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).

Some authors, particularly from the imperative language community, use the term "pure" for all functions that just have the above property 2 (discussed in § Compiler optimizations below). ^[3]

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

  voidf(){staticstd::atomic<unsignedint>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

  intf(){staticintx=0;++x;returnx;}

• because of return value variation with a non-local variable

  intf(){returnx;}

  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

  intf(int*x){return*x;}

• because of return value variation with an input stream

  intf(){intx=0;std::cin>>x;returnx;}

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

• because of mutation of a local static variable

  voidf(){staticintx=0;++x;}

• because of mutation of a non-local variable

  voidf(){++x;}

• because of mutation of a mutable reference argument

  voidf(int*x){++*x;}

• because of mutation of an output stream

  voidf(){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

  intf(){staticintx=0;++x;returnx;}

• because of return value variation with an input stream and mutation of an input stream

  intf(){intx=0;std::cin>>x;returnx;}

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. ^{[4] [5]}

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

Memoization

staticintfact(intn){returnn<=1?1:fact(n-1)*n;}intfact_wrapper(intn){staticintcache[13];assert(0<=n&&n<13);if(cache[n]==0)cache[n]=fact(n);returncache[n];}

C program for cached computation of factorial [6]

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). ^[7]

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.

Compiler optimizations

Functions that have just the above property 2 – that is, have no side efects – allow for compiler optimization techniques such as common subexpression elimination and loop optimization similar to arithmetic operators. ^[8] 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::strings="Hello, world!";inta[10]={1,2,3,4,5,6,7,8,9,10};intl=0;for(inti=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:

• In Fortran and D, the pure keyword can be used to declare a function to be just side-effect free (i.e. have just the above property 2). ^[9] The compiler may be able to deduce property 1 on top of the declaration. ^[10] See also: Fortran 95 language features § Pure procedures.
• In the GCC, the pure attribute specifies property 2, while the const attribute specifies a truly pure function with both properties. ^[11]
• Languages offering compile-time function execution may require functions to be pure, sometimes with the addition of some other constraints. Examples include constexpr of C++ (both properties). ^[12] See also: C++11 § constexpr – Generalized constant expressions.

Unit testing

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

See also

• Compile-time function execution  –The evaluation of pure functions at compile time
• Deterministic algorithm  –Algorithm that, given a particular input, will always produce the same output
• Idempotence  –Property of operations whereby they can be applied multiple times without changing the result
• Lambda calculus  – Mathematical-logic system based on functions
• Purely functional data structure  – Data structure implementable in purely functional languages
• Reentrancy (computing)  –Executing a function concurrently without interfering with other invocations

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. Here are the fundamental properties of a pure function: 1. A function returns exactly the same result every time it's called with the same set of arguments. In other words a function has no state, nor can it access any external state. Every time you call it, it behaves like a newborn baby with blank memory and no knowledge of the external world. 2. A function has no side effects. Calling a function once is the same as calling it twice and discarding the result of the first call.
2. Brian Lonsdorf (2015). "Professor Frisby's Mostly Adequate Guide to Functional Programming". GitHub. Retrieved 2020-03-20. A pure function is a function that, given the same input, will always return the same output and does not have any observable side effect.
3. "Common Function Attributes - Using the GNU Compiler Collection (GCC)". gcc.gnu.org, the GNU Compiler Collection. Free Software Foundation, Inc. Retrieved 2018-06-28.
4. 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.
5. 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.
6. assert() aborts with an error message if its argument is false; on a 32-bit machine, values beyond fact(12) cannot be represented, anyway.
7. 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.
8. "Common Function Attributes - Using the GNU Compiler Collection (GCC)". gcc.gnu.org, the GNU Compiler Collection. Free Software Foundation, Inc. Retrieved 2018-06-28.
9. Pure attribute in Fortran
10. Pure attribute in D language
11. "Common Function Attributes". Using the GNU Compiler Collection (GCC. Retrieved 22 July 2021.
12. constexpr attribute in C++