TOML

L[toml] is every text that is one TOML document. Membership is decided by the standard library's tomllib, so nothing extra is needed on Python 3.11 and later; on 3.10, pip install "mathema-language[toml]" brings tomli, the same reader under its earlier name.

Which TOML that is depends on the reader. tomllib up to Python 3.14 reads TOML 1.0; tomli from 2.3, and tomllib from Python 3.15, read TOML 1.1, which also accepts a trailing comma and line breaks in an inline table, a time without seconds, and the \e and \xHH escapes. mathema_language.text.toml_language.TOML_VERSION says which one the installed reader reads. With a 1.1 reader, those documents are hazards, since a 1.0 reader elsewhere refuses them; with a 1.0 reader, they are outside the language.

TOML has one reading, unlike YAML, so the gap worth a language is between what a reader returns and what the code handling it expects. Several plain-looking values come back as something other than text, a number or a table:

Written	Read as
released = 2026-10-10	a datetime.date, which json.dumps refuses
at = 2026-10-10T09:00:00	a datetime with no time zone
opens = 09:00:00	a datetime.time
version = 3.10	the float 3.1
limit = inf, ratio = nan	floats that JSON has no spelling for
id = 99999999999999999999	a Python int, refused by readers in other languages
server.host = "db"	{'server': {'host': 'db'}}
"a.b" = 1	{'a.b': 1}, a key containing a dot
[[items]]	a list of tables

These are the language's hazards, visited before any random document, with the others a config file meets in practice: underscores and octal in integers, a literal string where a backslash stays a backslash, a multi-line string whose first line break is dropped, Windows line endings, an empty document. Outside the language are the texts no TOML reader accepts: a key or a table given twice, a value with a leading zero, a bare word as a value, a date that does not exist, a byte-order mark.

A worked claim

The shop's status page shows the service settings as JSON, from examples/shop/settings.py:

def settings_json(text: str) -> str:
    """The settings a TOML file gives, as the JSON the status page
    shows."""
    return json.dumps(tomllib.loads(text))

Claiming every settings file gets a page:

f = settings_json
for text in L[toml], is_language_defined(text)
    falsified   text = 'a=0006-10-10' (inside L[toml]) raised TypeError…

A date is a valid setting, and json.dumps has no spelling for a datetime.date, so the page fails for any settings file that records when something was released. The witness is shrunk to the shortest document that still fails; the first hazard, released = 2026-10-10, fails the same way.