The problem

Comparing ASCII strings is simple -

1. Normalize both strings by converting them to lower-case
2. Compare the strings

# ascii string comparison
def compare_ascii(str1: str, str2:str) ->bool:
    return str1.lower == str2.lower

On the other hand, unicode string comparison is much harder to do. The strings cannot always be normalized by a simple uppercase/lowercase conversion. Eg - There are scripts that don't even have the concept of uppercase/lowercase, but still have different representations for the same character.

Note : Scripts and languages are different things.

Eg - The language Hindi is written in Devanagari script. The language english is written using Roman (Latin) script.

Here is comparison of 2 different representations of the letter 'a' in different scripts:

print('a')=='𝒂'
>> False

What makes unicode string comparison hard?

The source of the problem is -

• Multiple representations of the same character in different scripts
• Multiple representations of the same logical characters in the same scripts

Multiple representations of the same character in different scripts

Example:

There is the letter 'a' written in different scripts:

ａ 𝒂 ᵃ 𝘢 𝖆 ª 𝓪 𝚊 𝑎 𝗮 ₐ ⓐ 𝕒 𝖺 𝒶 𝙖 𝐚 𝔞

To us humans, these are the letter 'a'. But to the computer, these are all wildly different characters.

And when you do naive comparison these characters, the comparison will fail.

# compare `𝖺` and `ａ`
print('𝖺'=='ａ')
>> False

# compare lowercase representations
>>> print('𝖺'.lower()=='ａ'.lower())
False

Multiple representations of the same logical characters within a script

Example - In the German script 'ß' and 'SS' are equivalent. But, they cannot be directly compared.

'ß' == 'SS'
>> False

'ß'.lower() == 'SS'.lower()
>> False

So, to compare such strings, you need a smarter comparison system. The system should know which characters are logically equivalent. The python unicodedata module helps with this.

Solution

The solution has 2 steps:

1. Normalize the unicode strings
2. Make the normalized strings caseless
3. Compare the normalized & caseless strings

from unicodedata import normalize

def check_equality_unicode(str1: str, str2:str) -> bool:
    str1_normalized = normalize("NFKC",str1)
    str1_normalized_caseless = str1_normalized.casefold()

    str2_normalized = normalize("NFKC",str2)
    str2_normalized_caseless = str2_normalized.casefold()

    return str1_normalized_caseless == str2_normalized_caseless

This function is universal - It works for both Unicode and ASCII strings.

"NFKC" used above is a normalization form. There are 4 standard unicode normalization forms, each with different behaviours. More on them later.

Test cases

There are 3 test cases that you can put into in your codebases:

1. check_equality_unicode('Σίσυφος', 'ΣΊΣΥΦΟΣ') should equate to True
2. check_equality_unicode('a', 'ａ') should equate to True
3. check_equality_unicode('abc', 'ABC') should equate to True

Normalization in depth

The 4 normalization forms

There are 4 normalization form available for unicode:

1. NFD - Normalization Form D - Characters undergo canonical decomposition
2. NFC - Normalization Form C - Characters undergo canonical decomposition, followed by canonical composition
3. NFKD - Normalization Form KD - Characters undergo compatibility decomposition
4. NFKC - Normalization Form KC - Characters undergo compatibility decomposition, followed by canonical composition

Legend to understand the naming scheme:

• NF = Normalization Form
• D = Decomposition
• C = Composition
• K = Compatibility

A table makes their differences clearer -

The decomposition can be canonical or compatible. But the re-composition is always canonical.

More details are available in unicode's documentation - unicode.org - Unicode Normalization Forms

Choosing a normalization form

Choice of normalization form depends on the application. The decision is made by answering by two questions:

1. Which decomposition does the application need - canonical or compatibility?
2. After the characters are decomposed, should the characters to be re-composed canonically?

Canonical vs compatibility decomposition

The compatibility decomposition is built over canonical decomposition, by putting in additional rules. The compatibility conversion transforms characters into their more common forms. This "simplification" using more common forms leads to some information loss. This is the reason why all canonical sequences are compatible, but all compatible sequences are not canonical.

Following is an example from the original unicode.org document.

Notice how the exponent 5 gets converted into a simpler integer 5 by the Compatibility Decomposition algorithms of NFKD and NFKC. This simplification causes information loss - when looking at the normalized string, there is no way to know if the 5 originally was an exponent 5 or a normal 5.

Information loss in normalization

Normalization causes information loss. Once a string is normalized, it cannot always be converted back to the original string.

Here's an example - Suppose an ASCII string "HelLO TheRE" is converted to lowercase - "hello there". During this operation, the information that told which characters are uppercase got lost. So now, the lowercase "hello there" cannot be reverted back to the original "HelLO TheRE".

A similar thing happens during unicode normalization. Once a string is normalized, it cannot always be converted back to the original form due to information loss.

There are several reasons for this. Some of them are:

• Information loss caused during to the "simplification" performed by the compatibility form of character representation
• Information loss caused during to composition and decomposition

Here is an example from stackoverflow discussion on NFC vs NFD normalization - stackoverflow - When to use Unicode Normalization Forms NFC and NFD?

U+0387 GREEK ANO TELEIA (·) is defined as canonical equivalent to U+00B7 MIDDLE DOT (·) This was a mistake, as the characters are really distinct and should be rendered differently and treated differently in processing. But it’s too late to change that, since this part of Unicode has been carved into stone. Consequently, if you convert data to NFC or otherwise discard differences between canonically equivalent strings, you risk getting wrong characters.

When to and when not to use normalization

WHEN TO USE?

Normalization is required when two strings are being compared. Especially when dealing with non-english strings in multi-lingual apps.

• String comparison - eg - checking if a username is already taken
• De-duplication in datasets - strings are normalized strings before checking for duplicates in datasets. Typically used in llm training datasets, where the paragraphs are normalized and then their hash is then used to detect duplicates.

WHEN NOT TO USE?

By default, never normalize during data storage. If you're overriding this default, you should have a very good reason for it. If you're normalizing a string before storing it into a database, check if it is feasible to store both versions of the string - original(un-normalized) and normalized.

If you have good argument for normalization before storage, only then change this default, and store the strings normalized.

Don't use normalization during storage in use cases where the information loss due to normalization can cause problems. Normalization can change the way a string looks.

Some examples are:

• Normalization will cause problem in user typed strings. Eg - profile names, profile description, comments etc. The user might say "why is this text not looking like what I typed?".
• You may also break regulation in some strictly regulated industries, where storing data as-it-is is extremely important. Eg - legal document storage.

Resources

Further reading

• Tonsky.me - The Absolute Minimum Every Software Developer Must Know About Unicode in 2023
• Hn article
• W3C Standard Document: Character Model for the World Wide Web: String Matching
• Microsoft.com - Using Unicode Normalization to Represent Strings

Sources

• Stackoverflow - Normalizing Unicode
• Python - unicode lib documentation
• Stackoverflow - lower() vs. casefold() in string matching and converting to lowercase
• Stackoverflow - How do I do a case-insensitive string comparison?