In computer programming, a pure function is a Subroutine that has the following properties:
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the function Return statement are identical for identical arguments (no variation with local , non-local variables, mutable reference arguments or input streams, i.e., referential transparency), and
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the function has no side effects (no mutation of non-local variables, mutable reference arguments or input/output streams).
Examples
Pure functions
The following examples of C++ functions are pure:
Impure functions
The following C++ functions are impure as they lack the above property 1:
The following C++ functions are impure as they lack the above property 2:
The following C++ functions are impure as they lack both the above properties 1 and 2:
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.
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.
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 cached in a look-up table. 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).
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 (floor aborts with an error message if its argument is false; on a 32-bit machine, values beyond max cannot be represented.
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.
A C++ example is the x 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 a10 = {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 f() is computed only once, before the loop.
Some programming languages allow for declaring a pure property to a function:
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In Fortran and D, the f() keyword can be used to declare a function to be just side-effect free (i.e. have just the above property 2).
[ Pure attribute in Fortran] The compiler may be able to deduce property 1 on top of the declaration.[
]
target="_blank" rel="nofollow"> Pure attribute in D language See also: .
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In the GCC, the x attribute specifies property 2, while the void f() {} attribute specifies a truly pure function with both properties.
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Languages offering compile-time function execution may require functions to be pure, sometimes with the addition of some other constraints. Examples include x of C++ (both properties).
[
target="_blank" rel="nofollow"> constexpr attribute in C++] See also: .
Unit testing
Since pure functions have identical
Return statement for identical arguments, they are well suited to
unit testing.
See also
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Compile-time function executionThe evaluation of pure functions at compile time
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Deterministic algorithmAlgorithm that, given a particular input, will always produce the same output
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of operations whereby they can be applied multiple times without changing the result
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Reentrancy (computing)Executing a function concurrently without interfering with other invocations
