CODEWITHSUNDEEP
functionidempotentpure-function
Lai Yu-Hsuan
Lai Yu-Hsuan

Reputation: 28141

Are idempotent functions the same as pure functions?

I read Wikipedia's explanation of idempotence. I know it means a function's output is determined by its input. But I remember that I heard a very similar concept: pure function. I Google them but can't find their difference...

Are they equivalent?

Upvotes: 81

Views: 13609

Answers (8)

Mateen Ulhaq
Mateen Ulhaq

Reputation: 27271

Definitions:

  • Pure: f(x) always returns the same value for a given x.
  • Idempotent: f(f(x)) = f(x).

Examples

Not pure, and not idempotent

def f(x):
    return random()

Check:

f(0) = 0.2171
f(0) = 0.3142       # Thus, impure.

Pure, but not idempotent

def f(x):
    return x + 1

Check:

f(0) = 1
f(0) = 1  # Thus, pure.
f(1) = 2  # Thus, not idempotent since f(0) != f(f(0)).

Pure, and idempotent

def f(x):
    return round(x)

Check:

f(0.3142) = 0
f(0.3142) = 0  # Thus, pure.
f(0) = 0       # Thus, idempotent.

Visualization

graph diagrams

Each arrow denotes an application of f.

Notice that the idempotent graph ends up in a 1-cycle after one application of f.

What about "not pure, but idempotent"?

Impossible. Proof by contradiction:

Assume f is impure and idempotent. Impure f implies there exists x such that if f(x) = a and f(x) = b, then it is possible that a != b. Say that happens. Now, by idempotency, f(a) = a and f(b) = b. But then:

a = f(a) = f(f(x)) = f(b) = b

...so, a = b. We have reached a contradiction. Clearly, f cannot be simultaneously impure and idempotent!

Upvotes: 6

SocraticMathTutor
SocraticMathTutor

Reputation: 45

As others have said, the word "idempotent" has multiple distinct meanings.

In a pure-functional context, idempotent means f(f(x)) == f(x). But in an impure context, this bifurcates into two different conditions, due to the fact that f(f(x)) == f(x) may evaluate to True for all x values, despite that the overall effect of f(f(x)) may be different to the overall effect of f(x), making f(x) and f(f(x)) non-interchangeable from a compilation perspective.

To add insult to injury, idempotent can also mean side_effect[f(x); f(x)] == side_effect[f(x)]. Furthermore, if this condition is satisfied, then the definitional bifurcation described in the previous paragraph doesn't occur. Note that f is pure if and only if side_effect[f(x)] == side_effect[]. From this we see that a pure function is automatically idempotent in the final sense of the word.

Upvotes: 0

Ibrahim ben Salah
Ibrahim ben Salah

Reputation: 733

I've found more places where 'idempotent' is defined as f(f(x)) = f(x) but I really don't believe that's accurate. Instead I think this definition is more accurate (but not totally):

describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed. A projection operator is idempotent.

The way I interpret this, if we apply f on x (the subject) twice like:

f(x);f(x);

then the (side-)effect is the same as

f(x);

Because pure functions dont allow side-effects then pure functions are trivially also 'idempotent'.

A more general (and more accurate) definition of idempotent also includes functions like

toggle(x)

We can say the degree of idempotency of a toggle is 2, because after applying toggle every 2 times we always end up with the same State

Upvotes: 0

lkm
lkm

Reputation: 621

A large source of confusion is that in computer science, there seems to be different definitions for idempotence in imperative and functional programming.

From wikipedia (https://en.wikipedia.org/wiki/Idempotence#Computer_science_meaning)

In computer science, the term idempotent is used more comprehensively to describe an operation that will produce the same results if executed once or multiple times. This may have a different meaning depending on the context in which it is applied. In the case of methods or subroutine calls with side effects, for instance, it means that the modified state remains the same after the first call. In functional programming, though, an idempotent function is one that has the property f(f(x)) = f(x) for any value x.

Since a pure function does not produce side effects, i am of the opinion that idempotence has nothing to do with purity.

Upvotes: 5

jhuni
jhuni

Reputation: 425

Functional purity means that there are no side effects. On the other hand, idempotence means that a function is invariant with respect to multiple calls.

Every pure function is side effect idempotent because pure functions never produce side effects even if they are called more then once. However, return value idempotence means that f(f(x)) = f(x) which is not effected by purity.

Upvotes: 6

Brent Arias
Brent Arias

Reputation: 30215

No, an idempotent function will change program/object/machine state - and will make that change only once (despite repeated calls). A pure function changes nothing, and continues to provide a (return) result each time it is called.

Upvotes: 12

Anon.
Anon.

Reputation: 60033

A pure function is a function without side-effects where the output is solely determined by the input - that is, calling f(x) will give the same result no matter how many times you call it.

An idempotent function is one that can be applied multiple times without changing the result - that is, f(f(x)) is the same as f(x).

A function can be pure, idempotent, both, or neither.

Upvotes: 28

SLaks
SLaks

Reputation: 888187

An idempotent function can cause idempotent side-effects.

A pure function cannot.

For example, a function which sets the text of a textbox is idempotent (because multiple calls will display the same text), but not pure.
Similarly, deleting a record by GUID (not by count) is idempotent, because the row stays deleted after subsequent calls. (additional calls do nothing)

Upvotes: 83

Related Questions