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Why empty string is on every string?

I wonder why Python returns True whenever I check if the empty string is in a string, and why its index is zero.

For instance:

  • '' in '' => true
  • ''.index('') => 0
  • '' in 'notEmpty' => true
  • 'notEmpty'.index('') => 0

I noticed it when I was writing a ROT13 function, and testing it I found that when I call it on an empty string, it returns 'n' ('n' is index13 in the alphabet).

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3 Answers 3

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A string S is a substring of the string T if and only if there exist an index i such that T[i:i+len(S)] == S. When S is the empty string you have T[i:i] = '' = S so all the results are correct.

Also note that T.index('') returns 0 because index returns the first index in which the substring appears, and T[0:0] = '' so that's definitely the correct result.

In summary, the empty string is a substring of every string, and all those results are a direct consequence of this.

Also note that this is peculiar to strings, because strings are sequences of characters, which are themselves strings of length one. For other kind of sequences(such as lists or tuples) you do not get the same results:

>>> (1,2,3).index(())
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: tuple.index(x): x not in tuple
>>> [1,2,3].index([1,2])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: [1, 2] is not in list
>>> [] in [1,2,3]
False

That's because list and tuple only check for members, and not for sub-lists or sub-tuples, because their elements can be of arbitrary type. Imagine the case ((1,2),1,2).index((1,2)). Should index check for "sub-tuples"(and thus return 1), for members(and thus return 0) or do some ugly mixture(e.g. first check for sub-tuples and then for members)? In python it was decided to search for members only, since it is simpler and it's usually what you want. Checking for sub-tuples only would give really odd results in the general case and doing "mixtures" would often yield unpredictable results.

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5 Comments

More generally, index returns the start value if it's less than or equal to the length of the string: 'spam'.index('', 4) == 4. But 'spam'.index('', 5) raises a ValueError.
@eryksun I'd consider that a bug. The find doc states that: Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation. So the ValueError seems inconsistent to me(the index doc simply points to find's).
I suppose you're right. If a substring is in the corresponding slice, then find should return the first index.
I think it's worth noting that this behavior is peculiar to strings because substrings (and even single characters or empty strings) are still strings whereas single elements from other data types aren't guaranteed to be the same type. eg. mytuple[0] is not typically a tuple.
@mgilson Yes, that's what I meant. I'll edit my post to make it clearer.
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Another way to look at it is that x in y should return True if it's possible to find two strings s1 and s2 such that the following holds:

s1 + x + s2 == y

When x is the empty string it will always give True. This is because you can choose s1 = '' and s2 = y.

Of course the actual implementation of in doesn't work in this way, but the result is the same. It just gets that result in a more efficient manner.

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well, the answer is simple really. you are searching for "" which really, is not a character at all....

and the first time there is no character in a string, is right at the beginning... at [0]

it gets confusing, because you would think that [0] is the index of the FIRST character. this is true, but you must also think that in this case the segments between characters are also something "tangible" and so of course nothing is in something, its also in nothing. and if you were to check subsets of a string, you would find it anywhere you chose, in the first location possible.

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