Pure function

In computer programming, a function may be considered a pure function if both of the following statements about the function hold:

The result value need not depend on all (or any) of the argument values. However, it must depend on nothing other than the argument values. The function may return multiple result values and these conditions must apply to all returned values for the function to be considered pure. If an argument is call by reference, any parameter mutation will alter the value of the argument outside the function, which will render the function impure.

Pure functions are required to construct pure expressions. Constant expressions are pure by definition. An expression consisting of a function subexpression applied to one or more argument subexpressions is pure if both these statements about the subexpressions hold:

Typically the function subexpression is simply a function identifier. Pure expressions are often referred to as being referentially transparent.

Evaluation of a given pure expression will yield the same result regardless of when or how many times evaluation occurs during program execution. This property is what makes it meaningful to talk about an expression's "value". It also makes it possible to replace an expression with the corresponding value (or it with an equivalent alternative expression) without changing the meaning of a program.

A function can perform input or output and still be pure if the sequence of operations on the relevant Input/Output 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 input/output in pure functional languages.

The definitions above still allow some laxity with regard to purity. It is possible for a pure expression to yield an impure function (or more generally a value which contains one or more impure functions).

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