mutation of an input stream
```int f() {
int x = 0;
std::cin >> x;
return x;
}
```

## I/O in pure functions

I/O is inherently impure: input operations undermine referential transparency, and output operations create side effects. Nevertheless, there is a sense in which a function can perform input or output and still be pure, if the sequence of operations on the relevant I/O devices is modeled explicitly as both an argument and a result, and I/O operations are taken to fail when the input sequence does not describe the operations actually taken since the program began execution.[clarification needed]

The second point ensures that the only sequence usable as an argument must change with each I/O action; the first allows different calls to an I/O-performing function to return different results on account of the sequence arguments having changed.[3][4]

The I/O monad is a programming idiom typically used to perform I/O in pure functional languages.

## Memoization

The outputs of a pure function can be precomputed and cached in a look-up table. In a technique called memoization, any result that is returned from a given function is cached, and the next time the function is called with the same input parameters, the cached result is returned instead of computing the function again.

Memoization can be performed by wrapping the function in another function (wrapper function).[5]

By means of memoization, the computational effort involved in the computations of the function itself can be reduced, at the cost of the overhead for managing the cache and an increase of memory requirements.

A C program for cached computation of factorial (`assert()` aborts with an error message if its argument is false; on a 32-bit machine, values beyond `fact(12)` cannot be represented anyway.[citation needed]

```static int fact(int n) {
return n<=1 ? 1 : fact(n-1)*n;
}
int fact_wrapper(int n) {
static int cache[13];
assert(0<=n && n<13);
if (cache[n] == 0)
cache[n] = fact(n);
return cache[n];
}
```

## Compiler optimizations

Functions that have just the above property 2 – that is, have no side effects – allow for compiler optimization techniques such as common subexpression elimination and loop optimization similar to arithmetic operators.[6] A C++ example is the `length` method, returning the size of a string, which depends on the memory contents where the string points to, therefore lacking the above property 1. Nevertheless, in a single-threaded environment, the following C++ code

```std::string s = "Hello, world!";
int a[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
int l = 0;

for (int i = 0; i < 10; ++i) {
l += s.length() + a[i];
}
```

can be optimized such that the value of `s.length()` is computed only once, before the loop.

Some programming languages allow for declaring a pure property to a function:

## Unit testing

Since pure functions have identical return values for identical arguments, they are well suited to unit testing.

## References

1. ^ Bartosz Milewski (2013). "Basics of Haskell". School of Haskell. FP Complete. Archived from the original on 2016-10-27. Retrieved 2018-07-13.
2. ^ Brian Lonsdorf (2015). "Professor Frisby's Mostly Adequate Guide to Functional Programming". GitHub. Retrieved 2020-03-20.
3. ^ Peyton Jones, Simon L. (2003). Haskell 98 Language and Libraries: The Revised Report (PDF). Cambridge, United Kingdom: Cambridge University Press. p. 95. ISBN 0-521 826144. Retrieved 17 July 2014.
4. ^ Hanus, Michael. "Curry: An Integrated Functional Logic Language" (PDF). www-ps.informatik.uni-kiel.de. Institut für Informatik, Christian-Albrechts-Universität zu Kiel. p. 33. Archived from the original (PDF) on 25 July 2014. Retrieved 17 July 2014.
5. ^ Aley, R. (2017). Pro Functional PHP Programming: Application Development Strategies for Performance Optimization, Concurrency, Testability, and Code Brevity. SpringerLink : Bücher. Apress. p. 109. ISBN 978-1-4842-2958-3. Retrieved 2024-02-04.
6. ^ "Common Function Attributes - Using the GNU Compiler Collection (GCC)". gcc.gnu.org, the GNU Compiler Collection. Free Software Foundation, Inc. Retrieved 2018-06-28.
7. ^ Pure attribute in Fortran
8. ^ Pure attribute in D language
9. ^ "Common Function Attributes". Using the GNU Compiler Collection (GCC. Retrieved 22 July 2021.
10. ^ constexpr attribute in C++