Pure Functions: Does "No Side Effects" Imply "Always Same Output, Given Same Input"?

The two conditions that define a function as pure are as follows:

1. No side effects (i.e. only changes to local scope are allowed)
2. Always return the same output, given the same input

If the first condition is always true, are there any times the second condition is not true?

I.e. is it really only necessary with the first condition?

Here are a few counterexamples that do not change the outer scope but are still considered impure:

• function a() { return Date.now(); }
• function b() { return window.globalMutableVar; }
• function c() { return document.getElementById("myInput").value; }
• function d() { return Math.random(); } (which admittedly does change the PRNG, but is not considered observable)

Accessing non-constant non-local variables is enough to be able to violate the second condition.

I always think of the two conditions for purity as complementary:

• the result evaluation must not have effects on side state
• the evaluation result must not be affected by side state

The term side effect only refers to the first, the function modifying the non-local state. However, sometimes read operations are considered as side effects as well: when they are operations and involve writing as well, even if their primary purpose is to access a value. Examples for that are generating a pseudo-random number that modifies the generator's internal state, reading from an input stream that advances the read position, or reading from an external sensor that involves a "take measurement" command.