As per Wikipedia: In computer programming, a function may be described as pure i

Question

As per Wikipedia:

In computer programming, a function may be described as pure if both these statements about the function hold: The function always evaluates the same result value given the same argument value(s). The function result value cannot depend on any hidden information or state that may change as program execution proceeds or between different executions of the program, nor can it depend on any external input from I/O devices. Evaluation of the result does not cause any semantically observable side effect or output, such as mutation of mutable objects or output to I/O devices.

I am wondering if it is possible to write a function that compute if a function is pure or not. Example code in Javascript:

function sum(a,b) {
    return a+b;
}

function say(x){
    console.log(x);
}

isPure(sum) // True
isPure(say) // False

Explanation / Answer

Yes, it is possible, depending on the language.

In JavaScript, you can tell if a function is pure by the following criteria:

It only reads parameters and locals;

It only writes locals;

On non-locals, it calls only pure functions;

All functions it calls implicitly are pure, e.g., toString; and

It only writes properties of locals if they do not alias non-locals.

Aliasing is not possible to determine in JavaScript in the general case, because you can always look up properties of an object dynamically (object["property"]). Provided you never do that, and you have the source of the whole program, then I think the problem is tractable. You would also need information about which native functions have side-effects, such as console.log or most anything involving the DOM.

The term

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